lsquared on area conversions

lsquared writes:

I'm really wishing for a national curriculum right now--or at least a series of textbooks that goes K-10 instead of K-6 and another for 6-8.

I'm doing math with a friend's daughter. She's homeschooling, so I get to pick the book, and we're using a Singapore text. Our most recent section is converting units of area: cm² to m² and that sort of thing. So, I thought to myself, this is the US, we should also do problems with in² and ft²--I'll go look through the elementary and middle school texts in my library (I have 2-3 full series of each sitting outside my office door at work). Guess what? None of the books teach the topic at all. Aargh! Everyone is assuming someone else is teaching it, and no one is.

The first time I saw anything about area conversions was in the Saxon Math books I used to teach myself math a few years ago.

I learned inch-to-centimeter and inch-to-foot-to-yard conversions in school, but I learned nothing about area or volume conversions, and I continue to find volume conversions slightly confusing.

Speaking of Saxon Math, I've been thinking I need to get back to my books. I had almost finished the second book in the high school series when I was diverted to whatever I was diverted to. At the time, I was finding logs difficult to deal with in the "shuffled" organization of Saxon Math, especially since I wasn't studying every day.

Speaking of logs, I was emailing with Barry G. earlier today and I compiled a list of all the topics I was never, ever exposed to in high school math or college statistics.

I'll post tomorrow when I'm at my other computer.

The list is too long to remember off the top of my head.

is Saxon Math different?

Jean wrote:

It's my understanding that the new look also reflects a new owner and a different approach--not so "Saxon-y." Some folks are quite annoyed about this. I'm not sure what I'll do--my daughter is in 76 and I'm a fan, and I'm wondering if I'm going to like the new editions as much.

Art Reed wrote:

I have never seen a "Math Cat" before although several of my senior high school calculus students thought they were "Cats."

If you would take a look at the January 2010 news article at Using Saxon Math I believe your question about which editions of John Saxon's books are still valid - and will be for several decades - will be answered.

If you still have questions you can reach me at my office at (580) 234-0064 (CST) during normal office hours.

new look

Googling Saxon Math a couple of posts back, I learned that the Saxon books have "a different look."

source: 
Barb's People Builders

They sure do.

My books look like these.

source:
Buy used Saxon Math

I need a cat.

as smart as a 5th grader

source:
Competition Math: for Middle School (Volume 1)
p. 48

More evidence that "repeating the same lesson over and over" works as well as Howard Gardner's Chinese teachers said it does. I knew how to solve this problem within a few seconds of looking at it, and the reason I knew how to solve this problem within a few seconds of looking at it is that I used the difference of two squares to rationalize denominators many, many times while working my way through Saxon Math.

$83 million

from Saxon Math Warrior:

It was one thing for John Saxon to take on the mathematics education establishment. It was another for him to take on a special interest group whose followers were bankrolled by the federal government. With $83 million in federal tax dollars being pumped into the math education reformists’ camps during the 1990’s, any entrepreneur not in the chosen circle, who opposed reform math methods, and who was publishing his own math textbooks would have to battle more than their high-dollar funding. He would have to challenge the political ideology that guided all their decisions regarding America’s math program.

Saxon Math Warrior

from Education News:

John Saxon was hated by the math education establishment from the time he published his first algebra book in 1981. He still is, 14 years after his death in 1996. A West Point graduate with three engineering degrees, he declared war on those he blamed for creating the “disaster in American math education.” He insisted that math leaders had overseen this debacle and there was no personal accountability being demanded for the results of their radical ideology.

In John Saxon’s Story, a genius of common sense in math education, readers learn about his battles, his strong and colorful personality, and how his historically-based traditional math program made him, much to his surprise, a multimillionaire. This was in spite of high-powered and politically-connected math leaders’ efforts to destroy him.

The author, Nakonia (Niki) Hayes, is a retired math teacher and principal who used the Saxon program. She says she wrote the biography because John Saxon made a valuable and positive impact on thousands of American children. Go to Saxon Math Warrior for more information about how to order this original biography.

wow!

MSMI2010 was amazing.

Amazing!

