The National Council of Teachers of Mathematics issued a news release announcing their new Curriculum Focal Points. What’s this? I wondered. They anticipated that I’d want to know, and they published a Questions and Answers page to satisfy me and anyone else who might want to learn what this has to do with the Mathematics Standards. NCTM’s president, Francis (Skip) Fennell, made a multimedia presentation to orient us to the reformed Reforms. From what I saw it’s a powerpoint lecture, but the audio couldn’t beat the noise of kids eating lunch in my classroom (which is not the high point of my day) so I couldn’t hear what was said.

NCTM recognizes the difficulty of working with a math curriculum that covers topic areas “a mile wide and an inch deep,” and I am grateful for their acknowledgment. Rather than changing the standards, NCTM is attempting to prioritize them by focusing on areas for study at different grade levels.

In the introduction to the Focal Points, NCTM says:

The long-term opportunity…is for mathematics leaders at every level to use Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics [pdf 18.9 MB] to launch an ongoing, far-reaching, significant discussion with the potential to guide the thinking of the profession in the development of the next generation of curriculum standards, textbooks, and tests.

It bothers me, since this is supposed to be about opening a discussion, that according to an article in the New York Times, conservative critics of current instructional practices are celebrating this as “a back-to-basics victory….and moving away from the constructivist approach some educators prefer,” There is no justification for this political rapture, because NCTM isn’t doing that.

In order to understand what this new turn might be about, I read Alan Schoenfeld’s paper, The Math Wars. It is a comprehensive history and analysis of math reform in US education policy. Schoenfeld notes that there are at least three “master narratives” about education in the US:

  • education for democratic equality (to promote citizenship);
  • education for social efficiency (to fuel the economy);
  • and education for social mobility (to serve the needs of individuals);

He warns that curricular issues can become social issues, resulting in new curricula being rejected out of hand by the public, or corrupted by teachers, if either or neither is prepared for them. While he admits the validity of a viewpoint which holds that mathematics competence is related to factual and procedural knowledge, and that this knowledge increases with study and practice, he calls this point of view naive in that it does not account for more complex dimensions of mathematical competence.

The metacognitive processes required for effective problem-solving, for example, are critically important. He sums up his middle-ground position in favor of both process and content by saying that “Students need to learn to think mathematically as well as to master the relevant mathematical content.”

Schoenfeld maps out a middle-ground position in the process vs. skills trench war. His position would not satisfy the discovery learning purists, and he doesn’t yield to the direct instruction traditionalists. He beleives that students should:

  • compute single-digit numbers, integers, decimals, and fractions, efficiently and accurately;
  • solve problems with calculators and computers;
  • understand how to use the basic laws of algebra when solving mathematics problems;
  • explain and justify their reasoning and understand the reasoning of others;

And he argues that teachers should learn mathematics throughout their careers.

Schoenfeld is critical of the polarized rhetoric which places discussion of the merits of process and product in an ‘either/or’ frame. He argues for the reasonable inclusion of both, recognizing that facts without understanding are meaningless, while process without skills leaves students helpless and incompetent. NCTM’s standards documents were written from the perspective of the master narratives of social mobility and democratic equality. Perhaps this new move is an effort to give some ground to the social efficiency camp, but it shouldn’t be seen as a retreat. If anything, it’s a healthy attempt to reach consensus on how we can get “there” from “here.”