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12 Jan 2006 - 02:27
hoo boy, that was fun fun, fun, fun TRAILBLAZERS is going down bye-bye
UPDATE 9-19-2006: TRAILBLAZERS isn't going anywhere. don't listen to me.
a TRAILBLAZERS spiral I'll condense the story and post tomorrow, but I wanted to get this down tonight. After the meeting, Ed was talking to the Dows Lane (K-3) mom who's been agitating against TRAILBLAZERS. Her kid is a math-brain. Maybe both her kids are. She told Ed that in 2nd grade TRAILBLAZERS teaches kids how to construct graphs. Then, in 3rd grade, TRAILBLAZERS teaches kids how to construct graphs again — the exact same lesson — except that, this time around, they teach the kids TO LABEL THE AXES.* She didn't say whether they teach labeling the axes to mastery.
it's all becoming clear now All of it. The huge books, the grinding overwork, the ever-expanding gap between our kids and every other math student on the planet...... I get it. I have found the basic principle, as Temple would say. Start from the premise that nothing will be taught to mastery, and everything else follows. Big books, big gap, big backpacks, 11-year old kids breaking down in tears in the middle of a 'quiz.' It all makes sense. That big sucking sound you hear? That's the spiral curriculum Hoovering up the kids, the mom, the dad, the KUMON operator, and the kindly folks at ktm into the effort to teach basic algebra to just one boy. I don't like it.
No one at the meeting knew what the term 'spiralling' meant. Now they do. Until one year ago, I had never heard the term 'spiral' applied to a curriculum. I had no idea. I still had no idea after I had heard it. But once you start to really work your way through it....once you start to understand that schools deliberately teach skills and concepts so that children do not master them and then grade them on their 'performance'..... slow burn
* She thought it was 2nd & 3rd grades, but it might be 1st and 2nd grades.
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Here's another arrow for the quiver. Pagesplatter and animations = bad. When Static Media Promote Active Learning : Annotated Illustrations Versus Narrated Animations in Multimedia Instruction. Mayer, Richard E.; Hegarty, Mary; Mayer, Sarah; Campbell, Julie; Journal of Experimental Psychology: Applied. Vol. 11(4) December 2005. pp. 256-265. Abstract: In 4 experiments, students received a lesson consisting of computer-based animation and narration or a lesson consisting of paper-based static diagrams and text. The lessons used the same words and graphics in the paper-based and computer-based versions to explain the process of lightning formation (Experiment 1), how a toilet tank works (Experiment 2), how ocean waves work (Experiment 3), and how a car's braking system works (Experiment 4). On subsequent retention and transfer tests, the paper group performed significantly better than the computer group on 4 of 8 comparisons, and there was no significant difference on the rest. These results support the static media hypothesis, in which static illustrations with printed text reduce extraneous processing and promote germane processing as compared with narrated animations. The link was forwarded by Dan Willingham on the DI listserve. -- KDeRosa - 12 Jan 2006
Also set your dvrs for John Stossel's Stupid in America on Friday Night (1/13) on ABC: 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. -- KDeRosa - 12 Jan 2006
The mantra of all spiraling curricula: "Don't worry [that little Johnny got a 36 on the unit test]. He'll see this again next year." -- CarolynJohnston - 12 Jan 2006
"Also set your dvrs for John Stossel's Stupid in America on Friday Night (1/13) on ABC" Purely out of the kindness of my heart, I'm going to point Mike in Texas at the Stossel piece. -- VerghisKoshi - 12 Jan 2006
Meanwhile 36 does wonders for little Johnny's self-esteem and 'appreciation' for math — both watchwords of progressive educators. -- CatherineJohnson - 12 Jan 2006
We have children crying in the middle of math tests. -- CatherineJohnson - 12 Jan 2006
It's unconscionable. -- CatherineJohnson - 12 Jan 2006
I hope I spelled that right. -- CatherineJohnson - 12 Jan 2006
In terms of spiralling, Everyday Math does the same thing. In addition to not teaching traditional long division, they use the exact same example to teach forgiving division in the 4th grade and in the 5 th grade. One example, both the same. I am now starting my second round of Math Booster classes. Even though I have a very small sample size, I am a Bayesian, so I am going to go out on a limb: about 50% of my fifth graders cannot do long division. I mean that they cannot do it at all. They just sit and stare at the problem and have no idea what to do or how to do it. The other 50% are completely proficient. I don't know what this means yet. But I will go out on a limb and say this: someone is teaching certain children long division and making sure that they know it to mastery. The other children are left completely in the dark. They know that they don't know it. You can tell by the level of tension on their faces when you try to explain the procedure. I even had a child cry in my class last session, and he was a math brain!!! So I have a strategy to teach them. I'll let you know how it works. -- AnneDwyer - 12 Jan 2006
Anne, How long has your school system been using EM? What has been the reaction of the parents to EM? Our county just adopted EM. The major complaint from the parents is that they didn't phase it in. Kids who were using Scott-Forseman Addison Wesley for grades 1-4 are now facing EM this year. The few homework pages I have seen for the 5th grade have concepts that the kids have already learned under Forseman, so I'm sure that the parents will see an immediate improvement in grades. In fact, the one student I help (a 5th grader) made the honor roll for the first time this year, no doubt because he's just reviewing early 4th grade Forseman concepts. EM fans will no doubt take the credit. -- NicksMama - 12 Jan 2006
Spiraling "... nothing will be taught to mastery ..." Mastery requires grade-level expectations. Mastery requires practice. Mastery requires testing. Spiraling (as it is applied in these cases) is used to avoid mastery (a.k.a. Drill and Kill) Spiraling is used as a pedagogical excuse for social promotion. (no tracking and no holding kids back either) This is OK, because they think that there is no linkage between mastery and understanding. They think that everything will work out in the end. They want their pedagogy and eat it too. Please note that this is not what I would call spiraling, which is a fine technique for both learning and solving problems. Sometimes, when a design project is very large (building, bridge, car, ship), you cannot start at point A and go to point B to finish the design. You start with a conceptual design phase, spiral around through a preliminary design phase (same analysis, but with more details), and then go on to a detailed design phase. It's called a design spiral. (each step of which could involve a complex calculation that is done using only one BEST algorithm) Problem solving in the real world is so much more complex than any silly talk of only one answer or many ways of doing things. I think that educators have "mastered" the art of saying whatever sounds good just to do whatever they want. They argue with generalities, but they get to define the details. They do not want you to see the details! -- SteveH - 12 Jan 2006
My children's district has been using Mathland for several years. From what I can see, the teachers (at least in our school) are supplementing the Mathland curriculum with more and more of their own materials. At this point, I would have to describe the approach as a hybrid. It seems to be working, although I suspect it ends up being much more difficult for the teachers than it would be if they were starting with a stronger curriculum. Starting with a stronger curriculum would also result in greater uniformity from class to class and school to school, which I think is important. So many kids move in and out of the school during the course of a year -- I shudder to think of the gaps (and repetition) that results. Most of the supplementation comes in the form of timed drills, for addition and subtraction in the earlier grades, and for multiplication at the end of third grade and beginning of fourth. One thing that I think has worked. My son, a fourth grader, was taught "forgiving division" earlier this year. They did a reasonable amount of practice with it, while I was reading all the negative comments here and wondering what, if anything, to do. In the last few days, though, they have been taught the traditional algorithm, and last night's homework required using the traditional algorithm. To me, that's a reasonable way to use forgiving division -- as a starter, an introduction. -- DaleA - 12 Jan 2006
"In addition to not teaching traditional long division, they use the exact same example to teach forgiving division in the 4th grade and in the 5 th grade. One example, both the same." No! My son is in 4th grade and we just went over partial quotients in EM. If they cover the same stuff next year (sizzle, burn, pop, aaarrrrggghh!) ... my brain is turning to mush. Help! -- SteveH - 12 Jan 2006
Starting with a stronger curriculum would also result in greater uniformity from class to class and school to school, which I think is important. So many kids move in and out of the school during the course of a year -- I shudder to think of the gaps (and repetition) that results. Hi Dale! absolutely I'll have to rustle up the studies on that very issue this is one of the HUGE causes of extremely poor performance in disadvantaged kids they move far more often than middle & upper-middle class kids, and they're constantly joining classes in the middle Talk about no coherence -- CatherineJohnson - 12 Jan 2006
"I mean that they cannot do it at all. They just sit and stare at the problem and have no idea what to do or how to do it. The other 50% are completely proficient. I don't know what this means yet." I would say that for anything you teach, some kids will pick it up quickly, some will get it at home or with tutoring, and some won't get it (at home or school). The percentages for each category will vary depending on many factors, but 50 percent who don't understand the material indicates a major failure for the school. -- SteveH - 12 Jan 2006
They did a reasonable amount of practice with it, while I was reading all the negative comments here and wondering what, if anything, to do. In the last few days, though, they have been taught the traditional algorithm, and last night's homework required using the traditional algorithm. To me, that's a reasonable way to use forgiving division -- as a starter, an introduction. Obviously, we are FULLTIME complainers around here, but one thing I ought to say more often — and this has finally come up on another thread — is that I personally, because of Temple (Grandin), have become an 'outputs' person. That is, I don't care what the inputs are if the output is sound. If my child is learning math on par with his peers in Singapore, I don't care how they teach it. Forgiving division may very well be a good introduction to division; that makes sense to me. I've also seen, from my own experience of re-learning math, that teaching a concept or a procedure in 2 or at most 3 different ways has made math much more comprehensible to me this time around. So to me it makes sense that starting with forgiving division and then moving to the traditional algorithm — or starting with the traditional algorithm and using it to demonstrate that forgiving division works on the same principles — would be a good idea. What I love about Singapore Math & Saxon Math, though, (and probably Engelmann's math books, too) is that there are no wasted moves. Each concept or procedure is taught for a specific length of time, for a specific reason. The material is field tested, and then refined. -- CatherineJohnson - 12 Jan 2006
