kitchen table math, the sequel: Our schools do ruin Singapore Math

Friday, June 8, 2012

Our schools do ruin Singapore Math

SteveH has said a few times "Our schools would ruin Singapore Math." Well, we can dispense with the "would". Schools routinely ruin Singapore Math, just as they ruin every other initiative brought in. Not all schools do, of course, but badly run schools ruin everything --professional development, curricula, assessment, leadership initiatives. Bringing in good materials to a bad school doesn't work at fixing the school. (Whether it saves an individual student here or there is an open question.)

I have now seen schools ruin Singapore math. They do this by not reading Primary Math's own materials, not understanding or seeking out anything about how Singapore taught using Primary Math, by not getting their staff any professional development at all for using Singapore Math. So their teachers know nothing about how the lessons are supposed to be taught, what "Concrete->Pictorial->Abstract" means, and teach math the same way they taught before. Typically, they don't even get them a full complement of materials. I've seen schools where the teacher NEVER read the teacher's guide, and just assumes that since the textbook looks simple to them, there's nothing more to it.

Then they ruin it some more by teaching it out of order to "match the state standards"(more on this in an upcoming post next week.) Since nearly everything in Primary Math is carefully predicated on what has been taught before, this makes no sense at all.

I've now seen schools ruin Lemov's Teach Like a Champion, too. They do this by using it as a micromanagement tool--lesson plans must look exactly like this, word choice must sound exactly like this,   etc. to beat the teachers into submission. Then they ruin it some more by using the lack of techniques present during a class to penalize a teacher during an evaluation.  Nothing like making the teachers hate the administration, or that their lesson planning is a waste, or that all "teacher improvement" is really just a cover for a method for trying to fire a teacher to make the school function!

I've now seen schools ruin PLCs, too.

What is the common denominator?  cargo cult education.  To shamelessly quote myself:
Unless they understand what's underneath the "lessons of the high performing school" (the high performing parents, the high performing teachers, the high performing students) then it won't matter. Unless the "lessons" they grab are that they need teachers who already know classroom management skills and content, need solid curricula that can be built to mastery, need ability grouping rather than differentiated instruction, need schools that already enforce discipline and control their students' behavior, need raised expectations for all students, and more, then they will be missing something essential."
In each case, these schools have no idea what the actual function of teaching is, what knowledge you're supposed to impart to the students. So they grab PLCS, or TLAC, or Singapore Math, but it's just coconut shell headphones. Their teachers don't know that their students don't know 10/9 is a fraction; their teachers don't know that you can't teach the chapters of a math book in another order; their teachers don't know why place value works. Their principals don't know that their teachers haven't read the Teacher's Guide at all; their principals don't know that "accountable talk" isn't the same thing as explaining your bar model; their principals don't know that their teachers didn't follow any scope and sequence this year; their principals don't know what their teachers and students don't know. And they may test prep their way to better scores, but their students will still not know enough to succeed in high school, let alone college.

The real question is: can you find a school that isn't practicing cargo cult education? How would you know?

46 comments:

SteveH said...

Ironically, it's kind of like rote education. They slavishly adhere to ideas like different learning styles without really thinking about what it means or how to apply it. They fail at what they profess to teach.

I think many parents know, but what would you say to the school? Many parents know that differentiated instruction doesn't work. Many teachers on the front lines know that it doesn't work.

My son had to do over 100 3X5 crayon drawings of science terms in 6th grade. He could memorize the meanings in an instant, but took 40 minutes to draw each card. The teacher was amazed that it took him so long, but she loved his results. However, when he took only the suggested 10 minutes, he got a lower rubric grade. Forget whether he really remembered and understood the science terms.

What do you say to the school/teacher about that?

Then there was the whole issue of portfolios. Nothing came home. It went straight into the portfolio kept at school. If we wanted, we parents could make individual appointments with teachers to meet with them after school to review the portfolio. Of course, how many parents can go to a school on a regular basis at 2:40 pm just to get what should have been sent home? After talking to the principal about this, she had no solution. That was just their (rote) policy.

What do you say when you're in a restaurant and the waiter asks you how everything is/was? If you end up back in the same restaurant, does that mean you can't tell the difference?

Anonymous said...

I've seen homeschoolers ruin Singapore Math as well. They get the workbooks and just teach the algorithms by winging it. I am certain if our district were to adopt SM, this is essentially what would happen, which I think is probably worse than adopting an algorithm driven program and teaching it as intended.

Auntie Ann said...

We need some help.

Our school (which is the sort of school that can ruin anything) has decided to dump Everyday Math (yay!) in favor of Singapore "Math In Focus" (why not SM "Primary"? No clue.) However, they will only be doing it next year for Kindergarten and 1st Grade, 2nd-5th will have to wait another year.

