October 18, 2006

Everyday Math on Long Division

The authors of Everyday Math do not believe it is worth the time and effort to develop highly efficient paper-and-pencil algorithms for all possible whole number, fractions and decimal division problems.…It is simply counterproductive to invest hours of precious class time on such algorithms. The math payoff is not worth the cost, particularly because quotients can be found quickly and accurately with a calculator.
-- from the Everyday Math Teacher's Guide

This quote is from Barry Garelick's article A textbook Case of Textbook Adoption in which he describes the games played by the publishers of Everyday Math and used by the Washington DC school board (and many other school boards) to justify the adoption of this controversial elementary math program.

In case you forgot. Out of the 61 studies touted by the proponents of Everyday Math, none fully met the What Works Clearinghouse's criteria. Four studies met with reservervation, and 57 did not meet at all. Out of the four studies that met with reervations, three had statistically insignificant results and the fourth was conducted by a researcher affiliated with Everyday Math and has refused to release his data.

My school district adopted Everyday Math just this year. There was no protest by parents or a fight of any kind. They're all sheeple. Needless to say, I'm teaching my son math at home.


Anonymous said...

It's interesting to note the comments in the following paper:


See the paper called

Algorithms and Everyday Mathematics
by Andrew C. Isaacs

"Reducing the emphasis on complicated paper-and-pencil computations does not mean that paper and-pencil arithmetic should be eliminated from the school curriculum. Paper-and-pencil skills
are practical in certain situations, are not necessarily hard to acquire, and are widely expected as an outcome of elementary education. If taught properly, with understanding but without demands for “mastery” by all students by some fixed time, paper-and-pencil algorithms can reinforce students’ understanding of our number system and of the operations themselves."

" ... not necessarily hard to acquire ..."

" ... but without demands for “mastery” by all students by some fixed time ..."

Not hard to acquire? Mastery only for some students? No fixed time? EM is designed as a spiraling (circling) curriculum with no fixed grade-level expectations. It seems to me that this is the main driving force behind EM. This is pure rationalization just to meet the needs of full inclusion, not math education. This author also has admitted that EM is not for the "elite". I wonder how he defines that? They saw a market: progressive education, and they filled the need with all of the proper happy talk and appropriate "research".

"Exploring algorithms can also build estimation and mental arithmetic skills and help students see mathematics as a meaningful and creative subject."

But not one that requires a lot of hard work and mastery of skills. As for estimation and mental arithmetic skills, what's better than long division.

Divide 9427 by 231. Which requires more estimation and mental arithmetic skills, forgiving division (as taught in EM), or the traditional approach?

It doesn't matter because the key problem for them is mastery - drill and kill. They don't even require mastery of forgiving division.

They don't require mastery of ANYTHING.

Read the whole paper. It's obviously and after-the-fact rationalization for something they wanted to do in the first place.

KDeRosa said...

I like the way they mis-cite the research on distributed learning to justify their steep spiral.

Anonymous said...

"They're all sheeple."

I've been struggling with this for a long time. My conclusion is that since there is no school choice, parents spend little time thinking about what kind of education they want for their kids. They just react to what comes home in the backpack. Many parents know things are not right, but there is no choice and they have a hard time countering the Ed School party line. However, many that I talk to see that the big problem is low expectations and fuzzy ideas of education.

I know a lot about math and have a clear idea of proper grade-level expectations. (This doesn't help much because they don't have to do a darn thing.) However, this is not true in English. I can't evaluate my son's vocabulary and spelling books. I have a parent-teacher conference tomorrow with his English teacher and I don't know how to discuss/evaluate learning how to write.

And, I don't know what goes on in class. How does the happy talk translate to what happens in class?

I will get a lot of Ed School happy talk, and like math, it won't matter. This conditions parents to either not bother, or, if they have enough money, go to another school. As a (now) private school parent, my conclusion is that private schools are never worth the price, but, then again, public schools can extract a high negative price for a variety of reasons. We couldn't imagine having our son do little during the day at public school and then come home to our teaching and work - on top of his other school work. We are paying for differential education. If we had more than one child, this argument would be moot.

