KTM User Pages
16 Nov 2005 - 15:40
from Siegfried Engelmann, on designing and field-testing a textbook:
...the amount of practice that we've had to provide to meet our goal [all children in the program 'learn evereything the teacher teaches'] is possibly five times the amount provided in other published programs that teach the same subject.
War Against the Schools' Academic Child Abuse
That's where we are: desperate for Extra Practice. Last night Christopher was assigned 4 problems for homework; he missed 3 of them. The reason he was assigned only 4 problems, I assume, was that he had a Math Project to do; he had to create a 'Wanted poster' for a famous mathematician. He chose Gauss because we both love the story of Gauss adding the integers 1 to 100. (I taught it to my Singapore Math class this week.) btw, the only reason Christopher knows any famous mathematicians is that, IIRC, Saxon Math taught a lesson on Gauss. He's heard nothing about famous mathematicians at school; the kids were supposed to go out on their own, find a famous mathematician, & created a Wanted poster. (Last week they had to find some information on Fibonacci numbers & bring that in.) So Christopher knew about Gauss, thanks to Saxon Math, and thanks to me. To come up with a reason why Gauss would be wanted for arrest, he used a story that wasn't in Saxon. Supposedly, Gauss, when told his wife was dying, said 'Wait a minute' because he was in the middle of a problem. I have no idea whether this tale is apocryphal. Christopher Found It On The Internet, and Ms. Kahl can deal with it. So he had 4 problems to do, and missed 3. This on top of his 74 on the Chapter Two test. Which had already led to a second math explosion in our household yesterday morning. It was a big one, maybe you guys heard it. I have now had the blinding revelation that Direct Instruction would be extremely good for my marriage. Imagine! A school dedicated to the concept of teaching to mastery! Not challenge. Not it's up to the kid. Not it's up to the parent. And certainly not a challenging and supportive learning environment in which each student attains his or her highest potential for academic achievement, critical thinking and life-long learning. No! Forget all that! All I ask is that my child's school decide to teach to mastery.
Well, thank God for the internet yet again. This morning I managed to track down what I believe is the student workbook for Prentice Hall Mathematics Explorations and Applications. I'm in reactive teaching he**, only with a difference. I can find pre-algebra workbooks; I've joined edhelper, Susan's find, and it's terrific. I recommend it. But what I need are problem sets designed specifically to support, extend, illustrate, and practice exactly what he's learning in class today. Not something pretty close to what he's learning today. Exactly what he's learning in class today. Those are the problem sets I need. And I need lots of them. I need 5 times the number supplied by the textbook, at least.
inflexible knowledge, part 2
What I'm seeing is that you must practice exactly what you're learning in class before you branch out to other variants of the material. Inflexible knowledge seems to begin as a highly circumscribed 'set' of factoids & procedures in the brain. So, for example, in Chapter 3 Christopher is learning 'decimals and equations.' Well, number one, he's forgotten how to divide decimal numbers. (For that, I'm pulling edhelper sheets.) Number two, this means I need tons of problems like the 4 he was assigned to do last night. Exactly like those problems. Generic pre-algebra workbooks, as good as a couple of them look, aren't going to cut it. Very soon I will have morphed into a CRANK on the subject of Direct Instruction. I can feel it coming on.
a whole new regime
My friend Debbie's folks got divorced back before divorce was common, and she and I were talking about what it was like one day. She said every so often her mom would go on a rampage around the house, Restoring Order and Planning The Future. "There's going to be a whole new regime around here," she would say. Then that would last a couple of weeks.
I bring this up because, thanks to Math Blow-out number 2, we have a Whole New Regime. I think this one's got a fighting chance; any thoughts you all have, I'd like to hear. The plan now is to schedule homework and 'afterschooling' time tightly.