This another example of the educrats co-opting a perfectly good term - "spiraling" and demolishing it's meaning. As Steve points out, there is good spiraling and bad spiraling. Most schools employ bad spiraling mostly for social promotion reasons. The telltale sign of bad spiraling, as Engelmann points out, is that material isn't taught to mastery and as a result extensive review of old material is required. This review is just as ineffective as it was the first time the material was presented because knowledge has a very short shelf life. If material isn't mastered when taught it will quickly be forgotten. -- KDeRosa - 12 Jan 2006
Engelmann on the shelf life of learned material Typically about 60 school days pass before any topic is revisited. Stated differently, the spiral curriculum is exposure, not teaching. You don't "teach" something and put it back on the shelf for 60 days. It doesn't have a shelf-life of more than a few days. It would be outrageous enough to do that with one topic-- let alone all of them. ...Don't they know that if something is just taught, it will atrophy the fast way if it is not reinforced, kindled, and used? Don't they know that the suggested "revisiting of topics" requires putting stuff that has been recently taught on the shelf where it will shrivel up? Don't they know that the constant "reteaching" and "relearning" of topics that have gone stale from three months of disuse is so inefficient and impratical that it will lead not to "teaching" but to mere exposure? And don't they know that when the "teaching" becomes mere exposure, kids will understandably figure out that they are not expected to learn and that they'll develop adaptive attitudes like, "We're doing this ugly geometry again, but don't worry. It'll soon go away and we won't see it for a long time"? The Underachieving Curriculum judged the problem with the spiral curriculum is that is lacks both intensity and focus. "Perhaps the greatest irony is that a curricular construct conceived to prevent the postponing of teaching many important subjects on the grounds that they are too difficult has resulted in a treatment of mathematics that has postponed, often indefinitely, the attainment of much substantive content at all." -- KDeRosa - 12 Jan 2006
DaleA "My children's district has been using Mathland for several years." Wow! There is another town besides ours that still uses MathLand! MathLand, the curriculum that is so bad and trashed by so many that even the publisher dumped it and you can't find any mention of it on their web site - not even information on how to move up (?) to the Everyday Math they now push. If MathLand (or Everyday Math) is so good, then why are schools across the nation taking so much time supplementing them? As my wife says: "Why are they using a curriculum that they have to supplement?" Sometimes the supplementing is superficial and comes no where near mastery. With long division, it's one thing to teach the traditional algorithm, but quite another to expect mastery. My son is being taught partial quotients or forgiving division, but he gets maybe 4 or 5 problems to do every so often. I can't quite figure out the reasons behind the jumping around. I think they have moved on to graphing and division is over for the year?!? Mastery is the key, not just conceptual understanding. A lot of basic math is mastered doing the traditional long division algorithm. "Most of the supplementation comes in the form of timed drills, for addition and subtraction in the earlier grades, and for multiplication at the end of third grade and beginning of fourth." One thing I am beginning to notice is that schools know that talking about timed drills and supplementing gets parents off their backs. But, the devil is in the details. I don't see a lot of supplementing lately and I wonder what will happen when they get to fractions and decimals, where supplementing is not as easy as timed basic math drills. It's not just supplementing; it's teaching differently. "In the last few days, though, they have been taught the traditional algorithm, and last night's homework required using the traditional algorithm. To me, that's a reasonable way to use forgiving division -- as a starter, an introduction." That's fine. Forgiving division is the same as the traditional algorithm except that you aren't required to find the largest factor. They problem is mastery. They might be teaching the traditional approach because they think that will make parents happy. But, the goal is mastery, not conceptually learning a new method. -- SteveH - 12 Jan 2006
I don't think they are supplementing to get parents off their back. As far as I can tell, I'm the only parent making any noise. I think the teachers are supplementing because they want to make sure the kids are learning the things that the teachers think they need to know. I think the teachers are in a difficult position, burdened with a curriculum they don't like. From what I see, they are doing their best to work around it. As for learning to mastery, I don't know. I know that my kids will have mastered the traditional algorithms, because I'll make sure of it. Luckily, both of my kids think arithmetic is fun, and the bigger the numbers are, the better. I don't know how I'd get them to do extra practice if it weren't so. It also brings us back to the discussion of equity for those kids whose parents aren't giving them extra practice. -- DaleA - 12 Jan 2006
"Stated differently, the spiral curriculum is exposure, not teaching." Actually, you should see our schools' curriculum guides. ITRE Every topic for every subject is shown on a grade-level time line. The 'I' stands for the year(s) you introduce the the topic. The 'T' stands for the year you teach (whatever that means) the topic, the 'R' are the years you refresh the topic, and the 'E' is they year by which the student is exepcted to know (?) the material. ALL topics cover multiple years. It's a big notebook (just for math) filled with these time lines. It also states that up to 20 percent of the students are allowed to go on to the next grade even though they don't know (?) the topic in the year that it is taught. This is pedagogically-defined social (developmentally appropriate, of course) promotion. It is quite incredible that they went to all of this effort when none of the topics and mastery criteria are quantified at all. I'm sure it's almost completely ignored by the teachers. It teaches kids that very little is expected of them. State testing is the ONLY thing now that forces any expectations on the school and students, and they are pretty low expectations. After all of these years of study I am still astounded. -- SteveH - 12 Jan 2006
"I think the teachers are in a difficult position, burdened with a curriculum they don't like. From what I see, they are doing their best to work around it." This is not true in our area. Most of our teachers love the curriculum. There is a big difference of opinion over what constitutes a proper K-8 math education. Some teachers may be in difficult positions, but this is about the kids and not the teachers. "It also brings us back to the discussion of equity for those kids whose parents aren't giving them extra practice." Yes. Even with supplementation. -- SteveH - 12 Jan 2006
I was just reading an article by a longtime teacher about successful practices for teaching braille to beginning readers and ran across this great quote that applies to teaching to mastery in any subject: "No matter how repetitive texts may appear to the teacher, over-learning is vital." Spiral learning isn't over-learning, it is just repeated under-learning. -- SusanJ - 12 Jan 2006
About Everyday Math in our school district: our school has been using EM for 9 years. The other elementary schools in our district have been using it for less time. They now all use EM. The school district did research last year where every 5th grader and 8th grader took some standardized test that is norm referenced (or some such educational jargon). Their conclusion: we perform better than national average and all of our students from different programs, traditonal and non traditional, perform the same. So they are going to be standard with EM. The problem with the data (what little I saw of it) was that it was all already compressed together and averaged. That is, they give a percentage of students who score over a certain line. Like, a certain percentage of the students exceed expectations, a certain percentage meet expectations etc. When you group all the data like that, you loose any nuances in the data. Be that as it may, the school will now use this as a club to tell parents that the program works. With a program like EM, the teacher is absolutely all important. However, by the time you get to fifth grade, a teacher does not have the time or discretion during class time to help a student who has not mastered a specific skill. They do spiral back to long division in fifth grade. But they spend even less time on it. If the student has not mastered it, the teacher has to go on. By the way, my students introduced me to Does McDonalds? Sell CheeseBurgers? last night. This is a mnemonic for long division: Divide, Multiply, Subtract, Check, Bring Down. Some kids had other ones, but this was my favorite. (Although, I will add, one student asked me how to spell multiply!!) -- AnneDwyer - 12 Jan 2006
"Spiral learning isn't over-learning, it is just repeated under-learning." Great line! I detect a candidate for the Wit and Wisdom file. -- CharlesH - 12 Jan 2006
Arrgh--I just lost my post, so I'll try to summarize--- What I've noticed in EM is that they never finish the material in any year. Last year, in 3rd grade, the teacher never got to multi-digit multiplication. So now, in 4th grade, we are just finishing that unit. The last unit covered in 3rd grade was fractions, and she rushed through that, definitely leaving my daughter behind. Even given that "slower" pace, there are still so many topics covered, none of them well. All of them are under-learned. In most years, the teachers give out supplemental "review packets". Yet I know we will hear the same arguments from the district--last year, 68% of 3rd grade exceeded standards, and 30% met them. Of course, in 5th grade 25% exceed and 64% meet, dropping to 31% exceeding, 45% meeting, and 24% below standards in 8th. -- KathyIggy - 12 Jan 2006
Spiral learning isn't over-learning, it is just repeated under-learning Charles beat me to it. Excellent line, Susan. I'm going to memorize it and use it. -- SusanS - 12 Jan 2006
Anne they use the exact same example to teach forgiving division in the 4th grade and in the 5 th grade. One example, both the same The funny thing is, I recently went through huge quantities of TRAILBLAZERS teacher guides. They not only used the same example over and over again, they used the same chunks of prose over and over again. It got so I couldn't tell for sure whether I had actually scanned through to another page in the document, because the passages were identical. -- CatherineJohnson - 12 Jan 2006
They had this one passage about facts 'not being gatekeepers' — something like that — that they just plopped in everywhere. -- CatherineJohnson - 12 Jan 2006
Where is the DI listserve????? -- CatherineJohnson - 12 Jan 2006
STUPID IN AMERICA! whoa — THANKS FOR THAT LINK! — I'll send it to the PTSA Exec committee Also...Friday night, right? That's the first informal get-together of the kernel of our group. -- CatherineJohnson - 12 Jan 2006
To Join the Listserv for Direct Instruction/Effective School Practices, email to: MAJORDOMO@LISTS.UOREGON.EDU this message: SUBSCRIBE DI -- KDeRosa - 12 Jan 2006