It's hard to fight a well-oiled pedagogical, political, and union machine. They also do a great job of focusing the attention on "us" versus "them". Notice the "Save Our Schools" bumper stickers. What is that supposed to mean? Money.

The focus is on those who are fighting for better schools (teachers aligned with parents) and those in town who just want their taxes to go down. "Better schools" means whatever the teachers and schools want - usually more money, smaller class size, and more sports. Lost in this argument is the third leg of the triangle - those parents who want a better education and higher expectations for their kids. Many send their kids to private schools, are ignored, or labeled as elitist. Twenty to twenty-five percent of the kids in our town go to other schools. They leave and wash their hands of the problems. Few are left to fight the machine.

Also, in our town, there is the tension created by full inclusion. Parents feel that their more able kids are used as window dressing for the lower ability kids. This is a very touchy subject. So, the result is "differentiated instruction", which is fundamentally flawed (and many teachers know it). They lower grade-level expectations, spiral the curriculum, and mix the best kids in with the borderline autistic kids. One nice happy family. Right? Just try and discuss acceleration of material or tracking by ability - even in 8th grade!

In some sense, forget constructivism. In our town, it's about full inclusion. It's about developmentally appropriate. It's about conceptual understanding. It's about absolutely no tracking. There have been complaints about the difficult transition for many kids between the fuzzy ed world of lower grades and the tracking, higher expectation high school. "Our kids hold their own." "Their are issues, but we are working on them."

This system creates "sheeple". The only solution is school choice.

Brett Pawlowski said...

I can empathize with the frustration expressed by steveh in his second post, and I expect that millions of other parents share his feelings. There are entire books written about this issue (one great one is "Is there a public for public education" by Dave Mathews of the Kettering Foundation), so I won't dive into reasons or implications.

What I will say is that, while I agree with pushing for school choice, it's going to take years if not decades for choice to be widely implemented in any meaningful way, far too late for our own kids to benefit. The only alternative left to us is to become educated on education and to be really noisy about what we find - at PTA/PTO meetings, school board meetings, with the press, with community groups, and so on.

One resource I'd recommend for good information is the Education Consumers Foundation - http://www.education-consumers.com. Good information on lots of different education issues, and a growing focus on original research. (The director, John Stone, was the first one to demonstrate that the NBPTS emperor had no clothes.)


Anonymous said...

" ...far too late for our own kids to benefit."

Of course, but I don't do this for my son. I do this for other kids. If I only cared about my son, I would just smile with the satisfaction that it will be easy for me to help him get to the top of the heap. And, I would save myself all of this time on the computer.

" ... and to be really noisy about what we find - at PTA/PTO meetings, school board meetings, with the press, with community groups, and so on."

It doesn't help when you are dealing with fundamental assumptions about education. I have been on a number of our school parent-teacher committees. Nobody wants to address these assumptions, let alone curriculum. The superintendent said I could be on their Citizen's Curriculum Committee that was being reestablished. The committee was never formed and they decided to continue to use MathLand, a program so bad that it was dropped even by the publisher - not a clue left on their web site. There is no process. There is no leverage. There is no choice. Some will say that parents have to be part of the solution; not part of the problem. What they mean is that we parents have to be part of THEIR solution.

There is also the very touchy subject of full inclusion and differentiated instruction. This makes it even more difficult to complain about low expectations and poor curricula. If I were to write a letter to the editor about low expectations, bad curricula, and no opportunities for more able students, I would be (quietly) hailed by part of the population and loudly trashed by the other. What would be my goal? To get the school to do something they will not do? There is a reason people quietly take their kids and put them in other schools.

"One resource I'd recommend for good information is the Education Consumers Foundation - ..."

I don't need more resources. The assumption is that one can work witin the system to get it to work. The assumption is that modern educational pedagogues will be swayed by research. The assumption is that you can force schools to do what they really don't want to do. NCLB is even a poor tool for doing this. As in our state and schools, they define very low proficiency levels and they shift resources away from the better kids.

Choice guarantees nothing. Even private schools are awash with fuzzy educational ideas. However, it is a process where parents have real (more?) power. And, choice (charters & full vouchers) can have an immediate benefit for many urban students and parents right now who are doomed to educational incompetence.

Anonymous said...