It's astounding the way an 11-year old can work the system. Any system. We've gone through various schemes (excuse me, Whole New Regimes) and Christopher has managed to foil all of them. Martine (she's been with us for 11 years) and I came up with a similar schedule, which broke down because Christopher would race through his homework, finish early, then demand a 'break,' which would turn into the rest of the night. This of course led to scenes of Christopher doing Megawords at 8:30 or 9:00, when he is Officially Too Tired To Work. Screaming, crying, tantruming. This led to Ed 'putting his foot down' and imposing a strict curfew on study time. After 8:30, Christopher was to be done, no matter what. You can imagine what this led to. Number one, it led to the accurate perception that Daddy had put his foot down on Mommy, not on Christopher. Number two, it led to whopper levels of Playing Out The Clock. Suppose Christopher and I are sitting at the homework table, doing whatever we're doing.....Christopher gets up, goes to the bathroom. Twenty minutes later, he's not back. Meanwhile, I'm Distracted. I'm on the computer, I'm teaching Andrew to write letters, I'm doing my own math homework.....TIME HAS SLIPPED BY. Christopher counts on this. He counts on me to forget, and....I FORGET. (I talked to my neighbor yesterday. Her son does exactly the same thing.) Meanwhile I have the added dimension of being lobbied by one and all to stop being so demanding. Martine thinks Christopher is doing far too much work; 'poor thing,' she'll say. This about a kid who's doing maybe half an hour of schoolwork a night. She told Ed a couple of weeks ago that Christopher should never work late at night; then she told me she'd told Ed. This is how much respect I get! People go behind my back and then they tell me they went behind my back! I'm not CEO material, that's for sure. oh that reminds me So Christopher gets some football game where you can 'choose' your parents. For his dad, he chooses a professional football player. For his mom, he chooses a CEO. Excuse me, THAT IS A SIGN. Alright, so back to the math explosion. Thank God my husband is as brainy as he is. After he had 20 minutes to calm down he said, 'The 9:00 o'clock deadline is a good idea, but it isn't working. So we have to come up with something else.' That's impressive. Twenty minutes to completely repudiate The Whole New Regime you yourself came up with and wanted to do. If anyone is wondering how two people stay married when they have 2 autistic kids & 1 non-mathematically gifted kid in accelerated math, this is it. So Ed & I came up with the new schedule, and we've agreed that the instant Christopher figures out how to game the system we'll make changes. The other elements are:
We both see that it's high time Ed fight some of the Homework Wars himself. We've completely polarized our roles, and it's no good. I'm the villain who enforces homework and study; Ed is the fun guy who comes home, plays with the kids, and reads a book at bedtime. It's nuts. So we have a whole new regime. Last night, it worked great.
Siegfried Engelmann's website
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Catherine, This is exactly the same situation I was posting about in 'Six weeks on'-- the need for More Practice in some very targeted areas. Saxon, fabulous though it is, was just not giving quite enough in some cases. I have just been making them up -- scrawling them out on scratch paper in my own handwriting because a. that's the fastest way to crank them out and b. Our printer isn't working right now anyway because the computer we were using as a server died. I did not hear your Math Blowout the other morning, but I'm a deep sleeper. Did you know that Gauss's face is on German currency? Isn't that cool? -- CarolynJohnston - 16 Nov 2005
Just think if a regular kid needs more practice, how much more the struggler or LD child needs. I'm having the same issues. I need to stop to make sure my Saxon 6/5 kid really has something in his head. I'm trying not to make extra work up because it's so time consuming, but I'm surprised that this isn't easier to find. I've finally broken down and joined both sections of edhelpers. It definitely helps speed up the process of finding the right practice sheet, but in terms of LD, some very obvious things need to be practiced, but not with 25 problems at one time, and in bigger print, with more space to work. Can't find long division with lots of space for the life of me. -- SusanS - 16 Nov 2005
Did you know that Gauss's face is on German currency? Isn't that cool? Whoa, neat! -- CatherineJohnson - 16 Nov 2005
I did not hear your Math Blowout the other morning, but I'm a deep sleeper. You'd have to be. -- CatherineJohnson - 16 Nov 2005
