Kitchen > HomeSchooling

select another subject area

# Entries from HomeSchooling

SummerSupplementTimePart5 02 Jul 2006 - 17:49 CatherineJohnson

In SummerSupplementTimePart4 I mentioned that I think I have useful advice for 3 groups of kids:

• kids who, for whatever reason, have fallen significantly behind their classmates

• kids who are right on track, doing well, and you want to keep their math skills in shape over the summer

• kids whose parents want to accelerate their math learning -- in particular, to get them in position to take and master algebra in the 8th grade

My own strategy for kids who have falllen behind (Christopher's situation last summer) is in that post.

These are the ideas I've come up with working with one child, and talking to a group of 4 people (Carolyn, Ed, my neighbor & friend Laura, and my friend Debbie), with as many on-the-fly advice sessions as I could get with Christopher's teachers thrown into the mix.

One of the main reasons I wanted to do a bliki with Carolyn was to find out what other people are doing!

### avoiding summer regression

For kids who are doing fine, here are my thoughts.

Assuming the research I've found (pdf file) is to be trusted (it makes sense to me, for what it's worth) there are two points to bear in mind:

• summer loss equals about one month of a child's learned skills and knowledge from the previous school year

• summer vacation is more detrimental for math than for reading, and most detrimental for math computation and spelling

I find the math-versus-reading factoid ironic given that schools universally hand out summer reading lists, not summer math lists.

So here's my own stab at a summer maths list. (I think the British plural works for this.)

### summer maths list

• 'mad minute' worksheets daily (be sure to include fractions, decimals & percents if your child has gotten that far)

• a word problem or two each day, if you feel ambitious (Carolyn is posting problems from the Singapore series)

• a Math Olympiads word problem each day, if you feel really ambitious (I'll probably post some of these)

### books (worksheets)

I did a quick scan of the various 'Mad Minute' books on Amazon, and folks seem to like this one best:

The Mad Minute covers Grades 1 through 8, and includes fractions & percents.

If any of our teachers or parents have used this book, let us know.

• Saxon Math Tests and Worksheet Booklets for each grade level. 120 'fast fact' worksheets to be completed in under 5 minutes. These are the worksheets that finally got Christopher up to speed, and we're doing them again this summer. Cost for the Tests & Worksheets book alone is around \$20, probably less at the Homeschool Super Center. If you're just going to use the worksheets you don't need to buy the textbook or the solution manual.

### books (story problems)

• Singapore Math Challenging Word Problems series. These are terrific books. Almost 300 story problems in each, grouped according to subject area (e.g. measurement, time, multiplication-and-division, etc.) All problems are multi-step, & all answers are in the back. \$7.80 plus shipping.

caution: your child almost certainly needs to use a book 1 or 2 grades younger than the one he's in. So you might want to have your child take the placement test before ordering.

• Math Olympiad problems -- you can find Math Olympiad books all over the place. They're expensive, so try to rustle up a used copy.

• Math League Contest Books from Math League. Wayne Wickelgren strongly recommends these books for everything from building your child's math achievement to preparing for SAT's. I love them, too. Filled with the kinds of problems, including logical reasoning, children are going to need throughout their lives & much more 'sensible' than the showy problems from Math Olympiads. Each book spans 3 grades, and all answers are in back. \$12.95 a book plus shipping.

### virtual worksheets & problem-solving

I've mentioned that I'm leery of online learning, but you can't beat it for convenience and speed. I like Saxon's offerings:

• Saxon Math 'fast facts' generator The page is clean, simple, and visually compelling. You decide which math-fact problems you want to do, how difficult the problems should be, and how many to do in one set. You can choose between a timed & untimed option. That's great, because kids love seeing their times get faster.

• Check out 5th grade activities.
Saxon now has online exercises for each grade. They tell you which activities to do after which lessons in the book, and you can download the activities for use when you are not online.

• Saxon has lots, lots more, so take a look

• Batter's Up Baseball Game I can't find the 'addition facts baseball games' the kids at school love so much, so here's another one. Christopher told me just now that he loved playing online 'addition baseball' when he was in 2nd grade.

### I found it!

The kids at school were crazy about Funbrain, especially math baseball.

Also check out Singapore math's Intensive Practice books. These books cover all sorts of fun things including word problems, computation, puzzles and patterns etc... They are not joking when they call it intensive. Some problems are extremely difficult (and some are quite easy too) and we cover them orally and together with the view that exposure to these types of problems will only expand abilities!

I agree. I have two of these books, and they're terrific. [Catherine]

FreeWorksheets

SummerSupplement
SummerSupplementTime
SummerSupplementTimePart2
SummerSupplementTimePart3
SummerSupplementTimePart4 (resources for kids who have fallen behind)

SaxonPlacementTestsAndGuides
SingaporeMathPlacementTest

and:

Summer Supplement Time
linking decline in high school scores to elementary school
research on summer regression
the time costs of not teaching to mastery
U.S. fourth graders not doing as well as thought
Phase 4 topic list, grade 6 class

LoneRangerHomeschoolerReportsIncredibleMathProgress 11 Apr 2006 - 20:55 CatherineJohnson

Lone Ranger just left this report on her daughter's progress using Singapore Math:

I started homeschooling my daughter in August 2004. She had been in public school since kindergarten and was a rising 4th grader when we started homeschooling. She had suffered through 3 years of "Math Their Way" and then 1 year of "Everyday Math" before I woke up to the fact that she was not learning math well. Her third grade test scores showed her to be working at the 50% in math. Well, after one year of homeschooling using only Singapore Math Levels 2B- half of 4A and supplementing with Singapore Math's Intensive Practice her total math score on the Iowa Test of Basic skills is now at the 99%!! More importantly her confidence, fluency, and ability to work through difficult problems have gone through the ceiling as well. Happy 4th of July - Lone Ranger

Congratulations!

That is incredible.

Your daughter has moved from the 50 percentile to the 99th in 11 months.

Incredible.

Good work!

### update

This should give those of us who aren't working in math-related fields more confidence about using Singapore Math with our kids.

It certainly does me--

Comments thread on what 'Lone Ranger' did with her daughter's math education & why.

MoreFromLoneRanger

MoreFromLoneRanger 11 Apr 2006 - 20:55 CatherineJohnson

I wanted to make sure everyone saw this follow-up (I've added bullets & formatting because Jakob Nielsen told me to):

• I used Singapore math books 2B, 3A, 3B and half of 4A before having my daughter take the ITBS test Iowa Test of Basic Skills.

• She completed the 2B placement exam but took 3 times as much time to complete it as was recommended. I thought better to start her slightly below her level to build confidence, learn the rod diagrams, and build speed and fluency with her facts and basic procedures.

• We also used Intensive Practice books 2B, 3A, 3B, and part of 4A (not every problem though)

• I made the decison to use Singapore because through my research 2 titles kept appearing over and over: Saxon and Singapore. Saxon is expensive and did not seem to be a good fit for my youngest daughter. Singapore seemed to be the best one to try first, since I wouldn't be out a lot of money if it flopped! Not very scientific or glamorous but the truth. [ed: Saxon at Home School Center may not be more expensive; I'll check.]

• Once I worked with the program and saw the children's response to it I was sold.

• I am average in my math ability and studied through Trig in college. I think at first Singapore can be intimidating, but after working with it, I find it is fairly straightforward.

• I used the Instructor Guide for 2B and have not really used it since.

• I try to work out all the rod diagrams, and boy am I getting good at them. [ed: oh! are these what I call 'bar models'? If so, I'm getting incredibly good at them myself.]

• Jenny, at the Singapore Forum board, is a great help if I am hopelessly stuck. All problems at this level can be solved without using algebra and Jenny is very helpful for teaching people how to set up the rod diagrams. (singaporemath.com)

• I also am learning much along with my daughters. [ed. note: based in my own experience, I think it's a good idea for parents to learn & re-learn elementary maths along with their children.]

• I think Saxon is also a great program and a few of my homeschooling friends' kids are doing very well with it.

• I am going to look into the Russian Math program too.

LoneRangerHomeschoolerReportsIncredibleMathProgress

ScienceWithoutCalculus 15 Dec 2005 - 20:37 CatherineJohnson

Samantha just left this comment:

Incidentally, from what I've read about science, it's near impossible to teach real science without calculus already - most of what they doing in school before students do calculus is just junk science.

Is this true?

Offhand, it sounds true to me.

But I have no idea.

HomeschoolCurriculumForAProdigy 19 May 2006 - 21:18 CarolynJohnston

Here's a letter that LoneRanger found on another list and posted on our requests page. It's an interesting story about a homeschool mom with a brainy kid who sort of rolled her own math curriculum. My advice would be "don't try this at home". I don't really like the bit about 'real math not being sequential little increments' and 'the usual order is arbitrary pedagogy', either; it's a mistake to try to make broad sweeping generalizations from your experience with a single child.

But with those caveats, it's kind of interesting to see what she did.

My son is now 19 and a freshman at MIT majoring in math and computer science. He is extremely talented at math. He has never been to school. We've never worried about doing anything sequentially. I've always used the Tetris model of homeschooling with the random pieces falling from the sky, never the traditional beads-on-a-string approach. Here's what we did for math. It might not work for less-mathy kids, but it sure worked for us. It is sort of like learning a foreign language by moving to the country and having to survive, rather than learning a foreign language by studying 10 new vocabulary words a day and introducing 2 verb tenses per semester. I think S would have done much less if we had insisted on a sequential approach. "Real math" is not sequential little increments. "The usual order" is something totally arbitrary that pedagogues came up with.

Elementary PK-5
I used to say we had a "game-based curriculum". We played a lot of dice, card and board games that involved math. Get "Games for Math" by Peggy Kaye for ideas. We owned every math computer game on the market back then. The best ones are the ones where you need to use math to play the game. I avoided the ones where you are drilled for a few problems, and then "rewarded" by shooting a few spaceships or something. We talked a lot about mathy stuff in the car or waiting for food in restaurants. There was no agenda to it. We would just talk about anything off the top of my head to keep him entertained. We did not use a traditional math textbook with formal homework assignments until 9th grade, when he did AP calculus. But we used a lot of children's math books from the library ("Number Devil", "Al Gebra", etc). I also had all of those "What Your Nth Grader Should Know" books, and I went thru the math sections like a check list to make sure he had all of it. We bought all the Doug Downing "Easy Way" books (algebra, trig, calculus) and I read them to him like story books. Whenever he got bogged down in the explanations, I just skipped ahead to where the story picked up. A year or 2 later I would go through it again, with the explanations, a year or two after that we would make the final pass and include all the footnotes and end-of chapter problems. These all overlapped. We did the first pass on the algebra one in 3th grade, and the first pass on the trig and calc ones in 4th grade. We did all the teaching company videos. But I never asked him to do any problems with them. He would just watch them. Also the old Square One on PBS. He never memorized the multiplication tables (neither did I). I taught him the little tricks I figured out as a kid to compute them on the spot, and he invented some new ones. The tricks involve a much higher level of mathematical understanding than memorizing the table, plus they also work for bigger numbers than 12X12.

