David M. Bressoud April, 2008
On March 13, 2008, The National Mathematics Advisory Panel released its report . The Panel, established by President Bush in 2006, was charged with providing advice to the President and to the Secretary of Education, drawing on “research relating to proven-effective and evidence-based mathematics instruction” in order to recommend policies that will “foster greater knowledge of and improved performance in mathematics among American Students.” The Panel included many people for whom I have great respect, including Deborah Ball, Francis (Skip) Fennell, Joan Ferrini-Mundy, and Hung-Hsi Wu.
The report begins by explaining the importance of good mathematical preparation for all students and the crisis we now face because too many students are not graduating with the skills that they need. While the report stresses the importance of computational skills, it is in no sense a repudiation of the NCTM Standards (1989, 2000) or a condemnation of the efforts of those who have worked within the reform movement. The Panel calls for curricula that are focused and coherent, and that emphasize proficiency. They then define these terms: focused means including—and engaging at adequate depth—the topics that undergird success in Algebra; coherent means that there is an effective and logical progression of topics; and proficiency means understanding key concepts, achieving automaticity with basic number operations, developing flexible, accurate and automatic execution of standard algorithms, and using these competencies to solve a variety of problems.
These are to be understood within the context of the admonition that “The curriculum must simultaneously develop conceptual understanding, computational fluency, and problem-solving skills. Debates regarding the relative importance of these aspects of mathematical knowledge are misguided.” (p. xix)
The purpose of the Standards (1989, 2000) and most
of the various “reform” curricula always was to correct a historical
under-emphasis on conceptual understanding and problem-solving skills, not
to eliminate the requirement for computational fluency. However, some of the
reform curricula have lost sight of the goal of bringing all students up to
the level of proficiency with the material of Algebra and the necessity for
computational fluency in order to achieve this. This report is a very useful
The focus on Algebra is one of the most striking aspects of this report. The report asserts that the primary responsibility of Elementary and Middle School mathematics is to give students the mathematical foundations that are essential for success in Algebra. These Foundations include proficiency with whole number operations, the use of fractions (including rational and decimal fractions and percent), and particular aspects of geometry and measurement. The Panel’s recommendations with regard to preK–8 mathematics closely parallel those found in the NCTM’s Curriculum Focal Points . They also emphasize that all students must have access to an authentic  algebra course—which might be titled “algebra” or included within an integrated curriculum—and that mastery of the topics of Algebra should be expected of all high school students. On the controversial issue of when students should be expected to take Algebra I, the Panel recommends that more students should be prepared to study it in grade 8; the Panel does not go so far as to recommend that this should be the norm.
The other striking aspect of the report is that the Panel really did try to base their recommendations on existing research, and that they found this research to be extremely thin. Thus, many of the recommendations describe areas in which further research is needed.
One of the few areas in which there is very solid research is the effect of the quality of teachers, an essential ingredient that also was identified by the McKinsey Report of which I wrote in last month’s column . The Panel was able to state with confidence that the difference between student achievement after a single year of instruction by a teacher in the top quartile of effectiveness and student achievement following a year taught by a teacher in the bottom quartile is at least 10 percentile points, even after controlling for all other factors. By definition, those teachers in the top quartile do a better job of improving student achievement than those in the bottom quartile. What is significant is how much of the difference in student performance is attributable to teacher effectiveness alone, especially when you consider that the Panel considers the 10 percentile points to be a lower bound, this effect is cumulative, and the effect of teacher quality is most pronounced at the earliest grades
What is less clear is what it takes to produce an effective teacher. Certification alone appears to have little correlation with effectiveness. For teachers before 9th grade, there also is no clear correlation between which courses have been taken and teacher effectiveness. The name of the course matters much less than the actual mathematical knowledge of the teacher. While depth of understanding of the mathematics and knowledge of mathematical pedagogy are clearly key to producing effective teachers, the specific knowledge that an effective teacher needs is still imperfectly understood, and the Panel reports that we do not yet have a good means of measuring it directly.
I approached this report with particular interest in the Panel’s recommendations on the use of technology. There are signs that Computer Aided Instruction for drill and practice—with the immediate feedback that it can provide—is useful. Regarding calculators, the Panel found the research to be inconclusive: “A review of 11 studies that met the Panel’s rigorous criteria (only one study less than 20 years old) found limited or no impact of calculators on calculation skills, problem solving, or conceptual development over periods of up to 1 year.” (p. 50) It is not clear that calculators either help or hurt. That should not be too surprising. I have seen technology used atrociously. I have also seen it used to great advantage, but recognize how much effort needs to go into using it effectively. Teasing out the influence of the technology from that of the teacher will always be difficult. The Panel restricts its recommendation with regard to calculators to the need for high-quality research. They did observe that many high school Algebra teachers are concerned by a lack of computational fluency among their students. While it did not rise to the level of an official recommendation, the Panel warned that use of calculators must not impede the development of computational fluency.
In summary, I find this a reasonable and balanced report within the focus that it has chosen. I appreciate its emphasis on Algebra and agree that we need to streamline the topics introduced in preK-8 mathematics while enriching student understanding of and fluency with the basic competencies they will need if they are to succeed in the study of Algebra.
The report leaves us with a great deal to do, much of which requires the involvement of the mathematics community. From assessment and curriculum development to the training and support of teachers, mathematicians need to be educated about what has been done as well as what can and should be done. They then need to bring their perspectives and expertise to bear in a collaborative effort with those in Mathematics Education and with preK–12 teachers to improve the instruction of mathematics at all levels. The stakes are high. We must be engaged.
 The Final Report of the National Mathematics Advisory Panel, US Department of Education, 2008. www.ed.gov/about/bdscomm/list/mathpanel/index.html
 Curriculum focal points for prekindergarten through Grade 8 mathematics: A quest for coherence. NCTM, 2006. www.nctm.org/focalpoints
 The report clarifies the meaning of authentic by listing on page 16 the major Algebra topics that should be mastered by all students.
 How to Fix K-12 Education, David Bressoud.MAA Launchings column, March, 2008. www.maa.org/columns/launchings/launchings_3_08.html
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David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College in St. Paul, Minnesota, and president-elect of the MAA. You can reach him at firstname.lastname@example.org. This column does not reflect an official position of the MAA.