But this gives you some idea how much pressure Christopher's school puts on our household: I'm not a yeller. I'm just not. Ed doesn't yell, I don't yell. -- CatherineJohnson - 16 Nov 2005
Just think if a regular kid needs more practice, how much more the struggler or LD child needs. I'm having the same issues. I need to stop to make sure my Saxon 6/5 kid really has something in his head. I'm trying not to make extra work up because it's so time consuming, but I'm surprised that this isn't easier to find. I've finally broken down and joined both sections of edhelpers. It definitely helps speed up the process of finding the right practice sheet, but in terms of LD, some very obvious things need to be practiced, but not with 25 problems at one time, and in bigger print, with more space to work. Can't find long division with lots of space for the life of me. lol! I haven't 'broken down' yet, but I'm on the verge! You mean you joined the high school section, right? It is IMPOSSIBLE to find worksheets with workspace. It's driving me crazy, and it is LUDICROUS. When you're printing things out from a website, why in he** shouldn't there be space on the sheets? -- CatherineJohnson - 16 Nov 2005
You know, we should probably just start making up some decent sheets as we go along & posting them. Christopher's not LD, but he needs worksheets WITH SPACE TO DO THE PROBLEMS. Not just space, but quadrille graphing squares. -- CatherineJohnson - 16 Nov 2005
It's so frustrating, because his friend Marc got a 96 on the test. Marc probably is naturally brainy at math, and, interestingly, he has naturally good handwriting. All his numbers line up perfectly; he doesn't have to stress & strain to do that. Marc's twin, Drew, has very poor handwriting, and it's hard for him to line up numbers—and he isn't as good at math as his brother! (Though Drew is quite good, too.) -- CatherineJohnson - 16 Nov 2005
The irony to me is that by getting my child into 'accelerated' math I've managed to basically 'invent' a learning disability he doesn't have; I've managed to create the conditions & appearance of ld. I can really see, in my own life, Engelmann's point about all these non-ld kids in special ed who are there because they were taught so badly. Christopher is easily smart enough to master pre-algebra at age 11. BUT he has to have superb teaching &, even more importantly, superb instructional practice. -- CatherineJohnson - 16 Nov 2005
Carolyn yeah, I'm gonna have to scrawl out problems in my own handwriting that should be possible now that we've got the Ironclad time rule -- CatherineJohnson - 16 Nov 2005
SusanS?: "Can't find long division with lots of space for the life of me." How many problems would you like to have on an 8-1/2 x 11" page, and how big would like the the divisor and dividend to be? It should be easy enough to build a random worksheet generator to spec. FWIW, an update on my use of random worksheets: I'm still using random addition worksheets with my son, but have added a short session with flash cards right before using the worksheets. I'm using the flash cards as an opportunity to revisit speed strategies, and it seems to help. Last night he did 25 questions in 5:15 with only one mistake. Nowhere near automaticity, but definite progress. -- DougSundseth - 16 Nov 2005
Space for work on the sheet is a real issue. If left to himself, Ben will use up a whole sheet for every problem, and he'll write in huge symbols. All preprinted worksheets have too little space, byt too much space isn't what you want either; the amount has to be just right. At this point, on my homemade worksheets, I'm putting between 4 and 6 problems per sheet, and splitting the sheets with big black lines to keep him in the spaces. Basically, Catherine, you already have the perfect worksheets in your Saxon set; print out a bunch and put problems on them by hand as you go, and I predict that will help Chris' putative "LD" a great deal. -- CarolynJohnston - 16 Nov 2005
The are notebooks and pad of paper that have white lines interspersed with blue or shaded lines. Daniel uses this at school. Then his handwriting fits inside the line. This would also help in lining up numbers for math problems. I'm not at home, so I can't give you the website, but I will later. -- AnneDwyer - 16 Nov 2005
I'm putting between 4 and 6 problems per sheet, and splitting the sheets with big black lines to keep him in the spaces. Basically, Catherine, you already have the perfect worksheets in your Saxon set; print out a bunch and put problems on them by hand as you go, and I predict that will help Chris' putative "LD" a great deal. Yup. That's what I'm going to have to do. -- CatherineJohnson - 16 Nov 2005
