Reasoning and Sense Making Task Library
order for high school students to be engaged in reasoning and sense
making in the classroom, the task—what students are asked to do—is
critical. However, each item in this task library contains much more
than a student work sheet. While linking the task directly with NCTM’s Focus in High School Mathematics: Reasoning and Sense Making, NCTM’s Principles and Standards for School Mathematics, and the Common Core State Standards, each item addresses:
Taking a Spin
Eruptions: Old Faithful
Fuel for Thought
As the Crow Flies
Over the Hill
Cash or Gas
fluency is a critical component mathematical proficiency and is more than
memorizing facts and procedures.
Algebra is not confined to a course or set of courses but is
a strand that unfolds across a pre-K–12 curriculum.
that support access and equity require comprehensive understanding and require
being responsive to students’ backgrounds, experiences, cultural
perspectives, traditions, and knowledge.
To ensure that all students can gain access to, interpret,
and share information fluently, teachers must address multiple dimensions of
Young learners’ future understanding of mathematics requires
an early foundation based on a high-quality, challenging, and accessible
is important in shaping and developing the next generation of teachers,
particularly as expectations for students become more rigorous.
The Common Core State Standards offer a foundation for the
development of more rigorous, focused, and coherent mathematics curricula,
instruction, and assessments that promote conceptual understanding and
reasoning as well as skill fluency.
Computer science should be incorporated into the curriculum in a way that enhances, rather than limits, students’ college and career readiness in mathematics.
development courses and workshops for future and current teachers need to model
effective pedagogies for teaching statistics, in addition to focusing on
developing understanding of statistical concepts, mastery of statistical
content, and knowledge of the essential ideas of statistical thinking and
problem solving. (A
joint position statement of the American Statistical Association and the
National Council of Teachers of Mathematics.)
Collaboration between researchers and school personnel
provides integrated perspectives for addressing critical issues in mathematics
teaching and learning.
ultimate goal of the K–12 mathematics curriculum should not be to get students
into and through a course in calculus by twelfth grade but to have established
the mathematical foundation that will enable students to pursue whatever course
of study interests them when they get to college. (A joint
position statement of the Mathematical Association of America and the National
Council of Teachers of Mathematics.)
Large-scale mathematics assessments are only one of a
variety of measures that should be used when making high-stakes decisions that
significantly impact schools and students.
Much of the achievement gap in mathematics is a function of
differential instructional opportunities. 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.
Both teachers and students stand to benefit from a
comprehensive system of teacher evaluation that considers data from multiple
domains of professional practice over time.
Strategic use of technology strengthens mathematics teaching and learning.
hold high expectations means to engage all students in cognitively challenging
tasks that are within reach and rich enough to stretch students as far as they
When implementing interventions, teachers must possess
strong backgrounds in mathematical content knowledge for teaching, pedagogical
content knowledge, and a wide range of instructional strategies.
Calculators in the elementary grades serve as aids in advancing student understanding without replacing the need for other calculation methods.
Students need to develop an understanding of metric system
units and relationships, as well as fluency in applying the metric system to
elementary school should have access to an elementary mathematics specialist to
enhance the teaching, learning, and assessing of mathematics to improve student
joint position of the Association of Mathematics Teacher Educators [AMTE], the
Association of State Supervisors of Mathematics [ASSM], the National Council of
Supervisors of Mathematics [NCSM], and the National Council of Teachers of
Mathematics [NCTM] in response to the release of Elementary Mathematics
Specialists: A Reference for Teacher Credentialing and Degree Programs [AMTE,