Math Proficiency

The Five Strands of Mathematics Proficiency

DEVELOPING MATHEMATICIANS

strands
National Research Council. (2001). Adding it up: Helping children learn mathematics. J Kilpatrick, J. Swafford, and B. Findell (Eds.). Math Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.

For  more info http://books.nap.edu/catalog.php?record_id=10434

Click on each strand for classroom structures that promote this strand:

The Five Strands of Mathematics Proficiency

(1) Conceptual understanding

refers to the “integrated and functional grasp of mathematical ideas”, which “enables them [students] to learn new ideas by connecting those ideas to what they already know.” A few of the benefits of building conceptual understanding are that it supports retention, and prevents common errors. (NRC, 2001, p. 116)

Modeling Mathematics

Mathematics Vocabulary

Concept mapping

(2) Procedural Fluency (a.k.a. Computing)

is defined as the skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.Mental gymnastics- Flexibility with numbers

Challenge 24-Flexibility with numbers

Peer Coach-explaining how to

Math Detective-detecting error patterns

(3) Strategic competence

is the ability to formulate, represent, and solve mathematical problems. (NRC, 2001, p. 116)

Strategy cards

mathematics discourse

Questioning guide

Got Tools

Stand up, Pair up, Share (trade)

(4) Adaptive reasoning

is the capacity for logical thought, reflection, explanation, and justification.(NRC, 2001, p. 116)

Poster Proofs

Convince me

Questioning

Math talk

Reflection on problem solving

(5) Productive disposition

is the inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy. (NRC, 2001, p. 116)(NRC, 2001, p. 116)

Math Happenings

Literature and Math

Arts and Math

Movie in Math

Puzzles in Math

Junior Architect

Core Teaching Practices from the Principles to Action, NCTM (2014)

Implement tasks that promote reasoning and problem solving. Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.

Cognitive Demand 

Support productive struggle in learning mathematics. Effective teaching of mathematics consistently provides students, individually and collectively, with opportunities and supports to engage in productive struggle as they grapple with mathematical ideas and relationships.

Productive Struggle

Build procedural fluency from conceptual understanding. Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.

Establish mathematics goals to focus learning. Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional decisions.

Use and connect mathematical representations. Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.

Facilitate meaningful mathematical discourse. Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments.

Pose purposeful questions. Effective teaching of mathematics uses purposeful questions to assess and advance students’ reasoning and sense making about important mathematical ideas and relationships.

TeacherQuestions
DevelopingMathThinking

Elicit and use evidence of student thinking. Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning

http://books.nap.edu/catalog.php?record_id=9822

Jennifer Suh, Assistant Professor, Graduate School of Education, College of Education and Human Development teaches an EDCI 552 course, Mathematics Methods for the Elementary Classroom, at George Mason University's Fairfax Campus. Photo by Alexis Glenn/George Mason University

Jennifer Suh, Assistant Professor, Graduate School of Education, College of Education and Human Development teaches an EDCI 552 course, Mathematics Methods for the Elementary Classroom, at George Mason University’s Fairfax Campus. Photo by Alexis Glenn/George Mason University