Standards-Based
School Mathematics Curricula: What are They? What do
Students Learn?
Edited
by Sharon L. Senk and Denisse R. Thompson
In
Standards-Based School Mathematics
Curricula: What are They? What do Students Learn?, Sharon L. Senk and Denisse R. Thompson provide documentation that addresses
the question of how mathematics curricula impact student learning. The studies
presented in this volume discuss 12 standards-based programs that were produced
in response to the 1989 NCTM Curriculum
and Evaluation Standards for School Mathematics.
The
book is divided into five sections. The first and last sections consist of one
chapter each. The first chapter presents the historical context for the development
of the 12 programs as well as a discussion of research issues related to
curricula. The last chapter provides a critical analysis of the findings
presented in the book and the nature of the task of evaluating the impact on
curricula on student learning.
Each
of the three additional sections focuses on one of the grade spans elementary,
middle or high school. Each of these sections begins with an overview chapter
that presents summary data on student mathematics achievement at that level and
information on the NCTM Curriculum and
Evaluation Standards for School
Mathematics’ expectations for that grade span. Chapters that address research findings on a particular standards-based
program and student outcomes follow this introductory chapter. The section
concludes with a chapter that discusses common themes across the programs as
well as issues related to the research presented.
Four
programs, Math Trailblazers, Everyday
Mathematics, Investigations, and
Number Power are discussed in elementary programs section. The middle
school section presents information on Connected
Mathematics, Mathematics in Context (MiC), and Middle Grades MATH Thematics: the STEM Project. At the high school level The Core-Plus Mathematics Project, MATH Connections, Interactive
Mathematics Program, SIMMS integrated Mathematics, and
the UCSMP Secondary School Curriculum are the programs detailed.
So,
did the programs “work?” Jeremy Kilpatrick (p. 483) in the final chapter states
that the research presented demonstrates “… the tendency of students in new
curricula to perform at the same level as comparison students on standardized
tests and to perform at higher levels on specifically designed tests.” These
results, he points out, mimic the results found when evaluating the curricula
from the new math era. He, as did the authors of the summary chapters for each
grade span, offers a detailed analysis of problems with the research designs
for the studies presented. Some of the causes of concern were the
appropriateness of the measures used, the comparability of the experimental and
control groups of students, and the impact of teacher effects.
Given
the lack of rigor of the research studies reported and the dated nature of the
material (We now have a new NCTM standards document.), is the book worth
reading? To that question I give an unqualified yes. The true value of this
volume is not in what is reported but how the information in the book is
presented. This book is a gold mine. It allows mathematics teacher educators to
have a one-volume resource from which their students can learn some of the
recent history of mathematics education while sharpening their research
evaluation skills. Following are some of the serendipitous treasures in this
book.
The
first chapter by Senk and Thompson and the last chapter by Kilpatrick provide
new comers to mathematics education a brief introduction to the history of the
“new math” and the “math wars.” Part of the history tells that the role that
the National Science Foundation played in creating mathematics curricula. It
also provides readers with a sense of why NCTM’s 1989 Curriculum and Evaluation Standards for School Mathematics was such a revolutionary document.
Kilpatrick (p. 474) provides a concise comparison between the new math and
current standards-based mathematics curricula. The curricula from both eras
deemphasized procedures and emphasized understanding. The critical difference
between the programs from these two eras is they way the programs attempt to
achieve these goals. The new math used mathematical structure and the
standards-based programs used mathematical problems that had a real-world
context. The analysis of this statement and how it played out could be the
subject of a semester long analysis of the history of mathematics education
from the Sputnik age to today. It also provides a frame of reference for
discussions about the role of mathematicians in mathematics teacher education
and curriculum development.
Here
are some more tasks we could assign our graduate students if they had Standards-Based School Mathematics
Curricula: What are They? What do Students Learn? Almost
all of the 12 programs were designed in response to a NSF call for proposals.
One could ask to what degree the programs addressed the NSF guidelines. What
goals did each program establish for itself? Did they attempt to measure all of
these goals? How did they measure these goals? In what ways was the
instrumentation appropriate or inappropriate? How did the programs attempt to
have a control group? In what ways were their efforts problematic?
Our
students could also examine the mathematics in these programs. Each program
presents some mathematics that is representative of its curriculum. In many
ways, these examples of what standard-based mathematics can look like provide a
common basis for discussions of what good mathematics is.
And,
for us as mathematics teacher educators, there are many implications for our
work. One key issue in evaluating the evaluation results reported by the
programs is to what degree did teacher effectiveness and loyalty to the
curriculum impact the results? All these programs required, to a greater or
lesser degree, professional development in both mathematics and pedagogy. What
role do we play in providing this professional development? If those of us who
prepare mathematics teachers prepare them to deliver standards-based teaching
no matter what program they teach (even when teaching _ _ _ _ _ Math), how will
those evaluating the impact of mathematics curriculum separate the effects of
the content of the program from the pedagogy of the program?
As
I read Standards-Based School Mathematics
Curricula: What are They? What do Students Learn? by Senk and Thompson, I kept finding more and more questions
that I wanted to discuss with my colleagues or have my students explore. This
book is a valuable resource for a mathematics teacher educator’s bookshelf, but
not necessarily for what it purports to do.