I'd like to respond to Steve H's suggestion that Everyday Math's spiraling approach is meant to facilitate inclusion for lower end and special needs kids.

I don't know the rationale for the EM curriculum, but I do know that kids who have learning difficulties in math are the ones who suffer most under Everyday Math. They are the ones who need to be taught to mastery. A kid who catches on quickly may be able to manage the "spiral," but the slower ones get lost in the dust and require expensive tutoring, if their parents can afford it.

One of the reasons school districts like spiraling is that there is a lot of student mobility in this country. Since we don't have a national curriculum, schools need to ensure that new kids learn material already covered. They think spiraling addresses this issue. I think spiraling is awful and schools should teach to mastery and have remedial strategies for kids who aren't up to speed.

Anonymous said...

The "sheeple" got very upset in my District when EM was proposed. Despite the highest turnout in the history of the Bd of Ed, most in vocal opposition, the Bd approved the program anyway. Most Bds seem to be full of people that are intimadated by educrats. A lot of deference is shown to those with a Ph.D.

"One of the reasons school districts like spiraling is that there is a lot of student mobility in this country."

I don't think so. They like the spiral because it gets them off the hook for accountability. For Any Kid. With no reasonable benchmarks for learning, schools can tell parents not to worry that their kid can't add fractions -- it spirals, they'll cover it several times this year. They don't mention that there is no time in the spiral where competency with fractions is expected or tested.

Anonymous said...

"I do know that kids who have learning difficulties in math are the ones who suffer most under Everyday Math. "

I agree 100 percent. It's a bad math curriculum and it doesn't do what they want it to do. I call their spiraling technique "repeated partial mastery" (or, rather, no mastery, just repeated introduction). It's kind of like what you have to do at the beginning of each school year to get kids up to speed, except that you do this over and over and over, even though some kids have mastered the material and need to move on.

We have a stable population, but spiraling allows our school to pass kids along to the next grade without knowing the material. It seems that if kids have trouble learning the material, it's not because of the material and how it's taught (or not), it has to do with the developmentally appropriate level of the student. With this definition, they can't ever tell if they are doing a good job.

Anonymous said...

"With no reasonable benchmarks for learning, schools can tell parents not to worry that their kid can't add fractions -- it spirals, they'll cover it several times this year. They don't mention that there is no time in the spiral where competency with fractions is expected or tested."

Our schools uses something called ITRE. For each topic and grade level (I can't believe they went to all of this trouble), they define the year(s!) it is introduced (I), the year it's taught (T), the year(s) it is refreshed (R), and the year by which it is expected (E) to be mastered. I've seen this document. I have also seen on their web site last year a comment about how parents have to help their kids because they are expected to master their adds and subtracts to 20 by December. This is third grade!

This may work for really basic skills, but, as anon says, this is unlikely to happen for something like fractions. There is no final mastery test in the "E" year. Too many kids fall through the cracks. What is does allow is a much greater spread of student capabilities. This makes it much more difficult to teach the kids without acceleration of the material or ability tracking. It's really about lower expectations and accountability.

MassParent said...

Brett, school choice is available in some places, like my kid's local school. We've been a popular destination for parents from other rural towns nearby; and we've had incredible parent involvement.

However, this year, we were forced to adopt new math curriculum selected by our regional superintendent, because of a scathing report by the state to fulfill NCLB curriculum mandate. The extent of state involvement was to rate our district of several towns poor on alignment. At the district central office, that just meant forcing us to order new textbooks and put them into use this fall with no training. Many parents and teachers objected. Our best math teacher left the school to consult on math curriculum for a top ten district in the state.

Our math scores came in with a third year of significant improvement in a row this fall, because our school did have its act together. NCLB forced us to drop our successful program.

Our kindergarden enrollment this year is the lowest in 100 years - down by half from last year. Single classroom of less than 15 kids.

NCLB has reduced choice, and has taken away local control, in our town.

Anonymous said...

Not all communities are "sheeple". There are communities in which informed parents have protested against adoption of Everyday Mathematics. In the case of DC, the hearing was held on very short notice, and the textbook adopted SO quickly and quietly that even teachers were surprised when they found out in the fall that they were to be using Everyday Mathematics. It was the first many had heard of it. The point of my article was to show how school boards operate. Even in cases where there are no "sheeple", the school board does whatever it damn well pleases. The DCPS school board is typical of many.

