Draft 2004 Mathematics Framework for NAEP

Tom Loveless

Thank you for the opportunity to testify. I believe that the 2004 draft framework is seriously flawed. I urge you to reject it for four reasons.

More items are needed in number and operations at grades 4 and 8. The previous and current (1990 & 1996) NAEP frameworks followed the NCTM’s 1989 Curriculum and Evaluation Standards for School Mathematics The five NAEP strands are an NCTM invention. They represent the NCTM’s model curriculum. Accordingly, the percentage of NAEP items devoted to each strand have reflected NCTM’s 1989 priorities. For several years, those priorities have been under intense criticism—most prominently, by mathematicians and parent groups—for de-emphasizing arithmetic and basic math skills.

In response to that criticism, the NCTM moderated its position in the 2000 Principles and Standards for School Mathematics, declaring number and operations “the core of mathematics education for the elementary grades” (p. 32). The draft of the 2004 NAEP framework shows no corresponding moderation. The current NAEP framework (1996) recommends a 70% ceiling and 40% floor for the proportion of items assessing the number strand at fourth grade and a 60% ceiling and 25% floor at the eighth grade. These were reductions from the 1990 framework and were designed to “move NAEP assessments ever closer to the vision embodied in the NCTM curriculum Standards” (Mathematics Framework for the 1996 NAEP, p. 14).

The 2004 framework continues pushing NAEP toward NCTM’s 1989 vision. The draft framework keeps the fourth grade weighting at the minimal level of 40% and drops the weighting at the eighth grade to 20%, below the previously established floor. The under-weighting of the number strand in NAEP is grounded in the thinking of late-1980s NCTM math reform, a position that even the NCTM has seen fit to modify.

Weighting of items does not reflect current classroom practice. On page 8, the draft framework states “these numbers continue to be a reasonable reflection of the relative weights of each of these content areas at that grade level.” This is inaccurate according to NAEP’s own data. In the 2000 NAEP, teachers were asked the amount of emphasis they give to each strand in their teaching. The percentage of fourth grade teachers reporting “heavy” emphasis: number and operations, 87%; measurement, 25%; geometry, 21%; data analysis/probability/statistics, 19%; algebra, 17%. By far, number receives the most emphasis from fourth grade teachers.

At the eighth grade, the percentages are: number and operations, 72%; measurement, 18%; geometry, 25%; data analysis/probability/statistics, 22%; algebra, 64%. Number and algebra share honors as the most emphasized strands. If NAGB is serious about reflecting the emphasis of classroom teachers, the fourth grade NAEP should be weighted much more towards number. At the eighth grade, the weighting of the number strand should also be increased—to at least as much as algebra. It certainly should not be reduced to the same weighting as geometry when three times as many teachers say they give heavy emphasis to number than geometry. The weighting of the number strand at fourth and eighth grades is directly opposed to current classroom practice.

Report scores for whole number operations, fractions, decimals, and percentages. NAEP scores are not reported for topics that are recognizable or useful to parents and teachers. At fourth and eighth grades, NAEP should report student performance in whole number operations, fractions, decimals, and percentages. In the next few weeks, teachers across the country will be holding conferences with parents. Imagine the following conversation between a teacher and a parent.

Parent: Does my child know how to add, subtract, multiply, and divide whole numbers?

Teacher: I don’t know. But I can tell you how she’s doing in number.

Parent: How about adding, subtracting, multiplying, and dividing fractions?

Teacher: I don’t know. But she’s doing fine in measurement.

Parent: Does she know that 1/4 equals .25? Can she convert fractions to decimals and vice versa?

Teacher: I can’t really tell you. But she seems to have a little difficulty with geometry and spatial sense.

Parent: Can you tell me if she knows that 50% of 8 is 4?

Teacher: No, I don’t know, but she’s doing great in data analysis, statistics, and probability.

Parent: Will you be able to answer any of these questions in the spring?

Teacher: No, but I’ll be able to tell you how she’s doing in algebra and functions.

This parent would be alarmed at both the obscure categories that the teacher is choosing to evaluate and the important topics on which no information is available. That is the status of today’s NAEP test. The NAEP should report scores for math skills that parents, teachers, and the public believe are important.

Continued adherence to the tenets of NCTM math reform is inappropriate. The marriage of the NCTM and NAEP originated in the 1990 math framework prepared by the Council of Chief State School Officers, continued through the 1996 framework prepared by the College Board, and persists in the draft framework we are discussing here today. It is time for a divorce. In terms of NAEP and NAGB’s reputations, the relationship was a mistake from the start. In the 1980s, the NCTM cast itself as the champion of a particular kind of mathematics curriculum and a particular kind of teaching in American schools. The NCTM’s version of math reform is not the first political movement aspiring to change K-12 mathematics. It won’t be the last. Reform movements inevitably spawn criticism and counter-movements. Two states, California and Massachusetts, have adopted math frameworks that explicitly depart from the prescriptions of NCTM. The proper stance of a federal assessment—and of the independent body that governs it—is to remain rigorously neutral in such disputes. Why is this important? The data collected by NAEP may settle many of the most important questions in the debate. And the NAEP test offers information on the crucial question of whether NCTM math reform is good for American students’ learning of mathematics. Unfortunately, because of more than a decade of testing math achievement while supporting NCTM principles, NAEP and NAGB cannot credibly claim impartiality on questions about NCTM math reform. When it comes to NCTM math reform, the nation’s report card plays favorites. It always has. It continues to do so with the proposed 2004 framework.