Anne I mean that they cannot do it at all. They just sit and stare at the problem and have no idea what to do or how to do it. The other 50% are completely proficient. I think you should just ask them when & where they learned it, and how much practice they had (appropriately phrased, obviously). None of my gifted fourth graders could do long division. That may be wrong.....there was one super-bright child who had gone to a private school, and may have learned long division there. He also has two math brains for parents (I would say — certainly very math-friendly people) as well as an older brother who likes math & is good at it. -- CatherineJohnson - 12 Jan 2006
Be sure and fill us in on your long division approach! -- CatherineJohnson - 12 Jan 2006
I hope Stossel doesn't only talk about urban schools. I assume he won't.... -- CatherineJohnson - 12 Jan 2006
Nick's Mama & everyone The few homework pages I have seen for the 5th grade have concepts that the kids have already learned under Forseman, so I'm sure that the parents will see an immediate improvement in grades. In fact, the one student I help (a 5th grader) made the honor roll for the first time this year, no doubt because he's just reviewing early 4th grade Forseman concepts. I think it would be terrifically useful to have a precise understanding of the scope & sequence of constructivist math texts compared to non-constructivists. So whenever you see examples of EM being behind Foresman, let us know if it's not too much trouble.... Thanks. I haven't posted this yet, but I'm now actively pressing the time & opportunity costs of a constructivist, spiralling curriculum. -- CatherineJohnson - 12 Jan 2006
How do you spell 'spiraling'? I was assuming two l's, but now I'm thinking just one.... -- CatherineJohnson - 12 Jan 2006
Steve As my wife says: "Why are they using a curriculum that they have to supplement?" It's worse than that here. The district is now contemplating hiring a(nother) Math Enrichment Specialist. This person's job will be to pull the brainy kids out for enrichment. (Or maybe she'll join them inside their class, so it won't technically be a 'pull-out.) We've bought a constructivist curriculum that not only requires supplementation, it requires two new Math Enrichment Specialists in a tiny district to deal with the math-brain kids. We're not just Xeroxing stuff. We're creating new positions and hiring new staff members. This is a curriculum so bad you have to invent new job categories to implement it. -- CatherineJohnson - 12 Jan 2006
"Yet I know we will hear the same arguments from the district--last year, 68% of 3rd grade exceeded standards, and 30% met them. Of course, in 5th grade 25% exceed and 64% meet, dropping to 31% exceeding, 45% meeting, and 24% below standards in 8th." In our state, the public school hierarchy selects the test and calibrates the results. The fox is guarding the hen house. It's very difficult to see sample tests and understand how they decide who meets or exceeds standards. All that the schools have to do is to worry about minor relative changes up or down. All they have to do is compare themselves with other towns who have the same poor curricula. -- SteveH - 12 Jan 2006
From the Investigations web site, discussing supplementation, this bit jumped out at me: Note that encouraging teachers to implement the curriculum as written for the first year or two is not an effort to deny that teachers must make decisions and adaptations based on the needs of their children. Teachers must do what is right for the particular group of students in the class. Teaching the units mostly as is, in the beginning, can help with several early "implementation issues": Sometimes teachers "get stuck" in a unit, spending much longer than suggested because they are teaching for mastery, unaware that a concept will be revisited in later units. ...The key to supplementing with integrity is knowledge of the curriculum, and the mathematics it uses. Teachers need to know what is and is not in the curriculum at their grade level and even at the grade level before and after. Then they can consider how to adapt a particular lesson for students who are struggling, for those who need a greater challenge, or to include a topic they need to teach that is not in Investigations at that grade level. How to adapt, or Whether to adapt??? And is this "mau-mauing"? -- BeckyC - 12 Jan 2006
Wit and Wisdom -- CatherineJohnson - 12 Jan 2006
"This is a curriculum so bad you have to invent new job categories to implement it." Instead of replacing the curiculum with a proven one that is shown to work on a international basis, they want to fix, supplement, balance, or add to the poor, but politically correct curriculum they have. They can't just admit that they are fundamentally wrong. -- SteveH - 12 Jan 2006
oh right, ITRE I'd forgotten that. This is in your public school? -- CatherineJohnson - 12 Jan 2006
Instead of replacing the curiculum with a proven one that is shown to work on a international basis, they want to fix, supplement, balance, or add to the poor, but politically correct curriculum they have. I think I'm getting better at this stuff. Ed and I both, separately, jumped on the Math Enrichment Specialist as an opportunity to say we have excellent teachers; the curriculum is the problem. It was obvious (almost) everyone in the room either already agreed with this the instant these words came out of our mouth, or was going to. -- CatherineJohnson - 12 Jan 2006
I need to learn how to do my own statistics SOON. It doesn't have to be pretty. I just need to be able to do rough and ready analyses & sling the lingo. I don't want to be told our TONYSS scores 'went up' ever again without having a SERIOUS comeback. (My current comeback — TONYSS went up all over the state — works fine, but still.) -- CatherineJohnson - 12 Jan 2006
WOW BECKY FANTASTIC FIND!!!! -- CatherineJohnson - 12 Jan 2006
I don't think that's mau-mauing. Do you have a link for the INVESTIGATIONS quote??? Talk about a smoking gun. -- CatherineJohnson - 12 Jan 2006
LET THIS SINK IN OUR SCHOOLS ARE DELIBERATELY NOT TEACHING TO MASTERY OUR SCHOOLS ARE DELIBERATELY EXPOSING CHILDREN TO MATERIAL AND THEN MOVING ON KNOWING THE CHILDREN CAN'T DO IT AND WON'T REMEMBER IT THE NEXT TIME THEY SEE IT AND IN MANY CASES OUR SCHOOLS ARE ALSO GIVING TESTS AND GRADING CHILDREN ON MATERIAL THE SCHOOL INTENTIONALLY DID NOT TEACH TO MASTERY In theory, I've 'known' this for at least a year. But until yesterday it hadn't hit me that this is academic child abuse, as Engelmann says. I suspect that without our miserable experience in Phase 4, where you have children crying in class & at home over homework, I might not have come to this. -- CatherineJohnson - 12 Jan 2006
got it -- CatherineJohnson - 12 Jan 2006
"Sometimes teachers "get stuck" in a unit, spending much longer than suggested because they are teaching for mastery, unaware that a concept will be revisited in later units." The problem is that some of the students master the material quickly and others are at various levels. The next time through the spiral, with perhaps a different teacher, some of the kids are bored and rest (and the teacher) have to spend time to get back up to speed. People worry about the time it takes to get up to speed after the summer. Spiraling has this same problem for each topic all of the time. Instead of spending a little more time getting everyone to mastery, they have to spend much more time later doing the same thing. There is also a big difference between introducing a topic and partial learning. Everyone can think of examples where it would be nice to get a general overview of a topic before you get down to the dirty details. In Everyday Math, however, they seem to be moving on before my son had a good chance to get very far in long division. One, it's frustrating to stop in the middle of learning something, and second, they might have to restart almost at the beginning the next time through the loop. At best, the added (lost) time would be minimal for two loops of the spiral. For each additional time through the loop, more time will be wasted. For those who have already mastered the topic the waste is 100 percent. I think of our MathLand public schools that are finally enforcing mastery of adds and subtracts to 20 in third grade. What are the other students doing while this is going on? A more appropriate approach to spiraling is if you master a topic during each loop of the spiral. Then, the next time through the loop, you use that mastered knowledge in some more advanced way. This is not what these spiraling math curricula do. They do only partial mastery looping, with more wasted time and no guarantees that every student will ever master the topic. -- SteveH - 12 Jan 2006
ITRE "This is in your public school?" Yes. -- SteveH - 12 Jan 2006
"Ed and I both, separately, jumped on the Math Enrichment Specialist as an opportunity to say we have excellent teachers; the curriculum is the problem." Perfect. Compliment the teachers, but trash the curriculum. -- SteveH - 12 Jan 2006
"I don't want to be told our TONYSS scores 'went up' ever again without having a SERIOUS comeback." No matter what the test is, ask to see a sample test and the details of the grading system. Tell them you are interested in absolute results, not relative results. -- SteveH - 12 Jan 2006
Let's say it takes 1 hour to teach a topic. It might take, say, 3 hours to master that topic and move on. In the spiral, you may repeat the same 1 hour of instruction 3 times over 3 years and spend the same amount of time it takes to teach the topic to mastery. But due to the short shelf life of knowledge the end effect is usually much less than mastery even though the same amount of time was spent teaching. The presentation of the material makes all the difference in the world, and the curriculum controls the manner of presentation. Enrichment does nothing to remedy this fundamental deficiency in the spiral. -- KDeRosa - 12 Jan 2006
Steve Perfect. Compliment the teachers, but trash the curriculum. Thank you! It took me a little while to get to this (although in fact I've always thought most of our teachers were excellent). But once I realized I could separate the two out in the middle of a debate and do it succinctly, I had pretty much struck (rhetorical) gold......this phrase probably works in any context. School board meeting, PTSA Forum, soccer field conversations — you name it. It's short & clarifying. AND you completely de-personalize the issues, which in any public setting is important. -- CatherineJohnson - 12 Jan 2006
Steve Everyone can think of examples where it would be nice to get a general overview of a topic before you get down to the dirty details. Right. That is the heart & soul of pre-reading skills kids should learn. The HOW TO DOUBLE YOUR CHILD'S GRADES book teaches this brilliantly. That's one of my next projects: start teaching Christopher analytical reading skills — and then practice them to mastery. Very important. I also, yesterday, figured out the main note-taking programs:
It's:
-- CatherineJohnson - 12 Jan 2006
A more appropriate approach to spiraling is if you master a topic during each loop of the spiral. Then, the next time through the loop, you use that mastered knowledge in some more advanced way. That's Singapore Math. -- CatherineJohnson - 12 Jan 2006
-- CatherineJohnson - 12 Jan 2006
Look how clean and simple that is. Incredible. I had a WONDERFUL moment last night where, after we'd all finished with the TRAILBLAZERS & curriculum reform issue, a mom brought up backpacks & how heavy they are. I raised my hand and said, The backpack issue is a curriculum issue. The one thing I messed up on was that I forgot to bring my copies of PRIMARY MATHEMATICS 6th grade books & PRENTICE HALL PRE-ALGEBRA. I had planned to hold the books up, to show people how much leaner & cleaner the Singapore books are. That would have made a huge impression. -- CatherineJohnson - 12 Jan 2006
Now I'm thinking I should join the Superintendent's Wellness Committee and talk about how we need a Direct Instruction curriculum so our kids can carry their backpacks without injury. -- CatherineJohnson - 12 Jan 2006
bad news -- CatherineJohnson - 12 Jan 2006
