On March 13, 2008, The National Mathematics Advisory Panel released
its report [1]. 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
corrective.
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 [2].
They also emphasize that all students must have access to an authentic
[3] 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
[4]. 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.
[1] The Final Report of the National Mathematics Advisory
Panel, US Department of Education, 2008. www.ed.gov/about/bdscomm/list/mathpanel/index.html
[2] Curriculum focal points for prekindergarten through
Grade 8 mathematics: A quest for coherence. NCTM, 2006. www.nctm.org/focalpoints
[3] The report clarifies the meaning of authentic by listing
on page 16 the major Algebra topics that should be mastered by all students.
[4] How to Fix K-12 Education, David Bressoud.MAA
Launchings column, March, 2008. www.maa.org/columns/launchings/launchings_3_08.html
Access pdf files of the CUPM
Curriculum Guide 2004 and the Curriculum
Foundations Project: Voices of the Partner Disciplines.
Purchase a hard copy of the CUPM
Curriculum Guide 2004 or the Curriculum
Foundations Project: Voices of the Partner Disciplines.
Find links to course-specific software resources in
the CUPM
Illustrative Resources.
Find other Launchings
columns.
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 bressoud@macalester.edu.
This column does not reflect an official position of the MAA.