In the report, the NRC chose the term mathematical proficiency to

capture what it means for anyone to learn mathematics successfully.

Mathematical proficiency consists of the following five components, or

strands. [1]

• Conceptual Understanding:  The comprehension of mathematical

concepts, operations, and relations.

• Procedural Fluency:  The skill in carrying out procedures flexibly,

accurately, efficiently, and appropriately.

• Strategic Competence:  The ability to formulate, to represent, and to

solve mathematical problems.

• Adaptive Reasoning:  The capacity for logical thought, reflection,

explanation, and justification.

• Productive Disposition:  The habitual inclination to see mathematics

as sensible, useful, worthwhile, coupled with a belief in diligence and

one’s own efficacy.

The most important observation the committee makes and stresses is

that the five strands are interwoven and interdependent in the

development of proficiency in mathematics (NRC, 2001, p. 116).

1) Modeling Mathematics

Mathematics Vocabulary

Concept mapping

2) Mental gymnastics- Flexibility

with numbers

Challenge 24-Flexibility with

numbers

Peer Coach-explaining how to

Math Detective-detecting error

patterns

3) Strategy cards

mathematics discourse

Questioning guide

Got Tools

Stand up, Pair up, Share (trade)

4) Poster Proofs

Convince me

Questioning

Math talk

Reflection on problem solving

5) Math Happenings

Literature and Math

Arts and Math

Movie in Math

Puzzles in Math

Junior Architect