"bad news" It's a relative issue and they have their PR people out in force. Before (I am told), the math in our K-8 schools was bad (low expectations and some very poor teachers). Now, the teachers are better and they work harder for kids, especially at the lowest levels. Our average math scores are higher. This is with MathLand and no full course in algebra in eighth grade. Everyting is great, right? Except for the student who finds him/herself on a math track to nowhere in high school. Game Over. -- SteveH - 12 Jan 2006
And let's not forget that in all liklihood not one of these urban schools has more than about 20-25% of its students in the proficient and above range on NAEP even with the incease in scores. -- KDeRosa - 12 Jan 2006
Catherine, I picked up a copy of How to Double your child's grades, etc., and also the organized student, at our local B&N. It was the first time in history they had ALL of what I wanted to get. This weekend, I'll read! -- CarolynJohnston - 12 Jan 2006
"In Everyday Math, however, they seem to be moving on before my son had a good chance to get very far in long division." Right--just when my daughter begins to figure out a concept (and maybe even like doing a certain kind of problem), it's dropped, never to be seen again until next year, when it's repeated. Just last night, she asked why there weren't anymore "algebra" (open sentence) problems anymore. She had finally gotten the hang of solving for one variable. It's because they were covered for a few days, then on the test, never to be seen again until next year. -- KathyIggy - 12 Jan 2006
If teachers were held responsible for the aggregate performance of their kids in the following year... if teachers had to teach the same kids two years in a row, you can bet they would be On Board For Mastery -- nobody likes to double their own work. However, my understanding is that value-added assessment of teacher performance is highly unpopular. Fig leaf: a child's home environment. To the rescue: KIPP. -- BeckyC - 12 Jan 2006
they have their PR people out in force That's what I meant by 'bad news.' -- CatherineJohnson - 12 Jan 2006
People worry about the time it takes to get up to speed after the summer. Spiraling has this same problem for each topic all of the time. Instead of spending a little more time getting everyone to mastery, they have to spend much more time later doing the same thing. The cumulative effect has to be huge. -- CatherineJohnson - 12 Jan 2006
No matter what the test is, ask to see a sample test and the details of the grading system. Tell them you are interested in absolute results, not relative results. wait — what do you mean? I'm interested in absolute results.....don't I need a standard? or am I assuming the NY state standard is what matters? -- CatherineJohnson - 12 Jan 2006
Catherine, I picked up a copy of How to Double your child's grades, etc., and also the organized student, at our local B&N. It was the first time in history they had ALL of what I wanted to get. wow, cool! Christopher's ORGANIZED STUDENT system is holding up beautifully (it's only been two weeks, but my own systems are showing signs of strain after two weeks....) Those two books are going to be my Bible(s) for the next few years. I should have learned the reading method when I was 12. -- CatherineJohnson - 12 Jan 2006
Wit and Wisdom redux -- CatherineJohnson - 12 Jan 2006
If teachers were held responsible for the aggregate performance of their kids in the following year... if teachers had to teach the same kids two years in a row, you can bet they would be On Board For Mastery -- nobody likes to double their own work. hmm That's an interesting idea. It's true: I HATE it when I have to 'go back to square one' with Christopher. It's fun helping a child build on mastered skills. It's not fun discovering that he's retained nothing & you haven't taught to mastery. -- CatherineJohnson - 12 Jan 2006
How to Read a Book is really good too. Bonus Pink Question -- the second author was the subject of what somewhat recent movie? -- KDeRosa - 12 Jan 2006
I remember Van Doren being a figure at the center of the game show scandals of the 1950s, but I don't remember the name of the movie. -- DougSundseth - 12 Jan 2006
can I accept that? ... the judges say give it to him Quiz Show -- KDeRosa - 12 Jan 2006
You're an easy grader; I wouldn't have accepted it. 8-) -- DougSundseth - 12 Jan 2006
You got the important part right, so I let you slide. -- KDeRosa - 12 Jan 2006
I'm used to playing with people who won't accept a correct answer if it doesn't match the card answer. Even when the card answer is accepted as incorrect by everyone. It's a tough crowd. -- DougSundseth - 13 Jan 2006
The Moops! -- GoogleMaster - 13 Jan 2006
oh forget it all i'm gonna be able to say is, it was that movie about the guy who cheated on the quiz show and the guy from that show that was set in Alaska and had Janine Turner in it was the star -- CatherineJohnson - 13 Jan 2006
does that count? -- CatherineJohnson - 13 Jan 2006
The Moops? -- CatherineJohnson - 13 Jan 2006
wait! who are those other people.....the book on manners that was written back in the beginning of the 20th century... it wasn't the Moops, was it? -- CatherineJohnson - 13 Jan 2006
oh boy, I'm going to have to PRAY Christopher remembers the title -- CatherineJohnson - 13 Jan 2006
hey — that book does look interesting.... i'd seen it before, but it hadn't caught my interest -- CatherineJohnson - 13 Jan 2006
Northern Exposure -- CatherineJohnson - 13 Jan 2006
"The Moops" is in response to Doug's comment: I'm used to playing with people who won't accept a correct answer if it doesn't match the card answer. Even when the card answer is accepted as incorrect by everyone. -- GoogleMaster - 13 Jan 2006
goops and how to be them. -- VlorbikDotCom - 13 Jan 2006
"Right--just when my daughter begins to figure out a concept (and maybe even like doing a certain kind of problem), it's dropped, never to be seen again until next year, when it's repeated." I guess we've moved on from division to angles. Did you know that in Everyday Math a "turn" is a well-defined mathematical term? Guess how many degrees a turn is? 360. How about a lesson that combines angles, fractions, and graphing. Start at a point at the base of a tree (in the middle of a graph) and move north (up) by 3 steps. (I don't remember the details) Make a 1/4 turn clockwise and move 5 steps, etc. At one point it has the students do a "turn" and go 3 1/2 steps. Of course, the turn keeps you going in the same direction. I told my son that there is no mathematical term called a "turn". Most sensible people consider a turn to be 90 degrees. If you want to do a U-turn, you say 180. If you want to do a full rotation, you say 360, hopefully not referring to what your car did in the last snow storm. -- SteveH - 13 Jan 2006
I just had to put this information up on KTM: I had my first repeat students in a Math Booster class last night. Two math brain 5th graders who still need some work on division. They're great kids and a lot of fun. The other student in the class? The daughter of a school board member!!! How interesting is that? That being said, she definitely was proficient at long divsion. You can bet I will be asking her how she learned it so well. About Steve H comment on mathematical terms: one of the things I stress in my class is using the correct mathematical terms for everything I do. For EM, the main weakness are, of course, too many topics and spiralling. But the other weaknesses are not using any mathematical terminology (if the students learn it, they learn it from the teachers) and not putting in any problems that can't be solved by knowing your times tables. -- AnneDwyer - 13 Jan 2006
Vlorbik! THANK YOU!!!!! we loved that book when Christopher was little I have to see if Ed got rid of it (he goes on periodic de-cluttering binges, thank god.) -- CatherineJohnson - 13 Jan 2006
The other student in the class? The daughter of a school board member!!! heh -- CatherineJohnson - 13 Jan 2006
remember Mr. Liu patient and persistent I've decided not to get into a knock-down drag-out over my Singapore Math Course That's not the best use of my 'resources,' such as they are; it's not the best tactic (or strategy?) The best strategy is Patient and Persistent Spaced Repetition Drip, drip, drip Water wears away rock -- CatherineJohnson - 13 Jan 2006
Of course, dynamite works a lot faster -- CatherineJohnson - 13 Jan 2006
My kids memorized this poem (assignment from First Language Lessons by Jessie Wise). The Goops The Goops they lick their fingers, The Goops they lick their knives. They spill their broth on tablecloths They lead disgusting lives! The Goops they talk while eating and loud and fast they chew. That is why I am glad I am not a Goop Are you? -- NicksMama - 13 Jan 2006
I also had a talk with Temple that told me patient and persistent is the right strategy here (tactic?) -- CatherineJohnson - 13 Jan 2006
Nicks Mama THANK YOU! I HAVE TO FIND MY GOOPS BOOK! DO YOU HAVE THE POEM ABOUT THE GOOPS NOT LIKING CHURCH? -- CatherineJohnson - 13 Jan 2006
-- CatherineJohnson - 13 Jan 2006
No, I didn't know there was a whole book on the Goops! Man, with two boys fully armed with potty-humor, I could really use it! -- NicksMama - 13 Jan 2006
The other book your kids will LOVE is:
Every kid I've ever known, including me, was obsessed with this book. It's incredible. -- CatherineJohnson - 13 Jan 2006
"bad news" OK, I've spent quite a bit of time trying to discover if the 2005 Trial Urban District Assessments in Mathematics tell us anything good or bad about the fuzzy math curriculum. This is the official site: http://nces.ed.gov/nationsreportcard/mathematics/tuda.asp What this study did is compare NAEP mathematics and reading scores for students who were fourth and eighth graders in 2005 with scores for the different students who were fourth and eighth graders in 2003 in 10 urban districts. (At least) two things are fishy. (1) The scores went up in every single one of the 10 districts compared. (2) Only the math scores went up; not the reading ones. And yet when I looked at the few sample problems available, they all relied heavily on reading. Also, the sample problems seemed "fuzzy" to me so they might be more appropriate for children who've been taught this way the longest. Finally, the greatest improvement from 2003 to 2005 within a given district was only 4% but the spread between the best (Charlotte, NC) and words (Washington, DC) districts in 2005 is 18%. -- SusanJ - 14 Jan 2006
Oops, that's "worst districts", not "words." -- SusanJ - 14 Jan 2006
wow Susan thanks so much — I need to get this up front; I've been actively wondering about this myself — -- CatherineJohnson - 15 Jan 2006
more fun with spirals
hoo boy, that was fun fun, fun, fun TRAILBLAZERS is going down bye-bye
UPDATE 9-19-2006: TRAILBLAZERS isn't going anywhere. don't listen to me.
a TRAILBLAZERS spiral I'll condense the story and post tomorrow, but I wanted to get this down tonight. After the meeting, Ed was talking to the Dows Lane (K-3) mom who's been agitating against TRAILBLAZERS. Her kid is a math-brain. Maybe both her kids are. She told Ed that in 2nd grade TRAILBLAZERS teaches kids how to construct graphs. Then, in 3rd grade, TRAILBLAZERS teaches kids how to construct graphs again — the exact same lesson — except that, this time around, they teach the kids TO LABEL THE AXES.* She didn't say whether they teach labeling the axes to mastery.
it's all becoming clear now All of it. The huge books, the grinding overwork, the ever-expanding gap between our kids and every other math student on the planet...... I get it. I have found the basic principle, as Temple would say. Start from the premise that nothing will be taught to mastery, and everything else follows. Big books, big gap, big backpacks, 11-year old kids breaking down in tears in the middle of a 'quiz.' It all makes sense. That big sucking sound you hear? That's the spiral curriculum Hoovering up the kids, the mom, the dad, the KUMON operator, and the kindly folks at ktm into the effort to teach basic algebra to just one boy. I don't like it.
