National Math Curriculum: A Lesson from TIMSS

2002 was, by all appearances, a banner year for discussion of curriculum issues by the AFT. In A Coherent Curriculum: The Case of Mathematics, researchers compare the breadth and depth of math curricula in the "A+" countries that achieved top rankings in the TIMSS with those of 21 U.S. states. They found that the A+ countries covered fewer topics per year, focused in-depth on more topics per year, and taught each topic over fewer years than states in the U.S.

(For a quick overview, download the pdf United States vs. International Standards from this Education Week article.)

It is tempting to think that the effects of what is actually taught pale in comparison with other factors, such as teacher quality, school funding, or the socioeconomic status of the student body. But the fact is that what you teach is what you get.

One of the most important findings from TIMSS is that the differences in achievement from country to country are related to what is taught in different countries. In other words, this is not primarily a matter of demographic variables or other variables that are not greatly affected by schooling. What we can see in TIMSS is that schooling makes a difference. Specifically, we can see that the curriculum itself—what is taught—makes a huge difference.

So what lessons can we draw from this study?

First, the A+ countries had something of a consensus about when topics should be introduced. For example, none of the A+ curricula covered polygons and circles before grade 4. In contrast, 100% of the 21 state curricula specified that this topic be taught starting in grade 1. And so on.... For a total of 32 mathematics topics examined, all but five were introduced later in the top-achieving countries than in the U.S. states.

Second, the A+ countries had a sense that some topics should be mastered before children move on to more advanced topics. As such, a clear sequence emerges of early-elementary, late-elementary, early-middle, and late-middle grade content. In contrast, in the U.S. states,

Prerequisite knowledge doesn’t come first. For example, properties of whole number operations (such as the distributive property) are intended to be covered in first grade, the same time that children are beginning to study basic whole-number operations. This topic is first typically introduced at grade four (and not earlier than grade three) in the top-achieving countries.

In contrast, 100% of the 21 state curricula examined featured this topic in all of the grades from 1-7, and >83% also covered it in grade 8. That's a lot of polygons and a lot of circles! While the A+ countries introduced and taught each topic to mastery in a relatively short time, the U.S. covered...and covered...and covered...and covered the same topics, ad infinitum. The authors state:

The longer topic coverage combined with the absence of the three-tier structure suggest that state standards are developed from a laundry-list approach to mathematics that lacks any sense of the logic of mathematics as a discipline. For many of the individual states it seems that almost all topics are intended to be taught to all students at all grades. [emphasis added]

The report gives us a glimpse of what a coherent curriculum would look like, and I encourage you to read the whole thing (pdf), including the related articles (there is one by E.D. Hirsch).