Since our kid is going into 5th, and then off to junior high the follow year, this won't help him at all.

We are now in the middle of an argument with the school, trying to press them into a full roll-out next fall. They've essentially taken the strange position: Singapore Math is better, but your kids can't have it!

They have asked us for our reasoning for pushing Singapore over EM, and they want specifics.

For example, 5th is the year of really drilling in fractions, but it is my understanding that EM never does fraction division. I also know that at this same school, 6th grade uses Chicago Math's "Pre-Transitions" textbook, which is essentially a review of elementary math. Our sixth grader spent most of the first semester on addition and subtraction. That's the biggest indictment I can find against EM: after 6 years of the curriculum, kids still didn't have addition down cold.

Does anyone know what points would be best to focus on? And has anyone out there already done this kind of point-by-point comparison?

bky said...

Yeah, I know some homeschoolers misteach Singapore. One of the things that I have heard in talking with other homeschooling parents who don't get the curriculum or don't understand the math well enough is that they seem to think there are a lot of guess-and-check problems in Singapore, especially in the section on ratios that I think you would call "changating ratios". For example,the ratio of person A's trading cards to person B's trading cards is some given ratio, then when person A gives person B a specific number of cards their ratio is now some other specific ratio. A lot of parents don't both to learn the use of bar models and the idea of counting "units" in ratio problems, so they assume the student is suppose to try some numbers till they get it right. Wrong! There are methods.

Cassandra Turner said...

Auntie Ann : However, they will only be doing it next year for Kindergarten and 1st Grade, 2nd-5th will have to wait another year.

The challenge with adopting PM in the upper elementary grades is that it creates a ton of gaps in student knowledge. It's pretty rare to see a school adopt Singapore math curricula k-1, then grow each year,though, for exactly the treason you state. What school can tell their parent population, "We're giving your 1st grader the world's best math, but your 4th grader is still getting the same dreck we're dropping."

Schools that adopt k-6 and go all in with Singapore Math have a rough time of it the first year. Of course, it's rough on the teachers, because they have some assessing and backfilling to do. It's not so rough on the students. That's one reason that I always recommend a school get CONTENT-based professional development when adopting SM. If you get someone for PD who has taught the curriculum in a classroom,like, oh me for example,They know where those gaps will be. I always go over these trouble areas when working with a school adopting Primary Mathematics. And we make a plan to meet those student needs. Not saying every school does it perfectly, (Like Allison mentions), but at least they were informed.

"Math In Focus" (why not SM "Primary"? No clue.)
Based on what I've heard speaking to schools that have adopted Math in Focus, they cite the large company behind the materials (Houghton Mifflin Harcourt), and their sales staff. HMH provides pedagogical pd for the schools as part of the purchase package. CONTENT pd is extra. Many schools feel as though they've invested enough in the materials and don't get the additional content pd that they need.

Auntie Ann, feel free to email me.

Cassandra Turner said...

Allison said: their teachers don't know why place value works.

When teaching re-grouping on a place value chart, I once had a teacher (who had been teaching a long time) tell me that you could not ever have more than 9 ones in the ones column. "They'd need to be bundled up and made a ten." period.
"So..." I asked, "How do you teach subtraction with regrouping?"
"I don't in first grade."
"So...how do you expect the second grade teachers to teach it?"
"I have no idea."

Anonymous said...

Auntie Ann,

What Cassandra said.

Our district adopted Math in Focus a year ago. The explanation to the teachers was that this was the American version. The idea was that the average American teacher and student needs more help and supplementing than the Singapore student.

Some of the stuff I've seen has been somewhat confusing and nothing like what I've seen from the Primary books.

SusanS

Anonymous said...

Excuse my, uh, broken English. I hit "publish" instead of "preview."

SusanS

AmyP said...

"Some of the stuff I've seen has been somewhat confusing and nothing like what I've seen from the Primary books."

At our private school, we had Primary Mathematics when my daughter was in K-3. They switched over to the American version of Singapore this past year when our son was in 1st and our daughter was in 4th. I haven't seen any problems with my daughter, but my 1st grade son had many teary evenings trying to figure out what the assignment asked him to do. The things that gave him (and me) trouble generally weren't very sophisticated (once you understood what the heck they wanted), but I really missed the total clarity of the original Singapore workbook. My 7-year-old is an extremely mathy child, so he's the last person who ought to be suffering in 1st grade math. I talked to his teacher about the issues it sounded like the 1st grade teachers had eventually figured out the issues and were starting to supplement more and put more attention into figuring out if the kids were intellectually prepared for certain homework assignments.

Auntie Ann said...

Not knowing what the heck the workbooks are asking for seems to be common these days. I have a degree in physics, and sometimes had no clue what the EM workbooks wanted the kid to do.