And speaking of Andy Isaacs, who Steve H mentioned, I had an email exchange with him sometime back over the following statement which appears in the Teachers Reference Manual for EM: “In one study, only 60 percent of U.S. ten-year-olds achieved mastery of the algorithm using the standard regrouping
(borrowing) algorithm. A Japanese study found that only 56 percent of 3rd graders and 74 percent of 5th graders achieved mastery of this algorithm.”

I asked him what studies these were. He talked to his colleague Jim Flanders and between the two of them, they didn't know, the reference to it had been lost, apparently it was in a compilation of studies that a grad student was doing for them, and Andy, in an aside to Jim Flanders (I was cc'd) said that perhaps they should remove that statement from future editions of the reference manual because it wouldn't be good to rely on vaporous references.

If you go through the list of research materials for EM, which is on EM's website, you'll find a lot of studies by William Carroll who it turns out works for EM. Not that there's anything wrong with that...

Anonymous said...

" ... because of a scathing report by the state to fulfill NCLB curriculum mandate."

Show me the document that describes NCLB (content?) curriculum mandate.

It's up to the states to define the test. I agree that it seems like a fait accompli when the state defines a test that expects kids to know topics only taught in bad math curricula. This is happening in our state. Schools (although most like these curricula) say they can't use a curriculum like Saxon or Singapore because they are not aligned with the state test. This is just an excuse, and don't blame it on NCLB. Testing is not the problem. The people in your state who selected the test are the problem. This has nothing to do with any sort of "ruse" or "dismantling" theory you might have. The only state-level fights I have seen have been between those who like fuzzy math and those who don't. It's a fight over pedagogy and control of curriculum, not politics.

Which math curriculum was taken away and which one were you forced to use?

Then again, there has to be more to it then that. A town can always supplement their superior math program with the trivial material needed to meet any sort of minimal state test. Good schools should just laugh at these tests.

" ...school choice is available in some places, like my kid's local school."

Can you explain the school choice law for Massachusetts?

The Opinionated Homeschooler said...

A question to the experts here, on "spiraling": As homeschooling parents making it up as we go along, with a math-loving kid, we've developed by trial & error a 3-tier system for math, which sounds very much like "spiraling."

1. Leading edge: Learning advanced math concepts that Offspring is just able to grasp; this is the math she loves & keeps her on fire. (aka "math with Daddy")

2. Mastery: Eventually Offspring has to learn the math well enough to perform reliably, with only occasional (usually careless arithmetical) errors. By this time "leading edge" is on to something else. (aka "math with Mommy")

3. Review: Once-a-week "remember this?" math review. (aka "I hate review")

This system has worked very, very well for us, and Offspring is several grade levels ahead in math, by far her favorite subject. Isn't this the Spiraling described in posts above? Is there some crucial difference I'm missing?

Anonymous said...

Yes, you are missing something. With the Everyday Math spiral, schools don't teach to mastery. They expose the kids to a concept, spend a couple of days on it, and move on. Then they use distributed practice to review the concept.

For kids who have trouble with math, and need practice and drill to master a concept, this is a disaster. They don't get it the first time, and they're frustrated and confused when they see it again.


KDeRosa said...

Hi Opinionated Homeschooler.

You are doing "spiralling" the right way.

What you are doing is known as a stranded approach. New information is first taught via massed practice, Once the student understands the concept, the information is "downgraded" to distributed practiced where the skill is firmed with the solving of increasingly difficult problems. Once the skill is mastered, it is them "kept alive" either through periodic review and/or subsuming the skill into more difficult skills (e.g., single digit addition skills get subsumed into multi-digit addition skills).

I'm using Connecting Math Concepts with my son and it typically has ten strands or so going on at the same time. A few strands are new; most are review. The program offers a lot of practice. I routinely skip about every other lesson just because he doesn't need as much practice to master the material. He routinelt gets all the questions right on the cumulative tests. But, the program has been extensively field tested with lower performers and it goes to show you that average and below average students need a tremendous amount of practice to master math. Much more than you'd think. About 4 to 5 times the amount provided in the typical math program.

