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OneParentsConversion 29 Jun 2006 - 16:25 CatherineJohnson
Susan just pointed me to the most amazing personal story at Illinois LOOP. I'm bulletting the main points from the introduction for readability:
read the whole thing
By the end of elementary, we acknowledged to ourselves that something had gone badly wrong, though the causal link from early elementary instruction was not yet clear. It was easier to place blame on ourselves, on an exaggerated sense of homework neglect. Still, we took the precaution of moving the children to a private school billed as 'traditional' - only to eventually discover it to be an upscaled version of the progressivism offered at no extra charge by the public school next door. That discovery, too, was years in coming; I was so consumed with the career that paid the tuition that I barely took note of the continuing deterioration in scholastic achievement, much less delved deeply into the reasons why.
What was it that finally broke through my unquestioning faith and mindless optimism? A recognition that certain elements of a 7th grade math program were badly askew, some research for purposes of a teacher conference, and finding the Mathematically Correct website. A binge of research ensued which continues to this day. As full understanding of how progressivism had failed my children finally dawned, I was furious - more with myself than anyone else. But, I can no longer spare the emotional energy which anger consumes. It takes all I've got to stay attuned to three children from 3:00 to 10:30 p.m. sufficiently to correct Kumon math, direct grammar remediation, go over their SRA reading comprehension work, monitor the writing process program, and check assigned homework for the knowledge gaps which have undermined so much prior learning...and somehow attend to the non-tutoring aspects of parenting.
7th grade. That is horrifying. My perception—and I hope everyone will chime in on this—is that many parents hit the wall at the end of 4th or 5th grade. I've heard through the grapevine that there are lots of unhappy 5th grade parents here thanks to the TONYSS tests. (The TONYSS aren't mandated by the state, and aren't the same test everyone has to take in 4th and 8th. They're created by a private testing company, and purchased by individual school districts.) The TONYSS are graded on a scale of 1 to 4. Almost no one earned a 4 on the English language arts half. Only 2 children in Christopher's class of 19 kids got 4s, Christopher being one. (Poor thing. Christopher's glaring, obvious talent in life is not math. It's history & social science. Not surprising given that his father is a historian.) Back to the TONYSS. There were 4 or 5 kids in Christopher's class who earned 4s on math. It sounds like a lot of kids who had been getting good grades all school year suddenly came up with 2s & 3s on the TONYSS. I could be wrong about this. But that's what I'm hearing. For me, Christopher's '39' on Unit 6 at the end of 4th grade was a lucky break. Even Christopher said the same thing last fall. He actually said, 'If I hadn't gotten a 39 you wouldn't have started teaching me.' Up til the moment Christopher came home with that 39 I had no clue there was anything wrong with U.S. education that couldn't be fixed by moving to a super-expensive suburb and paying a small fortune in property taxes to get small class size and high per-pupil spending. When it came to education, the sum total of my sophistication was 'you get what you pay for.'
I've felt anger, but there are no easy targets. I knew every teacher and administrator involved. I knew that they had cared about my children and appreciated my work on behalf of the district; many of them are my friends. I saw them as well-intentioned, doing their best to use effectively the pedagogical tools to which they were limited by the progressivist reform vision that had been imposed from a policy level, one in which millions in professional development funds were being invested.
Check, check, & check. This is what I've come to realize: the problem is at the 'system' level... You can certainly have a bad teacher; I think we've had one so far. (She was a terrific lady; I feel bad saying anything publicly. But she didn't seem to be able to teach math out of the SRA book, something I couldn't do, either.) I love this, too:
If I have anger left for anyone, it is the educationalists who control accreditation standards that shape teacher training and professional development, and incidental to such, education policy. [snip] ...for all their power to effect or impede change at the critical level of teacher training, this is the last group to feel the heat of public accountability. They will never have to confer with the parent of a 4th grader who can't read. They will never see a performance review based on the achievements of their students. They will never face the electorate with their records. And they are, in a practical sense, insulated from legal liability for malfeasance.
I'd like to file a class action suit against Columbia Teacher's College.
KumonMathInDetroit 17 Nov 2005 - 13:28 CatherineJohnson
KUMON math program
KUMON reading program
I've had an amazing email from an engineering professor who learned of Kitchen Table Math while she was in China (!) (Apparently, not being listed on Google isn't a problem in China.) She also sent me a copy of her paper on Kumon supplementation in Detroit schools (the results were incredible), and I'm waiting to see whether it's OK to post. In the meantime, she says it's fine to post her email:
I'm sure you must have come across Kumon mathematics? I'm a professor of engineering at Oakland University, and so mathematics is obviously very important to me. As a consequence, to make up for the problems with the American school system I've had my own daughters in the Kumon program for about ten years each--between the ages of three and thirteen. Their math skills are far better as a result. I was so impressed with the ideas behind Kumon (it is an outstanding supplement that provides the additional practice missing from K-12 math), that I started a program using the Kumon method in a local inner urban school district, Pontiac. The results are described in the attached paper. Kumon provides the easiest, smartest way I've ever seen for a Mom to help her kids with math. I couldn't recommend it more highly. One last thought. I've taught in China as well as the US. The US is definitely way ahead on the "creativity" side. But we are so far behind in math that it is ridiculous--and it is potentially crippling for our source of engineers and other professionals. There are many aspects involved in good engineering, for example, where a good math background is critical. Most of the engineering professors where I work now (Oakland University), are foreign born. Although I greatly respect my foreign-born colleagues, it's really an indictment of the American system that we can so rarely grow our own any more. Thanks for your blooki, which I have bookmarked and will be following!
Actually, the woman who ran one of the Kumon centers I brought my children to originally got into Kumon because she saw how much it was helping a profoundly mentally disabled child who she was working with. So I suspect it may be surprisingly beneficial for Andrew. I couldn't have done the outreach in my local inner-urban outreach without the incredible help I got from Doreen Lawrence, the Vice President of Research for Kumon, North America. Her phone number is 248-755-2587, and her email is firstname.lastname@example.org. Doreen is a wonderful person who is deeply oriented towards helping children. I'm sure she'd be glad to answer any questions you might have about Kumon (she knows EVERYTHING about the program). You can feel free to post anything from my letter that might help. I just apologize for the poor writing. I just got back from China and am still jet-lagged. Over the next week or two I'll read through your website more carefully and get a better feel for what's going on (I just found out about your website while I was in China, but scarcely had any time available while I was there). I've a lot of thoughts and background information related to what you're doing, and have some interesting and relevent experience with national policy setters in academia on this topic, but am a little bogged down now working on a book, research papers, experiments, and grant proposals. You know, the usual academic stuff! So I will try posting some once I feel I understand more fully what you are doing and how you are doing it. Thank you ever so much for providing a forum for something that is so important to our children!
Her name is Barbara Oakley & she has had an amazing life (e.g., she met her husband at the South Pole.....) Plus--and I MUST post this--she's started a page of things she finds funny, which, thus far, has one link to a pdf file of what looks to be a PowerPoint presentation: Yours is a Very Bad Hotel.
All you World Traveling Kitchen Table Math denizens will relate.
dimensional dominoes and, now, send me an email out of the blue telling me I need to take Andrew to Kumon. That is exactly what I need to do. I need to take Andrew to Kumon. Andrew is my little locked-in boy; he's bright--so bright, it's there, you can see it--and I don't know how to reach him. The folks at Kumon may not know how to reach him, either, but it's obvious to me I'm supposed to give it a shot. If they don't know, something there will give me a new idea. It's a lead. I wasn't going to figure this out on my own. I was telling my neighbor about this today, complaining that I can't think of these things myself. I have to have complete strangers tell me: take your severely autistic son to Kumon Math. My neighbor said, 'You can never think what you're supposed to do about your own life.'
WhatIsConstructivism 14 May 2006 - 17:18 CarolynJohnston
AndyJoy asked on this thread: Can someone explain extreme constructivism to me? Is the problem that proponents never want to introduce the standard algorithm for a problem or make children memorize facts? The short answer is yes, but for the record, here is a fuller explanation. I think the best quick introduction to constructivism and its recent history in U.S. educational practice is Barry Garelick's An A-maze-ing Approach To Math, which appeared in Education Next this year. I'll excerpt a little piece of it to answer Andy's question, entirely without Barry's permission (but hopefully with his blessing).
Discovery learning has always been a powerful teaching tool. But constructivists take it a step beyond mere tool, believing that only knowledge that one discovers for oneself is truly learned. There is little argument that learning is ultimately a discovery. Traditionalists also believe that information transfer via direct instruction is necessary, so constructivism taken to extremes can result in students' not knowing what they have discovered, not knowing how to apply it, or, in the worst case, discovering (and taking ownership of) the wrong answer. Additionally, by working in groups and talking with other students (which is promoted by the educationists), one student may indeed discover something, while the others come along for the ride. Texts that are based on NCTM's standards focus on concepts and problem solving, but provide a minimum of exercises to build the skills necessary to understand concepts or solve the problems. Thus students are presented with real-life problems in the belief that they will learn what is needed to solve them. While adherents believe that such an approach teaches "mathematical thinking" rather than dull routine skills, some mathematicians have likened it to teaching someone to play water polo without first teaching him to swim. The Standards were revised in 2000, due in large part to the complaints and criticisms expressed about them. Mathematicians felt that the revised standards, called The Principles and Standards for School Mathematics (PSSM 2000), were an improvement over the 1989 version, but they had reservations. The revised standards still emphasize learning strategies over mathematical facts, for example, and discovery over drill and kill.So how does this fine-sounding idea play out in the classroom? Kids tend to spend too much deriving everything from first principles. What gets sacrificed is time spent learning advanced skills, as Barry shows:
Concept still trumps memorization. Textbooks often make sure students understand what multiplication means rather than offering exercises for learning multiplication facts. Some texts ask students to write down the addition that a problem like 4 x 3 represents. Most students do not have a difficult time understanding what multiplication means. But the necessity of memorizing the facts is still there. Rather than drill the facts, the texts have the students drill the concepts, and the student misses out on the basics of what she must ultimately know in order to do the problems. I've seen 4th and 5th graders, when stumped by a multiplication fact such as 8 x 7, actually sum up 8, 7 times. Constructivists would likely point to a student's going back to first principles as an indication that the student truly understood the concept. Mathematicians tend to see that as a waste of time. Another case in point was illustrated in an article that appeared last fall in the New York Times. It described a 4th-grade class in Ossining, New York, that used a constructivist approach to teaching math and spent one entire class period circling the even numbers on a sheet containing the numbers 1 to 100. When a boy who had transferred from a Catholic school told the teacher that he knew his multiplication tables, she quizzed him by asking him what 23 x 16 equaled. Using the old-fashioned method (one that is held in disdain because it uses rote memorization and is not discovered by the student) the boy delivered the correct answer. He knew how to multiply while the rest of the class was still discovering what multiples of 2 were.Now, consider the constructivists' argument for allowing this lack of 'domain knowledge' to persist -- kids develop deeper understanding, 21st century skills, bla bla bla -- after having read KDeRosa's "Terminator essay" on math education. That essay just puts this nonsense to death, don't you think?
smart constructivism post. Here are the 2 best passages. Smart constructivism says:
A common misconception regarding 'constructivist' theories of knowing (that existing knowledge is used to build new knowledge) is that teachers should never tell students anything directly but, instead, should always allow them to construct knowledge for themselves. This perspective confuses a theory of pedagogy (teaching) with a theory of knowing. Constructivists assume that all knowledge is constructed from previous knowledge, irrespective of how one is taught (e.g., Cobb, 1940)--even listening to a lecture involves active attempts to construct new knowledge.**Radical constructivism says:
It is possible for students to construct for themselves the mathematical practices that, historically, took several thousand years to evolve.
KumonPoll 17 Nov 2005 - 13:51 CatherineJohnson
Having hit the wall on afterschooling last night, I'm calling Kumon today. There's a Kumon center at the Barnes & Noble mall, which is pretty close. I figured I could get their number from the Kumon web site, so I clicked on the Find a Center link. There are 19 Kumon centers within 10 miles of my house. Are there that many Kumon centers surrounding ktm readers?
Of course, what I'd really like to know is how many kids from Masters School are also attending Kumon.
Interesting. There's a "Kumon Center" in walking distance of my house. I just called, and got a mom on the answering machine (obvious mom voice, that's how I know), saying, "Hi you've reached the X residence and Kumon Learning Center." This reminds me of my best friend in high school, whose mom ran a beauty salon out of their basement.
Top secret mom-operated Kumon Centers in Irvington. Strange.
KumonThreadMathForum 17 Nov 2005 - 13:33 CatherineJohnson
KumonInWAPO 17 Nov 2005 - 13:30 CatherineJohnson
from the Washington Post, April 7, 2005:
But most kids said they enjoy the feeling they get from doing well in their studies, figuring out tough problems and advancing to higher levels. "I don't know why, I just got interested in math here. Usually math is hard for me, but here it was really fun," said Marieclaire Alde, 10, of Wheaton, who goes to the Kumon Math & Reading Center in Rockville. Two years ago, Marieclaire was having trouble with multiplication, so her parents started her at Kumon. Now, the fifth-grader is able to do algebra normally taught in seventh or eighth grade. Kumon's self-guided learning style was developed in Japan 50 years ago. The math program involves lots of drills and memorizing -- and no calculators or computers. Thousands of work sheets cover 23 levels of math, from counting to calculus. (Kumon's reading program also takes a step-by-step approach.) Kids come twice a week and spend 30 minutes on a subject per visit. At the Rockville Kumon one recent afternoon, a dozen kids were busy with work sheets as four instructors peeked over their shoulders or checked papers nearby. "You can do it," read a yellow Post-it note an instructor had stuck on the table next to 7-year-old Austen Whibley. The Silver Spring girl was racing against the clock to meet her goal: a perfect math work sheet done in less than 25 minutes. She knocked it out in 22 minutes. "That is really good, Austen!" instructor Min Woo crowed. Kumon students who finish a work sheet with no mistakes on the first try get a star stamped in a little book. A bulletin board shows who is at what level, and high-level achievers get their names on a metal plaque.
"I would like to tell you about a scientific research on how to train your brain through arithmetic and reading. Have you heard of a book entitled “Train Your Brain”? It was written by the first researcher on the human brain in Japan, Professor Ryuta Kawashima from Tohoku University. Professor Kawashima has 4 sons. One day, he observed his elder son playing video games at home while his younger son was concentrating on his Maths worksheets. Wondering whose brain is doing more work, he decided to get research students from the university to participate in an experiment. Comparing the brain activity of one group of students playing computer games with another group who did addition sums of 1-digit numbers, he discovered interesting results. The brain activity of students doing simple arithmetic sums is more active than the brain of those playing computer games, which is active in only 2 areas; the visual area (controlling images) and the motor area (controlling movement). "The frontal lobe of the brain is the control centre of the entire brain. Activating this part of the brain amounts to training the entire brain. Reading aloud in English or Mandarin can achieve the same effect. "Our Singapore Office staff are working closely with instructors to help every student in Kumon to train his/her brain through reading, writing and doing arithmetic."
So this could be true. Or it could be dead wrong. I don't care. What I like about this passage is: this is marketing material. This is marketing material citing research on the brain. As opposed to marketing material citing, say, 21st century skills, real world contexts (Antopolis), making connections, balanced assessments, or the five myths that surround mathematics reform efforts and Standards-based curricula. I could go on. Souped up brain waves in children doing arithmetic sums may be nonsense on stilts. It doesn't matter. If you're going to pitch me, at least tell me something I want to hear.
OldWomanInKumon 17 Nov 2005 - 13:46 CatherineJohnson
Any program that promises to have me multiplying a 3 digit number by a 2 digit number in 3.5 years is fine by me.
Katherine Poit, 100, a long time Dobbs Ferry resident died November 16, 2004. She was born June 26, 1904 to Samuel and Jennie (Chatterton) Ingersol. She married Charles Poit in Poughkeepsie in 1929. Mr. Poit died in 1969. Mrs. Poit received her Bachelor of Science Degree from Vassar College and her Masters Degree in Library Science from Columbia University. Katherine was an honorary member of the Dobbs Ferry Women's Club and member of the Dobbs Ferry Hospital Auxiliary as well as a long time member and former Vestryman of Zion Episcopal Church.
Also, this (scroll way down).
Here's The Masters School. Can't find a photo of the Women's Club.
KumonFranchise 17 Nov 2005 - 13:45 CatherineJohnson
I've been Googling Kumon franchises and have found some interesting things:
First off, the LA Times has a brief but quite helpful run-down of positions for tutors.
Question: I am a former school teacher and have an interest in working part-time as a tutor. Do you have any suggestions on places I could work? What is the range of hourly fees paid to tutors?
Here's what they have to say about Kumon:
Kumon Math and Reading Centers
4th fastest growing franchise in the country in 2004. (pdf file) Subway was number 1, Curves was 2, and 7-Eleven was 3. I find that pretty shocking. Food and weight loss are radically more central to people's lives than 'supplemental education.'
what they're looking for in a franchisee: (pdf file)
In general, we are looking for someone who loves working with children, is a good communicator, strong math and reading skills, ties to the community and can dedicate their full-time effort to growing the Kumon Center. Satisfactory and adequate performance during the Preliminary Training Program is also a requirement. We usually require candidates to possess a 4-year college degree, but exceptions can be made in extraordinary circumstances.
Kumon math study guide (pdf file)
You Do the Math (1999).