No one at the meeting knew what the term 'spiralling' meant. Now they do. Until one year ago, I had never heard the term 'spiral' applied to a curriculum. I had no idea. I still had no idea after I had heard it. But once you start to really work your way through it....once you start to understand that schools deliberately teach skills and concepts so that children do not master them and then grade them on their 'performance'..... slow burn
* She thought it was 2nd & 3rd grades, but it might be 1st and 2nd grades.
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Here's another arrow for the quiver. Pagesplatter and animations = bad. When Static Media Promote Active Learning : Annotated Illustrations Versus Narrated Animations in Multimedia Instruction. Mayer, Richard E.; Hegarty, Mary; Mayer, Sarah; Campbell, Julie; Journal of Experimental Psychology: Applied. Vol. 11(4) December 2005. pp. 256-265. Abstract: In 4 experiments, students received a lesson consisting of computer-based animation and narration or a lesson consisting of paper-based static diagrams and text. The lessons used the same words and graphics in the paper-based and computer-based versions to explain the process of lightning formation (Experiment 1), how a toilet tank works (Experiment 2), how ocean waves work (Experiment 3), and how a car's braking system works (Experiment 4). On subsequent retention and transfer tests, the paper group performed significantly better than the computer group on 4 of 8 comparisons, and there was no significant difference on the rest. These results support the static media hypothesis, in which static illustrations with printed text reduce extraneous processing and promote germane processing as compared with narrated animations. The link was forwarded by Dan Willingham on the DI listserve. -- KDeRosa - 12 Jan 2006
Also set your dvrs for John Stossel's Stupid in America on Friday Night (1/13) on ABC: 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. -- KDeRosa - 12 Jan 2006
The mantra of all spiraling curricula: "Don't worry [that little Johnny got a 36 on the unit test]. He'll see this again next year." -- CarolynJohnston - 12 Jan 2006
"Also set your dvrs for John Stossel's Stupid in America on Friday Night (1/13) on ABC" Purely out of the kindness of my heart, I'm going to point Mike in Texas at the Stossel piece. -- VerghisKoshi - 12 Jan 2006
Meanwhile 36 does wonders for little Johnny's self-esteem and 'appreciation' for math — both watchwords of progressive educators. -- CatherineJohnson - 12 Jan 2006
We have children crying in the middle of math tests. -- CatherineJohnson - 12 Jan 2006
It's unconscionable. -- CatherineJohnson - 12 Jan 2006
I hope I spelled that right. -- CatherineJohnson - 12 Jan 2006
In terms of spiralling, Everyday Math does the same thing. In addition to not teaching traditional long division, they use the exact same example to teach forgiving division in the 4th grade and in the 5 th grade. One example, both the same. I am now starting my second round of Math Booster classes. Even though I have a very small sample size, I am a Bayesian, so I am going to go out on a limb: about 50% of my fifth graders cannot do long division. I mean that they cannot do it at all. They just sit and stare at the problem and have no idea what to do or how to do it. The other 50% are completely proficient. I don't know what this means yet. But I will go out on a limb and say this: someone is teaching certain children long division and making sure that they know it to mastery. The other children are left completely in the dark. They know that they don't know it. You can tell by the level of tension on their faces when you try to explain the procedure. I even had a child cry in my class last session, and he was a math brain!!! So I have a strategy to teach them. I'll let you know how it works. -- AnneDwyer - 12 Jan 2006
Anne, How long has your school system been using EM? What has been the reaction of the parents to EM? Our county just adopted EM. The major complaint from the parents is that they didn't phase it in. Kids who were using Scott-Forseman Addison Wesley for grades 1-4 are now facing EM this year. The few homework pages I have seen for the 5th grade have concepts that the kids have already learned under Forseman, so I'm sure that the parents will see an immediate improvement in grades. In fact, the one student I help (a 5th grader) made the honor roll for the first time this year, no doubt because he's just reviewing early 4th grade Forseman concepts. EM fans will no doubt take the credit. -- NicksMama - 12 Jan 2006
Spiraling "... nothing will be taught to mastery ..." Mastery requires grade-level expectations. Mastery requires practice. Mastery requires testing. Spiraling (as it is applied in these cases) is used to avoid mastery (a.k.a. Drill and Kill) Spiraling is used as a pedagogical excuse for social promotion. (no tracking and no holding kids back either) This is OK, because they think that there is no linkage between mastery and understanding. They think that everything will work out in the end. They want their pedagogy and eat it too. Please note that this is not what I would call spiraling, which is a fine technique for both learning and solving problems. Sometimes, when a design project is very large (building, bridge, car, ship), you cannot start at point A and go to point B to finish the design. You start with a conceptual design phase, spiral around through a preliminary design phase (same analysis, but with more details), and then go on to a detailed design phase. It's called a design spiral. (each step of which could involve a complex calculation that is done using only one BEST algorithm) Problem solving in the real world is so much more complex than any silly talk of only one answer or many ways of doing things. I think that educators have "mastered" the art of saying whatever sounds good just to do whatever they want. They argue with generalities, but they get to define the details. They do not want you to see the details! -- SteveH - 12 Jan 2006
My children's district has been using Mathland for several years. From what I can see, the teachers (at least in our school) are supplementing the Mathland curriculum with more and more of their own materials. At this point, I would have to describe the approach as a hybrid. It seems to be working, although I suspect it ends up being much more difficult for the teachers than it would be if they were starting with a stronger curriculum. Starting with a stronger curriculum would also result in greater uniformity from class to class and school to school, which I think is important. So many kids move in and out of the school during the course of a year -- I shudder to think of the gaps (and repetition) that results. Most of the supplementation comes in the form of timed drills, for addition and subtraction in the earlier grades, and for multiplication at the end of third grade and beginning of fourth. One thing that I think has worked. My son, a fourth grader, was taught "forgiving division" earlier this year. They did a reasonable amount of practice with it, while I was reading all the negative comments here and wondering what, if anything, to do. In the last few days, though, they have been taught the traditional algorithm, and last night's homework required using the traditional algorithm. To me, that's a reasonable way to use forgiving division -- as a starter, an introduction. -- DaleA - 12 Jan 2006
"In addition to not teaching traditional long division, they use the exact same example to teach forgiving division in the 4th grade and in the 5 th grade. One example, both the same." No! My son is in 4th grade and we just went over partial quotients in EM. If they cover the same stuff next year (sizzle, burn, pop, aaarrrrggghh!) ... my brain is turning to mush. Help! -- SteveH - 12 Jan 2006
Starting with a stronger curriculum would also result in greater uniformity from class to class and school to school, which I think is important. So many kids move in and out of the school during the course of a year -- I shudder to think of the gaps (and repetition) that results. Hi Dale! absolutely I'll have to rustle up the studies on that very issue this is one of the HUGE causes of extremely poor performance in disadvantaged kids they move far more often than middle & upper-middle class kids, and they're constantly joining classes in the middle Talk about no coherence -- CatherineJohnson - 12 Jan 2006
"I mean that they cannot do it at all. They just sit and stare at the problem and have no idea what to do or how to do it. The other 50% are completely proficient. I don't know what this means yet." I would say that for anything you teach, some kids will pick it up quickly, some will get it at home or with tutoring, and some won't get it (at home or school). The percentages for each category will vary depending on many factors, but 50 percent who don't understand the material indicates a major failure for the school. -- SteveH - 12 Jan 2006
They did a reasonable amount of practice with it, while I was reading all the negative comments here and wondering what, if anything, to do. In the last few days, though, they have been taught the traditional algorithm, and last night's homework required using the traditional algorithm. To me, that's a reasonable way to use forgiving division -- as a starter, an introduction. Obviously, we are FULLTIME complainers around here, but one thing I ought to say more often — and this has finally come up on another thread — is that I personally, because of Temple (Grandin), have become an 'outputs' person. That is, I don't care what the inputs are if the output is sound. If my child is learning math on par with his peers in Singapore, I don't care how they teach it. Forgiving division may very well be a good introduction to division; that makes sense to me. I've also seen, from my own experience of re-learning math, that teaching a concept or a procedure in 2 or at most 3 different ways has made math much more comprehensible to me this time around. So to me it makes sense that starting with forgiving division and then moving to the traditional algorithm — or starting with the traditional algorithm and using it to demonstrate that forgiving division works on the same principles — would be a good idea. What I love about Singapore Math & Saxon Math, though, (and probably Engelmann's math books, too) is that there are no wasted moves. Each concept or procedure is taught for a specific length of time, for a specific reason. The material is field tested, and then refined. -- CatherineJohnson - 12 Jan 2006
This another example of the educrats co-opting a perfectly good term - "spiraling" and demolishing it's meaning. As Steve points out, there is good spiraling and bad spiraling. Most schools employ bad spiraling mostly for social promotion reasons. The telltale sign of bad spiraling, as Engelmann points out, is that material isn't taught to mastery and as a result extensive review of old material is required. This review is just as ineffective as it was the first time the material was presented because knowledge has a very short shelf life. If material isn't mastered when taught it will quickly be forgotten. -- KDeRosa - 12 Jan 2006