Unknown said...

My school tried to implement Singapore in K-5 and had to take the upper grades out of Singapore altogether. Part of the problem was the lack of skill in the teaching staff. It was too much to learn the new curriculum and also backfill at one. The other problem was that the gaps were too great, especially for things like fractions, that I don't believe they develop very well for kids who aren't high functioning. Our younger kids are doing great, though, especially in the classes where the teachers really teach the problem solving the way it should be done. All to many elementary teachers don't have the number sense and mathematical skills to teach Singapore problem solving properly.

Unknown said...

Please ignore my iPad induced spelling errors.

Allison said...

Yes, many homeschooling parents fail to teach Primary Math well. In that case, almost always, they don't buy the home instruction guides or teachers guides, they don't understand Concrete->Pictorial-> abstract, they don't see how different Singapore's program is from "read the textbook, do the workbook".


But how would they know?
They are parents not teachers per se. It makes sense that they would not understand the value of the pedagogy, or know how to teach differently than they were taught. what is the school's excuse for not knowing that?

Second, MSMI's greatest demand right now is from exactly those parents who know they don't know how to teach Singapore math and want to learn more. They spend their weekends at workshops. They spend their own money. Not every Singapore-using home or after schooling parent wants to improve, but I've now personally taught a few dozen. In almost every case, they've sought me out, not the other way around. By comparison, Very few teachers have sought me out, and seldom do they get any support from their school when they do.

Auntie Ann said...

This is a partial draft of what we are planning on sending to our school's administration:

-------------

Spiral vs practice to achievement.
Everyday Math’s spiraling curriculum means that topics are repeatedly gone over lightly, and there is no attempt at making sure one concept has sunk in before progression to the next skill. While some math skills have no prerequisites, for the most part, math builds on earlier knowledge. Without fully building the foundation, subsequent levels don’t make as much sense and are harder to grasp. With Singapore, you do not progress until you have spent sufficient time to master a skill. That is a key difference: multiple, light coverage vs. practice to mastery.
In addition, the Everyday Math books were designed to work with a public-school calendar of roughly 180 days. Our private school's calendar is fully four weeks shorter, and usually one-quarter to one-third of the material in any given year is never covered. This is deadly in light of the spiraling nature of the curriculum—it means many skills never get presented enough times to really sink in, and students are forced to flail when they get to higher levels of math. At least with Singapore, if a previous year’s teacher doesn’t get to the end of the book, it is very clear where the class left off, and what skills they need to work on to make up the gap.
Standard algorithms
Everyday Math presents multiple algorithms for solving arithmetic problems—in most, four different methods are presented. Singapore instead focuses on one or two algorithms, and then takes the time to ensure the student achieves mastery. Using too many methods leads to a great deal of confusion, as kids can’t keep track of what to do in which.
Many of the algorithms taught (lattice being a prime example) are not robust enough and do not scale to more difficult problems. Try doing a lattice multiplication problem with four or five digit numbers, or with decimals; it quickly devolves into a mess. Using the classic algorithm for such problems—or even harder ones—is straight-forward, and you don’t have to waste time drawing the lattice. In third grade, when a teacher demonstrated in a side-by-side comparison how quickly the lattice method worked, and when our boy came home crowing about how fast it was, I had to point out to him that the teacher had cheated—he already had the lattice drawn up. I then showed him a real side-by-side comparison, where each algorithm started with a blank page. Lattice clearly lost the race, because so much time was wasted drawing the frame. The Everyday Math Teacher’s Reference Manual actually states that the lattice method was originally added for its “recreational value and historical interest,” not mathematics value, and that, “It is not easy to understand exactly why lattice multiplication works.” (K-3 Edition, 2001, pg 107.) In other words, it’s something to play with, but is hard to understand and not worth spending the kind of time that our school spends on it—time which could be spent actually working to master a robust algorithm. Obviously, Singapore doesn’t teach this at all.

Auntie Ann said...

