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A Position of the National Council of Teachers of
Mathematics
Question: What does it mean to hold high expectations for students in
mathematics education?
NCTM Position
To hold high expectations means to engage all students in cognitively challenging tasks that are simultaneously within reach and rich enough to stretch students as far as they can go. Holding high expectations does not necessarily mean accelerating coursework or presenting material that is more difficult or should be done faster. Teaching with high expectations for all students ensures greater understanding for every student.

Holding high expectations begins with the fundamental
assumption of equity—the belief that all students can learn and should be given
rich and challenging opportunities to do so. Holding high expectations means
assuming that all students, from prekindergarten through college, are able to
handle complexity and engage in mathematical reasoning and problem solving. It
is through tasks that challenge students to stretch and develop their reasoning
and problemsolving skills that they learn more. Furthermore, holding high
expectations involves recognizing that different students emerge as talented on
different types of mathematical problems and in different topics in
mathematics.
Challenging tasks are at the core of mathematical reasoning
and sense making, and they provide an introduction to content that students need
to learn. The appropriate introduction of this content helps motivate students
to learn more (Stein,
Remillard, & Smith, 2007; Silver & Stein, 1996; Stein, Grover, &
Henningsen, 1996).
Challenging tasks should not be postponed until the end of an instructional
unit; rather they should be used to launch and sustain learning throughout the
unit. Meeting high expectations requires effort from students (Willingham,
2009; Bransford, Brown, & Cocking, 2000). Teachers should challenge
students to persevere to experience the rewards of meeting high expectations.
Teachers should assume that students bring to the classroom a
diversity of mathematical understanding and backgrounds that can be tapped to
enhance learning for all students (Donovan
& Bransford, 2005).
Therefore, classroom experiences that build mathematical communities to solve problems,
communicate reasoning, and make sense of mathematics are key to high
expectations for all.
Holding high expectations means giving all students access not
only to challenging tasks but also to challenging courses and curricula (Stiff,
Johnson, & Akos, 2011; Tate, 2005). This does not necessarily mean
that courses are difficult or accelerated but does mean that they consistently make
problem solving the focus for all students. High expectations for all students
in mathematical reasoning, sense making, and communication enable students to
learn to identify assumptions, develop arguments, and make connections within
mathematical topics and to other contexts and disciplines.
References
Bransford, J. D., Brown, A.
L., & Cocking, R. R. (Eds). (2000). How people learn: Brain, mind,
experience, and school [Expanded ed.]. Washington, DC: National Academy of
Sciences.
Donovan, S., & Bransford,
J. (2005). How students learn: History, mathematics, and science in the
classroom. Washington, DC: National Academies Press.
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.
Stein, M. K., Grover, B. W.,
& Henningsen, M. (1996). Building student capacity for mathematical
thinking and reasoning: An analysis of mathematical tasks used in reform
classrooms. American Educational Research Journal, 33(2), 455–488.
Stein, M. K., Remillard, J.
T., & Smith, M. S. (2007). How curriculum influences student learning. In
F. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and
learning (2nd ed., Vol. 1, pp. 319–369). Charlotte, NC: Information Age
Publishing.
Stiff, L. V., Johnson, J. L.,
& Akros, P. (2011). Examining what we know for sure: Tracking in middle
grades mathematics. In W. Tate, K. King, and C. Rousseau Anderson (Eds.), Disrupting
tradition: Research and practice pathways in mathematics education (pp.
63–75). Reston, VA: National Council of Teachers of Mathematics.
Tate, W. F. (2005). Access
and opportunities to learn are not accidents: Engineering mathematical progress
in your school. Greensboro, NC: Southeast Eisenhower Regional Consortium
for Mathematics and Science Education.
Willingham, D. T. (2009). Why
don’t students like school? A cognitive scientist answers questions about
how the mind works and what it means for your classroom. San
Francisco: JosseyBass.
(October 2011)
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.