Still collecting my thoughts - will post - but in the meantime, Niki Hayes' John Saxon bio is out!
My copy arrived in the mail last week.

onward & upward

$28,354 per pupil

I learned how to figure percent increase from Saxon Math.

In case you were wondering.

Saxon Geometry

R. Johnston says:

For years a succession of Saxon publishers has honored the view of series creator John Saxon that (1) Geometry should not be a separate course, but instead, middle and high school students should be exposed to Geometry in bits and pieces across several years of their math studies, and (2) that the traditional core of classical Geometry, Euclidian logic and specifically "two column proofs," are unimportant. (Yes, there is a lesson on proofs in the Saxon Algebra 2 text, but if you blinked, you missed it.)

For just as many years, teachers have bought a Geometry text from another source (Jacobs in our case), depriving the Saxon publisher of a business opportunity and interrupting the instructional flow of students raised on Saxon. At last, the Saxon publisher du jour, Harcourt, has introduced this new text. It is excellent. It presents all of the traditional content, and presents it well, preserving the Saxon method of presentation, nightly problem sets, and continuous cumulative review.

John Saxon is turning over in his grave, but the students he has indoctrinated in a 13-year sequence of consistent instruction and practice no longer have to take a year off.

What do you know about Saxon Geometry?

point of information: I'm pretty sure the Saxon books have had only one publisher apart from Saxon himself.

interview with my cousin - July 2005

I did this interview with my cousin in summer 2005 & posted it to the original kitchen table math on July 11,2005.


part 1: how Everyday Math came to my cousin's town

The 2nd grade teachers had a grant and were very excited. I think the teachers were turned on by the program. So they started introducing it in the 1st grade.

Nobody else liked it. I hated it, and many parents complained.

Teachers in the upper grades didn't like it, either. The district was always having these huge teacher-board meetings to convince the other teachers that they had to adopt it, too.

Eventually, when the grade school kids got to high school, the high school teachers were in horror because the kids coming in couldn't calculate. They complained that the Chicago Math students had to spend all this time guesstimating and figuring out what the answer was to one small step inside a complex problem. The students were too slow; they were hung up on the basics.

This war went on for a decade. I don't know how it came out. I do know that for at least the first couple of years after Chicago Math came in they were not getting lots of kids proficient on the state tests. I'll ask my friend who teaches at the high school whether they're still using the books. She had 3 kids who went through the system, and she hated Chicago Math.^*


part 2: easier for mathematically talented kids?

One of my daughter's friends had a very easy time with it, and was successful at it. She really soaked it up. Someone told me that kids who are chronologically older and have math talent, maybe they respond to it better. My daughter was the youngest in the class.

My older daughter, though, had a babysitter who had Chicago Math at New Trier when we were living on the North Shore. She said it was a failure. The New Trier students were the first guinea pigs, because it was Chicago Math. She said Chicago Math came from a bunch of ivory tower people figuring the whole thing out and then trying to disseminate it to all these little children.


part 3: developmentally inappropriate

I once told the assistant principal that in the Saxon book, when you've done something wrong you go back. You can't advance until you get it right. I said that's what I like about the Saxon program.

He said, "Well children can do that with Chicago Math, too.' He was suggesting that my daughter had the ability to assess herself in Chicago Math, and that's what she should have done. She was a little adult who could self-assess.

But she couldn't. She was too young, and she didn't know enough about math to be able to assess how much she knew about math.

It's like driving. When you know how to drive, driving is built into your thinking process.

If you don't know how to drive, you're not going to have the confidence to figure out what your problem is. If you can't get from one corner to the next, you're not in a position to assess why not.


part 4: spiraling

Chicago Math gives you advanced math problems sprinkled in with the elementary math your child is learning. They slip it in.

They would have you guess at the answers for the advanced problems, but then they never gave you the answers so you didn't know if you guessed right or not. You're always a work in progress with Chicago Math. So you never get a definite answer. And you never had a sense of completion or success on a day-to-day basis.

But my pet peeve was that it sped you along at a rapid pace and you never mastered the material that you left the page before. When my daughter was in the 2nd grade one work page would be coins; the next day you'd be dealing with weather; the next day you'd be dealing with problem solving. My daughter had no sense of what a quarter or a dime was.