Middle School 6-8
At the beginning of 6th grade we discovered Mathcounts, and our lives changed. The math was an exact match for him. The problems are extremely challenging, varied, interesting, and combine multiple areas of math in one problem. They sometimes require stuff like combinatorics and number theory that I didn't see into college. Competition math is totally non-sequential. When newcomers start on Mathcounts, they just jump in the stream wherever everyone else is working. At first they can't do it. It takes about 100 problems of a solution book or person walking them through how to do it before they start to get the hang of it. Then, the first years can maybe get 20% of the problems. The second year, the problems don't get any harder, but the kids are better at it. Maybe they can get 50%. Third year maybe 70%. There is a tremendous amount of preparation material out there for contests. We have a huge supply of problem books with solutions, for contests at various levels. S learned by doing problems, with all the math mixed together.

High School Camp
- the summer after 8th grade S started attending USA-Canada Mathcamp. 5 weeks of math-nerd paradise! A huge smorgasbord of offerings at all levels. Kids pick and choose what they feel like doing every day. Some classes are one-lecture long, others might be 2 weeks, or the entire 5 weeks long. Topology, Field Theory, Optics, Problem Solving, Cryptography. A total mish-mash of subjects that the staff is interested in (often has Ph.D.s in) and makes available to the kids. It is totally non-linear. No pre-reqs, homework sets, exams, grades. The kids just jump in it and play around. Everyone is thrilled to be there and looks forward to it all year. 9th Grade - S had already had 3 passes thru Calculus the Easy Way spread over 5 years, plus watched some calculus videos. I got a bunch of AP review books and old AP problems. He worked through those, then took the AP Calculus BC exam at the end of 9th grade. I bought a calculus textbook, but he never used it. 10th grade - he did distance learning courses for Multivariable Calculus and Linear Algebra. This was his first experience actually working through a math textbook and dealing with homework sets and exams. He HATED that aspect of it (too much drill-and-kill even at this level). I had to force him to sit down and do it while he bitched bitterly, particularly on the multivariable which didn't involve as much new material as we had assumed. But he got through, and made As. He also read an AP Statistics review book and took the AP exam. 11th grade - started auditing grad level math courses at UT (Abstract Algebra, Algebraic Topology). 12th grade - Audited 4 grad courses. Because of conflicts with college visits, he was able to do varying amounts of the work, including attending. But he got something significant out of each of them. Also self studied differential equations using lectures and materials from MIT's OpenCourseWare site (free).

College Applications
We ended up with 10 AP scores (all self-study), 4 scores on SAT II subject tests (in addition to the regular SAT I scores), 3 grades from UT distance learning courses, 2 letters from UT profs stating what his grade would have been in their grad course if he had been allowed to register. I put everything together on one big master transcript. I included the things he studied at home, sort of arbitrarily bundled into "courses". I did not include any parent assigned grades. The transcript is 2 pages. There is an additional 5 page document with course descriptions (textbooks used, etc. Max few lines per course). There is also a one-page "school profile" describing our general educational philosophy. It makes it clear that we were homeschooling in order to attain the highest possible level of academic success, not for any religious reason. It also makes clear that the student had plenty of opportunity for social interactions. We got a rec letter from one of his math profs at UT, from one of the coaches of the USA Computing Olympiad, and from a homeschool parent who taught several classes that included my son. He also had an extensive list of national and some international awards in math, physics, computer science.

At MIT
We had a transcript and copy of the syllabus for the two UT distance learning courses he took, but he did not get automatic credit for any of the college level math he had done other than AP calculus. He was able to get credit for multivariable calculus by taking an MIT exam during freshman orientation. He expects to get credit for differential equations the same way, but they require kids to submit a semester's worth of homework assignments before they allowed to take the exam, so he hasn't gotten around to it yet. There are other courses that he has covered and could almost certainly get credit for by taking MIT's exam (linear algebra, topology). But he has decided not to bother since they are not required for the particular math major he is going for, and he expects to have plenty of credits. MIT is fairly loose about prereqs, so he won't have to repeat anything he has already covered.

OnceMoreWithFeeling 09 Jan 2006 - 17:47 CatherineJohnson

I should have homeschooled.

StupidInAmerica 12 Jan 2006 - 17:55 CatherineJohnson

Ken left a link to John Stossel's special 'Stupid in America' tomorrow night at 10. (January 13, 2006)

Jan. 9, 2006 — American students fizzle in international comparisons, placing 18th in reading, 22nd in science and 28th in math - behind countries like Poland, Australia and Korea. But why? Are American kids less intelligent? John Stossel looks at the ways the U.S. public education system cheats students out of a quality education in "Stupid in America: How We Cheat Our Kids," airing this Friday at 10 p.m.

"We're not stupid. & But we could do better," one high school student tells Stossel. Another says, "I think it has to be something with the school, 'cause I don't think we're stupider."

That's the question Stossel examines in his special report: What is it that's going wrong in public schools?

There are many factors that contribute to failure in school. A major factor, Stossel finds, is the government's monopoly over the school system. Parents don't get to choose where to send their children. In other countries, choice brings competition, and competition improves performance.

Stossel questions government officials, union leaders, parents and students and learns some surprising things about what's happening in U.S. schools. He also examines how the educational system can be improved upon and reports on innovative programs across the country.

"Stupid In America: How We Cheat Our Kids" with John Stossel airs Jan. 13, at 10 p.m.

I'm setting up the TIVO.

StupidInAmericaPart1 16 Jan 2006 - 18:39 CatherineJohnson

Of course I missed the show, but the message boards are a hoot.

This one is from sharpeteacher:

Stupid in America does not start in the schools. It is the stupid adults that produce these lazy, under-achievers. When the parent see no reason to act like civilized people why would you expect the children to. The problem I have in my classroom is parents. Parents support their disrespectful children. They defend them when they get suspended or act like fools. [ed.: true! case in point!] (Parents like the one on tv that said her child was in high school and could not read.) It is the parents responsiblity more than the teacher to be sure the child is progressing. Maybe if parents suck it up and quit being selfish, stupid people then there children would care and learn about the real world and do well in school. You are comparing these countries and states that do not have the same rules or even the same tests. If you take a test and I take another test we can not compare our scores because we did not take the same test. Parents do not care enough to change their childs school. What we need is for someone to stand up and broadcast a show about stupid parents in America!!!!!

I agree as an administrator we have more stupid parents that bad teachers. It only takes discipline.

Another satisfied customer:

It's funny, that only teachers are responding to this thread. Let me tell you that I have read to my 2 children since day one, have helped with homework every night, volunteered uncountable hours in the public school system and am probably over involved in my kids lives. But just recently I have encountered this problem. My 10th grader just dropped 2 grades in Geometry in 4 weeks and I did not know about it until the week before Christmas break. After a conversation with the teacher she tried to tell me that I "should have known" that my child was in trouble. She said that she had done everything she was supposed to do to inform me. She had sent a letter home at the beginning of the year, stating that she would eventually send a password home to log on to an account to check grades and that my son, "if he were doing his job" was keeping a running tab of grades. I never received either. She obviously does not have children, thinking that they are going to come to you, saying, "mom, I'm flunking Math". Give me a break! The teacher gets paid for making sure my child learns [ed.: a common misconception! no! she doesn't get paid to make sure your child learns! she gets paid to spiral!] and obviously, my child was not learning, and his teacher felt that I did not need a note concerning this fact. Hey, as long as she can pick up that paycheck for putting in those hours, what makes the difference whether my child learns or not. Let me also tell you that I am not an absentee parent. I have volunteered in the public school system for 13 years, and am always available. This "teacher" also went on to say that it was all three of our responsibilitys' to make sure that my son was progressing. [ed.: hey! I got the same line from the Study Skills teacher who hung up on me!] I can't fix what I do not know about. She also said that she had 132 students and couldn't keep track of everything. Well, then maybe she should only get part of her paycheck, if she is only doing part of her job. Let me also add, that in the week since we have found out about the grade drop, we have gotten him two tutors, (pretty bad when a child has to go to another teacher for tutoring), have helped him more at home and he has raised his GPA by 5% in one week! [ed: I Should Have Homeschooled, Part 100-something] Teachers are always saying that the student needs to take responsibility....just once I would like to see a teacher step up and take responsibilty for what they have done...or in this case what they haven't. Public Education in America really stinks!

why do new teachers quit within 5 years?

I spent three years as a high school teacher, getting a job at a public school straight out of college. Three other rookies started with me. One quit after one year; the second year another quit; I quit the third year; the other rookie is now the high school’s activities director, eyeing a vice principal position.

Most new teachers leave the profession within five years. Teachers like to point at this statistic as proof of how hard their job is. It isn’t. It’s proof of the job’s meaninglessness. It takes a month or so at the job to realize that it doesn’t matter how hard you work, or how well you do. Your students will appreciate it, a little, but they are gone when the bell rings, and at the end of the year, they’re out of your life. The administration will take no notice. Your pay isn’t attached to it in any way.

Beyond that, your class of 25 becomes a class of 40 with ten special ed students. You’ve got a future felon you’d like to throw out of your class but can’t, because no one cares how well you teach, but cares a lot if you deem one kid a bad apple. For someone young, who has visions of a rewarding career, it quickly becomes apparent that public school teaching is an empty profession.

Career public school teachers come in two flavors, both shown in the John Stossel special.

a) the lazy bum who likes the free ride. That teacher who had his geography students playing Monopoly isn’t the exception, he’s the rule. I guarantee you that the teachers on this message board and in your lives who speak of working 60 hours a week are LYING! At my school, all the teachers arrived five minutes before the first bell and left five minutes afterward, and didn’t take any work home with them. They ran personal errands during their prep periods, and milked the image of the overwork teacher to anyone who wasn’t in the club.

b) The activist. The Union President who made such a fool of herself on the show is the other model. This teacher is also prevalent in the schools. She doesn’t care that kids learn math, science, English, or history. She got in this business to become a brainwasher, and uses her classroom as her personal political forum.

I’ve left the profession, and now work for a corporation in a cubicle. And despite the fact that my job is much harder now, at least it feels like I am accomplishing something!

uh-oh

The sad state of affairs on this matter is that the majority of us have personally experienced a really bad teacher on more than one occasion. That's too many bad teachers!

Me? I personally spent from the beginning of my junior year to the month of February teaching myself AB Calulus. Why you ask? Because my teacher was too busy planning the annual math club ski trip during my class period. I also, by my choice, went to a local college that summer to take AB Calculus to be sure I was ready for BC Calculus my Senior year.

