National Council of Teachers of Mathematics (NCTM)

A Vision for School Mathematics

Imagine a classroom, a school, or a school district where all students have access to high-quality, engaging mathematics instruction. There are ambitious expectations for all, with accommodation for those who need it. Knowledgeable teachers have adequate resources to support their work and are continually growing as professional. The curriculum is mathematically rich, offering students opportunities to learn important mathematical concepts and procedures with understanding. Technology is an essential component of the environment. Students confidently engage in complex mathematical topics, sometimes approaching the same problem from different mathematical perspectives or representing the mathematics in different ways until they find methods that enable them to make progress. Teachers help students make, refine, and explore conjectures on the basis of evidence and use a variety of reasoning and proof techniques to confirm or disprove those conjectures. Students are flexible and resourceful problem solvers. Alone or in groups and with access to technology, they work productively and reflectively, with the skilled guidance of their teachers. Orally and in writing, students communicate their ideas and results effectively. They value mathematics and engage actively in learning it.

Such a mathematics program would be built on:

• Equity: High expectations and opportunities for all, accommodating differences, resources, and support

• Curriculum: coherent, organized and integrated, focused on important mathematics, well articulated across the grades

• Teaching: knowing and understanding mathematics, students as learners, and pedagogical strategies; a challenging and supportive learning environment; continually seeking improvement

• Learning: learning with understanding, actively building new knowledge from experience and prior knowledge

• Assessment: should enhance student's learning of important mathematics, for a variety of sources, used for making instructional decisions, useful to students

• Technology: enhances mathematics learning, supports effective mathematics teaching, influences what is taught