When I was taught math, each day you built on what you knew. When you did the coins you learned a penny, a nickel, a quarter. You kept going. Telling time, same thing. You work on time until you get it. You don't just have a flash of it one day.

In Chicago Math you had one page on one topic, then you went on to something completely different on the next page. There was no repetition. It was irresponsible, very ungrounded.


part 5: frustrating

They would want my daughter to guesstimate whether something was 50 or not, or 100 or not. And they wanted her to do that before she knew 25 and 25 was 50, before she knew what the building blocks that made a number were. It's hard to estimate something before you know that numbers are created.

To guesstimate is so frustrating. Math has a yes or no answer. And with math, when you go 5 x 7, it's 35. That's the answer. Children at a young age want to have something concrete. They learn from 'This is wrong' and 'This is right.' They like getting the right answer.

In Chicago Math, children don't get that reward.


part 6: demoralizing

First they give you an intuitive flash that of material that is above your level, that you aren't successful at. It's like a prelude.

The thinking is that when you get to the material for real, you've had a prelude. But on a day-to-day basis if you're always getting preludes, the child never has a sense of completion or success.

There was never a sense of mastery; there was never a sense of completing a task successfully before moving on to the new material that you were supposed to pick up intuitively.

Chicago Math was like trying to learn a foreign language by hearing tapes every day and intuiting what the words mean. Then 3 months later you're supposed to know what the tapes are saying.


Part 7: boring

It was too abstract and theoretical and boring. It's boring when you don't have the light bulb go off in your mind because, 'Oh! I got it right!'

The best you could think was, 'Well, maybe I got it right.

I think it's crippling.


Part 8: Saxon Math

I moved my daughter to private school after 4th grade. She's worked with the Saxon Math books ever since.

It took her awhile to get to a stable place in math because she had gaps in her knowledge, and because she didn't have confidence in the basics. She learned new concepts; she could understand them. But under testing she would crumble, because she didn't have confidence.

In Chicago Math, computation doesn't become second nature. I guess in new math they teach you all these steps you have to take. They make multiplication into 5 steps. Chicago Math makes learning to multiply real slow, and so damn confusing.

So she was bogged down in trying to do it in the new math way. It took her several years to overcome that, to get solid in the basics.

She improved greatly with the Saxon book. She's doing fine at the high school level. She just finished 9th grade, and she does well in math now.


^*Everyday Math was developed by the University of Chicago. Everyone in my cousin's town in MA called it 'Chicago Math.'

Saxon Math vs TERC

Student math achievement was significantly higher in schools assigned to Math Expressions and Saxon, than in schools assigned to Investigations and SFAW. Average HLM-adjusted spring math achievement of Math Expressions and Saxon students was 0.30 standard deviations higher than Investigations students, and 0.24 standard deviations higher than SFAW students. For a student at the 50th percentile in math achievement, these effects mean that the student’s percentile rank would be 9 to 12 points higher if the school used Math Expressions or Saxon, instead of Investigations or SFAW.

Achievement Effects of Four Early Elementary School Math Curricula: Findings from First Graders in 39 Schools

Here's the Education Week article, which is worth weighing in on.

Paul H on the toxic stew

more tales from the font:

Constructivism, as practiced by CMP is actually an amalgam of discovery learning, clothed in multiculturalism, with a dash of politically correct, story vignettes to 'connect' the child to real world problems. It's not that these things, in and of themselves are inappropriate, it's just that the program throws so much into a one day lesson, the math gets hijacked.

It's not atypical for one of these vignettes to have a dark skinned blue eyed child, named Ming lee, sitting in a wheel chair, talking in Spanish to her friend Sascha from Russia. Put that in front of a child who is reading at a third grade level as an introduction to a seventh grade lesson on solving proportions, and you have the makings of a nightmare. It's very hard at times to get by the intro.

Then when you get into the lesson's problem sets it is very often the case that the problems serve up a hodge-podge;fill out a table, look for a pattern, find equivalent fractions, make a graph, and on and on. It makes my head explode sometimes and I've been doing math forever.