...continued
_____

Level 5 EM still does not emphasize the standard multiplication algorithm.
Instead, it rehashes partial-products (which does have a great deal of value when just beginning to teach multiplication…in third grade,) but it doesn’t scale well to large problems—they become unwieldy. A simple 3X3-digit multiplication problem leads to 9 lines which have to be added together—and for kids, this means keeping their columns very straight, which many have a hard time doing; while the standard algorithm gets it done in 3. In addition, the partial products method gets much more confusing when you start throwing in decimal points, and are multiplying hundredths by hundreds.
Level 5 EM also continues to emphasize the lattice method, which, as I said above, is mathematically confusing and of little mathematical value. If the idea of favoring partial products, as Everyday Math does, is so that kids are always remembering that the digits stand for hundreds and thousands, etc, then the lattice method throws all that out in favor of a party trick.
Fractions
Much of Fifth Grade is taken up by fractions, including multiplying and dividing them. Instead of teaching that division is the opposite of multiplication and introducing the (quite simple) idea of a reciprocal, Everyday Math skips teaching fraction division entirely and teaches kids to reach for a calculator instead. It is hard to understand why EM skips over this, as fraction multiplication and division is so much easier than fraction addition and subtraction.
Algebra requires students to be able to work fluidly with fractions, including fraction division. It is difficult to find the square of a polynomial which includes fractions, if the only way you know how to do fractions is to reach for a calculator. Math skills build on one another, and skipping this simple, yet crucial, bit of fraction arithmetic handicaps EM-taught kids as they advance. Singapore Math does cover fraction division and doesn’t (ever) emphasize reaching for a calculator.
Exponents
On page 14 of the Singapore Math Primary Mathematics 5A workbook, there are already problems with exponents. Our daughter didn't get taught anything with exponents until probably 6th grade. Again, this is a very easy thing to learn—especially squares and most cubes—yet it is missing from Everyday Math. Just as multiplication is introduced as repeated addition, so too can exponents be introduced quite early as repeated multiplication.

Auntie Ann said...

...continued
_____
Circles
Everyday Math, at least as our kids have both experienced it at school, never gets around to the properties of circles until very late. When our fourth grader talked with his table mates about "pi", he was derided and asked if there was also a number called "cookie." This was near the end of fourth grade, yet most of his class had never heard of pi.
Volumes
Being able to calculate the volume of a rectangular prism—not to mention cylinders and spheres—is actually a useful life skill, yet this, again, seems to be missing from our schools current EM-based math program.
Surface Area
Similarly, how to find the surface area of solids is not taught.
Ratios and Proportions
Our sixth grader finally got around to being taught ratios and proportions this year (though we'd already done it at home.) This is a challenging topic, but it is also traditionally arrived at long before the end of 6th grade.
Mental Math
The mental math aspects of Singapore are great. They allow students to adopt ways of thinking about problems which speed up their calculations, increases accuracy, allows for students to tackle more complex problems easily, and always emphasizes the meaning of the numbers. These are the sorts of things which a student will use all of their life.
Singapore Bar Method
It is truly amazing how powerful the Singapore Bar method is. Using it, you can have kids in early grades essentially doing complex algebra and ratio problems that they would otherwise have to wait years to get to. It is really an impressive system, and of great value. Obviously, Everyday Math doesn’t use this at all.
Changing
Schools that have adopted Singapore Math often see tremendous gains in achievement in the first year, and the fifth graders next year would benefit tremendously from it. But you won’t let them have it, despite knowing it is the better program. Sixth grade math this year was largely a review of elementary school math, with chapters dedicated to addition, subtraction, multiplication and division. Instead of learning new things, and moving into pre-algebra, the students were stuck trying to finally learn the things that six years of Everyday Math failed to teach them. Perhaps that is the greatest indictment of Everyday Math—six years of it is not enough to fully learn addition.
Chicago Math trajectory
The biggest problem with a weak math program at school, is that it is closing the doors for students who want to, or are able to, go on to STEM careers. By being too far behind in 7th or 9th, they get placed on a slower track, which makes it very difficult to get to Calculus in high school—which is very important if you want a career in science, math, or engineering.

Crimson Wife said...

I've switched around the order of chapters in Singapore PM when dealing with a student who still needs more practice in math facts. There are a lot of measurement topics in the lower levels of PM that are pretty much self-contained. A student who is still working on mastering the addition facts or the times tables can do these even if the book has them scheduled later on in the level. The alternative is having to come to a grinding halt, and that's not something I'm willing to do.

Catherine Johnson said...

For months now I've been meaning to post an interview with a neighboring school that is using Singapore Math. Every time a reporter talks to the school's math specialist, or whatever he is, the guy says that "right answers don't matter."

Needless to say, I have never seen the slightest indication in my set of Primary Mathematics textbooks that the right answer doesn't matter in Singapore.

otoh, that district **is** sending teachers to summar school with ..... oh gosh. I don't remember his name now. They do professional development with one of the mathematicians who's been teaching teachers how to teach Singapore Math.

Catherine Johnson said...

It is absolutely true that ANYTHING can be scr**** up. Anything.

If a school doesn't know why they're doing what they're doing, the new initiative they've rolled out will be more of the same.

Allison said...

Auntie Ann,

i'd be happy to talk more offline too. or start at the msmi further reading list:

msmi-mn.org/

You said
---We are now in the middle of an argument with the school, trying to press them into a full roll-out next fall. They've essentially taken the strange position: Singapore Math is better, but your kids can't have it!

