Five Strands of Mathematical Proficiency

The “Depth of Knowledge” scheme was developed by Dr. Norman Webb at the University of Wisconsin and is used in our primary math resource, “Bridges in Mathematics” as a basis for designing instruction and assessment.In Lower Primary, we believe that students develop a deep understanding of math via exposure and practice with the FiveStrands of Mathematical Proficiency. These components work together, are interwoven and interdependent and form the overarching framework for our daily math practice.

Five Strands of Mathematical Proficiency

Conceptual Understanding: High achievers in mathematics understand the meaning of the operations and underlying math concepts of all areas of mathematics.Productive Disposition: High achievers in mathematics are persistent.Adaptive Reasoning: High achievers in mathematics can defend their thinking and critique the reasoning of others.Strategic Competence: High achievers in mathematics are good problem posers and problem solvers.Procedural Fluency: High achievers in mathematics can effectively, efficiently, and flexibly choose and use a variety of strategies to compute.Dr. Sandy Atkins. Parent Workshop “Creating High Achieving Math Students”. 2015The “Depth of Knowledge” scheme was developed by Dr. Norman Webb at the University of Wisconsin and is used in our primary math resource, “Bridges in Mathematics” as a basis for designing instruction and assessment.

Levels of Cognitive Demand

We want our young mathematicians to develop all strands of mathematical proficiency, to have conceptual understanding, procedural flexibility and fluency and the ability to apply math concepts in “real world” situations. In order to do this we are cognizant of the cognitive demand of tasks and strive to engage students in experiences that extend thinking.

Level 1: Recall and Reproduction

Recall, recognition; skill, behavior or sequence of behaviors learned through practice and easily performed(student writes 23 as twenty-three)

Level 2: Skills and Concepts

Engagement of some mental processing beyond recalling; the use of information or conceptual knowledge; requires making some decisions regarding how to approach a question or problem (student solves 45 + 29 with a place value model)

Level 3: Strategic Thinking

More sophisticated reasoning and analysis; deep understanding; students are required to solve problems and draw conclusions (student solves a two-step word problem and explains thinking using drawings, numbers and words to provide a solution that makes sense)

Level 4: Extended Thinking

Requires integration of knowledge from multiple sources and ability to represent knowledge in a variety of ways; usually requires work over an extended period of time (student collects data about height differences between second graders and middle school buddies, plots the data on a graph and makes some conclusions based on data)