I then spent my daughter's 6th grade year giving her the math lesson she should have been taught at school everyday by the teacher who couldn't stay off her cell phone long enough to teach. Her idea of teaching was handing out worksheets, reams of them, for the children to do without any lesson. The proverbial straw was the worksheet asking to calculate areas and perimeters of squares, triangles, parellograms, circles, etc. The worksheet had a diagram with measurements and an A = under each one. No formulas. I asked my daughter where her notes were from class on this. She said Mrs. Teacher didn't teach that day. They did worksheets with 5 digit numbers multiplied by 5 digit numbers...busy work.

helicopter parents of the world, unite

update

eduwonk likes this book, from Brookings:

Apparently the Wall Street Journal called it, "The education book of the year . . . an icon-smashing book on school reform."

There's a terrifically interesting-sounding (awkward modifier alert) list of books under "People who bought this book also bought":

the politics of vouchers (interview with Terry Moe)

ConstructivismAtHome 16 Jan 2006 - 21:24 CatherineJohnson

You will all want to order this book right away.

Teaching Your Child to Love Learning: A Guide to Doing Projects at Home

-- CatherineJohnson - 16 Jan 2006

SteveOnWhyKitchenTableMath 16 Sep 2006 - 20:28 CatherineJohnson

The only kids who are prepared to take a proper college prep math (esp. honors or AP courses) track in high school are those kids who are very smart or get help outside of the school. The current crop of fuzzy, low expectation, no mastery, discovery, spiraling math curricula are HARMFUL to kids. In the old days, traditional math may have been taught very poorly or inconsistently, but I don't think that was on purpose (perhaps incompetence and neglect played a part). Nowadays, perhaps there are more controls and teachers are more consistent (with the program), but the math curricula do not get students from point A (counting numbers in Kindergarten) to point B (a full course in algebra in eighth or ninth grade). This IS on purpose.

The problem of education is not some myopic teacher-perspective view of the problem. It is not "if only". If only we had more money. If only we had smaller class sizes. If only we didn't have to meet (trivial) state standards. If only the administration would get off my back. If only parents would get off my back. If only we had a better school culture. It is much more fundamental than that and it's not just about the teachers.

KTM exists because schools are not doing their jobs. Parents have to do it at home at the kitchen table. KTM is not ranting. It contains specific help for parents that they cannot get from the teachers, administration, school committee, or parent/teacher groups. Most of the regulars here have spent a whole lot of time working within their systems. It doesn't work.

After Christopher failed 2 of 6 units in 4th grade math, I had the Bayesian perception that unless I learned math myself, he would be out of the running for any career involving math in any way.

That perception may have been wrong. I'll never know how things might have turned out if I hadn't plunged into re-teaching Christopher his math, plunged into re-learning math myself, and ultimately plunged into writing and, more importantly, reading Kitchen Table Math.

Looking back, I think it's right to say that I myself was locked out of any career involving math in any way.

In my own school days, I was taught to mastery. That teaching stood me in good stead. I had 'shopkeeper's arithmetic' down cold, and I was able to start over again learning math in mid-life, and make quick progress.

But it wasn't enough to let me take math in college. And at that age, in college, I didn't know what I didn't know. I didn't know whether I liked math or not, whether I might be reasonably good at math or not, whether I should be doing something related to math or not....I didn't know anything. if I thought about it at all, I just figured I wasn't a 'math person.'

As one of Carolyn's old professors says, the last person you want making life decisions is a 19-year old.

When we were in Los Angeles over vacation, I spent time with the now-grown children of friends.

These kids have had fantastic educations, every one of them in private schools, including Catholic schools.

None of them is headed toward a math-related field at the moment (these kids are high school seniors & college freshmen) but each one of them could choose a math-related field if he or she wanted to do so. The door is open.

That's what I want for Christopher (and for Andrew, obviously, if I can get him there). I want the door to be open.

We've chosen to live in a high-tax suburban town with good schools. This was our version of choosing a private school. Talk about not knowing what you don't know.

The Irvington math track, thus far, isn't going to put Christopher in position to choose a math-related career.

Everyone says the high school is fantastic, and given the principal there I'm sure it is.

But when I talk to parents whose kids have taken AP calculus at IHS — and those kids are the only American kids who are competitive with their peers in other countries — what I hear is this:

His dad is really good at math, so he helped him all the way through.

In other words: my son made it through AP calculus because his dad knows calculus.

I have also heard this:

My son couldn't find a calculus tutor anywhere. He had to get through it on his own.

The woman who told me this has an advanced degree in math herself.

Carolyn says she finds it hard to believe that there could be no calculus tutors in all of Westchester County, and I agree.

But — and here's the point — I can't take the chance.

Maybe there'll be calculus tutors in Westchester when Christopher gets to Irvington High School, and maybe there won't.

Maybe Christopher would have gotten back on track without my turning into Math Mom, and maybe he wouldn't have.

I don't know.

I couldn't take the chance.

-- CatherineJohnson - 26 Jan 2006

MiniProblems 15 Jul 2006 - 16:33 CatherineJohnson

I've been complaining for months about the lack of word problems in Christopher's math class.

The kids memorize one procedure/rule/formula a day, do a few calculations, and march on. As a direct result, IMO, their knowledge really is rote as opposed to procedural. At least, Christopher's is. And I've had enough math talks with other kids in the class to know some of them are in the same boat.

Today I had a eureka moment reading a Comment left by Kathy Iggy:

The old math books I found (the same ones I used in grade school) have lots of what they call "mini problems" used to illustrate how a recently taught concept would be presented in a word problem. Megan likes these because of their brevity and she doesn't have to struggle with comprehension that much.

For example:

20 yards of ribbon. 1/4 used for dress. How much ribbon used?

That's IT!

mini problems

That's the concept, and the phrase, I've been looking for.

mini problems:word problems :: basic skills:higher order skills .

That's from Ken, and he's exactly right.

[update 4/23/2006: no! he's not right! Actually, he's write about using mini problems to teach word problems; I'm talking about mini problems to teach math - to teach the fundamental concept in a lesson. Awhile back I realized that word problems are the 'real manipulatives.' Now I know what I mean by that.

All concepts should be taught — illustrated — with mini problems. All concepts, every last one.

PRIMARY MATHEMATICS does this; SAXON MATH does it; KUMON does it. I'll post examples.

I've come to feel that the first word problems illustrating a new concept should be so simple children can do them in their heads.

For example, the very first ratio word problem a child does should be something like this:

Christopher bought one pencil for one dollar.
How many pencils can he buy for two dollars?

The question should be written this way, too: on two separate lines, so the child sees instantly that the first sentence is the set-up, and the second sentence is the question. Richard Brown's revision of Mary Dolciani's BASIC ALGEBRA, a book I like very much, does this for many of its word problems. I'll post some of those, too, as I get to it.

mini problems are applications

The problem with word problems is that, in the U.S., they're always hard.

Word problems are so hard people have apparently come to think that if a word problem isn't hard it isn't really a word problem.

I'm wondering if we ought to ditch the phrase 'word problem' (ditto for 'story problem') and adopt the word 'application.'

A better idea: we should think about the point of word problems.

Some word problems are written and assigned to give students practice.

Many word problems are written and assigned to assess whether students have developed flexible knowledge.

I'm talking about a third purpose, which is instruction. I'm talking about word problems designed to teach.

instructional word problems

A word problem is an application. A super-simple, starter word problem explains and demonstrates a mathematical concept by showing students how the concept is applied.

As a matter of fact, an instructional word problem shouldn't even be a 'problem.' It should just be a question, and the answer should be obvious.

A simple, instructional mini-problem should not test the child, should not challenge the child, and certainly should not trick the child.

It should teach.

examples to come

be sure to see Google Master's comment

how do you teach your child word problems?
mini problems (important)
arithmetic to algebra & mini-problems

-- CatherineJohnson - 07 Mar 2006

AmscoTeacherEdition 14 Mar 2006 - 06:34 CatherineJohnson

Go to Amsco School Publications & click on Homeschooling.

I am not a customer.

I am a taxpayer and potential test-cheat.

I can pay for a copy of the Teacher's Manual, or the Top Secret Glencoe Diagnose - Prescribe - Practice workbook, when my school places the order.

I can't actually own it.

So....if anyone knows where I can get a copy of the Teacher's Manual for INTEGRATED MATH COURSE I (3RD ED) by Edward P. Keenan & Isidore Dressler, let me know.

Teacher's Manual available (R 638 T) \$12.00
ISBN: 87720-230-3

Amsco protects its 'customers'
Glencoe Top Secret Test Prep

-- CatherineJohnson - 09 Mar 2006

StickingPointsInAreaAndPerimeter 09 Mar 2006 - 23:07 CatherineJohnson

I've finally found an image to explain one of the toughest concepts for kids:

Christopher has a dreadful time with figures like these, and so did my neighbor's son last year (no report on how he's faring this year).

Christopher simply can't 'see' that if all the angles are right angles, the right side equals:

8 ft + 5 ft

Nor can he see that the short horizontal line segment between the 8 & the 5 equals:

30 ft - 22 ft

I would like to have a few worksheets of figures like these.

taking a measure without starting at 0

Here's another category of problem that's incredibly hard for kids to do:

Doug, if you're around, and you feel like taking on another project, this is something I'll wager every grade schooler on the planet could use.

Christopher would be in much better shape today if he'd been given a bunch of 'simple' measurement problems in which the left side of the object being measured is placed somewhere other than 0 on the ruler.

For the life of me, I don't know why kids aren't bringing home such assignments as homework.

Some of you may remember that, last year, Christopher eked out a '4' on the TONYSS ('Test of New York State Standards,' a test schools in NY state can purchase from a private company to use in 'off' years). His score was one point above the cut-off.

The scale he flubbed was measurement!

I was shocked.

I'd been working around the clock with him (at an age when he was still willing to work with his mom) — and he flunks measurement! (Apparently, this was true of kids all over the state.)

Then we heard from teachers explaining that measurment is a difficult concept and skill to learn. Meanwhile the Singapore series takes measurement as one of its core subjects. They place huge emphasis on that topic.

Live and learn.

Now I see why measurement is a) difficult and b) incredibly valuable.

Think how much knowledge and skill goes into figuring out a problem like the line measurement above.

1
You can figure out the measure of the line either by adding or subtracting fractions.

2
The fact that you can figure it out by adding or subtracting reinforces the concept that addition and subtraction are inverse operations.

3
You can also figure out what the measurement is by counting-up using fractions instead of whole numbers. 'Counting by fractions' is an incredibly valuable activity. You almost can't not see that 'fractions are numbers' when you count by fractions. Saxon Math has numerous Mental Math tasks requiring students to count up (and, I think, back down) by fractions.