Truthfully, I don't recommend people change into Primary Math after grade 3 without serious reservations, and clarity on how much remediation they will be doing. And I can't think of an instance where a 5th grader could more from EM to Primary Math 5A cold. there is simply too much not already understood. there is a coherent deep pedagogy to Primary math that you can't just parachute into.

---They have asked us for our reasoning for pushing Singapore over EM, and they want specifics.

I would start with the NMAP final report on why mastery matters. But it's not as simple as "they do fraction division." on a they don't do fraction division." Students need to be taught math coherently, and they need to see why the formulas are true. Primary math has been building up conceptual understanding with its bar models for years before you hit fractions again in 5A. Schools are ill equipped to back fill the topics students need because they have not thought seriously about what is predicated on what. e.g. will a student entering 5 A from Em have seen equivalent fractions? When? with what proof? Will teachers wrongly teach it when back filling?


---Does anyone know what points would be best to focus on? And has anyone out there already done this kind of point-by-point comparison?

this depends on your goal. Is it to adopt the textbooks or get your students prepared for adoption? Is it to get the school to take content math development for the teachers seriously? Is it just to supplement?

Allison said...

CW said:
-I've switched around the order of chapters in Singapore PM when dealing with a student who still needs more practice in math facts.

I'm not sure what "switched around" means here, but I strongly caution against teaching Primary Math out of order.

There isn;t a lot of talk on the web about how you should use the Singapore PM texts, but the first thing to understand is the textbook is not the curriculum. the textbook is basically the "pictorial" phase if a three fold curriculum built on a pedagogy of Concrete -> Pictorial -> abstract. very roughly, using the textbook as the main curriculum only is like using a 1/3 of the program.

If you aren't using the teachers guide or home instructors guides, then you aren't seeing the rest of the program. you;re supposed to be introducing topics with conversations, examples, manipulatives, games, etc. once a concept is mastered concretely, then you move on to the oictorial (textbook) phase, and so forth.

You should be using the measurement chapters because they absolutely reinforce the arithmetic, and the problems are chosen specifically to do so. it's important to teach about units and grouping like terms because it reinforces place value. having to use lbs and ozs reinforces place value too by seeing how to count in non base 10 systems. practicing these subjects also gives time ti the student to "cook until dine" in their own heads.

but more, if you've been playing the games and other activities in the guides, then you should still be playing them through these chapters--you aren't relying on the workbook to be sufficient practice since it was never meant to be that--it's meant to be formative assessment to indicate what comes next for a student, and where you need to reinforce.

Crimson Wife said...

Oh, I definitely use the Home Instructors' Guide as I would be totally lost trying to teach PM without it.

What I mean by switching around the order is that I've run into issues where I cannot do the next chapter scheduled in PM because the student is still working on getting the relevant math facts mastered (addition, multiplication). The next chapter scheduled assumes mastery of those facts so it's either halt entirely or find some other chapter in the book on which to work on an unrelated topic while continuing to work on mastering the facts.

A student who has not yet mastered the addition facts can still do the chapter on telling time on an analog clock, for example, because that's a self-contained topic. And frankly, I don't see any logical reason why these self-contained measurement topics need to be done in any particular sequence.

gasstationwithoutpumps said...

We didn't exactly home school Singapore Primary Math—we sent him to school with the textbooks and workbooks and he did them on his own.

We had excellent results using just the textbooks and workbooks, without the teacher's guides. (I found out later that he'd done most of the workbooks without reading the text, only going to the text when he was confused about what was expected in the workbook.) Now it is true that we had a lot of mathematical games and conversations, but they weren't tied to Singapore Math curriculum.

One of the things I liked about Singapore Primary Math was its insistence on kids knowing everything that had already been done, without the endless mindless drill of alternatives like the Saxon books. The problems gradually increased in complexity and abstractness, but even in the Primary Math 1 text required more mathematical thought than many American 4th grade math books.

I'm sure it is possible to spoil the Singapore curriculum, but I'm not convinced that every home schooler needs to invest in the Home Instructor's Guide.

Chris said...

Doesn't this raise the possibility that the failures of math education aren't attributable to constructivism, but to something else inherent in the way schools function? In other words, it's easy to argue that Singapore Math in the ideal is better than constructivist math in practice, but isn't that comparing apples and oranges? So when constructivism flops, it's because it's constructivist, but when a more traditional curriculum flops, it's because they're just not doing it right?

I don't mean to make a pro-constructivist argument here. (I don't have a strong feeling one way or the other on constructivism.) But I do think it's important to consider the possibility that there are limits to what a huge bureaucratic enterprise can achieve in terms of making people learn things that they may have no interest in learning.

If Singapore Math ever becomes the dominant fashion, won't the constructivists point to the very things you're describing in this post to argue that constructivism (in the ideal) would be better?