I understand the need to make connections and provide spaced repetition but it should never get in the way of base understanding in the topic at hand. When it does, and the paradigm is discovery/group learning, the results are not pretty.

The math gets lost in a blizzard of roadblocks around; the weird names, and how come we saw that guy in the wheel chair last year, and are trees really alive, and why is the Chinese guy speaking Spanish to a Russian, do I really have to make a table, and on and on.

You mix this altogether and it's a toxic stew for behavior because each child is hung up on a different facet of the jewel. If you can't put all these fires out fast, really fast, the third of your class that is ADHD gets going with the third of the class that is laughing at the goofy names, while the last third passes notes about the day's scoop.

The math is lost. Instead of providing a structure to hang the practice and spaced reps upon, CMP rips the structure into tiny little pieces in the arcane hope that the kids will put it all together again.

C. and I used to laugh about the many and multi-splendored names of the children populating Saxon's word problems. The one I remember best was: Monifa.

Monifa?

Who in the world is named Monifa? (Apart from a pygmy hippo in Australia, that is.)

Of course today I wonder whether the choice of "Monifa" was John Saxon's little in-joke on multi-culturalism in math books.

Ted Nutting on the math mess

I'm a high-school math teacher in Seattle. When I hear Mark Emmert, president of the University of Washington, say that this state is "at the bottom in the production of scientists and engineers," and warn that our graduates "will be washing the cars for the people who come here for the best jobs," I know what the problem is. It's math. We are failing to educate our children in mathematics. I know how that came about, and what we can do about it.

The problem is national in scope, but in Washington state our difficulties can be traced principally to Terry Bergeson, superintendent of public instruction for the past 12 years. She oversaw the writing of our state's weak, vague math standards, basing them on a "reform" idea to promote "discovery" learning. This has turned teachers into "facilitators" who "guide" children in learning activities. It has promoted "differentiated instruction," placing students of wildly differing abilities together where some students cannot do the required work, often to the detriment of those who can.

She has moved away from rigorous testing. The "reform" math she champions encourages such things as journals, portfolios and group projects that tend to form large parts of classroom grading systems, while test results are relegated to a lesser role. The math portion of the Washington Assessment of Student Learning (WASL), aligned to her faulty standards, tests math skills at a low level. Even so, about half our 10th-graders fail it.

She has wasted millions of dollars on "professional development" to encourage teachers to put "reform" theories into practice. These theories are supposed to make it possible for all students to learn math. But few students know significant mathematics, and most know very little. About half of our students entering college now have to take remedial math. Many of our students who do succeed use private tutors, and the racial achievement gaps have widened. "Reform's" emphasis on equity and fairness has been revealed to be empty talk.

My experience tells me that we can fix this, and quickly. I am the Advanced Placement calculus teacher at Ballard High School. I don't teach Bergeson-style. I tell my students what they need to know, they do problems to understand how it works, and they demonstrate their knowledge and understanding through testing. Up until this year, we've insisted that our students who take AP calculus actually be able to do the work.

We at Ballard have by far the best AP calculus program in Seattle Public Schools, based on AP test scores. I have no special magnetism or charisma; I'm not a cult figure for teenagers. I have high standards and I require the students to work. If they don't work, they know they will probably flunk. But they do work, and I am proud of them. I also have the benefit of having an older textbook that doesn't fit the "reform math" model, and most of my students have had an excellent pre-calculus teacher the year before.

In most of our other math classes (and I doubt that Ballard is unique in this), we've tended to follow a "reform" model. We've passed students on from class to class; there is no meaningful threshold they must cross to enter a more-difficult class. Since we find that many students in our classes cannot do the work, we dumb down the courses. We say we are admitting unprepared students into our classes in order to "challenge" them.

But students should be challenged in the classes that they are qualified to take, not sent on to classes where they cannot do the work. Unfortunately, things are changing, even in our school's AP calculus classes: We're starting to admit unqualified students, and our program will soon begin to deteriorate.