Engelmann on the shelf life of learned material Typically about 60 school days pass before any topic is revisited. Stated differently, the spiral curriculum is exposure, not teaching. You don't "teach" something and put it back on the shelf for 60 days. It doesn't have a shelf-life of more than a few days. It would be outrageous enough to do that with one topic-- let alone all of them. ...Don't they know that if something is just taught, it will atrophy the fast way if it is not reinforced, kindled, and used? Don't they know that the suggested "revisiting of topics" requires putting stuff that has been recently taught on the shelf where it will shrivel up? Don't they know that the constant "reteaching" and "relearning" of topics that have gone stale from three months of disuse is so inefficient and impratical that it will lead not to "teaching" but to mere exposure? And don't they know that when the "teaching" becomes mere exposure, kids will understandably figure out that they are not expected to learn and that they'll develop adaptive attitudes like, "We're doing this ugly geometry again, but don't worry. It'll soon go away and we won't see it for a long time"? The Underachieving Curriculum judged the problem with the spiral curriculum is that is lacks both intensity and focus. "Perhaps the greatest irony is that a curricular construct conceived to prevent the postponing of teaching many important subjects on the grounds that they are too difficult has resulted in a treatment of mathematics that has postponed, often indefinitely, the attainment of much substantive content at all." -- KDeRosa - 12 Jan 2006
DaleA "My children's district has been using Mathland for several years." Wow! There is another town besides ours that still uses MathLand! MathLand, the curriculum that is so bad and trashed by so many that even the publisher dumped it and you can't find any mention of it on their web site - not even information on how to move up (?) to the Everyday Math they now push. If MathLand (or Everyday Math) is so good, then why are schools across the nation taking so much time supplementing them? As my wife says: "Why are they using a curriculum that they have to supplement?" Sometimes the supplementing is superficial and comes no where near mastery. With long division, it's one thing to teach the traditional algorithm, but quite another to expect mastery. My son is being taught partial quotients or forgiving division, but he gets maybe 4 or 5 problems to do every so often. I can't quite figure out the reasons behind the jumping around. I think they have moved on to graphing and division is over for the year?!? Mastery is the key, not just conceptual understanding. A lot of basic math is mastered doing the traditional long division algorithm. "Most of the supplementation comes in the form of timed drills, for addition and subtraction in the earlier grades, and for multiplication at the end of third grade and beginning of fourth." One thing I am beginning to notice is that schools know that talking about timed drills and supplementing gets parents off their backs. But, the devil is in the details. I don't see a lot of supplementing lately and I wonder what will happen when they get to fractions and decimals, where supplementing is not as easy as timed basic math drills. It's not just supplementing; it's teaching differently. "In the last few days, though, they have been taught the traditional algorithm, and last night's homework required using the traditional algorithm. To me, that's a reasonable way to use forgiving division -- as a starter, an introduction." That's fine. Forgiving division is the same as the traditional algorithm except that you aren't required to find the largest factor. They problem is mastery. They might be teaching the traditional approach because they think that will make parents happy. But, the goal is mastery, not conceptually learning a new method. -- SteveH - 12 Jan 2006
I don't think they are supplementing to get parents off their back. As far as I can tell, I'm the only parent making any noise. I think the teachers are supplementing because they want to make sure the kids are learning the things that the teachers think they need to know. I think the teachers are in a difficult position, burdened with a curriculum they don't like. From what I see, they are doing their best to work around it. As for learning to mastery, I don't know. I know that my kids will have mastered the traditional algorithms, because I'll make sure of it. Luckily, both of my kids think arithmetic is fun, and the bigger the numbers are, the better. I don't know how I'd get them to do extra practice if it weren't so. It also brings us back to the discussion of equity for those kids whose parents aren't giving them extra practice. -- DaleA - 12 Jan 2006
"Stated differently, the spiral curriculum is exposure, not teaching." Actually, you should see our schools' curriculum guides. ITRE Every topic for every subject is shown on a grade-level time line. The 'I' stands for the year(s) you introduce the the topic. The 'T' stands for the year you teach (whatever that means) the topic, the 'R' are the years you refresh the topic, and the 'E' is they year by which the student is exepcted to know (?) the material. ALL topics cover multiple years. It's a big notebook (just for math) filled with these time lines. It also states that up to 20 percent of the students are allowed to go on to the next grade even though they don't know (?) the topic in the year that it is taught. This is pedagogically-defined social (developmentally appropriate, of course) promotion. It is quite incredible that they went to all of this effort when none of the topics and mastery criteria are quantified at all. I'm sure it's almost completely ignored by the teachers. It teaches kids that very little is expected of them. State testing is the ONLY thing now that forces any expectations on the school and students, and they are pretty low expectations. After all of these years of study I am still astounded. -- SteveH - 12 Jan 2006
"I think the teachers are in a difficult position, burdened with a curriculum they don't like. From what I see, they are doing their best to work around it." This is not true in our area. Most of our teachers love the curriculum. There is a big difference of opinion over what constitutes a proper K-8 math education. Some teachers may be in difficult positions, but this is about the kids and not the teachers. "It also brings us back to the discussion of equity for those kids whose parents aren't giving them extra practice." Yes. Even with supplementation. -- SteveH - 12 Jan 2006
I was just reading an article by a longtime teacher about successful practices for teaching braille to beginning readers and ran across this great quote that applies to teaching to mastery in any subject: "No matter how repetitive texts may appear to the teacher, over-learning is vital." Spiral learning isn't over-learning, it is just repeated under-learning. -- SusanJ - 12 Jan 2006
About Everyday Math in our school district: our school has been using EM for 9 years. The other elementary schools in our district have been using it for less time. They now all use EM. The school district did research last year where every 5th grader and 8th grader took some standardized test that is norm referenced (or some such educational jargon). Their conclusion: we perform better than national average and all of our students from different programs, traditonal and non traditional, perform the same. So they are going to be standard with EM. The problem with the data (what little I saw of it) was that it was all already compressed together and averaged. That is, they give a percentage of students who score over a certain line. Like, a certain percentage of the students exceed expectations, a certain percentage meet expectations etc. When you group all the data like that, you loose any nuances in the data. Be that as it may, the school will now use this as a club to tell parents that the program works. With a program like EM, the teacher is absolutely all important. However, by the time you get to fifth grade, a teacher does not have the time or discretion during class time to help a student who has not mastered a specific skill. They do spiral back to long division in fifth grade. But they spend even less time on it. If the student has not mastered it, the teacher has to go on. By the way, my students introduced me to Does McDonalds? Sell CheeseBurgers? last night. This is a mnemonic for long division: Divide, Multiply, Subtract, Check, Bring Down. Some kids had other ones, but this was my favorite. (Although, I will add, one student asked me how to spell multiply!!) -- AnneDwyer - 12 Jan 2006
"Spiral learning isn't over-learning, it is just repeated under-learning." Great line! I detect a candidate for the Wit and Wisdom file. -- CharlesH - 12 Jan 2006
Arrgh--I just lost my post, so I'll try to summarize--- What I've noticed in EM is that they never finish the material in any year. Last year, in 3rd grade, the teacher never got to multi-digit multiplication. So now, in 4th grade, we are just finishing that unit. The last unit covered in 3rd grade was fractions, and she rushed through that, definitely leaving my daughter behind. Even given that "slower" pace, there are still so many topics covered, none of them well. All of them are under-learned. In most years, the teachers give out supplemental "review packets". Yet I know we will hear the same arguments from the district--last year, 68% of 3rd grade exceeded standards, and 30% met them. Of course, in 5th grade 25% exceed and 64% meet, dropping to 31% exceeding, 45% meeting, and 24% below standards in 8th. -- KathyIggy - 12 Jan 2006
Spiral learning isn't over-learning, it is just repeated under-learning Charles beat me to it. Excellent line, Susan. I'm going to memorize it and use it. -- SusanS - 12 Jan 2006
Anne they use the exact same example to teach forgiving division in the 4th grade and in the 5 th grade. One example, both the same The funny thing is, I recently went through huge quantities of TRAILBLAZERS teacher guides. They not only used the same example over and over again, they used the same chunks of prose over and over again. It got so I couldn't tell for sure whether I had actually scanned through to another page in the document, because the passages were identical. -- CatherineJohnson - 12 Jan 2006
They had this one passage about facts 'not being gatekeepers' — something like that — that they just plopped in everywhere. -- CatherineJohnson - 12 Jan 2006
Where is the DI listserve????? -- CatherineJohnson - 12 Jan 2006
STUPID IN AMERICA! whoa — THANKS FOR THAT LINK! — I'll send it to the PTSA Exec committee Also...Friday night, right? That's the first informal get-together of the kernel of our group. -- CatherineJohnson - 12 Jan 2006
To Join the Listserv for Direct Instruction/Effective School Practices, email to: MAJORDOMO@LISTS.UOREGON.EDU this message: SUBSCRIBE DI -- KDeRosa - 12 Jan 2006
Anne I mean that they cannot do it at all. They just sit and stare at the problem and have no idea what to do or how to do it. The other 50% are completely proficient. I think you should just ask them when & where they learned it, and how much practice they had (appropriately phrased, obviously). None of my gifted fourth graders could do long division. That may be wrong.....there was one super-bright child who had gone to a private school, and may have learned long division there. He also has two math brains for parents (I would say — certainly very math-friendly people) as well as an older brother who likes math & is good at it. -- CatherineJohnson - 12 Jan 2006