Anonymous said...

Chris --

You make an excellent point. There is a difference between a program on paper and a program in practice. I do think there are some teachers who *can* teach so there is great learning while using more constructivist practices and vice versa. In some ways there needs to be a good match of teacher, material and style.

At the elementary level the biggest problem, I think, is that many teachers are "afraid" of math and thus cling to the one thing that makes sense to them, even if it isn't the best way to teach.

I also have to say that my two oldest kids went through an EM system and did exceptionally well -- it really did work for them the way it was supposed to, they GOT why they were doing what they were doing, they understood concepts years younger than I remember "getting it."

But as a tutor and a teacher, I also saw pretty dramatically that it did NOT work for more of the kids than it did work for. And of course, I was at home, making sure that they had fast basic facts when I thought they should have them, which was well ahead of when the school did.

SteveH said...

"...the failures of math education aren't attributable to constructivism, but to something else inherent in the way schools function?"

"Failures" (plural) come from more than one source. KTM has had (moreso in the past) discussions about how some constructivism can be good and how some can be bad.

I've talked many times about what I call "brain research misdirection". If you can keep the discussion focused on thinks like how the brain works or the details of learning styles, you can avoid discussing basic competence issues like why bright 5th graders still struggle with the times table.


"But I do think it's important to consider the possibility that there are limits to what a huge bureaucratic enterprise can achieve in terms of making people learn things that they may have no interest in learning."

As Sheldon Cooper (from the Big Bang Theory) would say, "Do you want to just talk about that or do you want to do the math?" What is a graph of learning versus bureaucratic size? What learning are we talking about; shoelace tying? Adds and subtracts to 20? Fractions? What are the assumptions? Do you keep chair throwers in with the most able and willing kids? If you have two exactly the same classrooms and kids, but one is backed by a large bureaucracy and one is backed by a small one, what causes the difference?

The selection of Singapore Math could signal a change in educational thought or it could be a form of guess and check. As Allison would quickly point out (and what she is actively trying to solve), what K-6 educators need is a better understanding of math. Without that, almost any change is futile.

I couldn't talk to my son's K-6 teachers about math. They couldn't understand the linkage between mastery of skills and understanding. They have a very simplistic view about what math is.

So what will cause K-6 teachers to learn more about math? What are the driving factors? High school math requirements drove out CMP from our middle school, but the pressure stopped when it hit Everyday Math. Our state now requires subject certification for 7th and 8th grades, but I don't see that ever happening in K-6. Unfortunately, much of the damage in math is done in K-6.

For many of us at KTM, we know what the solution is. We are not fussing over direct instruction versus constructivism. It's not our fault that K-6 educators can't tell what will work and what can't. I don't expect our arguments will solve their ignorance of math.

Maybe, at best, we can get K-6 schools to hire teachers who know more math than ed school pedagogy. I'm not holding my breath, and CCSS will only institutionalize a math learning slope that's too low in K-6. I also have the worry that CCSS may reverse some gains in 7th and 8th grades.

SteveH said...

"I also have to say that my two oldest kids went through an EM system and did exceptionally well -- it really did work for them the way it was supposed to, they GOT why they were doing what they were doing, they understood concepts years younger than I remember "getting it.""

EM only works if you are bright enough (or with help at home) to learn the material the first time through the spiral. This is NOT how EM is "supposed to" work. It assumes that repeated partial learning will get the job done. It's designed for a full inclusion environment where the teacher can just keep moving and "trust the spiral". While the spiral might provide good review for those who already learned the material the first time through the loop, for those who didn't quite get it the first time, repeating the same material won't help.

Everyday Math is fundamentally flawed. It's not just a matter of learning how it's supposed to work.

Amy P said...

"EM only works if you are bright enough (or with help at home) to learn the material the first time through the spiral."

And if you learn it the first time through the spiral, won't subsequent trips round the spiral be a real drag?

Some years ago (around the time I first discovered KTM), I was considering moving us to Arlington VA and putting the kids in an Arlington parochial school. Fortunately, however, they had their math standards up on the web, and I was able to read the warning signs--namely, literally dozens of math topics every year in the elementary grades.

I showed the curriculum to my husband, who has a doctorate in probability. He thought that the math topics looked very interesting. Then I explained to him that they do basically the same topics every single year (just adding more topics each time round). He wasn't interested after that.

That's what K-6 looked like. Grades 7 and 8 were totally traditional pre-algebra, which must have been pretty jarring for the kids. There was obviously a Knievel (sp?) style math jump between grade 6 and grade 7, and I wonder how many kids didn't make it.

Barry Garelick said...

