by NCTM President J. Michael Shaughnessy
NCTM Summing Up, May 2011
Recently, I had the opportunity to participate in a working
conference on issues related to mathematics curriculum and assessment under the
new Common Core State Standards for Mathematics (CCSSM). Forty-four states have
now adopted CCSSM, launched by the Council of Chief State School Officers and
the National Governors Association Center for Best Practices in 2010. The
Department of Education has funded two consortia to develop assessment
instruments for CCSSM. Those assessments will go into effect in all states that
have adopted CCSSM in the 2014–15 school year. As we all learn more about the
Common Core Standards and the accompanying assessments, it is becoming increasingly
clear to me that they provide an opportunity for us to make deep changes in the
way that we teach and assess K–12 mathematics in our nation. However, as I
travel to meetings and conferences throughout the country, I sometimes hear
statements like, “Oh, our state already does the Common Core; it won’t be much
of a change for us.” Or, “We’re going to just wait and see what happens.” Let
me suggest that both of these extremes—one, an assumption that the changes called
for by CCSSM have already happened, and the other, an assumption that they will
come about on their own, or that CCSSM will quietly go away—are quite naïve.
Systemic changes in mathematics education will necessarily
accompany the Common Core State Standards for Mathematics because these standards are national in character. The individual
states themselves, as is their right under our Constitution, have, one by one,
decided to accept the Common Core State Standards. This is new in the United States—never before have so many states agreed to
base mathematics instruction on a common set of standards. Furthermore, these standards
include both Standards for Mathematical Content and Standards for Mathematical
Practice, and students’ mastery of both the content and the practices will be
assessed in the designs being created by the two assessment consortia. By the
way, the eight Standards for Mathematical Practice are not teaching practices—they
are student practices—processes that
students need to engage in and develop facility with as they learn mathematics
and solve mathematical problems. The fact that students will be accountable to the
Standards for Mathematical Practice is another systemic change for mathematics education
in our country. Although in the past individual states have included
performance tasks and extended constructed response items calling for student
work and reasoning, such assessments have been inconsistent, and sometimes not
persistent, in the United States. This will change.
In light of the national character of CCSSM and the new
types of accompanying assessments, we can start doing certain things now as we
think about curriculum, instruction, and assessment in the era of the Common
Core.
With respect to curriculum, we can begin to examine the
materials that we use to see how well they support the content and practice standards
in CCSSM. A project is now under way to develop tools that teacher leaders,
districts, and states can to use to review curricular materials to determine
how well they align with CCSSM—both with the content standards and the practice
standards. The tools from this project will be available to the public in the
next few months. One caveat in regard to curriculum: this is not the time for states to run off and write their own curricula
based on the Common Core State Standards. Quite a number of very
thoughtful, carefully tested and piloted curriculum projects and materials have
appeared over the past twenty years—many of them, in fact, have undergone
several updates and revisions. We actually do
have good curricula in this country—lots of them! Although the existing materials
will need some adjustments to improve their fit with CCSSM, building on
existing materials will be a much more efficient and effective process for
states and districts than inventing totally new materials on their own. A move
by individual states to reinvent the curricular wheel in a rush to implement
CCSSM is ill advised. States would do much better to work together with other
states on adapting existing curriculum materials.
With respect to instruction, implementing CCSSM’s Standards
for Mathematical Practice will call for engaging students much more in such processes
as—
- problem solving;
- communication of mathematical ideas in meaningful
classroom discourse;
- making connections across topics and to contexts;
- reasoning about and justifying solutions;
- developing a positive disposition toward
mathematics;
- creating and sharing multiple representations of
mathematical concepts and procedures; and
- modeling mathematical processes.
Excellent resources are available to teachers for instilling
and developing fluency in the mathematical practices in our students. At the
high school level, particularly useful resources include NCTM’s Focus in High School Mathematics: Reasoning
and Sense Making (2009) and the publications in the accompanying Focus in
High School Mathematics series. Valuable resources for teachers of mathematics
in prekindergarten–grade 8 include the grade-level books in NCTM’s Teaching
with Curriculum Focal Points series. In addition, grade-band books in NCTM’s rapidly
expanding Essential Understanding Series provide deep, cross-grade discussions
of the most important mathematical content and offer excellent resources for
teachers to use as they consider instruction based on the CCSSM.
Finally, with respect to assessment, we need to get a head
start to prepare both ourselves and our students for the new types of
assessment that will be used with CCSSM. The two assessment consortia funded by
the Department of Education, SMARTER Balanced Assessment
Consortium (SBAC) and the Partnership for the Assessment of Readiness
for College and Career (PARCC), have been sharing their respective plans for
assessment with the public, and we should all become familiar with them. Both
consortia plan to include extended mathematical performance tasks in their
instruments. You can download presentations on both assessment plans so that you
and your students can get involved in deeper assessment tasks right away, gaining
experience with such tasks well before 2014. Performance tasks are available
to the public from the MAP project on the MARS website and can be downloaded for
noncommercial use. The
Silicon Valley Mathematics Initiative also has made a collection of assessment tasks that can be downloaded.
In addition, NCTM
has an excellent portfolio of assessment resource materials, along with
accompanying support materials for teachers, including the Assessment Sampler series.
The bottom line for all of us is that under CCSSM, it is
not, nor will it be, business as usual. With the inclusion of the Standards for
Mathematical Practice, we have been handed an opportunity to make some
significant changes in our mathematics instruction. And for the first time we
have an opportunity to have cross-state, common mathematics assessment of our students’
progress in both content and mathematical practices. Together, let’s make the
best decisions we can as we proceed to implement these new standards.