Be sure and fill us in on your long division approach! -- CatherineJohnson - 12 Jan 2006
I hope Stossel doesn't only talk about urban schools. I assume he won't.... -- CatherineJohnson - 12 Jan 2006
Nick's Mama & everyone The few homework pages I have seen for the 5th grade have concepts that the kids have already learned under Forseman, so I'm sure that the parents will see an immediate improvement in grades. In fact, the one student I help (a 5th grader) made the honor roll for the first time this year, no doubt because he's just reviewing early 4th grade Forseman concepts. I think it would be terrifically useful to have a precise understanding of the scope & sequence of constructivist math texts compared to non-constructivists. So whenever you see examples of EM being behind Foresman, let us know if it's not too much trouble.... Thanks. I haven't posted this yet, but I'm now actively pressing the time & opportunity costs of a constructivist, spiralling curriculum. -- CatherineJohnson - 12 Jan 2006
How do you spell 'spiraling'? I was assuming two l's, but now I'm thinking just one.... -- CatherineJohnson - 12 Jan 2006
Steve As my wife says: "Why are they using a curriculum that they have to supplement?" It's worse than that here. The district is now contemplating hiring a(nother) Math Enrichment Specialist. This person's job will be to pull the brainy kids out for enrichment. (Or maybe she'll join them inside their class, so it won't technically be a 'pull-out.) We've bought a constructivist curriculum that not only requires supplementation, it requires two new Math Enrichment Specialists in a tiny district to deal with the math-brain kids. We're not just Xeroxing stuff. We're creating new positions and hiring new staff members. This is a curriculum so bad you have to invent new job categories to implement it. -- CatherineJohnson - 12 Jan 2006
"Yet I know we will hear the same arguments from the district--last year, 68% of 3rd grade exceeded standards, and 30% met them. Of course, in 5th grade 25% exceed and 64% meet, dropping to 31% exceeding, 45% meeting, and 24% below standards in 8th." In our state, the public school hierarchy selects the test and calibrates the results. The fox is guarding the hen house. It's very difficult to see sample tests and understand how they decide who meets or exceeds standards. All that the schools have to do is to worry about minor relative changes up or down. All they have to do is compare themselves with other towns who have the same poor curricula. -- SteveH - 12 Jan 2006
From the Investigations web site, discussing supplementation, this bit jumped out at me: Note that encouraging teachers to implement the curriculum as written for the first year or two is not an effort to deny that teachers must make decisions and adaptations based on the needs of their children. Teachers must do what is right for the particular group of students in the class. Teaching the units mostly as is, in the beginning, can help with several early "implementation issues": Sometimes teachers "get stuck" in a unit, spending much longer than suggested because they are teaching for mastery, unaware that a concept will be revisited in later units. ...The key to supplementing with integrity is knowledge of the curriculum, and the mathematics it uses. Teachers need to know what is and is not in the curriculum at their grade level and even at the grade level before and after. Then they can consider how to adapt a particular lesson for students who are struggling, for those who need a greater challenge, or to include a topic they need to teach that is not in Investigations at that grade level. How to adapt, or Whether to adapt??? And is this "mau-mauing"? -- BeckyC - 12 Jan 2006
Wit and Wisdom -- CatherineJohnson - 12 Jan 2006
"This is a curriculum so bad you have to invent new job categories to implement it." Instead of replacing the curiculum with a proven one that is shown to work on a international basis, they want to fix, supplement, balance, or add to the poor, but politically correct curriculum they have. They can't just admit that they are fundamentally wrong. -- SteveH - 12 Jan 2006
oh right, ITRE I'd forgotten that. This is in your public school? -- CatherineJohnson - 12 Jan 2006
Instead of replacing the curiculum with a proven one that is shown to work on a international basis, they want to fix, supplement, balance, or add to the poor, but politically correct curriculum they have. I think I'm getting better at this stuff. Ed and I both, separately, jumped on the Math Enrichment Specialist as an opportunity to say we have excellent teachers; the curriculum is the problem. It was obvious (almost) everyone in the room either already agreed with this the instant these words came out of our mouth, or was going to. -- CatherineJohnson - 12 Jan 2006
I need to learn how to do my own statistics SOON. It doesn't have to be pretty. I just need to be able to do rough and ready analyses & sling the lingo. I don't want to be told our TONYSS scores 'went up' ever again without having a SERIOUS comeback. (My current comeback — TONYSS went up all over the state — works fine, but still.) -- CatherineJohnson - 12 Jan 2006
WOW BECKY FANTASTIC FIND!!!! -- CatherineJohnson - 12 Jan 2006
I don't think that's mau-mauing. Do you have a link for the INVESTIGATIONS quote??? Talk about a smoking gun. -- CatherineJohnson - 12 Jan 2006
LET THIS SINK IN OUR SCHOOLS ARE DELIBERATELY NOT TEACHING TO MASTERY OUR SCHOOLS ARE DELIBERATELY EXPOSING CHILDREN TO MATERIAL AND THEN MOVING ON KNOWING THE CHILDREN CAN'T DO IT AND WON'T REMEMBER IT THE NEXT TIME THEY SEE IT AND IN MANY CASES OUR SCHOOLS ARE ALSO GIVING TESTS AND GRADING CHILDREN ON MATERIAL THE SCHOOL INTENTIONALLY DID NOT TEACH TO MASTERY In theory, I've 'known' this for at least a year. But until yesterday it hadn't hit me that this is academic child abuse, as Engelmann says. I suspect that without our miserable experience in Phase 4, where you have children crying in class & at home over homework, I might not have come to this. -- CatherineJohnson - 12 Jan 2006
got it -- CatherineJohnson - 12 Jan 2006
"Sometimes teachers "get stuck" in a unit, spending much longer than suggested because they are teaching for mastery, unaware that a concept will be revisited in later units." The problem is that some of the students master the material quickly and others are at various levels. The next time through the spiral, with perhaps a different teacher, some of the kids are bored and rest (and the teacher) have to spend time to get back up to speed. People worry about the time it takes to get up to speed after the summer. Spiraling has this same problem for each topic all of the time. Instead of spending a little more time getting everyone to mastery, they have to spend much more time later doing the same thing. There is also a big difference between introducing a topic and partial learning. Everyone can think of examples where it would be nice to get a general overview of a topic before you get down to the dirty details. In Everyday Math, however, they seem to be moving on before my son had a good chance to get very far in long division. One, it's frustrating to stop in the middle of learning something, and second, they might have to restart almost at the beginning the next time through the loop. At best, the added (lost) time would be minimal for two loops of the spiral. For each additional time through the loop, more time will be wasted. For those who have already mastered the topic the waste is 100 percent. I think of our MathLand public schools that are finally enforcing mastery of adds and subtracts to 20 in third grade. What are the other students doing while this is going on? A more appropriate approach to spiraling is if you master a topic during each loop of the spiral. Then, the next time through the loop, you use that mastered knowledge in some more advanced way. This is not what these spiraling math curricula do. They do only partial mastery looping, with more wasted time and no guarantees that every student will ever master the topic. -- SteveH - 12 Jan 2006
ITRE "This is in your public school?" Yes. -- SteveH - 12 Jan 2006
"Ed and I both, separately, jumped on the Math Enrichment Specialist as an opportunity to say we have excellent teachers; the curriculum is the problem." Perfect. Compliment the teachers, but trash the curriculum. -- SteveH - 12 Jan 2006
"I don't want to be told our TONYSS scores 'went up' ever again without having a SERIOUS comeback." No matter what the test is, ask to see a sample test and the details of the grading system. Tell them you are interested in absolute results, not relative results. -- SteveH - 12 Jan 2006
Let's say it takes 1 hour to teach a topic. It might take, say, 3 hours to master that topic and move on. In the spiral, you may repeat the same 1 hour of instruction 3 times over 3 years and spend the same amount of time it takes to teach the topic to mastery. But due to the short shelf life of knowledge the end effect is usually much less than mastery even though the same amount of time was spent teaching. The presentation of the material makes all the difference in the world, and the curriculum controls the manner of presentation. Enrichment does nothing to remedy this fundamental deficiency in the spiral. -- KDeRosa - 12 Jan 2006
Steve Perfect. Compliment the teachers, but trash the curriculum. Thank you! It took me a little while to get to this (although in fact I've always thought most of our teachers were excellent). But once I realized I could separate the two out in the middle of a debate and do it succinctly, I had pretty much struck (rhetorical) gold......this phrase probably works in any context. School board meeting, PTSA Forum, soccer field conversations — you name it. It's short & clarifying. AND you completely de-personalize the issues, which in any public setting is important. -- CatherineJohnson - 12 Jan 2006
Steve Everyone can think of examples where it would be nice to get a general overview of a topic before you get down to the dirty details. Right. That is the heart & soul of pre-reading skills kids should learn. The HOW TO DOUBLE YOUR CHILD'S GRADES book teaches this brilliantly. That's one of my next projects: start teaching Christopher analytical reading skills — and then practice them to mastery. Very important. I also, yesterday, figured out the main note-taking programs:
- Cornell note-taking system for lectures (invented by Walter Pauk at Cornell)
- SQR3 system for reading: Survey, Question, Read, Review and....I forget the 3rd 'r'
It's:
- Survey
- Question
- Read
- Recite
- Review
-- CatherineJohnson - 12 Jan 2006
A more appropriate approach to spiraling is if you master a topic during each loop of the spiral. Then, the next time through the loop, you use that mastered knowledge in some more advanced way. That's Singapore Math. -- CatherineJohnson - 12 Jan 2006
-- CatherineJohnson - 12 Jan 2006
Look how clean and simple that is. Incredible. I had a WONDERFUL moment last night where, after we'd all finished with the TRAILBLAZERS & curriculum reform issue, a mom brought up backpacks & how heavy they are. I raised my hand and said, The backpack issue is a curriculum issue. The one thing I messed up on was that I forgot to bring my copies of PRIMARY MATHEMATICS 6th grade books & PRENTICE HALL PRE-ALGEBRA. I had planned to hold the books up, to show people how much leaner & cleaner the Singapore books are. That would have made a huge impression. -- CatherineJohnson - 12 Jan 2006