1/5, 2/5, 3/5, 4/5, 1, 1 1/5, 1 2/5, 1 3/5, 1 4/5, 2

btw, Schoolhouse Tech has a very nice sheet of fraction number lines available for download. (pdf file)

update from Doug

Doug recommends drawing simple perimeter problems on quadrille paper, like this one from Enchanted Learning (I think you have to be a member to download the sheet):

I'm going to print out the sheet and see if Christopher readily transfers from the quadrille problems to problems written on blank paper.

from last year

I just found a number of comments about kids and measurement that I'd forgotten:

My first year teaching high school freshman (I just finished my 3rd year at a urban neighborhood school) I was completely shocked that none, and I mean none, of the kids could measure using an inches ruler.

How can they get out of middle school, or even grade school, not knowing how to measure? I still have no clue. I doubt its the constructivists fault due to their fondess for hands-on, manipulatives, and project, which all lend themselves to measurement.

What I have observed:

• Metric OK, Inches Not -- While the kids can't (or won't) measure in inches, many (but not all) can measure using a centimeter ruler. Fractions rear their ugly head again.

• Estimation, Schmestimation -- The kids do not know when it is, or is not, appropriate to estimate. The kids have trouble estimating measurements between the lines of the ruler. But the kids are very willing to make bad estimates to avoid having to figure out what the little lines mean. 2 5/16 inevitably becomes 2 1/2.

• What is a protractor? -- The kids REALLY don't know how to use a protractor (except as a frisbee). Most don't even know that its purpose is to measure angles.

A side note related, I believe, to measurement. Each year I do a lesson where we compare the kids height in inches to their shoe size. The majority of the kids do not know how tall they are, let alone how to convert the height in inches.

So by all means get a ruler, protractor, some measuring cups and spoons, and a kitchen scale (or even better a pan balance) and start measuring everything around the house!

Barry's reaction:
Interesting observation and good advice. I just purchased the Saxon Math 76 book for 6th grade, and I notice that many of the problems have a scale on the page (in inches, sometimes divided into 8ths, 16ths, etc depending on the problem), with a line above it and students are asked to give the length of the line. I thought it strange to have such measurement practice but now I don't.

(Obviously that's part of our problem around here. We skipped Saxon 7/6 and went directly from 6/5 to 8/7.

from Interested Teacher:

Learning to read/measure from an 'inch' ruler has to be incremental. Younger students can't look at a ruler and automatically discern what all of those marks mean. They have to be taught to find the 'half' mark and measure using the 'half' marks. Then add the 'fourth' marks, (Don't be surprised that students don't automatically know that the 'half' mark also becomes a 'fourth' mark.) Then have students measure using the 'fouth' and half' marks. And so on, going into 'eighth' marks, etc. Practice between each incremental step.

Practice is necessary so students develop the skill of disregarding the smaller (16ths and 32nds) marks. For some students, with visual discrimination problems, this is horribly difficult.

Saxon 6/5 covers through 'fourths' and I add a little 'eighths' for more advanced students.

I was looking through Passport to Mathematics,Book 1, a text that I am previewing for personal reasons, and I see lots and lots of metric work, but little with feet and inches. On pg. 32, students measure to the nearest inch, and nothing else that I can see until pg. 318. With no review of 'half' and 'fourth' inches, it jumps to 'eights' -- there is one problem.

-- CatherineJohnson - 09 Mar 2006

AreaAndPerimeterWorksheetsFromSmartestTractor 13 Mar 2006 - 04:13 CatherineJohnson

Wow!

Smartest Tractor comes through again!

Here are four area and perimeter sheets from schoolhouse teach:

THANK YOU!!!

I just tried Christopher on the page I printed out from Enchanted Learning. He couldn't do it at all. I can't tell if he totally doesn't get the concept, or what.

The graph lines seemed to get him even more confused....he kept counting interior lines....

So at the moment, I'm stumped.

This is reminding me of the Betty Edwards drawing boot camp, where you just have to keep at it.

Learning to draw, all drawing instructors universally say, is learning to see.

So you just have to keep trying to see the object you're drawing in the unnatural way you need to see it to draw it.

That may be all that's involved with Christopher.

-- CatherineJohnson - 09 Mar 2006

EmailToThePrincipal 08 Oct 2006 - 22:40 CatherineJohnson

back story here

Ed just talked to the principal on the telephone.

He was aggressive and unresponsive. The principal, I mean. Not Ed.

So.

Hi Scott —

I’m sending a detailed memo covering our experience with Ms. K’s class this year.

But I’d like to respond to one point immediately.

You observed that Ms. K does not know whether Christopher can do the calculations involved in constructing a scale drawing.

Scott, I agree.

Ms K does not know whether her students have learned the material she’s covered in class.

This is true for all of her students, including those who did record their mental math. We know of one child in the class who has earned grades of C and D on his tests, while scoring an unbroken string of As on the Extended Response problems he takes home to do.

What has that child learned about pre-algebra?

Can Ms. K tell you?

Punishing a child for failing to write down mental math is not teaching; nor is it information. Punitive grading is entirely negative. It demoralizes the child, angers the parents, and erodes trust.

We have two core problems with Ms. K’s teaching, one concerning her ability to inspire, motivate and lead her students to success in mathematics, the other concerning her ability to assess performance. It’s the latter that concerns me here.

Ms. K does not perform systematic, ongoing formative assessment.

She covers material, gives tests, and assigns grades.

And there her responsibility ends.

This year Ed and I have been fully responsible for seeing to it that Christopher actually learns the math Ms. K has ‘covered.’

This wasn’t the case at Dows Lane; nor was it the case with all but one of Christopher’s teachers at Main Street School. That teacher was not asked to return.

I would hope everyone involved in Ms. K’s tenure case would ask himself this question:

Suppose Christopher—or any other student in the class—does not know how to construct a scale drawing?

What happens now?

Ms. K’s answer is: Nothing. Once she’s recorded a grade, she’s done.

If Ms. K wanted to know whether Christopher can construct a scale drawing, she would have him do a simple scale drawing in her presence. She should do that with the entire class, because none of the kids I know was able to handle this assignment on his own. By rights, Ms. K ought to be finding out whether any of her students can do a simple scale drawing independently, without parent guidance.

Instead, it’s up to us to make sure Christopher has mastered this skill.

I will do so this summer when I reteach pre-algebra using Saxon Algebra 1/2.

If I’m going to do Ms. K's job, I want a refund. Ms. K, after two years of work, is going to be awarded lifetime employment, lifetime benefits, and a generous retirement, all funded by taxpayers like me.

Scott, I need to earn a living. I have two children with severe handicaps who will require lifetime care; I must fund my own retirement.

I need to be able to rely on our very well paid teachers to teach my son.

Instead I’m pulling worksheets, buying and studying textbooks, reteaching math lessons, preparing Christopher for the state test (Ms. K told the kids not to study because they ‘don’t know what’s going to be on the test’),* and helping Christopher’s friends in the class to boot.

This isn’t right.

Catherine Johnson

* Topics covered on the New York State tests are listed here: http://www.emsc.nysed.gov/ciai/mst/mathstandards/g6.html. These topics are also listed in the Glencoe Test Prep book Ms. Kahl sent home sporadically in the run-up to the test.

I am KICKING myself for not homeschooling.

Actually, it's not even at that level.

I'm kicking myself for not having a clue.

I'm kicking myself for not having the slightest idea what was wrong with our public schools.

I'm kicking myself for not even suspecting that, when it comes to public schools, money ≠ quality.

Christopher won't be doing any more 4-hour projects for Ms. K.

That's over.

My only concern now is: is he learning pre-algebra to mastery?

Everything else is noise.

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

keywords: performance indicators New York state tests New York state standards

-- CatherineJohnson - 27 Mar 2006

HomeschoolingQuestion 05 Apr 2006 - 22:15 CatherineJohnson

Does anyone happen to know, offhand, whether it's possible in New York state to homeschool for one semester?

I do know it's not possible to pull your child out of school for one course (other states allow this).

Can you pull your child for one semester?

Don't spend time on this!

I can do my own research (I'm SOOOO looking forward to doing YET MORE RESEARCH!)

I'm just asking in case anyone happens to know the answer off the top of his head.

A related question: is there one super-simple resource — such as a book or website — that answers questions like this quickly?

Thanks!

-- CatherineJohnson - 27 Mar 2006

LindaOnK12 10 Apr 2006 - 17:29 CatherineJohnson

from Linda P

I've never commented before, but I have a suggestion for the homeschooling option: the k-12 curriculum at k12. I homeschooled my daughter last year using it. She had an abysmal experience prior to that, and was behind in reading and math. After a year of that curriculum (albeit, taught poorly by me) she was on grade level - she is in 5th grade now. It is based on the core knowledge curriculum, but it goes beyond that. Being at home didn't suit her, so she is now enrolled at a local core knowledge charter school, is doing great (happy as a clam and feels good about herself academically - she used to call herself stupid), was advanced mid-year from 5th grade language arts to 6th grade l.a., and her teacher mentioned the possibility of also advancing her mid-year to 6th grade math (not sure I want to do that - she will have missed 5-6 months of 6th grade math content at this point).

Anyway, this is a long winded way of saying that k-12 might be worth looking in to. If you want to know more about my experience, you can email me. Or, ask Carolyn - she knows my daughter.

I'm SO glad to get this.

Quite awhile back I'd read a glowing reference to this group at eduwonk, I believe, and then I'd forgotten all about it.

Boy....this could be something that would make a move into homeschooling doable on relatively short notice. I'm going to have Ed look it over. He already admires the Core curriculum. I think if he felt like there was a 'Known Quantity' out there, an already developed and field-tested curriculum (no crass comparisons, pls.), he'd feel the whole concept is less radical.

Plus the fact that Linda — a real live existing person — did homeschool for a limited period of time is helpful.

Thank you!

science book recommendations from Verghis and Charles

Before I lose track of these titles, I'm posting them here, where I can find them again:

Verghis: Integrated Science, Books 1 & 2, by J. M. LeBel. Recommended by John Hubisz, and I took a look at Book 1.

Charles: Science books I like are the Concepts and Challenges in physical science, earth science and life science published by Globe Fearon. They focus wonderfully on concepts in bite-sized form and are all substance.

and a math group from Google Master

Catherine, do you follow the k12.ed.math newsgroup? It's moderated, and gets a lot of "how do I do this homework problem?" answers, but the moderators and denizens provide quite good answers and have lots of references.

Thanks!

update: more from Verghis

You might also look at Calvert, extremely impressive. In addition to their school, they also sell their stuff for homeschooling.

For an example of their English stuff, see the examples in "The War Against Grammar" by David Mulroy.

keywords:
middle school science textbooks
middleschoolscience

Linda P on K12
eduwonk op-ed in TIMES on virtual charter schools
Change Agent Me

keywords: marketing

-- CatherineJohnson - 29 Mar 2006

HomeschoolingInIrvington 31 Mar 2006 - 18:44 CatherineJohnson

I checked with Christopher's guidance counselor about whether he'd be able to participate in school activities if he is homeschooled.