The collision was horrific. In high school, mathematics had been easy for me—I could just sit for an hour and stare aimlessly while the instructor scrawled his cryptic chalk symbols. But when my lack of preparation met with my first college math exam, the twisted metal of my mind created a big fat F. A tutor changed my world. [snip] From my observations, the Kumon system, which originated in Japan, is a series of tests structured to create incremental success so every student feels like an achiever. These math and reading masters have created a learning structure based on constant repetition and measured growth. Students set their own pace, review their past work and then test again. Trainees take proficiency tests and are assigned homework. If you don't pass the exams, you'll see Kumon training methods up close and personal until you do. The homework requires many hours and is so intensive, even your kids will feel sorry for you. Your studies will also consist of creating a business plan. If your site is approved, you'll pay only $800 for the rights to open a Kumon Center, plus $200 for the training kit. [snip] It appears to me Kumon is more concerned with educating children than making money. It offers no protected territories and reserves the right to place both franchises and company-owned centers wherever it wishes. Furthermore, you're not allowed to operate more than two locations. Although educating America's youth is a laudable enough goal, let's do some math for the more hedonistic among us. Recommended tuition for a full-time student is about $75 per month plus a one-time registration fee of $30. Assuming you have 50 students by the twelfth month of operation—enough to get past your TLP—your gross revenues for the month would be $3,750, excluding registration fees. The franchisee I interviewed had 165 students, totaling $12,375 per month. Once you pass the TLP, you'll be required to pay the franchisor $28 per student per month. That leaves a gross profit of $2,350 with 50 students—$7,755 with 165 students. Subtract rent for about 1,000 square feet of space; marketing costs; and payroll for the local students who work for you after school. The result? Kumon can provide you with an income potentially better than that earned by the teachers you'll be supplementing. The franchisor is conscientious about assisting in your growth and will even help franchisees with rent for up to a 12-month period during the first 36 months of operation. Kumon—the top-ranked miscellaneous training systems franchise and No. 23 overall in Entreprenuer's 1999 Franchise 500®—is a low-cost opportunity that's been refined during its more than 40 years in business. The franchisor offers marketing and financial support, and boasted 2,617 franchise locations in North America as of March 1999.
BarbaraOakleyOnKumon 17 Nov 2005 - 13:45 CatherineJohnson
Using the Kumon Method to Revitalize Mathematics in an Inner-Urban School District (pdf file)
It is a compelling challenge to provide inner-urban K-12 students with the skills necessary for a career in engineering. A solid grounding in mathematics is the most valuable such skill and also the most difficult to develop. Many inner-urban programs meant to revitalize or strengthen mathematics education focus on students in middle or high school. At this grade level, many students already feel they have no skill with mathematics; they have a correspondingly poor attitude towards mathematics that makes any attempt to improve the mathematics curriculum more difficult. A more useful, if longer term, approach is to implement change from the bottom (elementary school level) up, rather than middle or high school, where ultimate change is so strongly desired. The authors have introduced a supplemental program in the Pontiac School District in Pontiac, Michigan to revitalize mathematics beginning with the elementary school level (K-5). The supplemental program, Kumon Mathematics, is used by millions of school children in Singapore, Japan, and Korea; countries that score the highest on worldwide mathematics achievement tests. Kumon Mathematics appears to provide an ideal structured support in mathematics for at-risk children who receive little or no help at home, and who present the teacher of any given grade with a great variety of achievement levels. It allows students to achieve frequent and repeated successes. This paper provides details of the Kumon Mathematics methodology as well as a description of the first year’s efforts in the program, which currently involves some 1,500 elementary school children in the Pontiac School District.
This is where we are, in my house. I can't create the level of practice Christopher needs, and I can't get it from Saxon 8/7 or edhelper.com (though edhelper is a terrific site). Actually, I probably could create the level of practice Christopher needs, but I haven't had 50 years' experience doing it, as Kumon has. The Kumon worksheets have been used & revised & used again & revised again. For years. Plus I'm sick of the battles. We had a Total Household Meltdown two nights ago—a total household meltdown involving triangulation, I might add—that left me hopping mad yesterday, and simmering mad today. That's not good.
reactive teaching stinks. Early on, working with Christopher, it was clear to me I needed to be teaching my own curriculum, separate from the school's. I needed not to be doing what Carolyn calls reactive teaching. When Christopher & I were working our way through Saxon 6/5, I was overseeing & teaching a coherent curriculum. I gave tests after each 10 lessons, and I could see whether he had learned the concepts or not. I had some means of assessing where he was. This year we don't exactly have time to do Saxon 8/7 along with Prentice Hall Pre-Algebra (or maybe Saxon-with-Prentice-Hall just doesn't seem appealing enough to devote the time to it. I'm not sure.) So I'm doing reactive teaching, and I'm not doing it very well. I guess the problem boils down to efficiency. Efficiency and child psychology. I'm 'dorking around in the dark' here, writing up Distributive Property Worksheets, having Christopher rehearse the definitions of the properties, etc....and who knows if I'm doing enough of this, too much, or too little? Plus every day is another battle, because Christopher loathes surprises. In this realm, he is One with his autistic brothers: He Does Not Like Change. (As a matter of fact, it's entirely possible both Jimmy & Andrew are more flexible when it comes to change, surprise, & transitions than Christopher.) Well, seeing as how I've never 'afterschooled' the subject of pre-algebra in my life, everything I write up for him is hideously new & unprecedented, by definition. It is a surprise. It is change. It is not what he expected. Kumon is going to be repetition to the max, and that's what we need.
KumonCenterLogPage 17 Nov 2005 - 14:17 CatherineJohnson
Spent a good 3 hours at KUMON today. What a trip. Only three white people showed up for the whole afternoon, & Christopher & I were two of them. Then there were two black kids. After that? Foreign nationals. Asians & Indians. And the Asians came as couples. That right there blew me away. The only time, in Irvington, you see both parents turn show up for an extracurricular activity, it's soccer or baseball. Not only did both parents show, they were dressed. One mom was wearing patent leather flats. I can't even remember the last time I saw a pair of patent leather flats. She looked like the kind of woman you see shopping in the Prada outlet at Woodbury Common. (If the kind of woman you see shopping in the Prada outlet at Woodbury Common doesn't instantly call an image to mind, think: Asian, young, great-looking, chic, and rich.) There are lots of foreign nationals in these parts, it seems, but they don't mix in much, or integrate. I keep hearing from other parents things like, 'they send their kids to Japanese school on Saturdays.' Which has always sounded like an urban legend to me. Japanese school? What is Japanese School? Where is Japanese School? Can I see the building from the road? Now I'm thinking: Japanese school. I better look into that. Christopher passed the test for 3rd grade, and flunked 2nd grade because he was too slow. (Speed and Accuracy, the Kumon mantra.) So he has to spend this week reviewing 2nd grade math facts, then take the achievement test again next Saturday. Assuming he passes, he starts grade 3 As for me, I was a Calculating Whiz. When I handed in my first test, the owner said, "That was fast." When I handed in my achievement test he said, "Done already?" Then he put me in fourth grade. More later.
KumonDay1 17 Nov 2005 - 14:22 CatherineJohnson
They weren't kidding about Kumon homework being easy. I did mine this morning:
Total number problems: 115
Total number correct: 112 (apparently, in the parallel universe that is my brain, 7 x 57 sometimes equals 64)
Total time: 6 minutes, 10 seconds
Total number correct: 210
Total time: 13 minutes
Part 2 begins when I come to and remember:
KumonMondayOctober24 17 Nov 2005 - 13:36 CatherineJohnson
I'm starting to see why, in the world according to KUMON, 4th grade math might be just about my speed. Timed multiplication tests are hard. Surprisingly hard. Especially when you have: a) fractured sleep
b) two large dogs whining & barking in your face
Sometimes I think it's a miracle my brain functions at all.
D6 a&b: 23 problems; 1:28; 0 errors
D7 a&b: 23 problems; 1:25; 1 errors
D8 a&b: 23 problems; 1:23; 1 errors
D9 a&b: 23 problems; 2:17; 1 errors
D10 a&b: 18 problems; 1:39; 0 errors
total problems: 110
total time: 8:12 minutes
total errors: 3
I hate errors.
The big red 0 here—and it has to be red—signifies a perfect score. A big, fat, red zero! That's not very friendly, I don't think.
And see Number 2 Pencil for another take on friendly numbers.
BarbOakleyOnKumon 17 Nov 2005 - 13:28 CatherineJohnson
The person who believes in constructivist approaches to math may be interested to learn that recent breakthroughs related to neuroimaging and learning are pointing towards the importance of automaticity in order to learn a subject well. In other words, you can "understand" how the chords work on your guitar, but to be able to play the guitar well, you have to have that automaticity of basic concepts that comes with practice. My daughter, who is in Chile now as an exchange student for her last year of high school, is telling me she's interested in a career involving math, because she likes it and everyone tells her how good she is at it. She wasn't one of those natural math whiz kids. It's just that the every day practice, (never too easy, never too hard) that she got over the years with Kumon made an enormous difference.
Good enough for me. My regret with Kumon is that we didn't start years ago. Especially seeing as how I have been placed in the 4th grade.
I thought you'd be interested to know that there was a group of students at Columbia University involved in an intense afterschool activity involving community outreach. They were all sitting around comparing notes about themselves, and were struck--the one thing they all had in common was that they had all been "Kumon" children. Their take on this unusual coincidence was that, because their background and comfort level in math was so high, they had a lot more time than other students to participate in after-school related activities. I heard this story from Doreen Lawrence, the Vice President of Kumon North America Research. The only bad thing is that "Kumon" children don't seem to grow up to be K-12 teachers. They're too busy becoming doctors, scientists, engineers, and businesspeople, because their top grades related to math have opened those doors for them.
Personally, I am hoping to grow up to become a K-12 teacher. It's obvious just from teaching my Singapore Math class that I'm going to need vastly more automaticity than I have now. You almost have to experience it to believe how much facility you need with elementary math to teach five 10-year olds.
Kumon math sequence
Kumon reading sequence
Apparently the goal, when a child starts young, is 'G by 5,' meaning the child completes level G at the end of 5th grade. The first word problems appear at that point, I believe:
Students are introduced to positive and negative numbers, as well as to basic algebra. Students use their previously learned four operations skills to master linear equations. A word problem set rounds off the level, allowing students to apply everything they have learned in Level G.
In Grade 6 you're doing worksheets that look like this:
Students will learn to solve simultaneous linear equations in two to four variables. Concepts of numerical and algebraic value are strengthened. Students are introduced to transforming equations, inequalities, functions and graphs.
This week Christopher is doing review sheets from Level B; I'm in Level D. We're a little behind.
KumonAverageStudentsBeyondGradeLevel 17 Nov 2005 - 13:25 CatherineJohnson
I've mentioned that one of the main differences between U.S. & Asian parents is that Americans see math as 'genetic.' You either have it or you don't. Asian parents recognize innate talents as well, but are far more inclined to see high math achievement as a function of hard work, not genes. Here's the KUMON company's take on the issue of advanced achievement for average kids:
Our aim should be to educate our students so well through the Kumon Method that they don't have to depend solely on classroom activities to be able to deeply understand the course content. Students who develop this capacity will have a good chance to enter leading universities. To make this possible, we must help students acquire the ability of self-study from an early age and accelerate their level of study beyond their school grade. (Emphasis added)This last line is the key. It follows that if Kumon teaches children to become independent learners, some of them will learn at a faster pace than their peers. This is certainly what happened to Mr. Kumon's own son, who was doing high school level work while still in the 5th grade. Multiply that times millions of students and you have a lot of children who are studying way beyond their "normal" school level. Mr. Kumon recognized that self-learners are motivated by their own progress. It is only natural when climbing a mountain to look up and see what lies ahead. Students don't need to be pushed to scale these heights, but they do need to recognize that there are concrete goals and interesting challenges ahead. For that reason, it is important to encourage study of materials above the current grade level. The biggest problem, in Mr. Kumon's view, was not getting children to want to tackle the challenges of advanced study, but getting parents and Instructors to believe that it was possible and desirable:The most important and difficult feature for people to understand about the Kumon Method is having students advance beyond their actual school grade. The majority of people don't have the experience of studying material beyond their school grade. Consequently, they don't believe that children have that ability. Even Instructors find this fact hard to believe at first. The history of the Kumon Method can be called the history of our efforts to convince people of this fact.That was written many years ago, but the same problem still exists. Many parents just don't believe that children can study beyond what is considered a "normal" level for them, or that it isn't "natural" for them to do so. If they see examples of children who are progressing at a faster-than-normal rate, they are inclined to say "The parents are pushing them too hard" or "That just isn't normal." In fact, advancing beyond grade level is a normal consequence of consistent, long-term Kumon study. Every year more and more young children in Kumon show that what we expect as "normal" for a certain age is more a reflection of the limits we have put on children than anything inherent in the child's ability to learn. More Kumon parents are spreading the word that what is really "normal" is for a child to be learning a wide variety of things, not under pressure or stress, but because children naturally enjoy learning about the world around them. [snip] Are most of the Kumon children who are studying one, two or three grade levels beyond their normal school level geniuses? I posed that question to Stan Laser, a former math and science teacher and later vice principal of Brooklyn High School in New York, where he was in charge of 1,200 students. Stan, who is now a Kumon Instructor, said that very few of the children who outperform later on are abnormally bright at an early age. "I sometimes ask the parents of children who turn out to be superstars in Kumon if those children were exceptionally bright when they were very young....In almost every case the parents say no, my child was just an average child." In other words, the great majority of the children who excel in elementary school or junior high are not geniuses. Their growth and success in attaining higher levels of ability has emerged through regular study. All of this would have Toru Kumon nodding and smiling with a knowing look on his face. Isn't it obvious, he would say to us? Children are not only capable of advanced study, but need to be given the opportunity to advance. But....it took time for him to understand this process:Initially, it was difficult to determine how children who advanced to higher levels would develop. Many Instructors worried that letting children advance so far would bring about other problems. But as children advance so far, they naturally develop self-motivaion and acquire self-esteem and self-confidence because of their abilities. Everyone thinks it is perfectly natural when children who were exceptional when they started Kumon eventually move beyond their actual school grade. But if Instructors see that children who had average abilities at the beginning also advance by the same process, they will have a more profound understanding of the learning effect of the Kumon method.
I believe this account, because I've seen it myself, throughout my adult life: slow and steady wins the race. Back when I was starting my dissertation, my advisor told me to write 500 words a day. Period. If I wrote 500 words a day for 6 months, I'd have a dissertation. I had already figured this out myself, but it was good to hear it from him.
I've also seen, in my own life, the effects of small amounts of effort put in on a daily basis. When KUMON says 'daily,' they mean daily. You do your KUMON worksheets every day of the week. No rest on Sunday. But the worksheets aren't hard. As far as I can tell, it's true that if you put in 10 minutes a day, day in and day out, you see shockingly high gains over time. Judging by the experience of folks around here, of course, this is not the case in grad school. And of course cognitive scientists have focused on the very high degrees of practice necessary to become, say, a virtuoso violinist. But that research isn't really relevant. Think about it. Is anyone trying to become a virtuoso of two-digit multiplication? No. What you're trying to do when you're learning elementary mathematics is to acquire speed and accuracy and then move on. That doesn't take 10 years of study. Nor does it take hours of drill. It takes 10 to 20 minutes a day for 6 to 8 weeks. I've come to feel that most people are missing how easy it can be to learn elementary mathematics when you have a coherent course of learning & practice.
keywords: drill and kill
KTMPollCostOfKumonInWestchester 17 Nov 2005 - 13:27 CatherineJohnson
Anne just sparked me to get this New KTM Poll posted:
Bear in mind that in my area SAT tutors are commanding fees as high as $800/hour.
BrianMickelthwaitOnKumon 17 Nov 2005 - 13:27 CatherineJohnson
I'm in the middle of reading Brian Micklethwait's terrific article about his experience as a KUMON instructor, but had to stop and post this passage:
There is also in Kumon what I think of as a very Japanese emphasis on the physical process of drawing the numbers and on physically handling the world generally. (Think of the Japanese fascination with hand-done graphics.) One of the ancillary games we get the children to play is simply placing numbers on a number board. This doesn’t just help them to understand numbers. It also helps them to get better at simply handling things, while thinking at the same time. As with so much of Kumon, doing the number board so that every number is where it should be is in principle very easy, so no child is humiliated by not being able to do it. But doing it fast isn’t so easy, so the cleverer ones are kept interested. (We also give the cleverer ones more complicated things, like “leave on the board only those numbers divisible by 3”.) This emphasis on the physical handling of the world also explains, I think, why the Kumon people are so reluctant to get involved with computers. To me, an Anglo-Saxon techno-nerd, Kumon absolutely shouts computers. Each child doing an individually selected clutch of repetitive problems. Relentless and potentially very tedious marking. Even more tedious analysis to tell you what each child should be doing next. A huge apparatus of collective, centralised analysis to see which methods work best and to tell the rest of the world. This is surely the sort of stuff that computers — and their recent combined offspring, the Internet — were invented to supervise. But I sense that the Kumon people resist such notions. There’s so far been no mention of computers in any of the Kumon back-up or sales literature that I’ve seen. Computers, I hear them saying, would only complicate things.
I've come to believe that paper-and-pencil math is math—that there's something necessary, at least when you're learning,* about the experience of actually holding a pencil or a pen in your hand and solving problems. Carolyn talks about the craft of math; Temple repeatedly & chronically encounters people who've learned to create scale drawings on computers and, as a direct result, cannot construct scale drawings. (Temple believes that the visusal processing and motor systems in the brain are connected. I won't be surprised to learn that she's right.) I've been surprised at how unmoved Americans are by the Singapore bar models. I fell in love the instant I saw them, and wanted to draw them. With Sybilla Beckmann, I think the bar models are probably the reason for the Singapore curriculum's success. I've mentioned several times that I've worked at least 300 bar model problems. I've said, too, that doing this changed my brain. I'd put money on it. The thing is, I really don't know why this should be the case. I'd been thinking maybe they develop spatial reasoning, which is connected to mathematical ability. It hadn't occurred to me that bar models might work simply because they involve lots more pencil-and-paper work than the traditional U.S. math curriculum. But the explanation may be as simple as that. When I first started drawing bar models, I badly wanted to paint one. I wanted to do a big, bold 'blow-up' of a Singapore bar model in oil, and hang it on the wall. Maybe one day I will.
Shouldn't we be as eager to end our obsessive love affair with pencil-and-paper computation as we were to move on from outhouses and sundials?
The answer is no.
*Temple says that older people who learned to draw by hand & then switched to CAD have no problems at all. The problems turn up strictly in the work of younger employees, who've never done physical scale drawing using pencil and paper.
Swoop and Swoop
the craft of math
KumonInWestchester 17 Nov 2005 - 13:26 CatherineJohnson
That's what KUMON costs in Westchester County. For that you get 150 worksheets a month, plus 4 visits to the center. You can't even get a haircut for $85 a month here. Best deal in town.
JUMP program, which I had never heard of. It sounds fascinating. I'm going to order JUMP's 6th grade workbook, as well as The Myth of Ability: Nurturing Mathematical Talent in Every Child by John Mighton, founder of JUMP. I bring this up here, because he begins remediation with fractions. That's where he starts. With fractions.
it has proven to be an extremely effective tool for convincing even the most challenged student that they can do well in mathematics. [snip] The various steps you will follow in teaching the material in this unit are outlined in great detail below, and also on the Fractions worksheets themselves. The individual steps are never more difficult than “count on your fingers” or “copy this symbol from here to here,” so the steps themselves will never be a barrier to weaker students. If you follow the instructions in this manual very closely, even your weakest students should achieve a mark of 80% or higher on the final diagnostic test (included at the end of the manual).
I haven't read through his material closely yet, but it seems that the reason he chose fractions as his jumping off point is that you can manipulative fractions using extremely friendly numbers. Which is true!
KumonIsASupplementalProgramOnly 17 Nov 2005 - 13:26 CatherineJohnson
Ken raised a question I'd been meaning to bring up: can KUMON be used as a primary curriculum? KUMON says no, and I agree. The KUMON worksheets are designed to be supplemental. There's no 'KUMON instructor,' even though everything you read talks about the 'KUMON instructor'; there's just you, your worksheets, and your mother, who grades the worksheets. What KUMON gives you is a highly structured, well-thought-out set of 200 worksheets per grade level—worksheets that have been used and revised over 40 years' time. One of the interesting aspects of working through the KUMON sheets as an adult is that they give you practice in things you didn't know you needed practice in until you started doing the worksheets. They're diagnostic, in a way.
Doing each one of these problems in sequence is going to give a 4th grader a sense of what a remainder actually is.
7 x 2 = 14 Seven twos are fourteen.
7 x 3 = 21 Seven threes are twenty-one.
and so on
Several of the pages have a set of 3 skip-counting problems: Fill in the blanks with the appropriate numbers. 7 14 21 28 ___ ___ ___
One page begins with this sequence of problems: 7 + 7 = ___
7 + 7 + 7 = ___
7 + 7 + 7 + 7 = ___
7 + 7 + 7 + 7 + 7 ___
The rest of the problems are all math facts written horizontally. Here's the rest of 37a, which is the page that opens with the times-7 facts listed in a table. The times-7 facts are written and solved in sequence. 7 x 1 = ___
7 x 2 = ___
7 x 3 = ___
7 x 4 = ___
7 x 5 = ___
7 x 6 = ___
7 x 7 = ___
7 x 8 = ___
7 x 9 = ___
KUMON has the kids do quite a lot of non-mixed practice. Russian Math does the same thing. (Can't remember, offhand, how much of this Saxon or Singapore do; I have a sense Singapore does quite a bit....)
KumonInstructionalPracticeInPrimeFactors 17 Nov 2005 - 13:26 CatherineJohnson
I love this. These are the first two pages of the prime factor worksheets.
I would like to know how, exactly, a person is supposed to do 24 problems like 111/16 in 3 to 4 minutes, without scratch paper? I don't know that you're not supposed to have scratch paper; that's what I assume since no one ever seems to be using scratch paper at KUMON. And the owner has expressly used the phrase 'side calculations' as a term of opprobrium So I'm thinking I'm supposed to be able to do 24 of these problems in 3 to 4 minutes using no side calculations. Well, that's not possible. I have to have scatch paper. I have to do side calculations. So I may be repeating the 4th grade. (The problems on the back are even worse.)
This is an exercise in working memory blowout, let me tell you. To do the page in 3 to 4 minutes, you have to either instantly recognize the GCF for a large proportion of the problems, or remember where you last saw the prime factors of 48 or 54 or whatever number you're trying to prime-factor-on-the-spot at the moment. You have to be looking for patterns in the numbers themselves and remembering the patterns, and you have to be looking for patterns specific to the worksheets themselves, and remembering those patterns. That's way too much remembering. I can't say I'm looking forward to 5th grade.
I wonder what else is out there I don't know about?
DiscoveryLearningWithKumon 17 Nov 2005 - 13:26 CatherineJohnson
picking up speed faster than you expect
Interesting. I've mentioned before that, in my experience, kids pick up speed on timed tests unbelievably quickly. I can't find the post I wrote about this, so I'll tell this story again. A friend of mine has a son who has math talent that isn't being recognized because he's a high-level special needs kid (so high that the school is trying to declassify him). He came to my after-school class last year, where I gave him a Saxon Math Fast Facts sheet to do. The time limit is 5 minutes. The first time he did one it took him 10 minutes. Something like that. He was so slow, I decided I would do his handwriting for him. I told him just to say the answer & I'd write it down. (He'd been in the multi-sensory class, which emphasizes handwriting, and now had beautiful but very slow & deliberate penmanship.) So the next time he came to class, probably a week later, I did the writing, and it took him 8 minutes to do the sheet. It didn't seem to me that my being the answer-writer was helping matters any, so the next week I had him do his own writing. He did the sheet in 5 minutes. He starts out with a time of 10 minutes; 2 sessions later he's hitting 5 minutes. With no practice in between.
♦ ♦ ♦ ♦ ♦
That is now happening to me. Last night it took me 7 minutes to do one of the KUMON fraction reduction sheets, which are supposed to be completed in 3 to 4 minutes. Today I'm down to 3 to 4 minutes. I got faster overnight.
The notion of efficient drill is something I never hear people talking about. Constructivists oppose timed tests & an emphasis on speed on principle:
De-emphasis of rote work. We believe that children must indeed learn their math facts, but we de-emphasize rote memorization and the frequent administration of timed tests. Both of these can produce undesirable results. Instead, our goal here is that students learn that they can find answers easily using strategies they understand.Math-content types like us, along with cognitive scientists, believe in practice, practice, practice: Q: How long does it take for Mozart to become Mozart? A: 10 years of 12-hour a day practice.
But this is looking at things the wrong way, I think. We're talking about math facts and procedures, not symphonies. The goal of practice in math, at least in the early years, isn't to become brilliant fraction-reducers. The goal is to become efficient and accurate fraction reducers. There's no reason to be talking about 10-year timelines of 12-hour a day practice in the context of students learning math procedures. The question we should be asking is: how quickly can a student learn math procedures to mastery? And: do some worksheets produce more efficient learning than others? I don't know the answer to either one, but I think I do know, at this point, that the focus on 'hard work' and 'practice, practice, practice' is distracting us from the question of efficiency and acceleration. I'm thinking the KUMON approach to creating worksheets, which is the opposite of the randomly-generated, mixed-practice approach American texts & web sites tend to take, may promote faster learning.
I think I've run into a snag with my KUMON worksheets, which is that I'm having to do a fair amount of discovery learning. This week's worksheets require the student to reduce fractions 'in one step.' I was never taught how to do that systematically. (Apparently, I was also not taught to READ THE DIRECTIONS FIRST. On sheet D195b, I didn't notice the line saying "Some fractions can be reduced by 13" until I posted it here on ktm.) The worksheets are designed to be supplemental, so I'm assuming that, in Japan, students must be taught to reduce fractions rapidly and systematically. I can reduce fractions rapidly, just because I'm fast. But I do it in two steps. If I don't instantly see the GCF, I start with the factor I do see, then work on from there. These worksheets expect a student to instantly see the greatest common factor. Last night, after my dismal 7-minute performance, I started thinking how a person would go about instantly seeing the greatest common factor. I came up with various things, none of which mean that I instantly see the greatest common factor, but all of which help. (I didn't get a chance to print out people's Comments on prime factorization last night, because the computer had locked up. So I was on my own.) For instance, First check to see if both numbers are even. Second, check to see if one number, when divided by 2, becomes a prime incapable of further reduction. Another one: if you've still got two even numbers after the first division, then the GCF definitely has a 4 in it. Look to see if the numerator itself is the GCF. And so on. This is all to the good; my conceptual understanding of prime factorization—which was already pretty good, thanks to Russian Math, is jumping. But it's haphazard, and I don't think it's probably what the KUMON folks had in mind.
I've mentioned any number of times now that it's extremely difficult to get a child—any child—to budge from a procedure he's learned to mastery. The problem is, all of the procedures kids learn when they're just starting out need to be pared down at some point. Christopher still, when he does the four operations, crosses out the number he's borrowing from, writes in a '9' or a '10,' etc. He does nothing inside his head. He doesn't need to keep writing in all those digits, but he does. I'm wondering whether Japanese curricula explicitly teach efficiency as a goal. If you tell a child, from the beginning, that the goal is to solve problems as efficiently as possible, might that be the grade school equivalent of mathematical elegance later on? And is that part of the point of the KUMON worksheets?
Susan on Mad Minutes; Carolyn on college kids who don't know their math facts
PenfieldInTheNewYorkTimes 17 Nov 2005 - 15:02 CatherineJohnson
Ken strikes gold: 'Innovative' Math, but Can You Count?
LAST spring, when he was only a sophomore, Jim Munch received a plaque honoring him as top scorer on the high school math team here. He went on to earn the highest mark possible, a 5, on an Advanced Placement exam in calculus. His ambition is to become a theoretical mathematician. So Jim might have seemed the veritable symbol for the new math curriculum installed over the last seven years in this ambitious, educated suburb of Rochester. Since seventh grade, he had been taking the "constructivist" or "inquiry" program, so named because it emphasizes pupils' constructing their own knowledge through a process of reasoning. Jim, however, placed the credit elsewhere. His parents, an engineer and an educator, covertly tutored him in traditional math. Several teachers, in the privacy of their own classrooms, contravened the official curriculum to teach the problem-solving formulas that constructivist math denigrates as mindless memorization. "My whole experience in math the last few years has been a struggle against the program," Jim said recently. "Whatever I've achieved, I've achieved in spite of it. Kids do not do better learning math themselves. There's a reason we go to school, which is that there's someone smarter than us with something to teach us." Such experiences and emotions have burst into public discussion and no small amount of rancor in the last eight months in Penfield. This community of 35,000 has become one of the most obvious fronts in the nationwide math wars, which have flared from California to Pittsburgh to the former District 2 on the Upper East Side of Manhattan, pitting progressives against traditionalists, with nothing less than America's educational and economic competitiveness at stake. In these places and others, groups of parents have condemned constructivist math for playing down such basic computational tools as borrowing, carrying, place value, algorithms, multiplication tables and long division, while often introducing calculators into the classroom as early as first or second grade. Such criticism has run headlong into the celebration of constructivism by the National Council of Teachers of Mathematics and such leading teacher-training institutions as the Bank Street College of Education. The strife has taken on a particular intensity here in Penfield, perhaps, because the town includes an unusually large share of engineers and scientists, because of the proximity of companies like Xerox, Kodak and Bausch & Lomb. Skilled themselves in math, they have refused to accept the premise that innovation means improvement, and in their own households they have seen evidence to the contrary.
This is about the worst I've ever seen school officials come off in a news article.
Susan Gray, the superintendent, attributed the criticism of the math program to "helicopter parents" who are accustomed to being deeply involved in all aspects of their children's lives. "Because the pedagogy has changed, the parents who knew the old ways didn't know how to help their children," she said. "They didn't have the knowledge and skills to support their children at home. There's a security in memorization of math facts, and that security is gone now."
helicopter parents unbelievable She opened her mouth and said helicopter parents to a reporter. Helicopter parents and a whole lot more; every word is hostile, belittling, and contemptuous—and she got busted for it. Next paragraph:
YET many of the dissident parents have extensive math backgrounds and thus the ability to criticize the curriculum. It is also true that most of them tolerated the constructivist program for its first several years, until bitter experience drove them into rebellion.
The article closes on this note:
Still, in the math wars, tweaking around the edges does not settle the issue. The dispute is fundamental. To its advocates, constructivist math applies the subject to the real world, builds critical thinking and rescues classes from numbing repetition. But to those parents in Penfield and elsewhere - who have children in junior high unable to do long division or multiply two-column numbers, who pay for private tutors or sessions at traditionalist learning centers like Kumon, who wonder why there are so many calculators and so few textbooks - the words of a recent graduate to the Board of Education ring tragically true. "My biggest fear about going to college," Samantha Meek said at a meeting last spring, "is attending introductory math courses How am I going to be able to explain to my professors that I do not understand what they are talking about, that I do not have the same math background as the rest of the students, and that I cannot do mental math and can barely do it with pencil and paper?"
Wipeout. Susan Gray is probably trying to remember how to walk and talk right about now.
one more thing
So Ed was going on about how Nicolas Sarkozy had no business calling the rioting beurs "thugs," and how destructive that is, throws gas on the fire, etc. OK, he's right. When you've got urban riots happening, it's almost certainly not the best strategy to call the rioters thugs. Ditto for school superintendents. Memo to Susan Gray. When you're in the middle of the Math Wars, helicopter parents is the wrong choice of words.
International Red Cross Symbol for Guess and Check
There's a link to the Penfield web site on the sidebar: Teach Us Math
Letter to the Editor
KumonReading 21 May 2006 - 13:16 CatherineJohnson
We're well on our way to becoming an all-KUMON-all-the-time household. Today Christopher wanted to take the KUMON reading test. He asked to take it. He aced the first test, then aced a second test. (He may even have taken 3 placement tests; I'll ask.) Then he placed into 5th grade (EI). In real life, he's in 6th. My thinking at the moment, in terms of what it is I think Irvington schools should do—and what some Irvington parents would sign on for: Irvington should have an American track, and an Asian track. That simple. The Asian track would incorporate the brilliant suggestions all of you left earlier.....or it would incorporate none of them (most likely), but would simply be a curriculum designed to teach to Asian standards. Not to American standards. Speaking of which, Christopher is a very strong reader. My guess is that he's not the best in the school, but he's close. I think there are two kids in the school who are better. Interestingly, those two kids are the ones who won the two Math Olympiads awards last spring. One is a boy, the other a girl, and I know both of them. The boy I know from way back in nursery school; the girl I taught the girl in my after-school knitting class. Another interesting thing: I ran into the boy's mom at back to school night, and after congratulating her on R.'s award, I said, "R. must really like math." Her reaction: "No, not really." This is probably the smartest kid in school, and one of the very best in math, and he doesn't really like it! OK, back to Christopher. Christopher taught himself to read. That's how good he is. IIRC, approximately 10% of kids, when given systematic phonics instruction, begin to read spontaneously. That was quite an event in our household, because shortly before Christopher began to read we had our teacher conference, at which we learned that Christopher was considered at risk for dyslexia because his handwriting was so bad. Bad handwriting is a risk factor for dyslexia, apparently because the area of the brain that manages handwriting directly borders the area that manages reading—something like that—and when one brain area isn't up to snuff there are often spillover effects. At least, that's what I remember of John (Ratey's) explanation. I'm guessing that probably all kids with dyslexia have bad handwriting, but not all kids with bad handwriting have dyslexia. (If someone knows the story on this, let me know & I'll revise this post.) Christopher's handwriting was horrific. It was so bad the school had been pulling him out for O.T. without even telling us—he was being given a 'free' special needs intervention without our having to fight tooth and nail to get it. That's bad. Naturally I was completely traumatized by this conversation; I was thinking, 'OK, two autisms and now one dyslexia, thank you very much.' Ed blew it off, which was seriously annoying (wives aren't fond of the Wife Filtering Mechanism, in case any of you were wondering), but he was right, because two weeks later lo and behold Christopher was reading. We haven't followed his reading scores closly (Short Attention Span Theater) but we did manage to get the word that he was reading at a 4th grade level in 2nd grade. Of course, when we actually got to 4th grade we had the Fourth Grade Slump everyone talks about, which led to my 'second-stage phonics' theory that you aren't done teaching decoding after you teach the phonemes. Second stage phonics: syllables. Megawords, a spelling program that teaches the syllabic structure of words, seemed to put Christopher back on track with reading, and he was one of the few kids in his school to earn a 4 on the TONYSS ELA last spring. It was a high 4, too, with a perfect score on the hardest section. My point being: he's a good reader. Yet he's still a full year behind grade level in KUMON. So it looks like he's going to start the KUMON reading program next week.
to be continued
update 5-20-06 I suspended Christopher's KUMON reading program today because it had become far too expensive once he cut back to doing just 1 sheet a day, if that. More on this later. We're sticking with KUMON math, which I continue to feel is worth its weight in gold. He's doing only 1 page of KUMON math a day, too, but it's worth it. I'll bump him back up to at least 3 a day this summer. Christopher completed one level of KUMON reading, E1, which corresponds to 5th grade. (He's nearing the end of 6th grade). Today I handed in sheets E11 18a & E1 185a. We've all slacked off on KUMON, so we need to get back on track. The sheets I picked up today say 4-15-06 on the front; today is 5-20. I've reached G40a. The G level introduces algebra, & I'm 40 lessons into Saxon Algebra 1, which has 120 lessons in all. So my KUMON worksheets are probably going to dovetail with the problem sets I do in Saxon & in Dolciani. (I'm suspending Saxon so I can work through Dolciani's chapter on functions, slope, and coordinate graphs. Then I'll go back to Saxon.) Andrew is at 3A46a in KUMON Math. I may start him in KUMON Reading this summer.
KumonReadingPart2 17 Nov 2005 - 13:25 CarolynJohnston
Catherine and I were talking yesterday about how it seems reading curricula are completely missing from elementary schools. Once a kid has the mechanics of reading, it doesn't seem there is a clear road forward; and it seems to have been that way for quite a while. As a kid in elementary school, for example, I didn't get grammar instruction; my husband did. Core Knowledge, at least, tries to standardize at least on the content of the reading kids do in elementary school, but it doesn't otherwise try to impose any teaching philosophy. Apparently kids like mine -- who get the mechanics of reading very early, are fluent readers and writers, but who have persistent problems with understanding what they are reading, and cannot organize a short theme to save their lives -- are pretty rare. That must explain the absolute absence of actual teaching on the subject, and the fact that Ben was always the odd man out in his special reading and writing groups in elementary school. They'd all be struggling with spelling and slow reading, and he was a perfect speller and a fast reader; but he'd misinterpret things he read literally. You'd be amazed at how typical kids are able to learn idioms by osmosis, for example; and you'd be amazed, too, at a very young autistic kid's response to phrases like "keep your eye on the ball". So the Kumon reading stuff looks kind of appealing, actually. Ben's been tracked into remedial reading and writing, and if I'm not careful, he won't surface. We've been addressing vocabulary, which is a good bit of his problem; he doesn't learn words in context, and needs explicit instruction in vocabulary (he picks it up quickly, but it needs to be explicit!). It doesn't look as though Kumon addresses vocabulary, but it addresses most of the rest of the issues he has trouble with: main ideas, reasoning, inference, comparing and contrasting. So, ironically, I may end up taking Ben to Kumon for reading.