Last night he did 25 questions in 5:15 with only one mistake. Nowhere near automaticity, but definite progress. wow! OK, I have to do the math.....what is 25 times 1:30??? 25 + 12.5 = 37.5 boy, that's fast is that right? 25 problems in 38 seconds -- CatherineJohnson - 16 Nov 2005
The are notebooks and pad of paper that have white lines interspersed with blue or shaded lines. Daniel uses this at school. Then his handwriting fits inside the line. This would also help in lining up numbers for math problems. I can't visualize this....white lines? Can't wait to see the website. -- CatherineJohnson - 16 Nov 2005
The reason he was assigned only 4 problems, I assume, was that he had a Math Project to do; he had to create a 'Wanted poster' for a famous mathematician. This is a typical trend ineducation. Students learn about the subject instead of learning the subject. Here, we learn about math (famous mathematicians) instead of learning math (practicing problems). -- KDeRosa - 16 Nov 2005
I'm confused. Alex did 25 questions in 5 minutes and 15 seconds, or 25 questions in 315 seconds. That's 12.6 seconds per question. I'd put automaticity at about 1 second per problem plus time to write the answer, and the answers are only one or two digits. Call it somewhere around 4 seconds with the writing (kindergarten kids don't write very fast), so somewhere under 2 minutes for 25 questions. I've promised him cash for performance ($1 if he can get under 4 minutes with 100% correct — so largely a token), but he was pretty happy with his feeling of accomplishment and our praise last night. Now that I think about it, maybe I should cobble up a certificate too. -- DougSundseth - 16 Nov 2005
I've just recently discovered this wonderful site--thank you so much. (I'm collaborating on a project to provide better means of inter-converting print and braille math which led to my discovering the poor state of math education for sighted kids and trying to learn more about it.) I didn't know until this post that you had autistic children. I don't mean to be patronizing but have you read "Siblings of Children With Autism: A Guide for Familes" or "What About Me? Growing Up with a Developmentally Disabled Sibling?" I'm wondering if part of Christopher's taking so long to absorb things is due to stress. SusanJ? -- KtmGuest - 16 Nov 2005
Oh man, Doug, I'm going to have to actually, gulp, measure. I can do this.. Okay, I've been taking graph paper that is 1 cm squared and making the division box run along 2 sides of the square perfectly. I make the numbers almost that size. He can handle anywhere from 4 to 6 long division problems (single digit divisor, multi digit dividend, with or without remainders) but he needs that space to keep from getting confused, although many times he's done it. That would be fantastic if you could come up with anything like that. -- SusanS - 16 Nov 2005
I'd like to also add that big graph paper and/or big print is helpful for young bright/gifted. My other son started long division at the end of first grade. He could not keep the columns straight for the life of him because of his age. He also had trouble with multi-digit multiplication, so his teacher had him practicing the entire next year with the same size graph paper. The large print/more space practice sheets help both the older LD and bright accelerated kids. Edhelpers.com asks if you have any questions or suggestion. I'll try to make sure I write something down next time I'm there, which will be any minute now. Catherine, I had to buy BOTH subscriptions 'cause the older one still needs grade school stuff and the younger one is in algebra. Go figure. I tried to avoid the algebra one as long as I could, but we still have problems with the occasional negative number and other little ticky things. Math kid always gets the hard ones that no one else can figure out, but never gets the super easy ones right. -- SusanS - 16 Nov 2005
I'm rather puzzled by why you are worried about space on worksheets. At school in NZ we very seldom had worksheets handed out that we actually wrote on. Even for tests we were normally given a sheet with the questions on and wrote the answers on lined paper (or graph paper for maths class). We could use as much paper as we liked, which was great for when I realised I'd done a problem completely wrong and had to re-do it from scratch. In external exams we were generally given: - a booklet with the questions - a booklet with blank pages for answering the questions And we could get more blank paged booklets if we wanted them. (When the booklets were being marked, the marker would put a line through any blank pages to stop someone getting their exam back, writing in the correct answers and then going for a re-mark). So why does Ben have to have space on the worksheets themselves for writing on? Does he forget the problem if it's not directly above where he's working? -- TracyW - 16 Nov 2005