Life on the Hill. When I was researching math education issues in a Senator's office years ago, I was telling a fellow staffer pretty much what SteveH said. "EM works if you're bright enough." As often happens on the Hill, she immediately connected the dots (incorrectly) and started lecturing me: "Oh, and so you think the solution is to dumb it down so that kids don't learn anything?" and on and on. Hard to get things done when everyone has all the wrong answers.

Anonymous said...

Aunt Ann, you seem to indicate that Singapore math introduces students to pi and the area of circles in 4th grade. When I checked out the sequence, it seemed to indicate that Singapore math introduces pi in 6th grade. Can someone who uses Singapore math clear this up for me?

Michael Paul Goldenberg said...

So if bad schools and/or bad teachers ruin Singapore Math, does that leave open the possibility that the progressive curricula decried by educational conservatives over the last two decades might not always have been well-taught or well-implemented, and that hence some of the vehement attacks on them might have been ill-considered and/or unfair? Or would it be fair to apply the same tactics and criteria to Singapore Math?

AmyP said...

"So if bad schools and/or bad teachers ruin Singapore Math, does that leave open the possibility that the progressive curricula decried by educational conservatives over the last two decades might not always have been well-taught or well-implemented, and that hence some of the vehement attacks on them might have been ill-considered and/or unfair?"

A strong teacher will be even stronger with a strong textbook, while a weak teacher will be even weaker with a weak textbook. You get results somewhere in between with a weak teacher/strong textbook and a strong teacher/weak textbook.

A lot of weaker teachers are going to have educational hubris with regard to their ability to manage without a strong textbook (or without a textbook at all), or their ability to take a strong textbook and "improve" it. Been there, done that. I haven't ever done that myself in math, but looking back, that was so true of me as a beginning EFL teacher (and indeed, true of nearly all the other Peace Corps people I trained with). Looking back, I desperately needed a good textbook to lean on.

AmyP said...

We were previously discussing the difference between Primary Mathematics (Classic Coke Singapore) and Focus on Math (New Coke American Singapore). Our school switched over this past year from the old to the new, and there was no comparison. Gone was the clarity of the original Singapore. Instead, my 1st grader (a very mathy child) was sniffling in despair over stupidly overcomplicated, poorly explained homework assignments. The 1st grade teachers eventually got a handle on the new textbook and were able to supplement to the point that the nightly weeping stopped, but it was a bad time. I think everybody was caught by surprise--nobody at school realized how different the two textbooks (which were purportedly very similar) really were, until it was too late.

Amy P said...

Interestingly, when we had the switch between Singapore Singapore and American Singapore last year, there were no issues at all with my 4th grader. She was fine. Here are a couple of possible explanations:

1) Maybe the new 4th grade book was better than the new 1st grade book? (I don't know--I never had to look at the 4th grade book, things were going so well.)

2) The 1st grade teacher was new to the school, hence we had a weak teacher/weak textbook situation.

3) The 4th grade class has a math specialist. So, it wasn't a spread-thin elementary teacher trying to teach a dozen subjects--the math specialist was able to familiarize herself with the new textbooks and make things run smoothly.

Cassandra Turner said...

Singapore math introduces pi in 6th grade.

That is correct. Scope and Sequence

4A introduces identifying radius and diameter.

Allison said...

--So if bad schools and/or bad teachers ruin Singapore Math, does that leave open the possibility that the progressive curricula decried by educational conservatives over the last two decades might not always have been well-taught or well-implemented, and that hence some of the vehement attacks on them might have been ill-considered and/or unfair? Or would it be fair to apply the same tactics and criteria to Singapore Math?

wow, an army of straw men!

short answer: teaching average kids Primary Math correctly leads to success in algebra. can anyone say the same for the average kid in everyday math or terc?

longer answer:
The vast vast majority of American mathematics k-8 textbooks program are bad.

They are bad when they are constructivist and bad when they are conventional. They are bad because they are mathematically incoherent, mathematically incorrect, and have stupidly low difficulty level.

Bad textbooks are not the only thing wrong with math education in k-8. the mathematical content knowledge of teachers is so poor that they cannot see the errors in their textbooks, cannot explain why the algorithms they teach work, cannot string together any clue of what mathematically depends on what.

but that's not all! then there are schools so poor that *just having teachers follow the bad text with fidelity* improves their scores--so they are so far down that they haven't noticed they can't reach the sky by climbing a tree.

yes, there are individual exceptions in teachers, schools, admins, districts. parents who have found such are deeply grateful.


none of that absolves the proponents of TERC or Everyday Math of their gross errors.

you cannot construct through discovery 6000 years of math in 12. you cannot make children into experts by having them mimic experts. and related: materials that lead an adult teacher to say Aha! do not necessarily lead their students to. you cannot prepare students for abstraction by analogy. you cannot mistake pedgagogy for content knowledge. you cannot prepare students for problem solving if they cannot recall on demand number facts.

you cannot build up difficulty by spinning around on the same material year in and year out. you cannot teach that math is coherent if you change the subject every 3 days.

these problems are fundamental to the texts. the other teacher knowledge and admin problems are systemic, yes, but the issues can be separated.

