Module 4: Strands of Mathematical Proficiency

EDUC 315 - Howard University

Nathan Alexander, PhD

School of Education

Module Overview

This module will deepen your understanding of generating mathematical lessons with a focus on fractions and decimals.

Goals for the module

One goal for this module is for you to come up with a set of ways to describe various ways to teach students’ properties and procedural fluency. We’ll use new examples and those from previous modules to guide you.

Decimals

Decimal Place Value

For each, underline the whole number part and circle the decimal (fractional) part.

  • 2.5
  • 1.23
  • 0.52
  • 0.002

Which digit is in the tenths place? Which is in the hundredths place?

True or False: Decimal Equivalents

True or False: 25 hundredths is the same as 2 tenths and 5 hundredths?

  • Draw a place value chart to prove your answer.
  • Write both numbers in fraction form.

Comparing and Ordering Decimals

Compare which is greater by identifying the digits in each decimal place (tenths, hundredths, thousandths).

  • 4.859
  • 4.869

Next, create your own set of three decimals and order them least to greatest.

Five Strands of Mathematical Proficiency

Five strands of mathematical proficiency

Kilpatrick and colleagues (National Research Council, 2001) identified five interdependent strands that together form a comprehensive definition of mathematical proficiency.

Procedural Fluency

Skill in carrying out mathematical procedures flexibly, accurately, efficiently, and appropriately.

  • Involves knowing procedures and using them correctly.

  • Includes the ability to select appropriate methods and apply algorithms based on the situation.

Procedural fluency

Conceptual Understanding

Comprehension of mathematical concepts, operations, and relationships.

  • Means having an integrated and functional grasp of ideas, not just memorizing facts.

  • Students should connect new knowledge with what they already know and represent mathematical situations in multiple ways.

Conceptual understanding

Adaptive Reasoning

Capacity for logical thought, reflection, explanation, and justification.

  • Enables students to explain and justify their strategies and solutions.

  • Supports the extension of knowledge from known concepts to unfamiliar situations.

Adaptive reasoning

Strategic Competence

Ability to formulate, represent, and solve mathematical problems.

  • Involves devising and using strategies for both routine and non-routine problems.

  • Encourages flexible thinking when approaching mathematical challenges.

Strategic competence

Productive Disposition

Habitual inclination to see mathematics as sensible, useful, and worthwhile, paired with a belief in perseverance and personal efficacy.

  • Nurtures a positive attitude and sense of efficacy towards mathematics.

  • Students believe that effort leads to understanding and success.

Productive disposition

Strand Key Aspect Description
Procedural Fluency Technical Performance Memorise and rehearse
Conceptual Understanding Classification, Definition Sort, classify, define and deduce
Representation Describe, interpret and translate
Analysis Explore structure, variation, connections
Adaptive Reasoning Argument, Proof Test, justify and prove conjectures
Strategic Competence Mathematical Model Formulate models and problems
Solution Employ strategies to solve a problem
Critical Commentary Interpret & evaluate solutions and strategies