Just heard back today:

I just found out from the district office that students who are home schooled can't participate in sports. Hope this answers your questions.

Griffin Murray

I need a lawyer.

-- CatherineJohnson - 31 Mar 2006

SignFromGod 05 Apr 2006 - 00:34 CatherineJohnson

I met my new agent yesterday (wonderful!) and discovered that:

a) she has a client who is homeschooling her two kids & is plugged into a network of semi-local homeschoolers including a homeschooling physics teacher

b) she herself is interested in homeschooling

c) she'll introduce me to her client

I'm in.

Ed's pretty close, too.

This morning he asked Christopher how he 'felt' about it, which is tantamount to asking 'What kind of dog would we get if we got a dog?'

Tonight he's trying to shine me on.

That never works.

a sign from God
Yahoo groups on K12
home charter schooling

-- CatherineJohnson - 05 Apr 2006

HomeCharterSchooling 08 Apr 2006 - 21:33 CatherineJohnson

So today I discovered that K12, which Carolyn's friend Linda told us about, and Calvert, which I think Verghis mentioned, are 'virtual charter schools.'

Now that sounds promising.

I can do a virtual charter school for as long or short a period as I like.

Christopher isn't keen on sitting around here with me all day, and Ed, as I mentioned, is fixing to resist the inevitable, so.....I'm telling everyone 6 months will do.

I'll have one semester to give Christopher a real curriculum without the character education, the No Name Calling, the styrofoam solar systems from Michael's, and the Kafkaesque assaults on my sense of reality. (for \$500 dollars: what is show your work?)

I can get a huge amount accomplished in one semester, and if Christopher's desperate to get back to his pals at the end of that time, fine.

If things are moving along, if we've tapped into a homeschooling network and he's met some new kids (which would be good in any case, because this is a tiny town)....we'll finish out 7th grade.

Here's a good article from the TIMES: A New Enterprise Joins Growing Community of Online Schools.

a sign from God
Yahoo groups on K12
home charter schooling

-- CatherineJohnson - 05 Apr 2006

WeathervaneMe 09 Apr 2006 - 01:39 CatherineJohnson

I've mentioned a couple of times that I'm almost bizarrely mainstream.

I'm also, due to general giddiness, I guess, an Early adopter type, and occasionally even an Innovator.

For my entire adult life, virtually every time I've developed a New Interest, 5 seconds later I find out everyone else has developed the same new interest, too. For instance, take the matched vests in this family photo.

These vests are from The Gap. I saw them one fall and fell in love with them, but they were too expensive. I wanted them desperately. I would go to Gap stores from time to time, just to check them out. They were lovely.

Eventually I more or less forgot about them....and then one day sometime around Christmas all of a sudden the vests were on sale at The Gap in Sherman Oaks — 2 vests in the twins' size, and 1 in Jimmy's!

I snapped them up, and my best friend Cindy took a Christmas photo of the kids wearing their matched fair isle vests from The Gap.

Immediately afterwards the vests turned up everywhere.

They were on the cover of TV GUIDE. (Somehow I'm remembering them as being associated with Don Johnson's cop show. Did he have a son in the show?? Was it the son who was wearing the vest? I remember a daughter....)

They appeared on a child in a soup ad in a magazine. (I think it was soup.)

The vests were on my children, in my Christmas photo, and they were everywhere else, too. Stylists had scooped them up and photographed ad campaigns and magazine covers of PEOPLE WEARING THE EXACT SAME GAP FAIR ISLE VESTS I'D JUST SPENT 3 MONTHS OF MY LIFE OBSESSING OVER.

I used to keep a running list of all the things I'd bought that TV stylists had bought, too. Our Limoges china (from Paris, no less, bought when the exchange rate was good, later destroyed in the Northridge earthquake) was on DALLAS. Our sofa pillow was on THIRTYSOMETHING. Our dishtowel with the blue-and-white checkerboard pattern and the little pig was on ROSEANNE. Later, when we moved to New York and bought a rug for the twins' room on sale at ABC Carpet and Home, the rug was on THE SOPRANOS. In the son's room.

My greatest triumph when it comes to Jumping On The Train First Not Last is math.

Eightteen months ago, I became obsessed with math — obsessed with math to the point of writing a blooki about math. That's really obsessed. I never wrote anything about the vests.

Five seconds later, the President of the United States is announcing math initiatives in the State of the Union speech.

This happens to me constantly. I call it Surfing the Zeitgeist. People should forget about forming focus groups and just get me to free-associate for a half hour or so about Stuff I'd like to Know, or Stuff I'd like to Buy, or whatever it is, then form their strategic plans accordingly. They'd make a fortune. I think.

Friday in the TIMES

So last week I decided to pull my kid out of public school and enroll him in a virtual charter school. (I've decided; Ed is in the process of deciding. Which is probably just as well. Not sure you want two early adopters in one marriage.)

Two weeks ago I'd never heard of virtual charter schools.

Last week Carolyn's friend Linda P clued me in, and the next week I hopped on the virtual charter train.

And now this op-ed in yesterday's NYTIMES:

Virtual Schools, Real Innovation
By ANDREW J. ROTHERHAM (aka eduwonk)
Published: April 7, 2006

A WISCONSIN court rejected a high-profile lawsuit by the state's largest teachers' union last month seeking to close a public charter school that offers all its courses online on the ground that it violated state law by depending on parents rather than on certified teachers to educate children. The case is part of a national trend that goes well beyond virtual schooling: teachers' unions are turning to the courts to fight virtually any deviation from uniformity in public schools.

[snip]

Virtual charter schools grab headlines, but they are actually relatively minor players. The Center for Education Reform reports that there are 147 online-only charter schools in 18 states, with 65,354 students. In other words, virtual schools make up just 4 percent of the entire public charter school sector. And a third of them can be found in just one state, Ohio.

Still, they are valuable for many students. For example, a student in a rural community with few schooling options who finds the curriculum in her school too limiting might be better served through an online program that allows her to learn at her own pace. So, too, might a ninth grader who finds unbearable the jock-and-popularity culture that still largely prevails in our high schools. And some parents may want to be more involved in their child's education than is possible in traditional public schools but don't have the time or resources to do fully independent home schooling.

[snip]

...virtual charter schools are just part of a larger debate about public education. There is a universal American desire for customization and variety in goods and services, and education must respond to that demand, whether the unions like it or not.

[snip]

This debate, like the ones over many other education issues, is fundamentally about who gets to have power. [ed: I'll say] Yet the power the teachers' unions now wield will be fleeting if public schools do not become more responsive to parents.

This is my best timing yet.

The change in customers as a technology matures. In the early days, the innovators and technology enthusiasts drive the market; they demand technology. In the later days, the pragmatists and conservatives dominate; they want solutions and convenience. Note that although the innovators and early adopters drive the technology markets, they are really only a small percentage of the market; the big market is with the pragmatists and the conservatives. (Modified from Moore [1995]).

Crossing the Chasm
The Innovator's Dilemma

keywords: marketing

-- CatherineJohnson - 09 Apr 2006

IowaTestOfBasicSkillsPartOne 11 Apr 2006 - 20:46 CatherineJohnson

Now that so many of our schools have dropped the norm-referenced tests they used to give in favor of the mysterious not-to-be-deciphered-by-mere-mortals annual state test, parents have even less sense of where their children stand in relation to their peers. A doctor friend of mine told me she studied math in college and statistics in med school - she did research before going into practice - and she has no clue what the NY test scores mean.

Awhile back Lone Ranger posted information about administering the ITBS to your own children, and I'm starting the process today. She writes about her experiences here and here.

I started homeschooling my daughter in August 2004. She had been in public school since kindergarten and was a rising 4th grader when we started homeschooling. She had suffered through 3 years of "Math Their Way" and then 1 year of "Everyday Math" before I woke up to the fact that she was not learning math well. Her third grade test scores showed her to be working at the 50% in math. Well, after one year of homeschooling using only Singapore Math Levels 2B- half of 4A and supplementing with Singapore Math's Intensive Practice her total math score on the Iowa Test of Basic skills is now at the 99%!! More importantly her confidence, fluency, and ability to work through difficult problems have gone through the ceiling as well. Happy 4th of July - Lone Ranger

Ed and I are watching this movie in reverse. Christopher isn't learning much math, and his confidence, fluency, and ability to work through difficult problems fall with each new 20-point deduction for failure to show all of his work. It's iatrogenic regression: loss of confidence caused by public schooling, not medical treatment.

RESEARCH SHOWS (in this case that much-abused phrase has meaning) that low-stakes formative assessment, aka assessment for learning, raises achievement.

Assessment for learning raises achievement because it tells the teacher and student what the student does and does not know.

So I'm getting started. I've just put in a call to Piedmont Education Services (got the phone machine) and I'm printing out the Iowa Test Administrator's Form (pdf file) from BJU Press.

I'm going to check 'yes' in the box for: I am willing to be contacted by home schoolers in my area who require the services of a test administrator.

This is the major source on formative assessment:

Inside the Black Box: Raising Standards Through Classroom Assessment by Paul Black and Dylan Wiliam

formative assessment in Hungary

-- CatherineJohnson - 11 Apr 2006

StanfordOnlineHighSchoolForTheGifted 13 Apr 2006 - 19:31 CatherineJohnson

via Joanne Jacobs
Stanford University's Education Program for Gifted Youth is taking the next logical step: launching what is believed to be the nation's first online high school for gifted students.

The virtual high school will offer a full standard curriculum -- and more -- for students in 10th through 12th grades, leading to a high school diploma.

The only restrictions? Students will have to prove their intellectual prowess -- and come up with the tuition of about \$12,000 a year. Applications are being accepted later this month, classes will begin in the fall.

Gifted students around the world already flock to the program at Stanford, in part because many schools are unable to offer everything that advanced students need.

``The gifted are among those left behind,'' said Patrick Suppes, a philosophy professor emeritus from Stanford who directs the Stanford program. ``For reasons that aren't bad policy, No Child Left Behind worries most about students who are underperforming.

I wonder what their writing program is like.

-- CatherineJohnson - 13 Apr 2006

QuizSite 06 May 2006 - 19:15 CatherineJohnson

terrific quizz site - includes a link to Selected Answers to Questions at Math Forum

-- CatherineJohnson - 06 May 2006

HomeschoolMomSaysParentsAreResponsibleAfterAll 15 May 2006 - 12:02 CatherineJohnson

music to my ears . . .

With regard to the April 25 letter "Defeated budgets ruin opportunities," I laughed at the writer's statement that those who voted against the school budget "failed (her) children."

