The article explains how Maryland's Montgomery County Public Schools (MCPS) system instituted a pilot program to test out the effectiveness of Singapore Math (SM), the curriculum responsible for catapulting the island of Singapore to top dog in 4th and 8th grade math achievement. The diferences between SM and your typical US math curriculum are profound.

Unlike many American math textbooks, such as Math Thematics, published by Houghton Mifflin, which are thick, multicolored, and multicultural, Singapore’s books are thin and contain only mathematics. There are no graphics (other than occasional cartoons pertaining to the lesson at hand), no spreadsheet problems, and no problems asking students to use a calculator to find the mean number of dogs in a U.S. household. With SM, students are required to show their mathematical work, not explain in essays how they did the problems or how they felt about them. While a single lesson in a U.S. textbook might span two pages and take one class period to go through, a lesson in a Singapore textbook might use five to ten pages and take several days to complete. The Singapore texts contain no narrative explanation of how a procedure or concept works; instead, there are problems and questions accompanied by pictures that provide hints about what is going on. According to the AIR report, the Singapore program “provides rich problem sets that give students many and varied opportunities to apply the concepts they have learned.”If you want to get a hands-on idea of how advanced SM is, I'd suggest comparing what your elementary school child is doing in math to what the students in Singapore are doing, as set forth in SM's placement tests. I'll wait until you're done crying to continue.

The AIR study frequently criticizes American math texts for being an inch deep and a mile wide, covering a great range of topics with little time spent on developing the material, including mastery of math facts. (One of the texts with which the AIR study compares Singapore’s Primary Mathematics series is Everyday Mathematics, a program developed with NSF funding and used widely in Montgomery County.)You remember Everyday Math (EM) don't you? I've written about EM recently. It is the fashionable "problem solving" curriculum that is the NCTM darling. It is THE constructivist math curriculum. Unfortunately, it also sucks. It has been the subject of much education research; none of it able to show that EM is effective (unless you include the researchers with a stake in EM), according to the WWC. Yet, it remains in widespread use.

Singapore’s texts also present material in a logical sequence throughout the grades and expect mastery of the material before they move to the next level. In contrast, mainstream American math texts and curricula frequently rely on a “spiral” approach, in which topics are revisited and reviewed. The expectation of that approach is that not all students achieve mastery the first time around. One Ohio school teacher familiar with the spiral approach summed up much of the criticism of the method on an Internet math forum, saying, students “can’t remember how to do it when [they] do return—or if they do remember it, it’s now being taught in a different way.”The spiral curriculum is not your friend when it comes to mastering math. Here is Zig Engelmann on the deficiencies of the spiral:

Teaching to mastery is a foreign practice to many experienced teachers because most programs do not require mastery. Instead of providing continuous skill development, these programs present topical or thematic units. Students will work on a particular unit for a few days and then it will be replaced by another unit that is not closely related to the first and that does not require application of the same skills and knowledge. This design, referred to as a “spiral curriculum,” is more comfortable for the program designers, teacher, and students; however, it is inferior for teaching skills and knowledge.It is as simple as that. Schools don't like accountability. Schools don't like being held accountable for student achievement or lack thereof. Instituting a curriculum like SM requires bringing students to mastery on each topic, which requires continual practice. It is hard work.

It is comfortable for the designers because the design does not have to be careful. The designers do not have to document that everything that is presented is “teachable”; the amount of new learning does not have to be carefully measured. The amount of time required for a “lesson” does not have to correspond precisely to a period, because the design assumes that different teachers will take different amounts of time to get through a particular “lesson” and “unit.” The amount of new material is not controlled. The expectations for student performance is low because teachers understand that students will not actually master the material. They will simply be exposed.

The accountability of the teacher is therefore more “comfortable” because the teacher is not expected to get through the material in a specified period of time or bring students to mastery. The spiral curriculum is more comfortable for students because they are not required to learn, use, or apply the skills from one unit to the next unit. They quickly learn that even though they do not understand the details of a particular unit, the unit will soon disappear and be replaced by another that does not require application of skills and knowledge from the previous unit. The design clearly reinforces students for not learning or for learning often vague and inappropriate associations of vocabulary with a particular topic.

Not unsurprisingly, MCPS dropped the SM pilot program within two years, despite some evidence of success. They opted instead for the warm confines of the EM spiral despite the fact that it had little evidence of success.

The same fate has befallen other mastery learning math curricula, such as Connecting Math Concepts.

In Philadelphia:

Based on the results of this study, the CMC implementation was expanded to districtwide adoption in grades 1 through 8 in the following year. The mean proportion of students performing above district-set criterion on district-developed tests in the spring of that year increased to 90% from 62% in the spring of the previous year. Two years later, the district terminated the program.And, in Michigan:

The impressive empirical results of the study, along with teacher and parent support, led to administrative support to continue and expand CMC implementation to 85% of the students the following year. Despite its success, the district subsequently terminated the program.One reason given for pulling SM was that it wasn't aligned with state standards.

Another complaint expressed by teachers and administrators in all four schools was that Singapore Math was not in line with state standards. Indeed, the state’s academic standards include data analysis, statistics, and probability, which Singapore’s texts do not address.I noted the same thing back in May. Maryland's state exam is heavily skewed to statistics and data analysis at the expense of math. I concluded:

The Singapore kids are well prepared for algebra. The Maryland kids are well prepared for a night at the blackjack table.(Barry left a lengthy comment at the bottom of that post which I suggest you read.)

Ultimately, however, it's the ideological differences which push out mastery learning programs like SM in favor of fuzzy programs like EM. And, the ideological puppeteer is none other than the NCTM.

Taking on a program like Singapore Math meant going against what many teachers believed math education to be about; surely, it was not what they were trained for. Since the success of Singapore’s programs relies in many ways on more traditional approaches to math education, such as explicit instruction and giving students many problems to solve, in some ways its very success represented a slap in the face to American math reformers, many of whom have worked hard to eliminate such techniques from the teaching canon.Gail Burrill, a former president of the NCTM, suggests quite bluntly that the success of Singapore Math cannot be imported. “These are books used by a different culture, a culture that is more homogeneous, and a culture that has a consistent way of thinking about mathematics.” And Cathy Seeley, a former president of the NCTM, hints as much by arguing that Singapore’s success (as well as that of other Asian countries) is not about the textbook. “We have to look beyond their textbooks to determine what these lessons are.”

As I stated up front, the NCTM has recently reversed its recommendations to be more aligned with the programs like Singapore Math. It's yet to be seen if and when schools will ultimately change their way of thinking when it comes to teaching math. I don't hold out much hope. Aversion to accountability and ideological agendas are still the elelphants in the room. I don't see schools voluntarily changing either without putting up a fight.

## 2 comments:

I'm a big proponent of basic stats in high school, though they taught no stats or probability when I was in high school. But if they are teaching stats in high school, in my experience at least, students aren't learning it because when they get to my class, they don't know anything about stats or probability. I've had students who did not know how to calculate a mean.

I agree, high school kids should know stats. I didn't get any either in high school.

The problem is that math is becoming a subset of stats at the pre-high school level. Things like long division and multiplication of fractions are being marginalized.

I believe the reason is that it takes 3-4 years of good math instruction to get students up to this level of math education. Whereas the baby stats that get taught K-12 require little math skills and only basic ones at that.

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