It's not just Ballard's AP calculus program that is successful, and it's not just the top students. North Beach Elementary in Seattle [was this Niki Hayes' school? will find out] switched its math curriculum to Saxon Math in 2001. This excellent series teaches real math and does not follow Bergeson's fuzzy, reform-oriented ideology. North Beach did this with reluctant agreement from Seattle Public Schools because the PTA paid for the books and because the superintendent supported site-based decision-making. North Beach's passing rate on the WASL rose from 68 percent in 2000 to 94 percent in 2004 — and yet, every year parents worry that real math will be scrapped. Recently, the school has had to seek waivers to avoid having to teach the district's "reform" math.

Legislators have begun to understand the problem. At the Legislature's direction in 2007, the state Board of Education reviewed our state's math standards, finding they were failing. The Legislature set up a system to fix the problems, but that system gave Bergeson the opportunity to sabotage the process. She stacked the committees selected to rewrite the standards with like-minded ideologues. The results were so bad the Legislature refused to accept the rewritten standards, sending them to the Board of Education to fix.

Bergeson then stacked the committees set up to select curricula for state approval. That process is not complete, but the first results are discour-aging. The Legislature had required that the new mathematics standards be based on (among other things) the standards of Singapore, consistently a leader on international tests, but Bergeson's initial submission of texts ranked Singapore Math, that country's official curriculum (and a superior one), dead last out of 12.

Most school-district administrations have gone along with Bergeson and share responsibility for this mess. Even as an uproar arose nationally against the programs Bergeson promotes, Seattle started using two of them in elementary and middle schools.

None of this is necessary. Students can learn math. My students learn it. If our education leaders would follow the lead of our Legislature, stop ignoring obvious successes and support what actually works, we would see major improvements in just a few years.

Ted Nutting is the Advanced Placement calculus teacher at Ballard High School in Seattle.

Copyright © 2008 The Seattle Times Company

A formula for lifting Washington out of its math mess

Students should be challenged in the classes they are qualified to take.

are you smarter than an 8th grader?

Thanks to Saxon Math, I am now smarter than an 8th grader in Singapore.

That's saying something.

brewhaha on the natural

Math is most unnatural - it is only after we understand it within its artificial axiomatic system that it seems natural. If math was so natural and could be learned in a completely natural setting we would have more mathematical geniuses out there and (at the very least) more people willing to forego maxing out their credit cards.
Brewhaha, commenting on spilt religion

John Saxon opens every one of his textbooks with an observation along these lines:

In this book we continue the study of topics from algebra and geometry and begin our study of trigonometry. Mathematics is an abstract study of the behavior and interrelationships of numbers. In Algebra 1, we found that algebra is not difficult—it is just different. Concepts that were confusing when first encountered became familiar concepts after they had been practiced for a period of weeks or months—until finally they were understood. Then further study of the same concepts caused additional understanding as totally unexpected ramifications appeared.

Didn't someone leave a similar observation from... Feynman?

Math Without Tears

Concerned Teacher has a blog!!!!

This is ASSIGNED READING, folks!

why worksheets may be better than flash cards

I've mentioned a few times that I had no luck using flash cards to teach C. his math facts. Paper flash cards didn't work; online flash cards didn't work. We futzed around with those things for what seemed like eons.

What worked - and worked fast - were the Saxon Fast Facts worksheets.

Maybe this explains it:

Mr. Karpicke's studies suggest that if you want to implant facts in long-term memory, it's best to receive feedback on a quiz after a short delay of 5 to 20 minutes. But flashcards (at least as they are ordinarily used) give feedback immediately.

In an experiment presented last month at the annual meeting of the Association for Psychological Science, Nate Kornell, a postdoctoral fellow in psychology at the University of California at Los Angeles, and Robert A. Bjork, a professor of psychology there, asked people to study 20 word pairs on flashcards during a one-hour period.

Half the participants reviewed the full cycle of 20 cards eight times. The other half broke up the pile into small stacks, studying five cards at a time, reviewing them eight times, then moving on to the next small stack.

Early in the experiment, the people using the small stacks felt pretty good about their progress. They predicted (on average) that on the final exam, they would remember 68 percent of the words. The people studying the full stack, by contrast, predicted that they would remember only 53 percent.