Parents are responsible for their children's education. With more and more families relying on two incomes to support a household, the public school districts have become a glorified day care system. If you are the type of parent who feels that educating your child is the burden of the taxpayers and local school district, you are the one who is failing your children.

The writer states that she wants her children to "have every opportunity." Then, give it to them. You can start by erasing the notion that taxpayers should foot the bill for extracurricular activities. Dip into your own pocket and support your offspring's endeavors.

With New Jersey's test scores dropping lower each year and incidents of violence in our schools on the rise, budgets that ask for new turf on football fields, additional sports teams and other nonessentials are irresponsible and asinine. If the money were going toward the basics — reading, science, history and mathematics — perhaps more people would consider voting "yes." But don't expect responsible parents and taxpayers to allow their pockets to be tapped once again to support noneducational agendas.

I am the parent of two children. I pulled them out of public school last year and began home-schooling this year because I realize as the parent, these children are my responsibility to educate. I taught them for less than \$2,000 this year. That figure includes books, manipulatives, bowling, tae kwon do, music lessons and field trips to places like Philadelphia and Plymouth Rock. Compare what my children have done this year to what other children were offered at an average cost that exceeds \$10,000 per pupil.

Unfortunately, I still pay the school portion of my property taxes. But don't expect me to vote "yes" when there is such a discrepancy in spending, overhead and test scores.

Lucille Kentner

I do think it's the state's responsibility to educate children, but seeing as how the state isn't doing it, I'm happy to read letters from mom's who are educating their kids on an annual budget of \$2000.

That's probably about what I'm paying to afterschool one child. That and the \$18,000 in property taxes.

Of course, that's not counting opportunity costs.

-- CatherineJohnson - 09 May 2006

AleksForSummer 31 May 2006 - 11:43 CatherineJohnson

This is exciting. I had asked Barry Garelick about ALEKS awhile back, and recently a parent sent him this account:

My child used ALEKS for Algebra and Geometry. IMO, it is a good solid math tutorial. A couple of years ago, I was looking for an inexpensive way for my child's classmates to learn mathematics, as opposed to what they were being taught in school (TERC and CMP). My child was taking an online algebra course (by Academic Systems) through Johns Hopkins' Center for Talented Youth (CTY). When he was about halfway through the course, I suspended the course and had him switch to ALEKS Algebra. The initial assessment indicated that he had mastered about half of the material in ALEKS Algebra, so in this sense it was comparable to the CTY course. Also, after he completed the ALEKS Algebra, I had him complete the CTY algebra course, which he did in about 2 weeks. That's about as fast as you could finish the course since it is linear (presented in a fixed sequence) and with video introductions and problem exercises which must be completed. My child thought the two courses were comparable. He also used ALEKS Geometry last year after he completed his high school "Honors" Geometry course. His initial assessment indicated that he had not mastered about 40% of ALEKS Geometry!

I know that ALEKS is used by a number of gifted children to accelerate in math. I know one parent, who coaches his local competition math team and has a child who is exceptionally talented in math (when he was in 8th grade the child had the highest score in his state on the AMC 10). The child uses Stanford's EPGY courses to learn math topics and then uses ALEKS to make sure he hasn't missed anything. That is a very strong endorsement in my book. Although I am most familiar with ALEKS being used by gifted student, it is not intended for gifted students, as is EPGY.

Being neither a mathematician nor a math educator, just a parent trying to provide his child with a decent math education, I heartily recommend ALEKS. A couple of years ago I asked for information about ALEKS on the nyc-hold list and got no response. I even wrote a couple of people offlist and asked them directly what they thought of it, but got little feedback. I hope someone else responds to your post with a more authoritative evaluation. If not, let me suggest that you try their free trial (see the top of the page you linked to). Pick a topic that you are comfortable with and incorrectly answer a couple of questions where you would particularly like to see what material they present and how.

ALEKS used to have a statement on their website to the effect that their program was designed to meet international math standards. I cannot find it now. I think they have intentionally rewritten the history of the development of ALEKS so that it would appear to be based on NCTM standards, "The practical development and implementation of an assessment and teaching system for Arithmetic based on Knowledge Space Theory began in 1992, financed by a 5-year grant from NSF." See Research Behind ALEKS. However, the history they used to have posted indicated that much of the original research began in the mid-80's, as I recall. You can learn more about ALEKS development and content by contacting ALEKS at 714.245.7191. You need to get beyond the customer reps (by asking for technical/content information they can't provide), but once you do the people are very helpful and knowledgeable.

Christopher's going to do ALEKS this summer.

Me, too, maybe. I'm thinking I can use it as a check on my self-teaching. Cost is \$19.95 a month, or \$99.95 for 6 months.

ALEKS as an inexpensive home-assessment tool

I think ALEKS probably works as a low-cost assessment tool for parents, based on this post from ParentPundit, whose daughter was languishing in Everyday Math:

In the summer at the end of 5th grade, I had her try the Aleks computer program in math, www.aleks.com. The Charter School in my town uses it, and I decided to try it for my own daughter. A tutor would have been expensive and less than optimal in this situation because my daughter does get concepts, she just needs more drill (how can most kids hone their number sense if they aren’t ever asked to multiply and divide numbers continuously), and she needs algorithms that have fewer steps so there is less possibility of error (everything that Everyday Math does not provide.)

According to Aleks, my daughter only knew 21% of a traditional 5th grade curriculum – and this was at the end of 5th grade. Talk about having a heart attack! This was soon remedied. My daughter is now in the 6th grade and she has completed the 5th and 6th grade curriculum according to Aleks. I’m looking forward to the tests at the end of the year to see if my intervention worked.

I'm trying to muscle Christian into taking an assessment test on ALEKS, too, but so far he's not enthusiastic. That's fine. The first project is getting him back in Westchester Community College. We got to work on that last night.

Then we'll deal with math.

I'm lying in wait.

I like this:

ALEKS is not a game, a toy, an art project, a virtual reality "space," a chat room, or a set of glitzy graphics with sprinklings of academic material. ALEKS is an interactive tutor which provides real assistance to anyone attempting to learn math.

Glencoe is now distributing ALEKS, which, based in my experience with their Parent-Student Study Guides (available free online), I think speaks well for it. You can still order ALEKS independently, however. No need to show your license.

ALEKS
parent report on ALEKS
ALEKS Graphic
formative assessment on wheels
ParentPundit uses ALEKS to fix Everyday Math
ALEKS question
ALEKS assessment coming right up

Glencoe math materials available free online
Glencoe Pre-Algebra Parent Student Study Guide
Glencoe Algebra 1 Parent Student Study Guide
Glencoe Geometry extra examples

Glencoe writing models available free online*

*good to know about in case your child's teacher is not at liberty to provide models of good student writing

keywords:
Glencoeparentandstudentstudyguide
Glencoewritingmodels
BarryALEKS

-- CatherineJohnson - 31 May 2006

MathTricks 31 May 2006 - 23:43 CatherineJohnson

Came across Math Tricks while looking for Math Teach and Math Learn. This is my favorite so far:

```From: Bob Stanarrow <Straitfromtheheart@aol.com>
To: Teacher2Teacher Public Discussion
Date: 2001030718:38:50
Subject: How to remember how many feet in a mile

I figured out a way to remember how many feet are in a mile.

Just say to yourself 5 tomatoes. Really there are 5,280 feet in a
mile, so you can remember that by saying 5 tomatoes.

5    to   mat  oes
( 5 ) ( 2 )( 8 )( 0 )
```

-- CatherineJohnson - 31 May 2006

SchoolsAndGroceryStores 02 Jun 2006 - 14:15 CatherineJohnson

I've been collecting essays I can have Christopher read and summarize.

Edspresso links to one of the clearest columns on economics I've ever seen:

Government K-12 schools, as now run everywhere in the U.S., will never excel at educating students. The reason is that each school gets its students and its budget without having to compete for them. Imagine if, say, supermarkets were run the same way we run schools. Everyone in my county would pay taxes to fund the county supermarket system; each one of us would then be assigned one specific county supermarket at which we are allowed to shop.

Of course, once in our assigned store, all the groceries that each of us gets are "free" -- meaning, we don't have to pay for them on the spot. If the products and services supplied by the supermarket are of poor quality, we're not allowed to switch to other county markets; we must, instead, complain to politicians.

The managers of the supermarkets will agree that their stores offer abysmal service and undesirable products; they will assert that this sad fact is caused by underfunding. We will be warned that only by paying higher taxes will we have any possibility of getting better supermarkets.

So our taxes will rise and funding for supermarkets will increase. But quality will remain poor -- and the excuses offered by the government-employed managers of the supermarkets will remain that they need yet more funding.

Author Donald J. Boudreaux, chair of George Mason's economics department, also has a nice passage on productivity in France and America:

Average worker productivity will be higher in those economies cursed by heavy government intervention into the labor market. Although at first this prediction might sound counterintuitive, it makes perfect sense. When government artificially raises the cost of hiring workers -- by mandating high minimum wages or by increasing the amount of red tape firms must endure in order to fire workers -- the workers that remain unhired are those who are least productive. Think about it: If the French minimum wage is the equivalent of \$10 per hour, then French workers who can produce no more than \$9 per hour of revenue for employers will not be hired, while in the U.S. such workers will be hired.

By pricing the lowest-skilled workers out of the labor market, European regulations ensure that only relatively high-skilled workers get jobs. So measures of average worker productivity will tend to show that workers in restrictive countries such as France and Germany are more productive than are workers in America. But this statistical outcome is a deceptive artifact of lamentable labor-market regulations whose burdens fall disproportionately on Europe's poorest peoples.

Can't wait to share that one with Ed, who has more than once told me French workers are more productive than American workers.

I've been wanting Christopher to go to George Mason ever since I read Alexander Tabarrok and Peter Boettke's column about it in SLATE.

Now I'm sure.

-- CatherineJohnson - 31 May 2006

MostEmailed 06 Jun 2006 - 21:25 CatherineJohnson

The number 1 most emailed article in the TIMES today is The Gilded Age of Home Schooling:

In what is an elite tweak on home schooling — and a throwback to the gilded days of education by governess or tutor — growing numbers of families are choosing the ultimate in private school: hiring teachers to educate their children in their own homes.

Unlike the more familiar home-schoolers of recent years, these families are not trying to get more religion into their children's lives, or escape what some consider the tyranny of the government's hand in schools. In fact, many say they have no argument with ordinary education — it just does not fit their lifestyles.

This is good news.

Once the TIMES starts writing about rich homeschoolers, homeschooling becomes an option.

An option for everyone, I mean.

This article is a case of synchronicity for me. Just last week a friend told me that an Irvington family has hired a 5th grade teacher, who retired from the Main Street School last year, to teach their kids at home.