SteveH said...

"wow, an army of straw men!"

MPG is just a troll. That's the best he can do.

SteveH said...

"There was obviously a Knievel (sp?) style math jump between grade 6 and grade 7, and I wonder how many kids didn't make it."

Lot's of kids don't make that nonlinear jump. Many don't even get the chance and are placed into the lower math track to nowhere. STEM career over! Worse yet, the kids will think they are not "math brains" or are just not good in math.

You can open up EM anywhere and see math that doesn't look too bad. However, you have to look at how the material jumps around and how it sets low expectations. It uses "Math Boxes" to help the students go over old material, but the onus is on them. Teachers can't possibly guide the learning process of a classroom of kids that are at different levels of the spiral. That's why they say "trust the spiral" to the teachers.

It doesn't work.

It only works if parents don't trust the spiral at home, and enough do so to hide the fundamental flaw of Everyday Math.

Crimson Wife said...

the mathematical content knowledge of teachers is so poor that they cannot see the errors in their textbooks, cannot explain why the algorithms they teach work, cannot string together any clue of what mathematically depends on what.

Bingo. The understanding of mathematical concepts of most Americans (including most teachers) is very, very shaky. I got A's up through calculus and >700 (pre-recentering) on my SAT-M and GRE-Q because I have a good memory. I didn't have a clue why the algorithms worked until I started homeschooling my kids using programs based on the Asian way of teaching (Right Start, Singapore, Math Mammoth).

Where I struggle with teaching Singapore is that the program assumes its teachers have a good conceptual understanding and it sometimes skips from point A to point D without first taking the student through the intermediate points B & C. The Home Instructor's Guide offers some guidance, but with certain topic I've had to put Singapore aside for a bit and use Math Mammoth. MM is also based on the Asian way of teaching math but is more incremental in its approach.

Anonymous said...

Obviously, it's not done on any large scale or most ES teachers would be better at math, but do ANY el ed programs require coursework to improve prospective teachers math mastery? Or demand passage of appropriate testing?

Crimson Wife said...

Testing wouldn't guarantee that the prospective teachers actually understand the underlying concepts. I could calculate the correct answer quickly, but it was all rote plug-n-chug. I would not have been able to explain why the algorithms worked because I had just memorized them procedurally.

A few ed schools are now offering Singapore Math training using the Parker & Baldridge book Elementary Mathematics for Teachers, but I'm, not aware of any that make it a requirement.

Cassandra Turner said...

If you haven't yet, I highly recommend this report to read from the NCTQ:
No common denominator: The preparation of elementary teachers in mathematics by America's education schools


I seem to recall it had a link to a sample test on what teachers need to know to teach vs. what students need to know that was highly enlightening.

Barry Garelick said...
This comment has been removed by the author.
Anonymous said...

Thank You, Thank You, Thank You! I love this post! When will someone wake up and smell the coffee? Maybe when there is no money to be made selling a new math program. Ugh. I was highly successful at teaching EM (And, I mean highly successful) but I had absolutely no problem placing my child into a private school that used Singapore Math. Boy, was Singapore Math ruined! Lesson learned: It is NOT about any one math program--it is about the teaching quality behind a program. Do not be fooled by the name on the math book! Jesh, I rather my child use some math book written in the 1920s and have a competent teacher at the front of the class than what he went through in a Singapore Math classroom! If I did not have the background I have, he would have gotten math anxiety from his Singapore Math experience!

SteveH said...

You won't find EM fans here. It's one of the reasons why KTM exists.

"If I did not have the background I have, he would have gotten math anxiety from his Singapore Math experience!"

I've seen it work more the other way. EM ruined the kids at my son's school. His fifth grade teacher had to NOT trust the spiral because bright kids didn't know the times table. My son was saved by my use of Singapore Math at home.

I tried to get that school to use Singapore Math, but they dismissed it because it wasn't right for "their mix of kids". Then again, they would probably still have kids get to fifth grade not knowing the times table with Singapore Math. A big issue in K-6 math is whether a school accepts the responsibility for ensuring all of the necessary basic skills on a grade-by-grade, no matter what the curriculum.

As a curriculum, Singapore Math is more rigorous and complete than EM, which is fundamentally flawed because they tell teachers to "trust the spiral". It gives them permission to pump kids along until there is little that can be done to fix the problems.

james abram said...

Singapore math tutorials should be taught differently than our regular mathematics. Changing the way of teaching it means lesser information absorbed by the students.