I'm rather puzzled by why you are worried about space on worksheets. Mostly, for ease of use. And also, so that no extra time is spent rewriting the problem. With my son, who is severely ADHD, writing the problems out adds to the time and he has a very short time in which he can focus. He writes very slow and can't hold much in his head so he has to look back a couple of times even for a pretty simple problem. He can actually work in a few more problems with sheets that he just starts working on over ones in which he has to rewrite and then solve. And many of his problems come from just writing the problem down wrong. I want to spend as much time just doing the math as I can. I will say that both of my children seem baffled that they can use scratch paper. The teachers never mention it and it drives me crazy. I always have it out and when he starts anything I mention that he's going to need extra paper. My more advanced son recently had a quiz in algebra where he missed one because of a calculation problem. I asked him if he worked it out on some paper and he said he wasn't allowed. I told him that I seriously doubted that any math teacher would not allow him to write it out on a piece of paper. Apparently, this has not been brought up in class which I find strange. In his mind it meant that he wasn't "allowed." I'm guessing that it's because he is supposed to have his calculator with him and so can check his work with his calculator. Neither child has apparently ever been told to grab a piece of paper to work math. I really find that odd. -- SusanS - 16 Nov 2005
Hi SusanJ, welcome to KTM! Both Catherine and I have autistic kids. Catherine has 3 kids -- two are autistic -- and I have one son with HFA. Catherine's typical son Chris and my son Ben (who are our 'guinea pigs' for math instruction at home) are both in 6th grade. Catherine is a past member of the board of NAAR, has written books about autism, and has teamed with John Ratey (author of "Driven to distraction") on a book about shadow forms of mental illnesses, and with Temple Grandin (well-known autistic animal scientist) on another recent book. Noone is more aware than she is that Chris' life is stressful -- or better equipped to reduce the stress as much as possible, which is only so much, I'm afraid, with autistic kids around (trust me, I know!). But actually, his difficulty with managing space (and his need for more practice than he gets in the normal curriculum) is not at all unusual. -- CarolynJohnston - 16 Nov 2005
I'm attaching an Excel spreadsheet to this page that generates random problems with divisors from 2-9 and dividends from 20-999 (both inclusive). You should also be able to open this with Open Office if you don't have Excel. There are only four problems per page, and the answer sheet and problem sheet are correlated with a random serial number. I chose not to provide a grid for the work (it looked awfully busy to me with grid lines), but it's easy enough to add. Just select the answer area that you want gridded, then choose Format>Cells and add borders with the tools on the "Border" tab. I set the spreadsheet up so that the cells would make a regular grid under each problem if you turn the borders on. If you need to change the parameters of the problems it generates, you'll either need to let me know or figure out some of the weird things I did to get the formatting prettier. It's not especially difficult stuff, but it's pretty kludgy. -- DougSundseth - 16 Nov 2005
Oh, I forgot to mention that F9 generates new random numbers for the problems. -- DougSundseth - 16 Nov 2005
Secoond stupid question - why does he need to rewrite the question? We just used to put the number of the question in so the teacher could tell which one we were tackling and then dive straight in. It must have taxed the teachers' and examiners' marking ability sometimes, as I'd do questions in different orders from the paper. I would also sometimes do a question, then when re-checking my work realised I'd approached it all wrong and didn't have space to do it again clearly, so cross out my working and direct the marker to the end of the paper, where I'd re-done the question. But I don't ever recall losing marks because an examiner couldn't work out which question I was answering. That's why I wondered if the reason why you wanted space on worksheets was that your son got confused having to switch back and forth between two pieces of paper - the one he was working on and the one with the question on. It's interesting how much kids need to be taught explicitly. We were told before exams that we could ask for more booklets, and also told that people's handwriting varied widely so just because your mate had gone up for a new booklet twice while you were still on your first didn't mean you were failing the exam. I now guess the teachers had had problems in earlier years with people not knowing this. -- TracyW - 16 Nov 2005