But on the final exam administered at the end of the hour, their performance was actually the opposite. The people who repeatedly studied the full cycle of cards had an average exam score of 80 percent, while the "small stack" participants scored only 54 percent.

Now, you might say that's just because the "small stack" participants had forgotten the words that they studied in their first batches, early in the hour. But even on the words they studied in their last batch, the small-stack participants scored just 68 percent, so their performance still trailed that of the full-stack group.

This is just the latest piece of evidence, Mr. Kornell says, that cramming doesn't work. When you study an unfamiliar fact again and again in immediate succession, he says, it feels much better embedded in your memory than it actually is. It's much better to create an interval between the times you study an item. (The people cycling through the full stack of cards studied each card every seven minutes or so, which is a decent interval.)
Why Cramming Doesn't Work

The Saxon Fast Facts worksheets are designed to be done in 5 minutes or less.

C. used to do his sheet in 3 or 4 minutes (it would be 5 or a bit more the first couple of times, but he always progressed quickly).

Then I'd futz around finding the answer sheet & read him the answers so he could correct his answers.

So: time delay of a few minutes.

Those sheets worked like magic with another boy who was classified SPED. (High-end SPED: the kind of kid who wouldn't be SPED if schools practiced direct instruction and precision teaching.) His progress from one week to the next was almost bizarre. First time I gave him one of the sheets to do he took 10 minutes at least. Second time - one week later - he was down to maybe 7 minutes.

Third and last time: he came in under five with no mistakes.

You can buy the Saxon Fast Facts books as stand-alones, but you have to buy the solution manual, too, I think.

inflexible knowledge redux

Another example of inflexible knowledge.

C. and his friend J. were assigned a "digit word problem" for homework. Example:

The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number.

source: purplemath

Neither of them had a clue how to do it. (I think digit problems had been taught in class that day for the first time. They'd both seen 1 or 2 worked examples.)

I tried to teach it by writing the number 23 and then, below that, writing a variable for each digit, then asking them something wildly imprecise like, "What would you have to do to these variables to get them to equal 23?"

Actually, as I think about it now, I don't know what words a person educated in mathematics would use to express this, so maybe you all can fill me in.

In any case, they did get the idea they were to let x equal 2 and y equal 3, and they were to write an equation using these values for x and y that would equal 23.



Looking at this arrangement of numerals and variables didn't help.

J. said, "x + y?"

"That's 5," I said.

"x times y?"

"That's 6."

They were stumped.

This is a classic case of inflexible thinking, for two reasons.

First of all, they've seen "plus" and "times" more often than they've seen 10x + y. Confronting a novel problem, their brains went straight to the more familiar instead of the less familiar.

Of course, that's what a brain ought to do: When you hear hoof beats on the bridge don't think of zebras.

The problem was that, pace Willingham, once they figured out the hoof beats weren't made by horses they didn't think of zebras next.

Both boys know how to set up word problems using letter variables; both boys are proficient (or close to) at solving number and consecutive integer problems. They can set up and solve coin problems, distance problems, and age problems; they can also set up and solve simple linear function problems.

They've been writing algebraic expressions for at least a couple of years.

And they were stopped cold by a simple digit problem.

I wish I'd taken notes on what I did next. I think I said something like, "What is the 2?" (That's imprecise, too, right? What's the correct language there? "What value does 2 represent"?)

I don't think I had to go as far as to remind them of the base-10 place system, but, on the other hand, maybe I did and I'm repressing it.

In any case, the moment it dawned on them that the key was recognizing the 2 as 20 they could both set up and solve digit problems rapidly and efficiently.

Knowledge transfer and generalization are core, unsolved problems in education.

update: Looking at this now, I think I should have had them start with the "3" and write an equation using y alone, then had them write an equation using x and 2 (or 20). If I wasn't simply going to show them a worked example myself (should I have? I don't know) I needed to break this down into the smallest, simplest possible steps. And I should have started with the ones digit, not the tens.

