Transitions in the Conception of Number: From Whole Numbers to Rational Numbers to Algebra

CONTENTS OF CURRICULUM UNIT 23.03.04

  1. Unit Guide
  1. Introduction
  2. Rationale
  3. Background Content Knowledge
  4. National Council of Teachers of Mathematics Process Standards
  5. Framework for Mathematical Discourse and Schema Building
  6. Strategies
  7. Activities
  8. Appendix on Implementing District Standards 
  9. Bibliography
  10. Notes

A Framework for Problem Solving: Schema Development and Discourse

Valerie Schwarz

Published September 2023

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Introduction

Children need to be mathematically literate, as their world is increasingly more dependent on technology, or they will be destined for a lower economic class.1

More than any other subject, mathematics filters students out of programs leading to scientific and professional careers. From high school through graduate school, the half-life of students in the mathematics pipeline is about 1 year, although various requirements hold some students in class temporarily for an extra term or year. Mathematics is the worst curricular villain in driving students to failure in school. When mathematics acts as a filter, it not only filters students out of careers, but frequently out of school itself.2

Currently, my school district is one of the lowest performing in the state of Virginia, and mathematics is no exception. The graduation rate for 2022 was 74.2%.3 The lack of mathematical literacy is an increasing problem across the country that has been compounded by the learning loss due to COVID. Students are acutely aware of their abilities regardless of their grade. Early experiences, successes and failures, impact not only students’ attitudes toward math, but their future relationship with math. Mathematics in elementary school lays the foundation for middle and high school. I hope this unit will engage students as they work collaboratively to examine word problems through mathematical discourse and the use of schemas.

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