When Nick Niell, an investment banker, and his wife, Sarah, moved to New York from East Sussex, England, for about a year in 2003, four teachers would come on weekdays to Mr. Niell's townhouse on 69th Street near Madison Avenue to teach his three school-aged children. Mr. Niell said he could not find a British school in the city and wanted his children to study the same things they would have studied in England. A floor of the house was converted into classroom space.

"It was quite good fun," said Mr. Niell, whose teachers came through Partners with Parents, a Manhattan in-home tutoring service.

That's it.

If the British are doing it, everyone's going to do it.

The cost for such teachers generally runs \$70 to \$110 an hour. And depending on how many hours a teacher works, and how many teachers are involved, the price can equal or surpass tuition in the upper echelon of private schools in New York City or Los Angeles, where \$30,000 a year is not unheard of.

Other parents say the model works for children who are sick, for children who are in show business or for those with learning disabilities.

"It's a hidden group of folks, but it's growing enormously," said Luis Huerta, a professor of public policy and education at Teachers College of Columbia University, whose national research includes a focus on home schooling.

The United States Department of Education last did a survey on home schooling in 2003. That survey did not ask about full-time in-home teachers. But it found that from 1999 to 2003, the number of children who were educated at home had soared, increasing by 29 percent, to 1.1 million students nationwide. It also found that, of those, 21 percent used a tutor.

Bob Harraka, president of Professional Tutors of America, has about 6,000 teachers from 14 states on his payroll in Orange County, Calif., but cannot meet a third of the requests for in-home education that come in, he said, because they are so specialized or extravagant: a family wants a teacher to instruct in the art of Frisbee throwing, button sewing or Latin grammar. A family wants a teacher to accompany them for a yearlong voyage at sea.

"Sailing comes up at least once or twice a year," Mr. Harraka said.

Parents say in-home teaching arrangements offer unparalleled levels of academic attention and flexibility in scheduling, in addition to a sense of family cohesion and autonomy over what children learn. To them, these advantages make up for the lack of a school social life, which they say can be replicated through group lessons in, say, ballet or sculpture.

Yup. That's sure the way I feel about homeschooling now. All of the above.

money 'graph

Companies that supply teachers and curricula are abundant, also making it easier for families to step away from traditional schools, experts say. And though many who follow the new model are wealthy, increasing numbers of middle class families more sociologically and racially diverse have begun to school their children at home, according to education officials and tutor-service companies.

Laurie Gerber, president of Partners with Parents, said she started to get requests for in-home teachers about three or four years ago.

"Our tutoring business started to become a huge percentage of home-schooling clients, as opposed to tutoring," Ms. Gerber said. "We started a whole home-schooling wing."

The teachers who are hired to home school say the job is great.

textual analysis

What does this teacher mean when she says, "This is pure teaching"?

Tiffany Wheeler's tutor, Nancy Falong, retired a few years ago after 32 years as a teacher in the New Jersey public schools. Now she works for On Location Education. Sitting next to Tiffany last week, their two world history books turned to the same page on the Marshall Plan, she expressed a sense of delight. "This is pure teaching."

Someone posted a comment on Math Forum saying that this teacher was talking about the breakdown of discipline in the classroom.

I don't think so.

Breakdown of discipline may be part of what she's talking about.

But I suspect she's talking about the wretchedness of public schools overall. The constant paperwork, the lack of authority given to teachers, the chronic churning of curricula by itinerant administrators....and perhaps the ban on direct instruction as well.

speaking of direct instruction...

Bank Street weighs in:

Jon D. Snyder, dean of the Bank Street College of Education in New York, said his main concerns about this form of education were whether tutors and students were a good fit, and whether students got enough social interaction.

"From a purely academic standpoint, it goes back to a much earlier era," Dr. Snyder said. "The notion of individual tutorials is a time-honored tradition, particularly among the elite."

Think Plato, John Stuart Mill and George Washington. Philosopher kings and gentleman farmers. Because of the cost of in-home tutoring, the idea will probably not spread like wildfire, and just as well, Dr. Snyder said.

"Public education has social goals; that's why we pay tax dollars for it," he said. "When Socrates was tutoring Plato, he wasn't concerned about educating the other people in Greece. They were just concerned about educating Plato."

I feel a letter to the editor coming on.

update from Tracy

When Socrates was tutoring Plato, he wasn't concerned about educating the other people in Greece. They were just concerned about educating Plato."

To the best of my knowledge, the only way this sentence is true is if we are talking about the moments Socrates was actually talking with Plato. Quite possibly Socrate's whole attention at that point of time was on tutoring Plato.

But this statement is not true of Socrates' life in general. Socrates didn't charge for his conversation. He was notorious for stopping all sorts of people, including slaves, and having ethical debates with them. He was eventually convicted and ordered to drink poison on the basis of having corrupted youth in general, not just Plato.

The further I go with all this, the more frustrated I become by my own poor education and general lack of knowledge. (Latest obsession: grammar. And Latin. History & "Bible literacy" are still on hold.)

It doesn't surprise me at all that the Dean of the Bank Street College would speak knowledgably about Socrates on the basis of precious little knowledge.

Krystal Wheeler, 18, right, studying with her tutor, Jennifer Jones, at the Wheelers' home in New York.
Krystal's sister is also home-schooled.

-- CatherineJohnson - 06 Jun 2006

BlowUpTheEdSchools 23 Jun 2006 - 15:59 CatherineJohnson

Eduwonk links to Mike Piscal again today. You should read and memorize all 3 of his posts, but at the moment I'm interested in this one:

Why can’t a future teacher get a bachelor’s degree in a field he/she loves, take an additional 7 or 8 classes on teaching while still an undergraduate, and graduate with a credential? The most elite private schools – Exeter and Andover and Choate, for example – hire teachers with that kind of preparation. So do the country’s network of successful charter schools. Why can’t public schools do the same?

In the words of Deep Throat: follow the money. A recent article in Education Week (March 16, 2005) sums it up: “Critics have long accused universities of using education schools as cash cows, generating more in tuition from a steady stream of students than the institutions actually spend to educate them. With the expansion of off-campus programs in educational administration taught mostly by part-time professors, the report warns, the problem is getting worse.”

A college graduate who wants to teach in public school must attend school fulltime for one or two additional years (in some cases for as much as \$20,000 a year), or she can go directly to work at a public school and take classes at night and on weekends for the next 3 to 5 years, also at her own expense. The time sacrifice is enormous. In the words of one Education Professor: "the opportunity costs of forcing half of the California Teaching workforce into "continuing their educations" in the name of credential seeking or renewal (AKA life-long learning) while attempting to teach a full day in the classroom, means that typically three days a week many of our teachers are not grading papers or preparing tomorrow's lessons. It means they are stuck in freeway traffic on their way to the next required credential college course, or they are at home writing the paper due tomorrow for that course. We don't train airline pilots WHILE they are flying commercial flights! Teachers are a different matter because, I guess, kids don't crash and burn."

[snip]

At my school, a teacher needs only a scholar’s zeal for the subject s/he studied in college, and a burning desire to lead the next generation. We’ll take it from there – from lesson planning to classroom management, from discipline to communicating with parents, she will learn from master teachers who are eager to lead and encourage the younger faculty. That’s how it works at Exeter – where tuition is thirty-eight thousand dollars a year – and that’s how it works in my school – where tuition is free.

Here in NY state, we're down to the wire (it seems) on the question of whether the cap on charter schools will or will not be raised.

The politics are astounding.

Nick Spano, our state senator & a Republican, presented Irvington with money for white boards or smart boards or something along those lines a couple of months ago. Then he delivered a blistering attack on vouchers, charter schools, and George Pataki.

Ed, who has voted for precisely one Republican in his life, came home scandalized.

"Isn't that guy a Republican?" he said. "He's attacking charter schools! He's attacking George Pataki!"

Ed's capacity to continue to be amazed is exceeded only by my own.

On the plus side, it's nice to know public school teachers are far better trained than the faculty at Exeter and Andover.

update: Joe Williams on NY charter school law

You can email Governor Pataki here after you read Wiliams' post, if you like.

blow up the ed schools part 1

View Park Preparatory Accelerated Charter Schools
Inner City Education Foundation

-- CatherineJohnson - 21 Jun 2006

LightningLiterature 13 Jul 2006 - 15:24 CatherineJohnson

Does anyone know anything about the Lightening Literature series?

I joined the Core Knowledge Homeschooling list serve, because I need more email to not read, and one of the parents had just gotten the books and teacher's manual & thought they looked great.

I am planning to get a post up about our summer activities around here, but until I do the 3 new books we're using are:

-- CatherineJohnson - 12 Jul 2006

JohnSaxonPrefaceAlgebra2 20 Jul 2006 - 17:25 CatherineJohnson

Preface to Saxon Algebra 2

This is the second edition of the second book in an integrated three-book series designed to prepare students for calculus. In this book we continue the study of topics from algebra and geometry and begin our study of trigonometry. Mathematics is an abstract study of the behavior and interrelationships of numbers. In Algebra 1, we found that algebra is not difficult—it is just different. Concepts that were confusing when first encountered became familiar concepts after they had been practiced for a period of weeks or months—until finally they were understood. Then further study of the same concepts caused additional understanding as totally unexpected ramifications appeared. And, as we mastered these new abstractions, our understanding of seemingly unrelated concepts became clearer.

Thus mathematics does not consist of unconnected topics that can be filed in separate compartments, studied once, mastered, and then neglected. Mathematics is like a big ball made of pieces of string that have been tied together. Many pieces touch directly, but the other pieces are all an integral part of the ball, and all must be rolled along together if understanding is to be achieved.

A total assimilation of the fundamentals of mathematics is the key that will unlock the doors of higher mathematics and the doors to chemistry, physics, engineering, and other mathematically based disciplines. In addition, it will also unlock the doors to the understanding of psychology, sociology, and other nonmathematical disciplines in which research depends heavily on mathematical statistics. Thus, we see that mathematical ability is necessary in almost any field of endeavor.

Thus, in this book we go back to the beginning –to signed numbers—and then quickly review all of the topics of Algebra 1 and practice these topics as we weave in more advanced concepts. We will also practice the skills that are necessary to apply the concepts. The applicability of some of these skills, such as completing the square, deriving the quadratic formula, simplification of radicals, and complex numbers, might not be apparent at this time, but the benefits of having mastered these skills will become evident as our education continues.

We will continue our study of geometry in this book. Lessons on geometry appear at regular intervals, and one or two geometry problems appear in every homework problem set. We begin our study of trigonometry in Lesson 43 when we introduce the fundamental trigonometric ratios—the sine, cosine, and tangent. We will practice the use of these ratios in every problem set for the rest of the book. The long-term practice of the fundamental concepts of algebra, geometry, and trigonometry will make these concepts familiar concepts and will enable an in-depth understanding of their use in the next book in the series, a pre-calculus book entitled Advanced Mathematics.