I think.


cumulative practice and problem solving

Speaking of which, I keep promising to write a post about one of the three most valuable papers I've ever read on the subject of teaching math:

The Effects of Cumulative Practice on Mathematics Problem Solving
Kristin H. Mayfield and Philip N. Chase

Here is the introduction:

Over 35 years of international comparisons of mathematics achievement have indicated problems with the performance of students from the United States. According to the latest international study, the average score of U.S. students was below the international average, and the top 10% of U.S. students performed at the level of the average student in Singapore, the world leader (Wingert, 1996). In addition, recent tests administered by the U.S. National Assessment of Educational Progress revealed that 70% of fourth graders could not do arithmetic with whole numbers and solve problems that required one manipulation. Moreover, 79% of eighth graders and 40% of 12th graders could not compute with decimals, fractions,
and percentages, could not recognize geometric figures, and could not solve simple equations; and 93% of 12th graders failed to perform basic algebra manipulations and solve problems that required multiple manipulations (Campbell, Voelkl, & Donahue, 1997).

These statistics reveal students’ deficits in the fundamental skills of mathematics as well as mathematical reasoning and problem solving. Indeed, poor problem-solving skills have been targeted by the National Council of Teachers of Mathematics (Carpenter, Corbitt, Kepner, Lindquist, & Reys, 1980; Carpenter, Kepner, Corbitt, Lindquist, & Reys, 1980; Kouba et al., 1988; National Council of Teachers of Mathematics, 1989, 2000). Thus, it seems appropriate that current behavior-analytic research in mathematics education should address problem-solving skills as well as basic mathematics skills (e.g., Wood, Frank, & Wacker, 1998).

I'm hoping I can get to this later on today.

But first -- must write chickens chapter!

EM success story

from the Dallas comments thread:

I am a student whose school used Everyday Math textbooks, and I was more than prepared for higher level math courses. However, this is because my math teachers had us put the books under our desk, and passed out real math textbooks, like Saxon Math instead. Because of the strong basic math foundation imparted by the traditional method, I have already been able to take both AB and BC calculus, and passed both AP tests with a five. I did see many other students struggling with the class not because they didn’t understand the theory, but because they were unable to perform the basic math operations. Everyday Math had crippled their basic math skills, and those are critical foundations for higher-level math.

Mrs. Wilson, you say that parents should help their kids review math, and I agree with you there. But the sad truth is, many parents don't care. The majority of students receive instruction solely in the classroom, and never receive the benefits that your daughters received. You should not focus on problem solving skills and "higher level thinking" if it prevents the students from actually learning any math. Removing Everyday Math from everyday usage is one of the best things possible for DISD's math scores.

Mrs. Wilson's comment:

my daughters 3rd grade teacher who has taught for over 25 years likes this book because it encourages higher level, multiple step thinking. People complain their kids aren't memorizing multiplication tables. Heres an idea for you, practice them at home with your child.

This comment is revealing, and wrong on every count:

• It assumes that learning = memorizing & teaching = one-on-one flash card practice
  
• It assumes that some content is "beneath" teachers and should be farmed out to parents who are also, presumably, beneath teachers
• It assumes that teaching a child the multiplication tables is in all cases a simple and easily accomplished task
  

I wish to heck I could find the post quoting a Soviet teacher on the precision methodology and timing they followed for teaching the times tables.

Since I can't, I'll quote the National Math Advisory Panel, which says that "most" American children do not achieve "fast and efficient retrieval of facts." (January 11, 2007 meeting)

It is not a simple matter to teach many children their math facts, nor is it a simple matter to "practice" successfully at home. My own efforts with flash cards came to naught; I was lucky enough to stumble onto the fact that, at least for my own child, worksheets were what was needed. I have since heard the same story from other parents.

And, in the n of 2 category, I've spoken with two parents of math-disabled adult children who tried and failed to teach the math facts at home. Both were educated and intelligent women; their kids are intelligent, too. No learning problems, no behavior problems, no ADD. One of the two scored a 780 on his SAT-V.

Remediating a bad math program at home is an extremely difficult proposition.

A good teacher is far more effective than the most intelligent and dedicated parent.

Saxon Math @ North Beach

For an unscripted kid talking about Saxon, you may want to see this one just for fun: