A Position of the National Council of Teachers of Mathematics
Question: How can we address differentials in access to
high-quality teachers, instructional opportunities, and expectations in
All students should have the opportunity to receive
high-quality mathematics instruction, learn challenging grade-level content,
and receive the support necessary to be successful. Much of what has been
typically referred to as the “achievement gap” in mathematics is a function of
differential instructional opportunities. Differential access to high-quality
teachers, instructional opportunities to learn high-quality mathematics,
opportunities to learn grade-level mathematics content,
and high expectations for mathematics achievement are the main
contributors to differential learning outcomes among individuals and groups of
Opportunity to learn remains one
of the best predictors of student learning (NRC, 2001). Differentials in
learning outcomes therefore are not a result of inclusion in any demographic
group, but rather are significantly a function of disparities in opportunities that
different groups of learners have with respect to access to grade-level (or more
advanced) curriculum, teacher expectations for students and beliefs about their
potential for success, exposure to effective or culturally relevant
instructional strategies, and the instructional supports provided for students
education is not just for those who want to study mathematics and science in
college—it is required for many postsecondary education programs and careers
(Achieve, 2005; ACT, 2006; National Science Board, 2008). Too many students—especially
those who are poor, nonnative speakers of English, disabled, or members of
racial or ethnic minority groups—are victims of low expectations for
achievement in mathematics. For example, traditional tracking practices have
consistently disadvantaged groups of students by relegating them to low-level
mathematics classes, where they repeat work with computational procedures year
after year, fall further and further behind their peers in grade-level courses,
and are not exposed to significant mathematical substance or the types of cognitively
demanding tasks that lead to higher achievement (Boaler, Wiliam, & Brown,
2000; Schmidt, Cogan, Houang, & McKnight, 2011; Stiff, Johnson, & Akos,
2011; Tate & Rousseau, 2002).
Wide variation in performance
among U.S. schools serving similar students indicates that existing learning
differentials can be closed and that demographic factors are not destiny when
students receive high-quality instruction and the necessary support to learn
grade-level content (McKinsey & Company, 2009). The National Council of
Teachers of Mathematics outlines a vision for high-quality mathematics
instruction in Principles and Standards
for School Mathematics (NCTM 2000) and Mathematics
Teaching Today: Improving Practice, Improving Student Learning (NCTM 2007).
Research indicates that all students can learn mathematics when they have
access to high-quality mathematics instruction and are given sufficient time
and support to master a challenging curriculum (Burris, Heubert, & Levin,
2006; Campbell, 1995; Education Trust, 2005; Griffin, Case, & Siegler,
1994; Knapp et al., 1995; Silver & Stein, 1996; Slavin & Lake, 2008;
Usiskin, 2007). “Equity does not mean that every student should receive
identical instruction; instead, it demands that reasonable and appropriate
accommodations be made as needed to promote access and attainment for all
students” (NCTM 2000, p. 12).
Rising to the challenge: Are high school graduates
prepared for college and work? Washington, DC: Author.
ACT. (2006). Ready for college or ready for work: Same or
different? Iowa City, IA: American College Testing Service.
Boaler, J., Wiliam,
D., & Brown, M. (2000). Students’ experiences of ability grouping—disaffection,
polarisation, and the construction of failure. British Educational Research Journal, 26(5), 631–648.
Burris, C. C.,
Heubert, J. P., & Levin, H. M. (2006). Accelerating mathematics achievement
using heterogeneous grouping. American
Educational Research Journal, 43(1), 105–136.
F. (1995). Project IMPACT: Increasing mathematics
power for all children and teachers (Phase 1, final report). College Park, MD:
Center for Mathematics Education, University of Maryland.
Trust. (2005). Gaining traction, gaining
ground: How some high schools accelerate learning for struggling students. Washington,
(2007). Examining disparities in mathematics education: Achievement gap or opportunity
gap? The High School Journal, 91(1), 29–42.
A., Case, R., & Siegler, R. S. (1994). Rightstart: Providing the central conceptual
prerequisites for first formal learning of arithmetic to students at risk for school
failure. In K. McGilly (Ed.), Classroom lessons:
Integrating cognitive theory and classroom practice (pp. 25–49). Cambridge,
MA: MIT Press.
Knapp, M. S., Adelman,
N. E., Marder, C., McCollum, H., Needels, M. C., Padilla, C., Zucker, A. (1995).
Teaching for meaning in high-poverty schools.
New York: Teachers College Press.
Company. (2009). The economic impact of
the achievement gap in America’s schools. Washington, DC: Author.
National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics.
Reston, VA: Author.
National Council of Teachers of Mathematics (NCTM). (2007). Mathematics teaching today: Improving practice,
improving student learning. Reston, VA: Author.
Research Council (NRC). (2001). Adding it
up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, & B.
Findell (Eds.). Mathematics Learning Study Committee, Center for Education,
Division of Behavioral and Social Sciences and Education. Washington, DC:
National Academy Press.
Science Board. (2008). Science and engineering indicators 2008 (2 vols.). Arlington, VA: National
H., Cogan, L. S., Houang, R. T., & McKnight, C. C. (2011). Content coverage
differences across districts/states: A persisting challenge for U.S. education policy.
American Journal of Education, 117(3),
Silver, E. A.,
& Stein, M. K. (1996). The QUASAR project: The “revolution of the possible”
in mathematics instructional reform in urban middle schools. Urban Education, 30(4), 476–521.
Slavin, R. E.,
& Lake, C. (2008). Effective programs in elementary mathematics: A best-evidence
synthesis. Review of Educational Research,
Stiff, L. V., Johnson,
J. L., & Akos, P. (2011). Examining what we know for sure: Tracking in middle
grades mathematics. In W. F. Tate, K. D. King, & C. R. Anderson (Eds.), Disrupting tradition: Research and practice pathways
in mathematics education (pp. 63–75). Reston, VA: National Council of
Teachers of Mathematics.
Tate, W., &
Rousseau, C. (2002). Access and opportunity: The political and social context
of mathematics education. In L. D. English (Ed.), Handbook of international research in mathematics education (pp. 271–299). Mahwah, NJ: Lawrence Erlbaum.
Usiskin, Z. (2007).
The case of the University of Chicago School Mathematics Project—secondary component.
In C. R. Hirsch (Ed.), Perspectives on
the design and development of school mathematics curricula (pp. 173–182). Reston, VA: National Council
of Teachers of Mathematics.
NCTM position statements define a particular problem, issue, or need and describe its relevance to mathematics education. Each statement defines the Council's position or answers a question central to the issue. The NCTM Board of Directors approves position statements.