Problems have been selected in various skill areas, and these problems will be practiced again and again in the problem sets. It is wise to strive for speed and accuracy when working these review problems. If you feel that you have mastered a type of problem, don’t skip it when it appears again. If you have really mastered the concept, the problem should not be troublesome; you should be able to do the problem quickly and accurately. If you have not mastered the concept, you need the practice that working the problem will provide. You must work every problem in every problem set to get the full benefit of the structure of this book. Master musicians practice fundamental musical skills every day. All experts practice fundamentals as often as possible. To attain and maintain proficiency in mathematics, it is necessary to practice fundamental mathematical skills constantly as new concepts are being investigated. And, as in the last book, you are encouraged to be diligent and to work at developing defense mechanisms whose use will protect you against every humans’ seemingly uncanny ability to invent ways to make mistakes.

One last word. There is no requirement that you like mathematics. I am not especially fond of mathematics—and I wrote the book—but I do love the ability to pass through doors that knowledge of mathematics has unlocked for me. I did not know what was behind the doors when I began. Some things I found there were not appealing while others were fascinating. For example, I enjoyed being an Air Force test pilot. A degree in engineering was a requirement to be admitted to test pilot school. My knowledge of mathematics enabled me to obtain this degree. At the time I began my study of mathematics, I had no idea that I would want to be a test pilot or would ever need to use mathematics in any way.

I thank Tom Brodsky for his help in selecting geometry problems for the problem sets. I thank Joan Coleman and David Pond for supervising the preparation of the manuscript. I thank Margaret Heisserer, Scott Kirby, John Chitwood, Julie Webster, Smith Richardson, Tony Carl, Gary Skidmore, Tim Maltz, Jonathan Maltz, and Kevin McKeown for creating the artwork, typesetting, and proofreading.

I again thank Frank Wang for his valuable help in getting the first edition of this book finalized and publisher Bob Wroth for his help in getting the first edition published.

John Saxon
Norman, Oklahoma

Beautiful.

The third editions of the Saxon books seem to have done away with John Saxon's prefaces; at least, that's the case with the 3rd edition of Algebra 1/2.

Thanks to our ktm Book Fairy, I have a copy of the 2nd edition of Algebra 1/2, so I'll post that preface, too.

The books themselves don't seem to have been changed in other bad direction. If you're interested in buying the 2nd edition, though, Rainbow Resource seems still to have them. So does Seton Books. I'm sure other homeschooling stores do as well.

Wilfried Schmid on procedures and understanding

''I'm a professional mathematician, and I myself very often use mathematical methods that I understand only imprecisely,'' he said. ''It is while I use them that I begin to understand. After a while, the use and the understanding are mutually supporting.''

source:
The New, Flexible Math Meets Parental Rebellion (scroll down)
By ANEMONA HARTOCOLLIS (NYT) 2403 words
Published: April 27, 2000

Carolyn on procedures and understanding

Carolyn has said more than once that she believes in teaching procedures first. Conceptual understanding follows. (I can't find any of her posts on this, so if I've misremembered I'll delete this.)

I was always a little skeptical of this, although my working assumption is that where Carolyn and I disagree, Carolyn is right.

I've now spent enough time working my way through Saxon to see what Saxon, Schmid, and Carolyn are talking about. When you practice a procedure you don't understand over and over and over again, at some point it "naturalizes." It seems right and inevitable. And it makes sense.

John Saxon stresses this idea in book after book. Math isn't hard; it's different. It's unfamiliar.

When you've done so much math that it no longer seems strange, it starts to seem easy — or at least not harder than other subjects.

Of course, the irony is that this naturalizing process leaves me unable to explain procedures to someone for whom math is still strange. It does, however, make me understand why "math brains" tend to say things like, "It just is" when I ask for an explanation!

I'll add that Saxon (and probably Carolyn & Schmid, too) rarely teaches a concept stripped of all meaning or explanation — though he does do so far more often in Algebra 1 than in the earlier books. A student using Algebra 1 must take a lot on faith.

If nothing else, meaning helps memory; it's easier to remember a procedure you understand. (I have references for this observation, but don't want to spend the time to dig them up just now.) I'd be willing to bet that meaning increases student motivation, too. I recall Steve H saying that students always want an explanation if they can get one. (Steve - am I remembering that correctly?) Every one of Saxon's explanations in 6-5 through 7-6 has been pure pleasure to read, and has made me want to learn more math. In contrast, my motivation sometimes flags as I work with Saxon's highly abstract Algebra 1, my motivation sometimes flags.

In short, I think it's probably always good to try to teach some conceptual understanding along with procedure. I also think, after living through Ms. K's Phase 4 math class, that it's essential to include mini word problems — although Saxon does not do so in Algebra 1. But John Saxon can get away with it, because he's a genius math textbook writer. If you're not a genius math text writer, or a genius math teacher, you can't.

Nevertheless, these caveats aside, math is first and foremost something people do. Barry says that constructivist math ends up teaching math appreciation, not math, and I agree.

Teach procedures supported by meaning where possible, and, where not possible, teach the procedure and practice it to mastery. Understanding will follow as "totally unexpected ramifications appear."

John Saxon & John von Neumann on math
preface to Saxon Algebra 2

-- CatherineJohnson - 15 Jul 2006

HowToTeachYourselfArithmetic 21 Sep 2006 - 21:51 CatherineJohnson

This may seem like a strange question coming from me.....can you teach yourself arithmetic?

UPDATE 10-19-2006: The answer is yes. You can. Christian is doing it now. Starting in Saxon Math 5/4.

I ask because Christian just got his placement test results — he passed reading!

I don't think we can credit the Yonkers school system for that, but the Mamaroneck schools may have had a hand in it. I say "may" because Christian's mom is college educated and has always subscribed to the New York Times, which meant that as a child Christian, like the rest of us it seems, was getting most of his vocabulary and exposure to print at home. He went to Mamaroneck schools through middle school, then moved to Yonkers where his 12th grade English teacher used the same book Mamaroneck used in 7th.

So I'm not giving Yonkers a lot of credit.

The bad news is math. We're looking at a pre-algebra placement.

(Can we sue the schools for not teaching yet?)

I'm in no mood to pay for two zero-credit remedial courses at Westchester Community College, and I don't know whether financial aid exists for pre-algebra. Even if it does, Christian needs two semesters' worth of remedial math (pre-algebra and high school algebra) before he can take a math or science course for credit. If that's what he has to do, then that's what he has to do, but he also has to support himself and stay motivated. The college completion stats don't show a lot of people who have to take two semester's worth of remedial math making it through.

I'd like to find another way if possible.

Naturally I'm thinking Saxon. Christopher's been moseying through Saxon Algebra 1/2 this summer. He's up to Lesson 15 and he's been getting all the answers right. Christian could probably teach himself fractions, decimals, and percents using Algegbra 1/2.

On the other hand, the Saxon books are huge. "Huge" meaning long and time-consuming. Long and time-consuming may be the only way to go here, seeing as how there's no royal road to geometry. But if anyone has thoughts, I'd like to hear.

update: I've just realized I'm going to have to get Christian to take the Saxon placement test.

If Saxon puts him into 8/7 or 7/6....I'm going to have to find another way.

computers & test anxiety

Christian says his mother was shocked that he passed the reading test.

I didn't get that at all until he told me he's always had a hard time taking tests. It sounds like he has some test anxiety; plus he's got some kind of fine motor "issue" (Carolyn's favorite word!) that tripped him up for years. He was classified special needs, along with all the other black kids, and his mom was constantly trying to get the school to provide him with a keyboard. Plus he's lefthanded.

So basically, he's never been able to take tests.

Apparently the reason he did well on the WCC test was that it's done on a computer terminal. He took the Accuplacer test, which I gather is being used in colleges all over the country. I had no idea the College Board is also in the remedial placement testing business. Apparently there's a whole Accuplacer test prep world out there, too. (It's aways worse than you think.)

Doing the test on the computer made Christian feel as if he wasn't doing a test. He was the second person finished; he just whipped through it.

ALEKS?

This is making me wonder whether ALEKS might be a good idea for Christian.

I'm certain Christian has math baggage (scroll down for Rudbeckia, Steve H, Carolyn, & Susan) and it seems pretty clear that looking at math on a computer will help him "break set."

On the other hand, I've been using ALEKS for a few weeks and while I find it highly motivating - addictive, almost - I don't find it highly illuminating. It's pretty much the ultimate in fragmented content, and the program offers no "metacognitive pointers" as Saxon does. You're on your own.

By "metacognitive pointer" I mean the kind of pointers people give when they're telling a delivery person how to get to their house. ALEKS doesn't give pointers. ALEKS just gives you the procedure, along with a lot of hyperlinks to other pages filled with other procedures & definitions, and that's the end of it. It's like learning algebra from Hal.

Years ago, when I interviewed nearly 100 couples for a book on marriage, I ended up dividing people into two categories:

• people who give good directions

• people who don't *

People who give good directions always tell you where you're going to be tempted to go wrong, how to tell if you have gone wrong, and what to do about it when you realize you did go wrong. A really good direction giver will say "You can't really see the driveway from the road, so if you get to the traffic light across from the church and the Sunoco station you've missed it."

That kind of thing. That's what the Saxon books do. Saxon lessons routinely tell students what mistakes they're likely to make and how not to make them. Often these pointers give you greater insight into the topics you've been studying.

Saxon Algebra isn't going to be addictive for most people.

But it is illuminating.

Any thoughts?

* When I first met Temple, she made exactly the same observation & for the same reasons.

Christianlearnsmath

-- CatherineJohnson - 31 Aug 2006

ScholasticAchievementOfHomeSchooledStudents 12 Sep 2006 - 22:28 CatherineJohnson

The grade equivalent score comparisons for home school students and the nation are shown in Figure 2. In grades one through four, the median ITBS/TAP composite scaled scores for home school students are a full grade above that of their public/private school peers. The gap starts to widen in grade five. By the time home school students reach grade 8, their median scores are almost 4 grade equivalents above their public/private school peers.

source:
Scholastic Achievement and Demographic Characteristics of Home School Students in 1998
Education Policy Analysis
Volume 7 Number 8
March 23, 1999

Maybe we should forget the ed schools and go hire some homeschooling parents.

-- CatherineJohnson - 08 Sep 2006

BankOfAmerica 28 Nov 2006 - 20:48 CatherineJohnson

hmmm

I actually kind of don't hate this.

It's possible I have completely lost what remains of my mind, at long last.

Or not!

-- CatherineJohnson - 22 Nov 2006

NationalInstituteForLiteracy 09 Dec 2006 - 01:57 CatherineJohnson

Is this what I think it is?

Is this a federal agency directing parents to a homeschooling website for help assessing their children's reading level?

and....

If it is....then why?

Is there a particular reason why our federal government can't provide parents with help assessing their children's reading level?

-- CatherineJohnson - 02 Dec 2006