KDeRosa said...

I'd be hesitant to call what EM does "distributed practice."

Distributed practice does not mean putting non-mastered material on the shelf for 60 lessons or so to wither and then coming back and then reteaching the skill again, usually in a different way.

Wash, rinse repeat.

The human mind does not retain information this way. Those who benefit by such instructional lunacy are the high performing kids who do grasp the concept when taught the first time and need little practice to get it into LTM. These kids were the ones who learned math under the traditional curriculum in any event, EM has neither increased their performance nor reached kids who didn't used to learn under the traditional curriculum.

Anonymous said...

"Wash, rinse repeat."

Repeated partial learning.

Some kids will master the material with little practice, while others need longer duration, concentrated practice, not the same short amount every 60 lessons or so.

Robyn is right. There is no requirement for mastery. Mastery is not in their vocabulary. From the paper I cited above, here is their philosophy:

" ... but without demands for “mastery” by all students by some fixed time ..."

EM: math without mastery.

Many schools know that this is a crock. They supplement EM with extra practice. But what happens when they spiral back to the same material after 60 lessons or so? If they helped all of the kids master the material the first time around, what do they do now? Skip the material?

Each loop of the spiral is not based on previously mastered skills. Each loop of the spiral (circle) reintroduces and reteaches the material.

Supplementing EM with mastery will not work because EM uses the spiral to avoid the need to practice to mastery. They assume that if you see the material enough times, mastery will just happen.

By 6th and 7th grades, this lack of mastery really begins to have an effect on the pace and depth of material covered. Set EM side-by-side with Singapore Math or Saxon Math books and the difference is obvious. This difference has nothing to do with conceptual understanding versus rote learning.

Anonymous said...

"Supplementing EM with mastery will not work because EM uses the spiral to avoid the need to practice to mastery."

Well, I'll answer my own comment here after coming back from a parent-teacher conference with my son's EM math teacher (new to the curriculum this year). EM supplementation apparently happens way after the fact - more like remediation. His fifth grade teacher is astounded by how many kids still count on their fingers and can't quickly figure out something like 15 - 7. There is no mechanism in EM for ensuring mastery. They spiral along and just hope that it happens. She can't teach what is even in the EM workbooks because kids do not have basic mastery skills.

I let her borrow my 5th grade Singapore Math books. She was very interested.

The Opinionated Homeschooler said...

Thanks, anonymous and kderosa for the clarification on "spiraling."

What had struck me about its description was the introduction of a concept without necessarily requiring mastery the first time around, and its similarity to the approach we use at home of introducing advanced concepts early without requiring mastery just then. Hsing math curricula we've looked at (Saxon, Singapore) seem to require mastery on first introduction, so I'd thought this "spiraling" approach might be more like the method we've used successfully. But the difference seems to be *never* requiring mastery. Which is clearly insane.

I thought public schools were upset because they had to "teach to the test"? Doesn't sound like this curriculum is teaching to anything.

Anonymous said...

From the article that was referenced somewhere in the beginning of the orginal post there is this comment from the so-called Georgetown Professor (Tom Bullock) who said Asian nations use spiraling: "There is spiral teaching as it is done in Singapore, and there is the spiral method as done by EM. The two are very different. Singapore revisits older material that has been mastered and builds upon it. EM’s “learn it later” spiraling is not used in the highest performing nations. Also, not addressed in [Bullock's] statement is the fact that if EM omits valuable material, no amount of spiraling will bring it in."

Anonymous said...

My bad. I didn't mean to say Bullock said all that. I meant to say he claimed EM's spiraling was the same as that used in Asian nations. The quote is from the article, not Bullock.


CrypticLife said...

I think my son's school uses a different text, but I'm not sure which -- what he brings home are pull-out pages (which are stamped with "Pearson Education, Inc." He goes to school in NJ. The school has not focused on using calculators yet (he's in first grade), but I'm afraid they will. He's invested considerable effort to learn the multiplication tables, and I'd hardly want it to go unrecognized (the teacher was rather dismissive when he showed knowledge of negative numbers).

Any comments on what the text might be, how good it is, and what I can do to help my son's education go smoothly?