Incidentally, on thinking over what Susan said, if handling two pieces of paper is too much for kids with ADHD then that would explain some of the poor results of the NZ school system. -- TracyW - 16 Nov 2005
Tracy, With a lot of things he doesn't need to rewrite anything. He just works it on a separate sheet and then puts the answer in. But with long division practice or multi digit multiplication he needs to rewrite the whole thing to see it, or he needs to have enough room just to work it on the page. It is interesting to me that I have to say it over and over about the extra paper. I don't remember having a problem with that as a child, but maybe the teachers kept reminding us and I don't remember. Most Boomers that I know immediately reach for a piece of paper to work anything out. It seems like common sense to me, but when my other son acted like it was some kind of exotic idea I knew something was up. Yay Doug, (I hope I can figure it out.) -- SusanS - 16 Nov 2005
"I hope I can figure it out." Let me know if you have any problems. You should be able to just open the spreadsheet, press F9, and print. Then press F9 and print again to get a new worksheet. (I just realized that I didn't ask whether you would be printing this on 8-1/2 x 11" pages. If you need to print on A4 paper, one of us will need to play with it a bit.) -- DougSundseth - 16 Nov 2005
I can print on 8 1/2 x 11. And I do have Excel, so I should be good to go. You're like the great and powerful Wizard. -- SusanS - 17 Nov 2005
I'm collaborating on a project to provide better means of inter-converting print and braille math which led to my discovering the poor state of math education for sighted kids and trying to learn more about it. Hi Susan J! boy, isn't that the story you get started down one path, and you end up at: math ed in America stinks! -- CatherineJohnson - 17 Nov 2005
Both the books you mention are great. Christopher isn't horrifically stressed, given the circumstances. For one thing, you'd be surprised at how 'normalizing' it is to have two autistic kids instead of just one. For another, he's absorbing his social studies material easily, and, last spring, won the academic award for 5th grade....so his learning is hanging in there. One problem, almost certainly, is that he has visual processing problems, and we are Vision Therapy drop-outs. That's a lot of what's going on with his handwriting, paper, etc., etc. Writing anything remotely resembling a straight column of figures is quite difficult, and I wouldn't be at all surprised to learn that seeing a straight column of figures is difficult. Now that we have our Whole New Regime, I'm going to start requiring him to do equation sequences, as Carolyn is doing with Ben, I believe. I insisted that he do one tonight, and he suddenly got the point. He'd been trying to solve equations mentally, holding variables & steps in his head... -- CatherineJohnson - 17 Nov 2005
Incidentally, on thinking over what Susan said, if handling two pieces of paper is too much for kids with ADHD then that would explain some of the poor results of the NZ school system. Oh, yeah.... I know NOTHING about New Zealand EXCEPT 'The Hypomanic Edge' guy has data showing that NZ may be even more bipolar than America. That means LOTS of hyper little kids with messy handwriting. -- CatherineJohnson - 17 Nov 2005
And I mean messy-to-the-point-of-psychotic messy. -- CatherineJohnson - 17 Nov 2005
It's interesting how much kids need to be taught explicitly. We were told before exams that we could ask for more booklets, and also told that people's handwriting varied widely so just because your mate had gone up for a new booklet twice while you were still on your first didn't mean you were failing the exam. I now guess the teachers had had problems in earlier years with people not knowing this. That's so cute! -- CatherineJohnson - 17 Nov 2005
"You're like the great and powerful Wizard." Pay no attention to that man behind the curtain. 8-) -- DougSundseth - 17 Nov 2005
You're like the great and powerful Wizard. You ARE! You are JUST LIKE the great and powerful Wizard! It's people like Doug who keep making me wish I had a Useful Skill. -- CatherineJohnson - 17 Nov 2005
I had finally started learning how to draw; then I got diverted to grade-school math. -- CatherineJohnson - 17 Nov 2005
Of course, grade school math is a highly useful skill, but I already knew grade school math well enough to have a useful skill in that arena. -- CatherineJohnson - 17 Nov 2005