Now I'm thinking I should join the Superintendent's Wellness Committee and talk about how we need a Direct Instruction curriculum so our kids can carry their backpacks without injury. -- CatherineJohnson - 12 Jan 2006
bad news -- CatherineJohnson - 12 Jan 2006
"bad news" It's a relative issue and they have their PR people out in force. Before (I am told), the math in our K-8 schools was bad (low expectations and some very poor teachers). Now, the teachers are better and they work harder for kids, especially at the lowest levels. Our average math scores are higher. This is with MathLand and no full course in algebra in eighth grade. Everyting is great, right? Except for the student who finds him/herself on a math track to nowhere in high school. Game Over. -- SteveH - 12 Jan 2006
And let's not forget that in all liklihood not one of these urban schools has more than about 20-25% of its students in the proficient and above range on NAEP even with the incease in scores. -- KDeRosa - 12 Jan 2006
Catherine, I picked up a copy of How to Double your child's grades, etc., and also the organized student, at our local B&N. It was the first time in history they had ALL of what I wanted to get. This weekend, I'll read! -- CarolynJohnston - 12 Jan 2006
"In Everyday Math, however, they seem to be moving on before my son had a good chance to get very far in long division." Right--just when my daughter begins to figure out a concept (and maybe even like doing a certain kind of problem), it's dropped, never to be seen again until next year, when it's repeated. Just last night, she asked why there weren't anymore "algebra" (open sentence) problems anymore. She had finally gotten the hang of solving for one variable. It's because they were covered for a few days, then on the test, never to be seen again until next year. -- KathyIggy - 12 Jan 2006
If teachers were held responsible for the aggregate performance of their kids in the following year... if teachers had to teach the same kids two years in a row, you can bet they would be On Board For Mastery -- nobody likes to double their own work. However, my understanding is that value-added assessment of teacher performance is highly unpopular. Fig leaf: a child's home environment. To the rescue: KIPP. -- BeckyC - 12 Jan 2006
they have their PR people out in force That's what I meant by 'bad news.' -- CatherineJohnson - 12 Jan 2006
People worry about the time it takes to get up to speed after the summer. Spiraling has this same problem for each topic all of the time. Instead of spending a little more time getting everyone to mastery, they have to spend much more time later doing the same thing. The cumulative effect has to be huge. -- CatherineJohnson - 12 Jan 2006
No matter what the test is, ask to see a sample test and the details of the grading system. Tell them you are interested in absolute results, not relative results. wait — what do you mean? I'm interested in absolute results.....don't I need a standard? or am I assuming the NY state standard is what matters? -- CatherineJohnson - 12 Jan 2006
Catherine, I picked up a copy of How to Double your child's grades, etc., and also the organized student, at our local B&N. It was the first time in history they had ALL of what I wanted to get. wow, cool! Christopher's ORGANIZED STUDENT system is holding up beautifully (it's only been two weeks, but my own systems are showing signs of strain after two weeks....) Those two books are going to be my Bible(s) for the next few years. I should have learned the reading method when I was 12. -- CatherineJohnson - 12 Jan 2006
Wit and Wisdom redux -- CatherineJohnson - 12 Jan 2006
If teachers were held responsible for the aggregate performance of their kids in the following year... if teachers had to teach the same kids two years in a row, you can bet they would be On Board For Mastery -- nobody likes to double their own work. hmm That's an interesting idea. It's true: I HATE it when I have to 'go back to square one' with Christopher. It's fun helping a child build on mastered skills. It's not fun discovering that he's retained nothing & you haven't taught to mastery. -- CatherineJohnson - 12 Jan 2006
How to Read a Book is really good too. Bonus Pink Question -- the second author was the subject of what somewhat recent movie? -- KDeRosa - 12 Jan 2006
I remember Van Doren being a figure at the center of the game show scandals of the 1950s, but I don't remember the name of the movie. -- DougSundseth - 12 Jan 2006
can I accept that? ... the judges say give it to him Quiz Show -- KDeRosa - 12 Jan 2006
You're an easy grader; I wouldn't have accepted it. 8-) -- DougSundseth - 12 Jan 2006
You got the important part right, so I let you slide. -- KDeRosa - 12 Jan 2006
I'm used to playing with people who won't accept a correct answer if it doesn't match the card answer. Even when the card answer is accepted as incorrect by everyone. It's a tough crowd. -- DougSundseth - 13 Jan 2006
The Moops! -- GoogleMaster - 13 Jan 2006
oh forget it all i'm gonna be able to say is, it was that movie about the guy who cheated on the quiz show and the guy from that show that was set in Alaska and had Janine Turner in it was the star -- CatherineJohnson - 13 Jan 2006
does that count? -- CatherineJohnson - 13 Jan 2006
The Moops? -- CatherineJohnson - 13 Jan 2006
wait! who are those other people.....the book on manners that was written back in the beginning of the 20th century... it wasn't the Moops, was it? -- CatherineJohnson - 13 Jan 2006
oh boy, I'm going to have to PRAY Christopher remembers the title -- CatherineJohnson - 13 Jan 2006
hey — that book does look interesting.... i'd seen it before, but it hadn't caught my interest -- CatherineJohnson - 13 Jan 2006
Northern Exposure -- CatherineJohnson - 13 Jan 2006
"The Moops" is in response to Doug's comment: I'm used to playing with people who won't accept a correct answer if it doesn't match the card answer. Even when the card answer is accepted as incorrect by everyone. -- GoogleMaster - 13 Jan 2006
goops and how to be them. -- VlorbikDotCom - 13 Jan 2006
"Right--just when my daughter begins to figure out a concept (and maybe even like doing a certain kind of problem), it's dropped, never to be seen again until next year, when it's repeated." I guess we've moved on from division to angles. Did you know that in Everyday Math a "turn" is a well-defined mathematical term? Guess how many degrees a turn is? 360. How about a lesson that combines angles, fractions, and graphing. Start at a point at the base of a tree (in the middle of a graph) and move north (up) by 3 steps. (I don't remember the details) Make a 1/4 turn clockwise and move 5 steps, etc. At one point it has the students do a "turn" and go 3 1/2 steps. Of course, the turn keeps you going in the same direction. I told my son that there is no mathematical term called a "turn". Most sensible people consider a turn to be 90 degrees. If you want to do a U-turn, you say 180. If you want to do a full rotation, you say 360, hopefully not referring to what your car did in the last snow storm. -- SteveH - 13 Jan 2006
I just had to put this information up on KTM: I had my first repeat students in a Math Booster class last night. Two math brain 5th graders who still need some work on division. They're great kids and a lot of fun. The other student in the class? The daughter of a school board member!!! How interesting is that? That being said, she definitely was proficient at long divsion. You can bet I will be asking her how she learned it so well. About Steve H comment on mathematical terms: one of the things I stress in my class is using the correct mathematical terms for everything I do. For EM, the main weakness are, of course, too many topics and spiralling. But the other weaknesses are not using any mathematical terminology (if the students learn it, they learn it from the teachers) and not putting in any problems that can't be solved by knowing your times tables. -- AnneDwyer - 13 Jan 2006
Vlorbik! THANK YOU!!!!! we loved that book when Christopher was little I have to see if Ed got rid of it (he goes on periodic de-cluttering binges, thank god.) -- CatherineJohnson - 13 Jan 2006
The other student in the class? The daughter of a school board member!!! heh -- CatherineJohnson - 13 Jan 2006
remember Mr. Liu patient and persistent I've decided not to get into a knock-down drag-out over my Singapore Math Course That's not the best use of my 'resources,' such as they are; it's not the best tactic (or strategy?) The best strategy is Patient and Persistent Spaced Repetition Drip, drip, drip Water wears away rock -- CatherineJohnson - 13 Jan 2006
Of course, dynamite works a lot faster -- CatherineJohnson - 13 Jan 2006
My kids memorized this poem (assignment from First Language Lessons by Jessie Wise). The Goops The Goops they lick their fingers, The Goops they lick their knives. They spill their broth on tablecloths They lead disgusting lives! The Goops they talk while eating and loud and fast they chew. That is why I am glad I am not a Goop Are you? -- NicksMama - 13 Jan 2006
I also had a talk with Temple that told me patient and persistent is the right strategy here (tactic?) -- CatherineJohnson - 13 Jan 2006
Nicks Mama THANK YOU! I HAVE TO FIND MY GOOPS BOOK! DO YOU HAVE THE POEM ABOUT THE GOOPS NOT LIKING CHURCH? -- CatherineJohnson - 13 Jan 2006
-- CatherineJohnson - 13 Jan 2006
No, I didn't know there was a whole book on the Goops! Man, with two boys fully armed with potty-humor, I could really use it! -- NicksMama - 13 Jan 2006
The other book your kids will LOVE is:
Every kid I've ever known, including me, was obsessed with this book. It's incredible. -- CatherineJohnson - 13 Jan 2006
"bad news" OK, I've spent quite a bit of time trying to discover if the 2005 Trial Urban District Assessments in Mathematics tell us anything good or bad about the fuzzy math curriculum. This is the official site: http://nces.ed.gov/nationsreportcard/mathematics/tuda.asp What this study did is compare NAEP mathematics and reading scores for students who were fourth and eighth graders in 2005 with scores for the different students who were fourth and eighth graders in 2003 in 10 urban districts. (At least) two things are fishy. (1) The scores went up in every single one of the 10 districts compared. (2) Only the math scores went up; not the reading ones. And yet when I looked at the few sample problems available, they all relied heavily on reading. Also, the sample problems seemed "fuzzy" to me so they might be more appropriate for children who've been taught this way the longest. Finally, the greatest improvement from 2003 to 2005 within a given district was only 4% but the spread between the best (Charlotte, NC) and words (Washington, DC) districts in 2005 is 18%. -- SusanJ - 14 Jan 2006
Oops, that's "worst districts", not "words." -- SusanJ - 14 Jan 2006
wow Susan thanks so much — I need to get this up front; I've been actively wondering about this myself — -- CatherineJohnson - 15 Jan 2006
| WebLogForm | |
|---|---|
| Title: | more fun with spirals |
| TopicType: | WebLog |
| SubjectArea: | IrvingtonMath, IrvingtonSchools, TrailBlazers |
| LogDate: | 200601112126 |