KumonInstructorsProfile 21 Nov 2005 - 23:05 CatherineJohnson
from the Dobbs Ferry/Hartsdale/WhitePlains Kumon Centers:
Susan and George, working as a husband-wife team, have been running Kumon centers since 1989. Their original motive for running a Kumon center was to help their three daughters improve their math and reading proficiency. All of them benefited from the program: Ada, the oldest daughter, graduated from Cornell Law School and is now an attorney at a Wall Street corporate law firm; Wendy, the second daughter, graduated from MIT and is now pursuing her PhD in Biomedical Engineering at Johns Hopkins Medical School; Jamie, their youngest daughter, graduated from MIT, majoring in Computer Science, is now a Software Engineer working for IBM. Both Susan and George are strong believers of the Kumon philosophy. They enjoy working with children and take great pride in helping students improve their math and reading skills, and develop good study habits that benefit them in all school subjects. Since becoming empty nesters, George and Susan spend almost all of their spare time working at the Kumon centers. Currently, they run 3 centers in Westchester with a combined enrollment of over 200 subject students. Recently, one of their students, Edward Zhang, an eighth grader, just completed the entire Kumon math curriculum – Level Q!* Mrs. Susan Liu holds an M.S. in Statistics from the University of Rhode Island and studied in the Ph.D. program of Statistics at the Wharton School, University of Pennsylvania. In addition to being a Kumon instructor, Susan is a technical programming manager at an advertising firm. Mr. George Liu received his M.S. degree in Industrial Engineering from the University of Rhode Island and studied Bio-statistics at the School of Public Health, Columbia University. Besides being a Kumon Instructor, George is also a vice president at a major financial institution.
Kumon math sequence
Kumon reading sequence
GoalOfKumon 20 Nov 2005 - 17:57 CatherineJohnson
this is interesting—
The aim of the Kumon Math Program is to prepare students so that they can excel in high school Math. The lower level Kumon worksheets are designed to build mastery of the four operations, addition, subtraction, multiplication and division, which are the basics of mathematics. Students with a mastery of addition, subtraction, multiplication and division can easily learn more complex operations such as long division, fractions, equation solving and factorization. Students who are struggling with math's are most often those with poor foundation skills. Kumon’s programs are structured in a linear fashion to ensure that students master one concept before moving onto the next. Kumon students are able to progress based on an assessment of their own needs and skills. This is one of the major differences between Kumon and school-based learning. The Kumon Math's program consists of 23 levels covering content from counting to calculus. It is suitable for preschool children through to senior high school students and those doing tertiary study. The Kumon Math curriculum has 460 steps: from counting practice for pre-scholars (level 7A) to college level mathematics (level Q). Within those steps it is easy to find one that is "just right" for any child. There are 10 worksheets for each step, totaling 4,600 worksheets in all. Kumon believes that if children are having a hard-time learning, they should not be blamed. The problem usually lies in the type of materials being used, or the type of instruction being given. Based on this philosophy, Kumon worksheets are constantly evaluated to iron out any shortcomings. The path to advancement is made even smoother by the focus on repetition. This focus gives children the chance to consolidate each topic area until they can get the correct answers quickly and effortlessly. This level of fluency and the focus on practice feeds into and complements the formal teaching that children receive in school.
4,600 worksheets. That oughta keep me busy for awhile.
department of veiled references
Enrolling your child in Kumon will mean concrete learning steps every day. Kumon learning is practical and relies on paper, pencil, eraser and daily practice. Most parents would be familiar with this focus on content rather than on the tools of computers, calculators or theories.
In truth, there's not a lot of time left over for erasing.
TheKumonStudent 24 Nov 2005 - 00:38 CatherineJohnson
Kumon students are organized, tenacious, modest and skilled. With strong study habits and long term, positive learning experiences they are well prepared for higher learning.
Mr. Liu liked the Brian Mickelthwait article I gave him. He told my friend Kathy, who brought her daughter to the center today, that it accurately describes Asian culture. Asian culture, he said, 'is persistent and patient.' Me, I've always had to rely on a double-dose of persistent. Which is not a bad work-around.
The Kumon Method
ChicagoTribuneOnBadCollegePrep 18 Nov 2006 - 22:22 CatherineJohnson
from Susan, an article in the Chicago Tribune:
In the lowest-level writing class at Columbia College, freshmen learn about the pitfalls of run-on sentences and the correct places for commas. In basic math, they learn about fractions, decimals and simple geometry. Sarah Rehder didn't expect to start college in either of these courses. A graduate of Curie High School in Chicago, she assumed she was prepared for college. But like many students in the state and nationwide, Rehder learned through a college placement exam that she wasn't ready for college-level coursework. Now she's learning--and paying for--material that she arguably should have mastered in high school. [ed.: high school?] "I thought high school was supposed to prepare you for college," said Rehder, 18, a photography major and the first in her family to attend college. "I'm just doing the same thing over again that I did in high school. I didn't learn anything."
It's interesting that she's the first in her family to go to college. Her parents would have had essentially no domain knowledge about college prep, so they left her education up to the schools. Big mistake. Trust but verify.
who's in charge here?
State report card data released this month show that about 40 percent of high school juniors failed to meet standards in reading this year, and 47 percent failed to meet standards in math. In Chicago public schools, 59 percent didn't pass the reading test, and 73 percent didn't pass the math test.
question for Susan Do Chicago city schools use constructivist curricula? That figure—73 percent—is awfully high. I don't know what the tests are like, but usually you see disadvantaged urban kids scoring higher on math than reading, I think. At least, math scores on NAEP have been rising, while reading scores have been relatively flat. (I'll have to fact-check...)
how much do we spent not teaching kids fractions in grade school, middle school, and high school?
"You want to put those scarce dollars toward new classes, financial aid, and not toward remediating students for the same skills they should have been taught in high school," said Kristin Conklin, who studies college readiness as a program director with the National Governors Association. "The big equity argument that shouldn't be lost is that these are the students who can least waste money on classes that don't count." [snip] Last school year, 21.3 percent of community college students in college credit programs took at least one remedial course, spending $106 million on the classes, according to the Illinois Community College Board.
This is one of Laurence Steinberg's themes.
this is what we call a catastrophic failure
At the seven campuses of the City Colleges of Chicago, where the majority of students come from Chicago public schools, 61 percent of students who took the placement test were below college level in reading, 69 percent in writing and 92 percent in math. The numbers are higher for Chicago Public Schools students. At the University of Illinois at Chicago, 16 percent of students took preparatory English and 57 percent took preparatory math in fall 2004. But of the Chicago Public Schools students, 25 percent took preparatory English and 73 percent took preparatory math. The math classes do not count toward graduation. Even at the state university's flagship campus at Urbana-Champaign, about 6 percent of freshmen are taking math courses this fall that won't count toward credits needed for graduation.
This sounds like a good idea—
State Sen. Edward Maloney (D-Chicago), chairman of the Senate's higher education subcommittee, said he would like to see colleges send their syllabuses to high schools.
Better send them to the parents, too. In fact, send them to the parents first.
City Colleges of Chicago bears the brunt of teaching students who leave Chicago schools unprepared. More than 95 percent of Chicago graduates test into remedial math, and 70 percent test into remedial English. About one-third fail the courses. Those students then become the least likely to graduate, with only about one in 10 students who start at the lowest level of math able to transition to college-level math courses.
algebra in 8th grade
Nationwide, 34 percent of students take algebra before high school, but only 7 percent do in Chicago, Gartzman said.
Wow. I'm thrilled to have this figure. The figure for Christopher's 6th grade class is 30%. Thirty percent of the kids in his class will take real algebra—algebra that allows them to move on to geometry freshman year in high school. At $18,000 a student, we're below the national average. That's going on the Irvington page. Here's the full passage:
The district also is trying to encourage more students to take algebra before high school so they can take more difficult math classes before they graduate. Nationwide, 34 percent of students take algebra before high school, but only 7 percent do in Chicago, Gartzman said.
Finally! I've got it. Every time I raise the issue of Irvington's math track, school officials & faculty give me the run-around by citing revised New York state standards requiring algebra in the 8th grade. They simply will not address either the glaring KIPP/Irvington disparity or the glaring Singapore/Irvington disparity. 'All students will take algebra in the 8th grade.' 'The new standards mean everyone takes algebra.' 'They're changing the whole thing, so none of this is relevant.' etc. I need to stop framing the issue as, How many Irvington students will take algebra in 8th grade? The question is: How many Irvington students will finish taking algebra in the 8th grade? Better yet, How many Irvington students will take geometry in 9th grade? Duh.
update from Susan
It's interesting that the article focuses a lot on how high school may not be preparing kids for college, but fractions and decimals are k-8 skills that should have been mastered before high school. As we've noted here on many occasions, the derailment starts there.
KUMON grade 5
200 worksheets on fractions. I am sick that I didn't get Christopher into KUMON in Kindergarten. If we'd been doing KUMON all this time, Christopher would be breezing through Pre-Algebra, and I kid you not. The interesting thing is, he has no problem learning the concepts of pre-algebra. So far, distributive property aside, they're pretty easy for him. It's the plug and chug that's hard. Christopher will say, 'I left out the minus sign.' And it's true: the digits are correct, the sign is incorrect. This is not a minor difference, but when he's doing computations, he doesn't see it. When he's just 'working on' the conceptual understanding of negative numbers, he sees clearly that there is a huge difference between, say, 100 and -100. He sees, clearly, that negative numbers are less than zero on a number line, on a thermometer, in your bank account, etc. It's not hard. Solving open equations with negative numbers is a different story. If he'd done 200 KUMON worksheets on negative numbers, he'd be blowing through his pre-algebra tests with 90% mastery and above, easy.
ScopedOutKumonToday 22 Nov 2005 - 03:01 CarolynJohnston
I stopped by the local Kumon Center today, just to figure out where it was. As I suspected, it's walking distance from my work. It was empty, of course. Our Kumon Center is open on Mondays and Thursdays, from 3 to 6:30. Intermittent hours are typical, apparently, judging from my experience and Catherine's (her Kumon Center is only open on Saturday, something I hadn't quite caught on to!). It's in one of the ubiquitous office-suite complexes that are dotted all over Boulder; this particular one was hard to find, since it was mostly hidden behind a bank building, and the entry is through the parking garage. This office suite is unique in that it has a huge Japanese sand garden taking up most of the center of the second floor (whenever I see those things, I want to get in them and run all around and make footprints). Also in the same extremely spiritual office suite is the "Tibetan Cranial Massage Center". Tibetan cranial massage is much more a Typical Boulder Thing than Kumon. The outside of the Kumon Center has a sign that says 'Kumon mathematics instruction.' Is there no reading program at this Kumon Center? Can individual Kumon centers opt out of a whole line of instruction? The inside (seen only dimly, through darkened windows) looked cozy. There was a sign that said, "Sshh, this is our classroom." I saw bean bags and stacks of books and other materials. There was a drop box out front for Kumon sheets and instructions on what to do over the Thanksgiving break. There was a photocopied article from the Denver Post out front that said that American 15-year-olds are no longer internationally competitive in mathematics. I figure that if you've gone to the trouble of finding the Boulder Kumon Center, you probably already know about the TIMSS results. Boulder is a city of almost 100,000, with a highly educated and wealthy populace, but it apparently supports only one small center. You wouldn't expect Kumon to be very popular here, though. Boulder is the only town I know of that doesn't have a waiting list as long as your arm for the local Core Knowledge charter school. In fact, they had to go scrape up some kids last year in order to have a second kindergarten class.
KumonFractions 26 Nov 2005 - 21:36 CatherineJohnson
A ktm guest asked about Level E fractions in KUMON. Here's my favorite page so far:
pattern and rhythm This page is tremendously reinforcing. It is instructional practice to the max; working your way through this sheet, you can't not see the meaning of a whole number divided by itself. My friend Kathy, this weekend, called the Kumon approach conceptual practice.
Levels D, E, & F
The Greatest Common Factor problems were very challenging. The student is asked to reduce fractions with numerators & denominators that are multiples of the numbers 11 - 19 in one step and with only seconds to spare. (And they don't tell you this. It took me awhile to figure it out. Discovery learning at KUMON!)
Here's Level E:
Students learn to add, subtract, multiply, and divide fractions. Proper intermediate steps are emphasized. At the end of the level, students learn basic fraction/decimal conversions.
And here is Level F:
Students continue calculations with fractions, now employing the order of operations. Level F contains a challenging section of word problems, as well as more work with decimals.
G by 5
There are 200 worksheets in each level, and my understanding is that level E corresponds roughly to grade 5—although the goal in KUMON is G by 5, to complete level G by the end of 5th grade:
Kumon does not push children to advance, but Kumon does encourage children to set goals for themselves. Kumon Instructors reward performance and they often find that the child's own sense of satisfaction is a prime motivator. In other words, children who do well want to keep doing well; children who begin to advance in their studies want to advance further. One potential goal for Kumon students is to reach Level G, which is a fairly advanced level, by the fifth grade in school, or approximately age 10. This "G by 5 or "G5" is something you may hear mentioned when you visit a Kumon Center. Instructors often talk about children attaining G5 or being "on track" to hit G by 5. However, you should not think that this is the whole focus of Kumon. [snip] There is another, quite serious aspect to G by 5, however. Level G is a key point in both the math and reading programs. In math, it marks the introduction of algebra, and in reading this is where students learn key summarizations skills. In many ways, Level G marks the beginning of higher-level study. Many students who have never experienced difficulty in elementary school math and reading may find junior high school work very challenging: the pace picks up, grading becomes stricter in schools, and students' social activities begin to compete with academics. By reaching Level G by the fifth grade—roughly two years ahead of grade level—Kumon gives students an edge when they need it most. It helps children to avoid the frustration that is so common in making the transition from elementary to junior high school, and guarantees that there are no dangerous gaps in learning as children begin to tackle advanced materials like algebraic equations and critical reading.
I believe this absolutely. We would be in so much better shape around here if Christopher had been going to KUMON for years. I can see why brain periodization theory came into being; middle school kids are tough. Remember what the homeschooling Commenters said?
...from what I've heard from the other moms at the Well-Trained Mind message boards, the kids are still spacey at that age, no matter where they learn. They turn 12 and act like their brains have rolled under the bed with the dust bunnies, not to be found again for 2-3 years. It's not uncommon for them to forget how to do stuff they mastered three years before. They discover the opposite sex. Some of them get moody, etc.
Check, check, and check. It would have been an enormous advantage for Christopher to go into middle school with complete mastery of every single aspect of elementary mathematics. Kumon would have given him that.
I left out the minus sign
If Christopher had completed level G before going into Pre-algebra, I wouldn't be hearing 'I left out the minus sign' on a regular basis. 'I left out the minus sign' as in: 'I got the answer right, I just left out the answer sign.'
Students are introduced to positive and negative numbers, as well as to basic algebra. Students use their previously learned four operations skills to master linear equations. A word problem set rounds off the level, allowing students to apply everything they have learned in Level G.
I'm starting Andrew in KUMON math after Thanksgiving.
Chris Adams Chris Adams is our resident expert on KUMON:
We really see the good effects of Kumon on the math abilities of our younger daughter. She started about 1 1/2 years ago and is now in 4th grade. I too wish we had started our 9th grader much sooner. The initiative to start the youngest came during a parent/teacher conference in 2nd grade. After Kate explained an addition problem (written horizontally with no carries), the teacher said something to the effect of... "Kate, that was very good, but you know next year you will need to do a better job of explaining each step of your work". That was the catalyzing moment to enroll her in Kumon. The downside is that 4th grade math is boring to her, but at least she has Kumon to keep her challanged. However, the progress is incremental enough that I don't think she feels especially challanged by it, but the results, at least comparing her to her peers are quite satisfying.
I'm curious about how kids doing KUMON, which is intended to be supplemental, jump beyond their grade level in school. I still don't really understand how the program works.
homeschoolers talk about pre-teens
KumonAndFormativeAssessment 22 Nov 2005 - 20:38 CatherineJohnson
The new trauma is that apparently Ms. Roth gave a practice ELA test to the class, and Christopher & his friend M. hosed it. Fortunately, M.'s mom is radically on the ball; nothing escapes her notice. She called me Saturday morning, majorly ticked off, and said she wanted to know how Christopher did, because ELA is 'Christopher's thing,' which is true. He's the standard to use. Well, of course, I didn't even know Christopher had taken a practice ELA, much less that he had scored 2-slash-3, so now I'm not happy, either. Not that I was brimming with good cheer and satisfaction before that, but still. The fact is, when there's a Cone Of Silence surrounding your child's school, it's impossible to know what's going on. Is Christopher learning what he's supposed to be learning? And what is he suppoed to be learning, anyway? (Which reminds me, time to finally hit 'Purchase' on my Amazon order. E.D. Hirsch's What Your 6th Grader Should Know has been sitting in my cart since summer.) So tonight, Christopher did his KUMON reading sheets, and I was shocked to find that he missed these items:
The newsletter that was available at the stores had advertisements in [it them] (Christopher picked 'them')
The parents enjoyed the school play because _____ children were in it. (Christopher wrote 'her')
I had no idea he could get questions this simple wrong. The first one he really did get wrong; the second one he probably misread, but either way.....he's at a level now where he has to learn to force himself to take in every word, whether he's got visual 'issues' or not. The point is, I have no way of knowing where he is in English language arts, whether he's on track, whether he's off track, what he knows, what he doesn't know, etc. With KUMON reading I'll know what's going on.
I desperately need KUMON for expository writing I'm starting to get some ideas on how to do it..... And I'm thinking KUMON reading may help.
I sprang for a copy of this book on Saturday:
Which I see has now dropped to 39 cents. sigh UPDATE 11-7-2006: ended up never using it; sold it back to somebody else on Amazon Marketplace this fall
ScopedOutKumonTodayPart2 22 Nov 2005 - 18:25 CarolynJohnston
Having figured out yesterday where the Boulder Kumon center was, I stopped by today during its open hours. There was a sign next to the Japanese sand garden that said "please don't step in the sand," and someone (the Tibetan cranial massage place?) was burning some incense. Boulder is overwhelmingly white, and so the Kumon center may be the most diverse place you'll find in Boulder. There was a freckled teenage girl, and an Indian family, and a cute little Asian boy in Crocs, probably in kindergarten or younger, working on a worksheet (in between writing short answers on the page, he was amusing himself by pressing the eraser end of his pencil against his nose). The promise of Kumon was being fulfilled; even the little tiny boy with the pencil was working on his own, without adult intervention. I spoke for a while with Ginny, the proprietor, about having Ben start the Kumon reading program. I told her that my son has Asperger's Syndrome, and asked her if she knew what that was; I was curious, because the thought style and problems of kids with HFA takes some getting used to. The teachers in his elementary school were rather nonplussed by his combination of strength in language mechanics and spelling, and weakness in inference and reading comprehension; by the time he left, they'd had 3 students with autism spectrum disorders and had figured things out. She was familiar with Asperger's Syndorme, and we talked for a bit about his needs. She gave me some detailed material about the order and structure of the program. The really amazing thing is the math program, which Ginny told me is actually older and more fully developed and calibrated than the reading program. It's amazing to see where it leads... the program begins with counting 1 through 3 and number boards, and ends years later with differential equations, probability and statistics, and matrix algebra and linear transformations. But the reading program looks good, too. Ben can be strange to teach reading, since he is so strong in some of its aspects and so weak in others. He'll be moving fast in some parts of the program, and with difficulty through others; that's okay. Kumon is self-paced. When I asked about her own background, Ginny told me that she was a major in Japanese, and that she had learned all the material taught in the Kumon program from doing the Kumon program herself. Ginny is a Japan consultant with long-term connections to Japan; that's how she got interested in Kumon ("the Japanese businessmen I worked with wanted to know why Americans were so crummy at math," she said). I gave Ginny my business card—and, in a fit of what-the-heck, wrote the KTM URL on the back of it. "This is you?" she asked. I simpered (recognition at last!). "Why yes, that's our website," I said. "Chris Adams told me about your website! I like your website!", she said (that would be our ChrisAdams, who is schlepping his daughters in from Longmont to attend the Boulder Kumon). Alas, KTM usability has been a problem for Ginny; I think the mixed-case stuff can throw people. Most places on the web, upper-case vs. lower-case doesn't matter all that much, but it does around here! Hopefully Ginny will come visit, and check out all the stuff that's been discussed on the Kumon program, teach us a little bit about how she teaches, and perhaps fill us in on teaching and learning in the mysterious East with which she is so familiar.
TrailblazersAndTheAlgorithms 29 Nov 2005 - 14:17 CatherineJohnson
I talked to a friend whose son is in second grade. He's a brainy kid who loves math, but he can't use the addition algorithm—because it hasn't been taught, apparently. If he's adding numbers smaller than 20, he counts on his fingers and toes. If the numbers are larger than 20, say 12 + 19, he draws 12 circles, then 19 circles, and finally counts them. Same process for subtraction, only in reverse. 63 - 19 means drawing 63 circles, then crossing out 19 of them. The kids have the triangular flash cards that portray number families, and her son is working on flashcards with numbers 1 - 10. A friend of hers whose child is in 3rd grade told her those children are working on the exact same cards. Adding and subtracting numbers 1 through 10. In third grade.
what the people who wrote TRAILBLAZERS have to say about this
Our approach is based on educational research and is supported by the National Council of Teachers of Mathematics’ Principles and Standards for School Mathematics (2000). It is characterized by the following: • Emphasis on problem solving. Students will learn the basic facts if they are encouraged to use a problem-solving approach. Students can invent their own strategies, learn from their peers, or learn from the teacher through class discussions. Students will discover the need to learn the facts as they encounter them in labs, activities, and games. • De-emphasis of rote work. Students learn their math facts, but we de-emphasize the use of rote memorization and in first grade we do not administer timed tests. These can produce an undesirable result—students perceive that doing math is memorizing facts and rules which “you either get or you don’t.” Instead, students should feel confident that they can find answers through the use of strategies they understand. Throughout first grade the focus remains on the use of strategies that are meaningful to students. Beginning in Unit 11, a systematic organization of the math facts is introduced via the Daily Practice and Problems. Facts are grouped together in ways that may help students think of them in a more efficient manner. However, students are still free to solve the problems using whatever strategies they wish. By the end of second grade, students in Math Trailblazers are expected to demonstrate fluency with the addition and subtraction facts. The first grade curriculum enables them to build to this fluency through experience with and understanding of the concepts of addition and subtraction.
This passage illustrates the difference between 'research' and 'field-testing.' TRAILBLAZERS is now being used in the field, here in Irvington. Do we see children demonstrating fluency with the addition and subtraction facts by the end of 2nd grade? I don't know the answer to that question. From what I hear, it doesn't sound like it. What I'd like to know is: does anyone have an answer to this question?
the kindness of strangers
My least-favorite reform-math slogan:
• Facts will not act as gatekeepers. Students are not prevented from learning more complex mathematics based on their fluency with the math facts.
All children of normal intelligence can learn math facts. No doubt many children with mild mental retardation can learn math facts as well. A responsible educator figures out how to teach math facts at the earliest possible age, and makes sure all children have learned.
source: TIMS Tutor grades 1 - 5 (pdf file)
HowCanCollegeFreshmenFillGaps 30 Nov 2005 - 18:34 CatherineJohnson
from Anne Dwyer:
Going back to the question of what to do with students who have large gaps in their background: We (someone, I forget who) once asked this question on this site: once you have these large gaps in your knowledge, can you ever catch up and close all the gaps? I think this is especially relevant at the college level. There is a basic math course at our community college, but it goes incredibly slowly. The prealgebra class gives basic lip service to large number problems, then goes straight into algebra. Towards the end of the course, the curriculum goes back to decimals and percentages and conversion factors. But, by then, many of the students are completely and totally lost. Then, they break basic algebra into two classes: elementary algebra and intermediate algebra. Even with a tutor, there isn't enough time to determine where the weaknesses are and to go back and correct while the student is taking the class. This would require them to work on parellel tracks: making up gaps and keeping up in class. Everything is geared towards students keeping up in class not preparing the student with the basics for the class.
This was a conundrum for me. I don't know the structure of mathematics well enough to be able to tell where I have significant gaps and where I don't; if I did, I (probably) wouldn't have gaps. This is why I decided to go back and re-learn everything from the beginning. That way, I figured, whatever gaps I didn't know I had would get taken care of. I didn't end up being able to do that, mainly because I had to keep up with Christopher. So I started in 5th grade, where he was. I'm wondering whether KUMON would be a good idea for students in this position. I started in Level D—roughly 4th grade—and moved to Level E after two weeks. Algebra begins in Level H. Each level has 200 worksheets, and you do 5 worksheets a day, 6 days a week. (I think you're supposed to do 5 worksheets a day, 7 days a week, but Mr. Liu only gives me enough for 6 days.) If you figure roughly 7 weeks per level, I'll move from Level E to Level H in 21 weeks. I can do that and easily do everything else; my KUMON worksheets are the least demanding part of my day. So I think an ill-prepared college student swamped with remedial work could do KUMON sheets and keep up with his classwork. I gather there are some adults taking KUMON; I wonder if any of them have written about it.
KumonForEnrichment 01 Dec 2005 - 00:11 CatherineJohnson
A friend of mine, back in Studio City, once told me that every time she read an article in the Los Angeles Times about a subject she knew well, the article was wrong. I've just had that experience with this Dallas News (pdf file) article on KUMON, but I'm quoting it anyway, in hopes that the material I don't know anything about is more accurate than the material I do know something about. Here's the glaring mistake:
Costs, which can range into the hundreds of dollars per month, often are determined by whether a child is in a remedial or enrichment program.
Wrong on both counts. KUMON never costs hundreds of dollars a month; the highest fee anywhere in the country is probably $100 per month. I pay $85. The fee has nothing to do with whether you are using KUMON to remediate a slow student or speed up an average or fast student. There's no difference one way or the other; it's the same program. For what it's worth, here's the passage that interested me:
These centers are not like in the past, when tutors were associated mostly with students who fell behind. Increasingly, centers such as Sylvan and Kumon cater to parents trying to give their kids an edge in more competitive classrooms. And now, more than ever, some see them as an educational necessity for little Timmy or Jane. Kumon’s Web site says it has more than 123,000 students in 1,200 U.S. centers. Sylvan boasts nearly 1,000 centers in the nation. “You’ll have children who are struggling, who failed the Texas Assessment of Knowledge and Skills,” said Ken Darden, who runs two Kumon centers in Dallas with his wife, Barbara. “But the other market, the one that is growing fast, is the ‘enrichment’ market, for parents who want to make sure their children get into private schools or stay at the top of their class.” The goal at Kumon, Mr. Darden said, is for students to be able to do basic algebra by the time they’re in fifth grade. Typically, students visit one of the centers once or twice a week for about an hour each time. They complete sequential worksheets and are graded based on accuracy and speed. Kumon also expects a student to complete a weekly packet of worksheets and to do timed assignments for 15 to 20 minutes a day, seven days a week. [snip] Plano parent Martha Boyd said she looks at supplemental education as a necessary investment. “It’s such a joy not to have them struggling in math,” said Ms. Boyd, who has sent her two daughters to one center for several years. “They’re so far above their grade level.”
I hope that last quote is right, for Christopher's sake and for my own. I would really like him to show up at his high school math courses ahead of the game. As I've mentioned, Wayne Wickelgren advises teaching your child 30% of the material in any accelerated math course before he enters the class. (I think most behaviorists would call this "priming.") KUMON does that. I'd like to be in the same boat when I finally take trig & calculus.
update: canaries in the coal mines Becky C has a wonderful line about KUMON parents being canaries in the coal mine. Apparently we are a growing population:
January 19, 2005 (Teaneck, NJ) - Driven by parent demand, the tutoring industry is expected to grow by 15 percent in 2005 according to the Education Industry Association. Higher expectations, low test scores and mounting competition for admission to top-tier universities is boosting student enrollment at tutoring centers across the country. At Kumon Math and Reading Centers, enrollment has increased by 55 percent over the past four years and as a result, the company expects to open 150 new centers in 2005 to meet the demand.
press release: ELEMENTARY SCHOOL PARENTS DRIVE DEMAND FOR TUTORING PROGRAMS
The tutoring situation is interesting in light of NCLB. Last year I read an interesting paper on NCLB written by, IIRC, Paul Peterson, published by Brookings. He argued that NCLB would not work in its 'hard form,' because schools wouldn't be adequately held to account. But he predicted that NCLB might well work in its 'soft form,' which was the public exposure of having to publish bad scores. NCLB would produce a shaming effect. I've begun to have my doubts about the shaming effect. But I'm beginning to wonder whether all the focus on test scores could be having an effect on parents. It's one thing to constantly read news stories about the 'crisis' in American public schools. This stuff goes in one ear and out the other a lot of the time. It's another thing to receive your child's Official Scores in the mail. The thing about state scores is, they're bad news no matter what. If the scores are low it's horrifying; if the scores are high it's also horrifying. I've now seen a copy of the 4th grade test here in NY state. Christopher got his 4s, but they'd be 2s in Singapore. A couple of years of this and you're in KUMON.
SadBeanKumon 18 Jan 2006 - 00:24 CatherineJohnson
A ktm guest left this. I love it!
KumonWriting 16 Dec 2005 - 22:07 CatherineJohnson
I've been forgetting to thank Carolyn for our new categories:
learning to write with KUMON Reading I've mentioned that Ben Franklin taught himself to write persuasive essays by reverse engineering other people's persuasive essays. He'd cut apart the sentences (IIRC), then try to reassemble them in proper sequence. I've tried this myself. It's much harder than it sounds. KUMON Reading (which I think is a superb program) does something similar, which I suspect would help any child develop a mature expository writing style. Here it is: Rearrange the words to complete the sentences. 1) A rocket is a spacecraft __________________________________.
[ that / space / allows / to / reach/ humans / outer ]
2) __________________________________ ,
the probe is navigated from afar.
[ are / humans / as / aboard / there / no ]
3) The universe is __________________________________ .
[ exist / matter / space / and / all / where ]
the scientist boasted.
[ now / we / " / " / have / technology / the / , ]
KUMON Reading worksheet E1 77a (5th grade)
answers: 1) A rocket is a spacecraft that allows humans to reach outer space. 2) As there are no humans aboard, the probe is navigated from afar. 3) The universe is where all space and matter exist. 4) "We now have the technology," the scientist boasted.
This is sophisticated prose, and it's difficult to teach to children, or to students of any age. Left to his own devices, no 5th grader—these are 5th grade worksheets—is going to produce sentences like these. Doing this exercise forces the child to focus on the 'smallest units' of writing, words and punctuation marks. It also directs the child's attention to the 'Exactly Right Words,' to see that the difference between the best composition and the next-best is the difference between lightning and a lightning bug (wasn't that the Mark Twain analogy)? Christopher, for instance, constructed sentence number 4 in this way: "Now we have the technology," the scientist boasted. That's perfectly fine. It's grammatically correct; it makes sense. But it's not as elegant as 'We now have the technology,' and in fact it doesn't work as well with the verb 'boasted.' This is a subtle point. Offhand I can't think of a better way to make it (or of any way to make it at all, as a matter of fact). The same principle holds with number 3. It would be grammatically correct to write, The universe is where all matter and space exist. But it wouldn't be as good I would imagine that the only time in school students are taught to pay such close attention to language would be in reading and writing poetry. Not expository prose. (If anyone knows expository writing programs that do teach the subtleties of style, let us know.)
learning to read expository prose I've often read educators saying that, in 4th grade, children must begin to read for content. Unfortunately, they haven't been taught to do this. The reading programs of elementary schools are fiction, fiction, and more fiction, along with a personal narrative or two. Children aren't taught to read and interpret expository prose. Another missing piece.
Andrew to KUMON I'm starting Andrew in KUMON math today. Mr. Liu saw him in action last week, and told me to bring him at 4. In preparation, I'm going to spend the rest of the afternoon chanting persistent and patient under my breath.
do narrative reading skills transfer to expository reading? The Direct Instruction folks say no, which would be my guess:
Narrative reading skills do not readily transfer to expository reading. Narrative and expository texts have been found to have differential effects upon readers, with narrative being easier to comprehend than expository (Zabrucky & Ratner, 1992.) The ability to comprehend and formulate expository prose is essential for achievement in school (Seidenberg, 1989).
articles, marketing material from EPS, College Board report Seidenberg, P.L. (1989). Relating text processing research to reading and writing instruction for learning disabled students. Learning Disabilities Focus 5 (1), pp. 4-12.
Zabrucky, K. & Ratner, H.H. (1992). Effects of passage type on comprehension monitoring and recall in good and poor readers. Journal of Reading Behavior 24, pp. 373-391. Writing Across the Curriculum Series by Patrice Cardiel, Ronda Cole, Mary Kay Hobbs, et. al. By Anna Cimochowski, Ph.D. research supporting the Writing Across the Curriculum Series published by EPS. You may have to Google to find it. This is marketing material, but often these papers are useful. Report of The College Board National Commission on Writing in America's Schools and Colleges, pdf file to download at EPS.
CreativeKumon 12 Dec 2005 - 16:30 CatherineJohnson
Well, Andrew is launched on his KUMON career, which means I should officially stop calling myself a writer & start calling myself a KUMON worksheet grader. Remember that mugged-by-reality mom Susan told us about? The one who threw herself into progressive education and didn't find out 'til 7th grade that her children weren't learning? One of my favorite passages from that story was this one:
As full understanding of how progressivism had failed my children finally dawned, I was furious - more with myself than anyone else. But, I can no longer spare the emotional energy which anger consumes. It takes all I've got to stay attuned to three children from 3:00 to 10:30 p.m. sufficiently to correct Kumon math, direct grammar remediation, go over their SRA reading comprehension work, monitor the writing process program, and check assigned homework for the knowledge gaps which have undermined so much prior learning...and somehow attend to the non-tutoring aspects of parenting...
I'm there. I'm so there that tonight I'm shaking in my boots because Christopher moved up levels today (from C to D) and I forgot to get a copy of the D Level answer book. This means I'll have to do all the calculations on my own worksheets and all the calculations on Christopher's worksheets in order to check his answers. I don't think that's going to be possible.
next thought We should find out what writing program that mom is using. (Though I tend to hate anything calling itself 'writing process.' No idea whether that's a rational prejudice or not.)
Mr. Liu meets Andrew Every once in awhile we get going on the creativity gap Asians seem to feel separates them from us. I tend to think there is a creativity gap, mainly because there's a bipolar gap, and bipolar disorder is associated with creativity. John and I said something along these lines 10 years ago (we said there was a hyperactivity gap, to be precise), and since then others have begun to talk about the manic roots of American creativity. For instance:
So today I saw it. I took Andrew to meet Mr. Liu. Andrew is adding simple sums now, and I took his schoolwork to show Mr. Liu. Andrew can't talk and he can't write, so in class he uses number stamps & an ink pad to record his answers. I have number stamps here at home, and I took those with me, too. I showed his work and the stamps to Mr. Liu. He peered down at them, and said, in his quiet voice, "I don't think he can do KUMON, because KUMON is all writing." I said, "Well, he can use the stamps." I was holding the stamp set in my hand, and Mr. Liu was looking at it. Mr. Liu said, "We don't have stamps here," and then looked partway around the room, as if to say, "You can see that we have no stamp sets." I said, "I have stamps." Mr. Liu carried on frowning at the stamps. He was thinking. I felt like a Martian, which is how I felt the first day I met Mr. Liu and presented my middle-aged self as a KUMON candidate. Somehow we maneuvered past this obstacle, and Mr. Liu found himself asking whether Andrew should start with the counting pages. This was an innovation. No KUMON instructor asks a parent where a child should start. The KUMON instructor gives the child a placement test, and places the child according to the results. That's what I thought Mr. Liu would do. That was obviously what Mr. Liu had thought he would do, too. Now, however, he was at a loss. Andrew was starting to jump, slap himself on the side of the head, and scream, which wasn't helping matters. This is where it's good to be a touch hypomanic. Mr. Liu was looking more doubt-filled by the moment, but when you're a touch hypomanic other people's doubt is not a problem. I asked for some samples of the Counting Level worksheets, and Mr. Liu obligingly handed me a sample book containing all 200 of them. I started showing them to Andrew. Boy, can that child count. He's way past the counting level. I was able to find this out thanks to my Native Creativity. I would flip open to a page at random (I hope Mr. Liu didn't have to witness that), ask Andrew to count the items, and then have him pick the appropriate number stamp but stop him before he actually stamped the page and ruined it. So now I have KUMON math for Andrew, too. Mr. Liu decided to try Andrew on some of the number-writing sheets, which I'm game for. Andrew is starting to write (physically write, I mean) and if I could get him on track to write on KUMON sheets that would be a good thing. I'm thinking, Let's forget all this creativity stuff, and just have Andrew write the numbers down on the worksheets like a normal human being. We'll see.
update "What was really amazing was the speed with which the Americans adapted themselves….They were assisted in this by their tremendous practical and material sense and by their lack of all understanding for tradition and useless theories." - Erwin Rommel, 1943 Andrewsullivan.com May 7, 2003
AlphaSmart (& letter to LA Times)
AlphaSmart & Andrew & KUMON
AlphaSmarts reduced 30%
CommentsToCome 15 Dec 2005 - 20:33 CatherineJohnson
I have a boatload of Comments to get pulled up front.....which means it's going to take awhile. I thought I'd mention that the reason I pull Comments up front is that a) I don't want casual visitors to miss the super-meaty ones and b) once a Comment is on the front page it's part of the Category thread, so anyone reading that thread will be sure to see it. (All Comments stay connected to the original blooki posts, but a person reading through the KUMON category, say, isn't necessarily going to have the patience to click on each post individually so he/she can read each Comments thread individually. So these things need to come up front..... I've finally begun disciplining myself to KEEP A LIST, and here's what I've got at the moment:
If there are things I've forgotten, let me know.
other Since I'm posting a public to-do list, I also need to:
I should probably go ahead and buy DON'T MAKE ME THINK....
IfTheStudentHasntLearned 23 Dec 2005 - 22:16 CatherineJohnson
revision From Catherine: Our new pretend-shirt specifically says "If the student hasn't learned, the school hasn't taught," not 'the teacher hasn't taught'. No more thoughtless (and unintended) teacher-bashing. Seriously. I'm the last person to want to make teachers feel blamed and bashed, seeing as how half my relatives have been or are currently teachers. I'm sure I'll be one again at some point, too. The problem is that, when you talk about schools, it's the teachers who are visible. They're in the trenches, so they get the blame. (I realize I'm not telling teachers anything they don't know.) I know better than that, but I've been sounding like I don't. Time for a course correction.
From Carolyn: Hey, my entire family on my mother's side were also teachers, every man and woman Jack of them. I've been a teacher too; so has Catherine. My observation is that policy flows downhill in a school, and the buck stops with the teachers. They get the responsibility, but not the authority; policy changes really have to start with upper management. We're here to put the pressure on upper management, and support the teachers in doing what they know how to do.
ReadingDiagnosticAtKumon 10 Jan 2006 - 14:47 CarolynJohnston
Ben and I visited Ginny at the Kumon Center tonight, so that Ben could take the diagnostic test for placement in the Kumon reading program. Ginny and I had a great time talking while Ben ground away at the diagnostic test (just kidding about the grinding-away part -- I just wanted to leave you with the accurate picture of Ginny and Ilaughing and yakking while Ben swotted away on his exam). She was a Japan consultant for a long time, working with American executives to help them learn to deal with Japanese executives. She started a Kumon franchise about 8 years ago because she really believed (and believes) in what Kumon can do for students. It looks as though Kumon might be able to do a lot for Ben. She gave him the primary 6 placement exam in reading, for 6th graders. When he sat down with it, he actually said, "Finally, some real language arts! With real grammar practice and writing! Not this stupid lit log stuff all the time." I was surprised to hear him say that. I know he's treading water in his language arts class -- I know he is not learning much, and he's doing no real expository writing at all. It's a joke, actually. He went to a Core Knowledge school, and they did extensive research reports on topics in history every year after 2nd grade. That was intense; maybe even a little too intense. But when it gets to the point where BEN HIMSELF is complaining about the lack of teeth in his language arts class -- then I sit up and take notice. I was delighted with his performance on the reading exam. She gave him the 6th grade diagnostic test and he went all the way through with one small error. It wasn't easy material, either. What really impressed me was one problem -- which he aced -- in which a short story had been broken up into 8 or 9 single sentences and rearranged; the testee was supposed to number them in their correct order. It wasn't a trivial task. What's amazing about the fact that he aced this question is that sequencing -- correctly ordering things -- was one of Ben's weakest areas, cognitively, as a young child. We spent hours with the Playskool stacking rings and stacking cups, trying to help him put them in the correct order; later, we worked with sets of 3 or 4 simple cards that told a story if you put them in the right order. It is something that typical kids do pretty easily, and we had to work hard to catch up. Eventually we left them behind and moved on with his childhood, because you have to, but to find that he has somehow magically more than caught up in this area is an extremely pleasant extreme surprise. He placed into a section in which he'll work on dependent clauses, mastering the main idea of a paragraph, and vocabulary. Extracting the main idea of a paragraph is one of the most difficult tasks for any autism spectrum kid -- as Catherine and Temple say, autism is a disorder of hyperspecificity. People with very high-functioning autism will seize on a million irrelevant details in a narrative, and completely miss its main point, something we typicals can extract almost without thinking. I am excited about Ben's starting Kumon reading; his success on the diagnostic test is a good omen. And it also did me good to hear Ginny say, "he does well." Because I've known in my heart for years that he does really well, and is someone to be proud of, but I'm often out there waving the flag all by myself.
(Comments thread: notes on DOUBLE YOUR CHILD'S GRADES by Eugene Schwartz — teaching your child to read analytically & take notes)
FunKumonProblem 16 Jan 2006 - 21:10 CatherineJohnson
1/2 + 1/4 + 1/8 + 1/16 source:
-- CatherineJohnson - 16 Jan 2006
INeedPaper 19 Jan 2006 - 02:40 CatherineJohnson
btw, I do need paper. I started having a terrible time with my KUMON worksheets just last week.... I discovered 2 things: a) I need strong light b) I NEED LINED PAPER
The problems I'm doing now are fairly complicated 3-fraction operations, sometimes with decimals thrown in, and all four operations on the same worksheet & often within the same calculation. To do such problems rapidly and accurately I need strong light and lined paper. I'm finding that I'm losing track of where I am and what I just did to what (especially since these problems always involve canceling)..... Temple told me that fully 1/3 of the brain is committed to vision & visual processing, a factoid I saw confirmed recently (though I'm not going to dredge up a source right now). That tells me that if our kids are doing complicated math problems on unlined paper.....they shouldn't be doing complicated math problems on unlined paper. You're eating up a whole lot of brain resources trying to keep track of fraction computations on unlined paper. (Apparently the NY state tests are all given on unlined paper, and the kids aren't allowed to use any paper but the test paper. Another smart edu-move!) Anyway, from now on I'm going to try to always take a look at the visual environment whenever Christopher or Andrew are having problems doing math (or any other academic subject).
I need paper
good lighting redux
-- CatherineJohnson - 17 Jan 2006
WhatSaxonAndKumonHaveInCommon 26 Jan 2006 - 20:37 CarolynJohnston
We're doing lesson 50 tonight, in Saxon Math 8/7... it would be cool if this were exactly halfway through the book, but it's not; there are 70 lessons to go. We'll celebrate when we get to lesson 60. We've long since settled into a routine; a teacher's aide works with him to get him started on a new section during his math period, and then he comes home and does the mixed practice set, which is the heart of every section and the most work-intensive part (the nightly Major Homework Fuss is also part of our routine, which may be more time-consuming than anything else). It consists of about 30 problems covering topics from previous sections, and presenting a couple from the current section (there is a much shorter 'targeted practice' problem set presenting only problems from the current section). If a kid is having a hard time with some concept, you'd have to be blind not to notice it with that much repetition. The Saxon program is wonderful. It's carrying Ben forward so gradually that acquiring the day's new bit of knowledge never feels like a strain; and yet, there's no doubt that Ben is learning a great deal from this curriculum, and rather quickly at that. Saxon isn't quite perfect -- the lessons are ordered a little incoherently for my taste -- but I'm very pleased with the skills and knowledge Ben is developing. Kumon is the same way; it builds slowly, and yet it really gets you there. Its approach may really be the ticket for getting autism spectrum kids working comfortably on their own. Kathy's daughter Megan finds its pace and regularity soothing enough that she's enjoying doing it, and actually asks for it; Catherine reports that her Andrew is enjoying doing Kumon math (though he's not asking for it yet). Ben has begun doing Kumon reading. He's been placed into a section where he's studying main and dependent clauses, and even with the amount of time he already spends doing homework, Ben is finding this little bit of added work unburdensome. It's easy; but until he started doing Kumon, he didn't know what main and dependent clauses were (and frankly, I wasn't so clear on the concept anymore, either). This is the strength of Saxon and Kumon; the 'incremental approach', where you build slowly, but don't leave topics behind when you take up new ones. For Saxon, at least, it means a higher volume of time spent working in the problem sets than most math curricula provide now. What's the average size of the homework set in the major curricula? In Saxon, there are about 40 problems a night to do -- but most of them are exercising well-established skills. Some might think that's boring -- but kids love to exercise their skills, as long as they can do it successfully. I noticed when Ben was little, and doing applied behavioral analysis, that if I gave him a task that was going to be difficult for him, he would balk at trying it. However, if I gave him 5 tasks in a row, 4 of which were easy and the fifth of which was the one I really wanted him to try, he would do the 4 easy ones and keep the momentum going right through the fifth, more difficult task. If I had to sum up the strengths of both Kumon and Saxon in a single word, that would be the one; they both build momentum. -- CarolynJohnston - 26 Jan 2006
AccelerationNotRemediation 16 Sep 2006 - 20:38 CatherineJohnson
Carolyn's dead right about Saxon: the program moves students along at a brisk clip.* I was thinking about it just last night, while I was doing my own Saxon lesson. I'd put money on it I'm learning lots more than Christopher, whose book is, technically speaking, more advanced. And I'd put money on it he'd end the year knowing more than he's going to know with Prentice-Hall if he were using Saxon, too.
slow and steady wins the race The conventional wisdom about 'behavioral' programs like Saxon Math is that they're remedial; they're for slow learners. Well, it's true. If I were teaching a class of slow learners, I'd choose Saxon Math in a heartbeat. But Saxon also moves fast learners through material at a fast clip. If you're a fast learner, you just work through the material more quickly. Back when Christopher and I were using Saxon 6/5, the 5th grade book, we were doing complete full lessons a day for a time. Only recently have I realized that Teaching to Mastery means accelerating a student's rate of learning. High achievers move faster with Direct Instruction:
Tarver and Jung reported that the Direct Instruction program was equally effective for lower and higher performing children who participated in the study. Other studies provide additional evidence that Direct Instruction programs accelerate the learning of high-performing students in language (Robinson & Hesse, 1981), reading (Schaefer, 1989; Sexton, 1989), and science (Vitale & Romance, 1992).
low achievers move faster, too Direct Instruction is, expliticly, a teaching approach designed to produce 'maximum acceleration' for all students at all levels. (see: Student-Program Alignment and Teaching to Mastery by Siegfried Engelmann) Not only can low achievers be accelerated, when they are accelerated their learning curves look like those of fast learners:
I find this counterintuitive and almost bizarre. When taught to mastery, low IQ students learn at the same clip as high IQ students? Hard to believe. On the other hand, I wouldn't be surprised. So many of our decades-old beliefs about students and learning are just pure ideology. So I hope Engelmann's right. Here's what he has to say:
Even students who would be predicted to have low levels of achievement benefit greatly from Direct Instruction. Gersten, Becker, Heiry, and White (1984) examined the yearly achievement test profiles of students in Direct Instruction classrooms to determine whether annual gains made by students with low IQ scores differed significantly from the gains made by students with average or superior IQ scores. Figure 2.11 [above] shows the yearly gains made by students in reading as measured by the Wide Range Achievement Test. As shown in this figure, students with higher IQ test scores started at higher achievement levels and ended with higher levels than their peers with lower scores. However, the pattern of growth of students with low IQ scores is remarkably similar to that of other students. The group with the lowest scores (under 70) gained nearly as much each year in reading as students with much higher scores. By the end of third grade, those students with the lowest IQ scores were performing at the 70th percentile, or a grade equivalent of 4.3. The results are even more pronounced in math as seen in Figure 2.12 [below]. This figure shows the students’ performance on the Metropolitan Achievement Test. The growth rate for all groups of students corresponds to one grade equivalent for each year in school.
These results provide evidence that Direct Instruction is appropriate for, and effective with, a wide variety of individuals including those with low IQ scores, those with IQ scores in the average range, and those with high IQ scores. In addition, because children in this study were taught in small homogeneous groups (having students with relatively the same skill levels), the gains of students with lower IQ scores were not made at the expense of other students nor the other way around. Several reviews of research focusing on the use of Direct Instruction with special education populations have all converged on the finding that Direct Instruction is measurably effective with these students. White (1988) reviewed 25 such studies and found that all comparisons favored the Direct Instruction group. Forness, Kavale, Blum, and Lloyd (1997) conducted an analysis of various intervention programs for special education and determined Direct Instruction to be one of only seven interventions with strong evidence of effectiveness. Perhaps because Direct Instruction programs have been so successful with students who have failed in other instructional programs, their use is commonly associated with children who are behind, who are failing, or who are at risk for failure. And some have questioned their appropriateness for general education. However, Figures 2.11 and 2.12 provide direct evidence of the effectiveness of Direct Instruction for students with IQ scores in the middle range and those in the upper range. Engelmann and Carnine (1989) found that typical second graders who had received 2 years of Direct Instruction scored an average 4.6 grade equivalent in reading on a standardized achievement test. The children’s average scores in science and math were 4.0 and 3.4, respectively. Other researchers have arrived at similar findings. Tarver and Jung (1995) investigated the effects of a Direct Instruction math program (Connecting Math Concepts) and a discovery learning math program on the math achievement and attitudes of general education students in the primary grades. They found that, at the end of second grade, the children in the Direct Instruction program scored higher on measures of math computation and math concepts than children in the comparison group. In addition, children in the Direct Instruction program had significantly higher scores on a survey of attitudes about math. Finally, Tarver and Jung reported that the Direct Instruction program was equally effective for lower and higher performing children who participated in the study. Other studies provide additional evidence that Direct Instruction programs accelerate the learning of high-performing students in language (Robinson & Hesse, 1981), reading (Schaefer, 1989; Sexton, 1989), and science (Vitale & Romance, 1992).
acceleration for all students through Direct Instruction in a nutshell
KUMON is an acceleration program, too Interestingly, KUMON adds the element of teaching children to become 'self-learners,' i.e. self-teachers:
Our aim should be to educate our students so well through the Kumon Method that they don't have to depend solely on classroom activities to be able to deeply understand the course content. Students who develop this capacity will have a good chance to enter leading universities. To make this possible, we must help students acquire the ability of self-study from an early age and accelerate their level of study beyond their school grade. (Emphasis added)
Here is the irony. When Ed and I told our 'Team' that we want the school to be responsible for Christopher's learning, as opposed to Christopher being responsible for Christopher's learning, the principal objected. Christopher has to learn to be responsible, he said. He'll need it in high school. It was another helicopter parent moment, though neither hostile nor critical. The essential meme in middle schools everywhere seems to be that helicopter parents don't 'allow' their children to grow up and become responsible for themselves and their studies. But KUMON says that a Teach-to-Mastery approach builds responsibility in children. I don't understand quite how that happens. But I believe that it does. I think this is one of those Bayesian issues where parents have the right idea, without knowing why they have the right idea. A parent sees his child floundering and failing, and knows this is a bad thing. The parent knows the child will be far better off if the school continues to 'coddle' and 'protect' him while he learns the material his teachers are teaching. But how do we know this? What are we basing it on? It's the same problem parents have 'knowing' fuzzy math is bad. The minute I heard about fuzzy math, I knew it was bad. But could I say why it was bad? No. Same thing with 'responsibility.' Obviously, I want Christopher to grow up to be a responsible person. And yet, somehow, I'm in the position of arguing 'against' Christopher being responsible. I know — in the Bayes way of knowing — I'm right. But I don't know why. UPDATE 10-20-2006: Now that my child has spent one year in a math class in which full responsibility was placed upon parents for reteaching and students for learning, this issue is no longer a mystery.
* ed. update 4-21-2006: Dan has some reservations on this score. It's certainly true that the Saxon books have a tremendous amount of repetition from one book to the next. Mike Feinberg of KIPP on spiral curricula
Steve and Susan J on spiral curricula
acceleration versus remediation
parents' stories about spiralling curricula
-- CatherineJohnson - 26 Jan 2006
DirectInstructionAndTheRigorConundrum 16 Sep 2006 - 20:39 CatherineJohnson
There's all kinds of good stuff in the various comments threads — in particular, Rick Ballard, who is amazing with statistics and polling, is trying to figure out what the 'Boy Problem' numbers actually mean. I'm all over the place on the Boy Problem, obviously. I don't like what I see as anti-boy bias in textbook development, and I think schools are too female-dominated. Those observations are pretty much incontrovertible. I also think schools over-reward clerical and organizational skills, while over-punishing the lack thereof. These perceptions are more debatable (especially seeing as how I don't know what middle school girls are experiencing). What I'm not at all sure of is whether there's a 'real' boy problem in districts like mine, where divorce is rare and dads are present. Here's what Rick's found so far:
I'm still working on the data sets but I'm not finding any clear distinctions - other than that men are more highly rewarded than women after college for the same level of performance in college. IOW - there is no economic payoff for any edge awarded to women during school. I'm beginning to wonder if the higher rate of matriculation and graduation might not be attributable to innate differences in the importance that each sex attaches to organizational skills. The "leveling of the playing field" back in the seventies may have just revealed women's superiority in completing tasks within an ordered environment.
This is exactly what I've been wondering. Is college just more of a 'girl thing'? (I say 'girl thing' neutrally in this case.) I was talking to Ed about this yesterday. He doesn't know what to think about the whole thing, either, but he pointed out that when you look at Continuing Ed, it's all women. It's true. I've tried to take a couple of continuing ed. courses (I always end up dropping out) and the ratio is 10 to 1, if that. For every 10 middle-aged women taking a continuing ed. course, there'll be 1 guy. Women like school! So I don't know. I think Rick's still looking into it.....I'm going to be interested to read what he comes up with.
There's lots of other good stuff, too, but I wanted to get this up front sooner rather than later. Here's Ken, on acceleration of normal students through Direct Instruction:
Engelmann also claims that in a low mobility school with sufficient number of high performers, these high performers can be accelerated at 3-4 times the usual acceleration rate that DI achieves. To do this you'd need an affluent suburban school to become a DI immersion school and there's esentially zero probability of that happening in the absence of outright parental revolt.
At this point, I'd like to know exactly how fast a high-achieving child taught via Direct Instruction can move. Toru Kumon, who wrote the KUMON worksheets and founded the company, had his own son doing calculus in 6th grade. Even though I haven't taken calculus myself (yet), I'll go out on a limb and say I believe it. Now that I've worked with Singapore Math a bit, and spent so much time immersed in K-8 math, it makes sense. Here in 6th grade, Christopher is being taught Algebra 1. That's what this course is. Algebra 1 and geometry (without the proofs). AND the kids have all started Algebra 1 without being anywhere near mastery of fractions, decimals, or percents. He's having a heck of a time, but it's obvious to me, sitting and working with him, that if John Saxon or Siegfried Engelmann were running this course he'd be learning the material. He'd be learning the material because it's not 'hard.' The fact that Christopher has apparently reached some kind of mastery on integers is evidence. He was utterly confused by integer operations at the beginning of the year; he's remained confused throughout the year (for 'the year' please substitute '3 months'); and now, all of a sudden, he can take a pop quiz on integer operations and score 20 out of 20 correct. If integer operations were hard, he'd be scoring 0. Because he has sure as heck not been taught to mastery. So how far and how fast can a high achiever go with Direct Instruction? Do we know?
the rigor conundrum For me, Direct Instruction and KUMON have solved the 'rigor conundrum.' The rigor conundrum is this. Many parents want their schools to provide a more rigorous curriculum. At the same time, parents don't want their kids homeworked to death. I'm not going to take the time now to pull all the evidence for this; you'll just have to trust me. There's plenty. Here's one: Tom Loveless, at Brookings, has some great stuff on the Homework Wars. All over the country you've got parents in open rebellion about how much homework their kids have to do — and when you look at it, it turns out nobody's doing any homework! We're doing less homework than other countries, and homework levels are the same as they always were. (This isn't strictly true; Loveless explains why parents believe homework demands have soared.) So the question is: which is it? Do parents want a more rigorous curriculum? Or do they want a less rigorous, lower-work-loads curriculum? Policy experts don't know; that's why you see Forums on the question of Will the American public support excellence in education & the like. Meanwhile, I've had a paradigm shift. More rigorous education versus Less homework is the wrong question. 'Rigor' doesn't mean '4 hours of homework' plus an Extended Response problem you have to know modular arithmetic to solve. I think Ken's expression for this is fake rigor. 'Rigor' means material is taught to mastery so students can accelerate their progress through the curriculum. and: Material taught to mastery is far easier to learn than material taught through exposure. What parents want is more rigor without more homework — without pointless, overwhelming, ditch-digging-in-San-Quentin levels of homework. I'd put money on it that if parents saw their kids being assigned more homework that obviously increased their learning and mastery they'd support it. But given what I've seen of KUMON, quantity shouldn't be the 'standard' in K-8 or perhaps even in K-12 (not sure about that). KUMON's philosophy is slow and steady wins the race. Ten to twenty minutes a day, and don't over-do it. They've shown that it works.
KUMON and 'responsibility' KUMON talks about self-learning.
Kumon students study independently at both Kumon Centers and at home. The role of instructors within the Kumon Method is focused almost entirely on the development of a student's ability to learn on their own. Kumon refers to the ability to set goals and solve unfamiliar and challenging tasks independently as "self-learning" ability. Instructors foster this "self-learning" ability in students by using worksheets that allow students to learn at one's own pace, moving forward when they are ready. The students' enthusiasm for learning is aroused in this process, as the goals they set are their own goals. In addition, this process awakens a desire in the students to take on new challenges. Instructors ensure that students can, without any hindrances, experience over and over a sense of accomplishment, thereby boosting confidence in their own abilities. Problem solving abilities are enhanced, and independent methods of solving problems are encouraged. Instructors must also observe the study behaviors of each student, get a sound idea of each student's particular learning situation and incorporate this into the method of instruction. Instructors routinely analyze the learning process. If problems become apparent, the instructors ask themselves pertinent questions about the problem before proceeding such as, "Is the student's pencil moving too slowly?" or "Is the student too lost in thought?" Through such careful observation of the student's learning, small obstacles are removed in a timely manner thus assisting the students in their self learning. Consequently, it is a uniform approach, using the worksheets, the instruction method, the input and analyses of the instructors, and the abilities of the students, which make the method a great success.
That's a terrific description of KUMON, Ideal Type. Around here, we're not experiencing KUMON, Ideal Type. Christopher isn't becoming a Self-learner via KUMON at this point; he'd quit today if I let him. Nor are we having a lot of helpful analysis of pencil grip. Doesn't matter. Christopher is practicing and learning every day. KUMON draws a connection between correctly paced teaching to mastery and the child's eventual independence and self-motivation. I believe it (and in fact I do see signs of it in Christopher at times). Here's Ken again (yes, we're having an all-Ken-all-the-time day here at ktm):
The reason why DI and Kumon create more independent learners by the middle school years is because they start with a high degree of student support in the lower grades and gradually fade the support structure by the end of the program. Still, many low performers always need some level of support over the average student. With other kids, the support can be faded even faster. Bear in mind that in any event the support is faded gradually and that the kids have been exposed to effective learning techniques over the course of many years off of which they can model their own learning. The rug just isn't pulled out from under them come sixth grade. There is no sink or swim, nor should there be at this age.
This is as good an explanation as I think I'm likely to see of how a 'passive,' 'spoon-feeding,' Directly-Instructing program like KUMON in fact leads to an active, independent, self-motivated and self-directed student over time. I want my school to adopt an educational philosophy and practice of teaching to mastery.
extended response problem from IL state test
extended response problem 1
extended response problem 2
extended response problem 6
extended response problems 7, 8, 9
direct instruction & the rigor conundrum
Dan's daughter reacts to extended response problem
defensive teaching of Singapore bar models
open-ended problems in math ed
problems that teach - "Action Math"
email to the principal
-- CatherineJohnson - 27 Jan 2006
NewWorldRecord 01 Feb 2006 - 21:35 CatherineJohnson
...set here at Kitchen Table math for most wrong answer:
#14, KUMON Math sheet F111b My answer: 66 2/3 Correct answer: 1/3
If it's not a world record, it's definitely a personal best.
-- CatherineJohnson - 01 Feb 2006
BarModelsInKumon 04 Feb 2006 - 21:02 CatherineJohnson
I just looked ahead in this week's packet of KUMON worksheets, and found KUMON bar models!
Saxon uses bar models, too I keep meaning to mention the fact that Saxon Math 8/7 uses bar models to teach fraction word problems. A Saxon student sees bar models in a number of lessons, then practices drawing them to mastery. Saxon, Singapore, & KUMON. We have a consensus.
Sybilla Beckmann's terrific article on bar models
Solving Algebra and Other Story Problems with Simple Diagrams: a Method Demonstrated in Grade 4-6 Texts Used in Singapore (pdf file) by Sybilla Beckmann.
Sybilla Beckmann Kazaz
also by Sybilla Beckmann:
-- CatherineJohnson - 04 Feb 2006
GbyFifty 13 Mar 2006 - 01:58 CatherineJohnson
I passed my Level F test today, thank God. Level F was not easy. Nor was the test. 50 fraction calculations, each one involving at least 3 fractions, each fraction with a different denominator AND order of operations stuff. To pass with a score that's considered 'excellent' you had to do all this in 20 minutes. I took 25, but I managed to miss only 2 which bumped me into the middle of 'good.' I took 25 minutes on purpose, because my accuracy rate was so lousy on the worksheets. I finally figured the only way to get through a Level F test would be to focus HARD and LONG on EACH NUMBER IN THE COMPUTATION. That worked, but my scored dropped from Levels D & E. I was exactly on the borderline between good and excellent on those tests.....which is making me wonder how long I can keep this up. If I'm too old to be a fighter pilot (source: READER'S DIGEST) I may be too old to do all 17 levels of KUMON. We'll see. There was a 6th grader next to me whipping through a set of worksheets for Level I. He must be one of those kids who got to G by 5. Meanwhile Christopher has managed to wangle his way down to a rate of 1 sheet per day. 1 sheet of math, maybe 2 sheets of reading. He says his goal is to stay in Level D forever, and never get to fractions in Level E. Even at this rate, he's dreaming. One way or another, he'll be doing KUMON fractions before next school year.
-- CatherineJohnson - 11 Mar 2006
KumonFractionLine 17 Mar 2006 - 00:45 CatherineJohnson
from H. Wu's Some remarks on the teaching of fractions in elementary school (pdf file):
It is widely recognized that there are at least two major bottlenecks in the mathematics education of grades K–8: the teaching of fractions and the introduction of algebra. Both are in need of an overhaul. I hope to make a contribution to the former problem by devising a new approach to elevate teachers’ understanding of fractions. The need for a better knowledge of fractions among teachers has no better illustration than the the following story related by Herbert Clemens (1995):Last August, I began a week of fractions classes at a workshop for elementary teachers with a graph paper explanation of why 2/7 ÷ 1/9 = 18/7. The reaction of my audience astounded me. Several of the teachers present were simply terrified. None of my protestations about this being a preview, none of my “Don’t worry” statements had any effect.This situation cries out for improvement.
I'll say. Here's one of my favorite passages from the 'Math Warrior' literature I've consumed thus far:
Let us look more closely at the way fractions are introduced in the classroom. Children are told that a fraction c/d, with positive integers c and d, is simultaneously at least five different objects (cf. Lamon 1999 and Reys et al. 1998): (a) parts of a whole: when an object is equally divided into d parts,
It is quite mystifying to me how this glaring “crisis of confidence” in fractions among children could have been been consistently overlooked. Clearly, even those children endowed with an overabundance of faith would find it hard to believe that a concept could be so versatile as to fit all these descriptions. More importantly, such an introduction to a new topic in mathematics is contrary to every mode of mathematical exposition that is deemed acceptable by modern standards. Yet, even Hans Freudenthal, a good mathematician before he switched over to mathematics education, made no mention of this central credibility problem in his Olympian ruminations on fractions (Freudenthal 1983).
I love his writing — very droll.
He goes on to say that:
...there are recurrent reports of students at the University of California at Berkeley and at Stanford University claiming in their homework and exam papers that
I have yet to make my way through Hu's 183-page opus (pdf file) on fractions & how they should be taught to elementary schoolchildren and elementary school teachers, but this point has stayed with me:
[Hu's approach] starts with the definition of a fraction as a number (a point on the number line, to be exact), and deduces all other common properies ascribed to fractions...from this definition alone.
I've been using this idea ever since I came across it. I point out to Christopher that fractions are numbers that can be located on a number line, just like whole numbers. I also remind him that whole numbers can be expressed as fractions. At some point in the near future I'll start bugging him about the meaning of the word 'rational' in rational numbers: a rational number is a number that can be expressed as a ratio. Hence any whole number, fraction, or integer can be expressed as a ratio. I've noticed that Saxon also approaches fractions as numbers-on-a-number line, although Saxon does this a bit differently: Saxon has kids use fractions for mental-math skip-counting, like so:
Count up from 0 to 5 and back down again by thirds.
I don't remember whether that particular exercise is in Saxon 6/5 or 7/6, but it could have been. I like it.
It turns out that KUMON Level G has fraction & decimal number lines:
Here's the whole sheet:
number line worksheets Schoolhouse Tech has a beautiful page of fraction number lines available free for downloading. And don't forget Doug Sundseth's downloadable number lines! 2 KUMON fraction & decimal lines
Chapter 2: Fractions by H. Wu (pdf file, 183 pages)
-- CatherineJohnson - 14 Mar 2006
FlexibleAbilityGrouping 07 May 2006 - 15:02 CatherineJohnson
from Dan (bulleted version below):
I happened to have a meeting with my daughter’s teacher yesterday about the kind of differentiated instruction that I like. It’s not enrichment or pull-out from the heterogeneous group. It’s actual homogeneous ability grouping. My daughter is in first grade in a K-5 public school. I don’t know if the school previously had some homogenous ability grouping for reading at the upper levels before or not. I do know that this is the first year that they’ve taken the grouping all the way down to the first grade level. So, four days a week, my six-year-old leaves her homeroom class and goes down the hall to a different first grade teacher for her “reading block.” There are four first grade classes in this school, so they have four levels of reading groups. Let’s call them A, B, C, and D, where the D group has the most proficient readers, and the A group kids were still shaky on the alphabet back at the beginning of the school year. They call it a reading block, but it also includes spelling and other activities. I can’t speak with certainty, because I haven’t done any thorough analysis. Still, I think that the results of this grouping have surprised the teachers. My daughter is in the D group (highest ability). Every week, these kids are learning spelling words that rival the difficulty of the words used in my other daughter’s fourth grade class. Here are a few of the words she brought home this week: Wednesday, beautifully, anniversary, rectangle. The reading teacher has also borrowed materials from a third grade teacher to have the kids do an invention convention, where they each designed some new invention, described it, prototyped it, and created a script for an advertisement for it. They also worked with their parents to research an existing invention and its inventor. Then, the child had to write a report on it. For all of these writing steps, the teacher had them turn in drafts, which she then corrected for them to rewrite. I think it turned out very well. They’ve also read and reported on biographies. They’ve learned alphabetization and dictionary skills. Any of these things, taken by itself, is perhaps not so amazing. I can’t imagine, though, that so many topics could really be covered—and understood—with this level of quality if pursued in the context of a heterogeneous ability class. My understanding is that the grouping is also quite successful for the lower groups. We were talking to my daughter’s homeroom teacher. She has the A group (lowest proficiency). I might be misremembering my numbers, but I think she said she began the year with 23 kids in her group. Several have moved up to other groups; she has 16 now. When the rest of the class is not leaving them behind, even the lowest performers can make real progress. I think it’s great that she has the fewest students at this point, because they probably need the most attention. The teacher also told us about a girl that had recently moved up from the C group to the D group. Nobody is locked in and held back. The reason we were meeting was to ask about next year. Given that our kid has done a project usually pursued in third grade and is handling spelling words that match those in fourth grade, how are they going to deal with her in second grade? The answer is that nobody is quite sure. This is also the first year that they’ve done ability-based reading groups in second grade. Next year, though, will be the first time they will be confronted with students coming out of ability-grouped first grade reading. I expect the second grade teachers to be blown away. We also face some uncertainty about math instruction in second grade. The first graders have not been regrouping for math. Instead, this is where some pull-out acceleration has been applied. My daughter is not yet automatic with her multiplication facts, but her teacher has started giving her some division problems. There’s no way they can start next year by asking her to plod along with Saxon second grade. It will be interesting, but I am very optimistic. To me, this is pretty close to the right way to do differentiated instruction.
I am firmly convinced, at this point, that flexible ability grouping - Susan's term - is tremendously helpful for average and slow learners. Here is Tom Loveless's description of tracking in a Catholic High School:
Reba Page’s 1991 study, Lower Track Classrooms, painstakingly reports on the daily activities of eight low track classes, documenting how they often function as caricatures of high tracks, how teachers and students in low tracks make deals to not push each other too hard so that they can cope with their environment. Low tracks may be used as holding tanks for a school’s most severe behavior problems. [snip] Intellectually stimulating low track classrooms do exist, however, and researchers have found the most productive of them in Catholic schools. Margaret Camarena and Adam Gamoran have described low track classrooms where good teaching, lively discussions, and ample learning take place. In 1990, Linda Valli published her study of a heavily tracked Catholic high school in an urban community. The school’s course designations publicly proclaimed each student’s track level. Textbooks and instruction were adapted for each track. Yet Valli discovered that "a curriculum of effort" permeated the entire school, even the lowest tracks. The school culture centered around academic progress, and the tracking system was but another facet of the school that served this aim. Students of all abilities were aggressively pushed to learn as much as they could. Every year, low track students were boosted up a level. By the senior year, the lowest track no longer existed. A judicious tracking system teaches low track students what they need to know and moves them out of the low track as quickly as possible.
in a nutshell:
sources cited by Loveless: Linda Valli, "A Curriculum of Effort: Tracking Students in a Catholic High School," in eds. Reba Page and Linda Valli, Curriculum Differentiation: Interpretive Studies in U.S. Secondary Schools (Albany: SUNY Press, 1990), pp. 45-65. Margaret Camarena, "Following the Right Track: A Comparison of Tracking Practices in Public and Catholic Schools," in eds. Reba Page and Linda Valli, Curriculum Differentiation: Interpretive Studies in U.S. Secondary Schools (Albany: SUNY Press, 1990), pp. 159-182. Adam Gamoran, "Alternative Uses of Ability Grouping in Secondary Schools: Can We Bring High-Quality Instruction to Low-Ability Classrooms?"
strategic plan for differentiated instruction
is there a research base for differentiated instruction?
timeline for implementing direction instruction & the administrator's career path
teacher's role in differentiated instruction
differentiated instruction in middle school
differentiated instruction & the pre-test
differentiated instruction in Steve's town
follow-up on DI in his town from Steve
pre-tests & post-tests w/o formative assessment
differentiated instruction & executive function
flexible achievement grouping & accelerating average children
acceleration for average & slow learners
Tom Loveless on tracking research
flexible achievement grouping in Dan's school
Wayne Wickelgren on math talent & when to supplement
Wickelgren on math talent
-- CatherineJohnson - 21 Apr 2006
AdjustableReservoirForIndoorPlants 22 Apr 2006 - 21:47 CatherineJohnson
I've been wanting something like this ever since my mom bought us an EarthBox two years ago. A few months back I found an expensive variant of this "adjustable reservoir" indoor pot, made in a Scandinavian company, in an online catalogue whose URL I seem not to have recorded. But that pot was designed mostly to be lovely to look at. This is the real thing:
gardeners.com has lots of EarthBox-type outdoor planters as well
I managed to kill one of my few house plants this winter, through inattention, general spaciness, and way too much multi-tasking. I've been feeling bad about it ever since, and naturally, being an American, I've been thinking Technology Can Solve My Problem. Speaking of technology solving my problems, I also missed a doctor's appointment this week, and will solve that problem by finally purchasing a PDA that links to my Mac, which my old PDA does not, or not smoothly enough at any rate for me to be willing to troubleshoot the software every time I need to synch. I don't know whether the adjustable reservoir will work as well for indoor plants as the EarthBox does for outdoor plants. However, I expect it will, assuming the reservoir holds enough water to tide my plants over on the days I forget they exist. I'm guessing that the reason the EarthBox works so well is the same reason producing your own insulin is vastly preferable to injecting yourself with insulin on a schedule. The plant gets the water it needs when it needs it, and it never gets too much or too little. It's a form of biological 'efficiency,' I guess.
efficiency in learning? It's the same kind of efficiency I want to see in education, including self-teaching.....what is the most efficient, most thorough and rapid way to learn a subject or a skill? And by 'efficient, thorough, and rapid' I don't mean the kind of brute-force Death March to Harvard schedules imposed on kids by elite private schools, which around these parts assign 9th graders 6 hours of homework a night. I think Seigfried Engelmann may be one of the few people on the planet with real insight into this question, and nobody listens to him. Well, Seigfried and Toru Kumon. I say 'I think,' because I haven't dug into this. It's entirely possible cognitive science has something to say about learning efficiency. Another item on my to-do list.
EarthBox investigation with Christopher
adjustable reservoir for indoor plants
self-watering pots and planters from Denmark
-- CatherineJohnson - 22 Apr 2006
SummerSchool2006 03 Jul 2006 - 19:43 CatherineJohnson
Still getting my act together on the summer program around here. Andrew's set. He's doing KUMON Math and, as of today, KUMON Reading. Amazing KUMON moment this week: I took a set of worksheets to school to show Andrew's teacher & aide how well he does with them. Good thing I did, because they had no idea whether Andrew can or cannot do beginning addition. The answer is that he can, and they're the ones who taught him. They were blown away when they saw him whiz through a sheet of add-ones problems. The problems were sufficiently mixed that it was clear he understood the principle; x + 1 means the next number up from x. The sheets I'd brought in had problems in the 30s, I think (30 + 1, 32 + 1, etc.). After he did a few of those I skipped ahead to the last sheet in the stack. The final problem was:
1000 + 1 =
Andrew frowned at this and hesitated. Then he typed "1000" on the AlphaSmart. I was mortified. I figured this was the moment where his teacher and aide would decide he was just learning by rote. But I was wrong. They were both watching him intently. I said, "No, 1000 plus 1." Andrew hadn't stopped frowning at the problem, which I think is part of what had his teachers so interested. He reached out his hand, and deleted the final zero, then typed in '1.' 1001 They couldn't believe it. The mistake was what convinced them he knew what he was doing. I don't know whether they've seen him self-correct before; they probably have. But watching him self-correct while doing a brand-new problem no one's ever shown him was the magic. As impressed as they were, they stilll wanted to know whether Andrew could add ones if you wrote them in a different way, on a different kind of paper. This is the "hyper-specificity" problem that's so frustrating with autistic kids, and that is the center of Animals in Translation. The reason they were so frustrated with his progress in class, apparently, is that his performance is inconsistent – and the inconsistency seems to be related to changing fonts or paper, etc. I’d never checked to make sure Andrew could do the same problems in different fonts and on different size paper (which I should have). They gave me a sheet of paper, and I hand-wrote a ones problem. Andrew answered it instantly. They were convinced. They were so convinced that they said they wanted to use KUMON as Andrew’s math curriculum this summer. We talked about what the problem might be for awhile, and none of us knows. I'm guessing the problem is that the school doesn’t have a math curriculum for Andrew, mainly because there isn’t one, although KUMON may serve. Clarice ordered Engelmann’s DISTAR program back when she was hired, and she gave it to me to take home. I got to spend two days holding the Presentation Book in my hands (I wish Ken had been there!) It looked like everything it’s cracked up to be, but it didn’t look like something a teacher could do with Andrew. I suppose you could type the script and have Andrew read it....which might be a good idea. I had to return the program the next day, and didn’t have enough time to think it through. What's happening in class is that Andrew will seem to have mastered an addition fact, but then later on will seem to have lost it. For the time being, I'm assuming that because they don't have a curriculum any one or all of 3 things has happened:
As to the first, KUMON's worksheets are the ultimate coherent curriculum. The child does many, many worksheets on adding one to a number before moving on to add 2s to a number. KUMON doesn't stop with the within-ten addition facts, either. Instead it takes the child all the way from 1 + 1 to 1000 + 1 before moving on to + 2. Clarice hasn't done that, I don't think. I think she had him learn all the various addition facts up to 10. She said Andrew will seem to have mastered 6 + 4 = 10, but then when they ask him 6 + 4 a week later, he doesn't know. I'm hoping the reason he forgets 6 + 4 is that 6 + 4 doesn't have the meaning it's going to have in KUMON. I'm also wondering whether "massed practice" — aka drill and kill — may be especially important or even critical for developmentally disabled kids. Everyone in the U.S., constructivists & cognitive scientists alike, seems to have decided that distributed practice is the key to the kingdom. (TRAILBLAZERS & EVERYDAY MATH both claim to give children distributed practice.) But I've always found I need to do a certain amount of massed practice in the beginning just to remember a concept well enough to be able to do distributed practice. Andrew is tough to deal with; I bet they haven't made him sit in a chair and do the same addition problems over and over again the way KUMON does. I wouldn't have. In any case, we're moving on to +2 in a couple of days, so at that point I'll start occasionally asking him to do a +1 problem to see if he remembers. We'll see. As to KUMON reading, this morning Andrew was aghast at the discovery that in addition to the 5 KUMON math pages he has to do every day he now has 5 KUMON reading pages, too.
summer school for Christopher First off, I've had my second abject failure in afterschooling books: Sentence Composing for Middle School: A Worktext on Sentence Variety and Maturity by Don Killgallon. I love this book — I even bought the college level one for me — and it's worthless for Christopher. The first exercises ask you to divide a sentence up at its natural breaks. For instance:
The only way to / keep your health is to eat what / you don't want drink / what you don't like and do what you'd / rather not.
The student is supposed to rewrite the sentence putting the slashes where they belong. Christopher can't do it. He's so far away from being able to do it that he doesn't even really get what he's supposed to be doing. The whole thing makes no sense to him at all. I thought he'd start to get the hang of it after awhile, but he didn't. He doesn't have an "ear." Some kids do. My friend Kris's little guy, Charlie, has an ear. I went over one day & he came running up to show me something he'd written. He was missing a comma, and when I pointed it out he stopped in his tracks and talked the sentence to himself under his breath, and he heard where the comma was supposed to go. "Oh yeah!" he said, looking happy. My other afterschooling flop was Daily Paragraph Editing, which I was using in 5th grade. I pushed Christopher through pages & pages of that book without his performance improving a jot. Finally I talked to his teacher, the brilliant Ms. Duque, and she said forget it. The book wasn't teaching him anything. I interpret these failures to be more grist for the direct instruction mill. Christopher needs to be directly taught punctuation and grammar. Period. Then he'll have an ear. I think he will, too. We've finished Megawords Book 3, and his ELA teacher, the other Ms. K, has been giving spelling tests all winter and spring. Ms. Duque taught spelling, too. So he's had a lot of spelling. Suddenly, Christopher is using spelling rules to spell words he doesn't know, and he's getting them right, too. Boy is that great. His spelling is so much better, it's amazing. Back in 3rd grade his spelling was A SCANDAL. It was almost psychotically bad, like those jokes about Eastern European languages with no vowels. These days he's starting to have normal not great spelling. In one paragraph of prose he might have two misspelled words, and those words will be misspelled logically. This is why I'm sure he'll develop an "ear." He's developed whatever the analogous form of implicit knowledge is for spelling; he'll do it for writing, too.
vocabulary, writing, math... So we're putting Killgallon on the shelf for the time being. Christopher will do Vocabulary Workshop, a book I like more and more as we go along. He does one page a day, which takes 5 minutes max. VW teaches words in 5 exercises:
There are 15 units in the book, and you review every three units. 20 words per list; 185 pages in the book. Efficient & effective.
We're big on vocabulary these days. At dinner I make Christian and Christopher learn Greek and Latin roots from English from the Roots Up. So far we've learned photos, graph, tele, metron, tropos, philia, phobos (predictable hilarity with metron, which instantly suggests the neologism metronsexual, philia & phobos), syn, and thesis, although Christian is having a horrible time remembering tropos. For quite a while there he was saying "line" whenever he heard it (too long to explain), so "line" has now become a running gag. I told Christian to come up with a mnemonic device for tropos, but unfortunately the one he came up with caused him to start thinking tropos means revolving, which come to think of it maybe it does. (Does it?) If anyone has a suggestion for a mnemonic device that connects tropos to turning, let me know.
I've also got an ancient copy of Word Power Made Easy (a Google Master recommendation, IIRC) next to the dining room table, so we may get to it, too, one of these days. Then last week Martine went out and bought a dictionary of New York slang, and we all learned the meaning of ace boon coon, a phrase Christian knew and had used. I'm having as much trouble remembering ace boon coon as he is remembering tropos (I can't remember the "ace" part), so we'll see who gets to the finish line first.
Christopher is supposed to take his ALEKS placement test today, so I've got to go figure that out. More later.
my boon companion
-- CatherineJohnson - 25 Jun 2006
AndrewDoesKumon 21 Sep 2006 - 12:28 CatherineJohnson
Email from Andrew's* teacher:
I had him do one of the Kumon sheets. He kept typing that 13+3=416. It looks like he is adding 1+3, writing down a 1 and then adding 3+3.
He's been giving this answer over & over again, so it's not an accident. He's also having trouble doing his KUMON worksheet problems on other worksheets printed in other fonts and formats. Hyperspecificity strikes again. Andrew's entered a horrifically obsessive stage focusing on the internet, which he wants Ed to spend hours surfing for images of various PBS & cereal box cartoon figures. It got so bad Ed finally decided to go cold turkey, and for the last 3 days he's refused to go on the computer with Andrew at all. A couple of nights ago he decided to do something else with Andrew, and Andrew got batty enough that Ed was driven to attempting to do some Singapore Math. Andrew couldn't do anything! Ed panicked, so I came in and discovered that, yes, Andrew could still tell us what number comes after 8. Finally Andrew started doing some math for Ed, so at least we know the Depakote, which he started taking this summer, isn't making him stupid. Depakote can do that. I particularly dislike Depakote, and now I have two kids taking it. grump
I've ordered a complete set of Primary Mathematics textbooks, Grade 1, for Andrew's teacher.
* For any newbies out there, Andrew is 12 years old and has autism.
-- CatherineJohnson - 20 Sep 2006
SorobanSchool 12 Oct 2006 - 02:22 CatherineJohnson
Ed and I were talking to a long-time math teacher the other night who said he's taking his child to the Soroban School to save him from Everyday Math. This came up because Ed asked him what he thought about Everyday Math and the other constructivist books. I wish I'd taken notes. His opinion went something like this: "I would take every single Everyday Math book in the country, and take them out in a field, and put them in a rocket, and launch them into outer space so I could get them as far away from children as they could possibly go." Something like that.
I'm going to check out the Soroban schools.
-- CatherineJohnson - 11 Oct 2006
HowToCureMathAnxiety 23 Oct 2006 - 00:00 CatherineJohnson
So I mentioned that the Yonkers school system graduated Christian from high school with a 3rd grade level of math knowledge — and that last week I'd started him on the 4th grade Saxon Math book, Saxon 5/4. It's working. He breezed through the first lesson. Then he breezed through the second lesson. Then he breezed through the third. Now he comes in, deals with the kids, and, after dinner, pulls out his Saxon Math books and does the lesson in 15 or 20 minutes while keeping an eye on Andrew & watching whatever Christopher has on TV. This is the way you cure math anxiety. I think. You cure math anxiety the same way you remediate gaps, by starting a student back before the point where math got hard. That's the Siegfried Engelmann way; that's the KUMON way. I don't know that Christian had a full-blown case of "math anxiety." I don't even know what "math anxiety" is, other than the predictable result of years of lousy math instruction. Christian was against math when he first started working with the kids. Now he's neither for math nor against it, as far as I can tell. He just comes in and does his math. Long live Saxon.
Speaking of living long, I'm a bit concerned. The Harcourt website seems to have pulled its online placement tests. yikes We need those. I have copies myself, and I've found two other websites that have them posted (links below). Harcourt has an online test, which is good, but it doesn't give you the flexibility you need and reading online is difficult. I hope they post those tests again.
Engelmann on student placement in curriculum
Rule 1: Hold the same standard for high performers and low performers. This rule is based on the fact that students of all performance levels exhibit the same learning patterns if they have the same foundation in information and skills. The false belief that characterizes the conventional wisdom about teaching is that lower performers learn in generically different ways from higher performers and should be held to a lower or looser standard. Evidence of this belief is that teachers frequently have different “expectations” for higher and lower performers. They expect higher performers to learn the material; they excuse lower performers from achieving the same standard of performance. Many teachers believe that lower performers are something like crippled children. They can walk the same route that the higher performers walk, but they need more help in walking. These teachers often drag students through the lesson and provide a lot of additional prompting. They have to drag students because the students are making a very high percentage of first-time errors. In fact, the students make so many mistakes that it is very clear that they are not placed appropriately in the sequence and could not achieve mastery on the material in a reasonable amount of time. The teachers may correct the mistakes, and may even repeat some parts that had errors; however, at the end of the exercise, the students are clearly not near 100% firm on anything. Furthermore, the teacher most probably does not provide delayed tests to assess the extent to which these students have retained what had been presented earlier. The information these teachers receive about low performers is that they do not retain information, that they need lots and lots of practice, and that they don’t seem to have strategies for learning new material. Ironically, however, all these outcomes are predictable for students who receive the kind of instruction these students have received. High performers receiving instruction of the same relative difficulty or unfamiliarity would perform the same way. Let’s say the lower performers typically have a first-time-correct percentage of 40%. If higher performers were placed in material that resulted in a 40% first-time-correct performance, their behavior would be like that of lower performers. They would fail to retain the material, rely on the teacher for help, not exhibit selfconfidence, and continue to make the same sorts of mistakes again. If students are placed according to their first-time-correct percentages, they tend to learn and behave the same way, whether they are “lower performers” or “higher performers.” In Project Follow Through, we mapped the progress of students of different IQ ranges. The results showed that regardless of students’ entering IQ, the rate of progress was quite similar across all children and across different subjects. Lower performers learned as fast as higher performers. They simply started at a different place, with material that higher performers had long since mastered. Note that this conclusion may be somewhat biased because we paid particular attention to the instruction for the lower performers. They tended to have better teachers and their instruction tended to be monitored very closely. In any case, they learned at a very healthy rate, one that paralleled that of students with IQs 40 points higher. The typical practices of placing and teaching students are completely opposed to appropriate placement and teaching procedures. At the University of Oregon, we place teaching-practice students in special-ed classrooms that use direct-instruction programs. During the years that we first offered these practica, we typically worked with teachers who were teaching DI but had not generally received much training. Before we arranged for a placement with a new supervising teacher, therefore, we made sure that the classroom was “appropriate” for our students, which means that the children the practicum students were to work with were placed appropriately and that the teacher was using and modeling appropriate practices. As part of the review of the new classrooms that were candidates for receiving practicum students, we checked the program placement of the students and changed their placement if necessary. Our estimate is that in the first 40 or more classrooms we used, the children were moved back in DI reading programs an average of 100 lessons—sometimes 120 lessons. The children, in other words, were placed about 3/4 of a school year or more beyond the optimum first-time-correct percentages. Nearly all teachers had children that were seriously misplaced. Furthermore, I don’t recall a single classroom in which children’s percentages required us to move children ahead in the programs. Children were always “over their heads.” source:
Children were always "over their heads." When you design instruction so that children are always in over their heads, you have poor instruction and bad student outcomes. Period.
in a nutshell
remediating math at the college level We've had a number of discussions about how to remediate the math knowledge of college kids. Rudbeckia Hirta has written about this often, along with Carolyn &, I think, Steve H. When Ed and I first discussed what to do about Christian's math, I said I didn't particularly feel like paying for Westchester Community College to teach Christian the math his mom already paid Yonkers to teach him back in grades 6-12. I said I was thinking about just giving him the Saxon placement test & buying him the books & seeing how it went. Ed thought that was a bad idea. (It's fun to be right! It's even more fun to be right on your own blooki.) Actually, "I told you so" isn't (really) the point. At the time I thought Ed was probably right. I thought handing Christian a couple of Saxon books and telling him to go teach himself math — or trying to teach him myself — was probably nuts. He doesn't (didn't) like math; he couldn't do math; he had no interest whatsoever in the whole question of math....none of this sounds like a recipe for success in self-teaching. The fact that I went ahead and gave him the Saxon placement test anyway was probably a Bayesian moment. I've been teaching myself math long enough now, and teaching Christopher math, and writing ktm, and reading the Comments that I probably "knew" at the level of the cognitive unconscious that Saxon was a better idea than a $500 "developmental" math course at a community college. The reason Saxon is probably a better idea (it's early days, I realize) is that the community college doesn't offer courses in 4th grade arithmetic. They're trying to remediate years of missing math instruction in one or two semesters. I just don't see how it can work no matter how good their teachers are (and I bet their teachers are good). In fact, the effort to close years of math gaps in one or two semesters seems almost inevitably destined to produce more math anxiety than a student had going in. I'm thinking that just as there is no royal road to geometry, there's no royal road to Algebra 1. People whose math education went completely off the rails back when they were eight have to go back to when they were eight. At least, that's what I'm thinking at the moment. We'll see how it goes.
Saxon middle grades online placement test
downloadable Saxon placement tests at Learning Things
downloadable Saxon placement tests at Sonlight Curriculum
Rainbow Resource (least expensive source of Saxon Homeschool texts I've found)
teachingtomastery teachtomastery programplacement
-- CatherineJohnson - 20 Oct 2006
NationalMathAdvisoryPanelLinks 21 Nov 2006 - 18:07 CatherineJohnson
about the panel
where you can find links I'm posting links to the Math Panel homepage, transcripts, & ktm posts here:
You can find both pages on the menu to the left. If all else fails you can search posts using the keyword nationalmathematicsadvisorypanel with no spaces between words. (Works pretty well with spaces, too.) I'm thinking this is about as findable and redundant as I can make the links now...unfortunately, you will have to remember some constellation of the words "national mathematics advisory panel" to find these links (that could be iffy for me these days....) But I think I've just raised the odds of re-finding the transcript links considerably.
panel members w/links
Polite agreement or something we can use?
National Math Panel announcement
National Math Panel update
short story by Vern Williams
-- CatherineJohnson - 07 Nov 2006