Improving Algebra Students' Number and Operations Sense, Conceptual Knowledge, Executive Control, and Algebraic Thinking Skills: A Supplementary Curriculum

Abstract

Since the National Council of Teachers of Mathematics (NCTM) wrote their Curriculum and Evaluation Standards for School Mathematics in 1989, the mathematics education community has focused on developing students' mathematical proficiency. In recent years, mathematics education has continued to receive a great deal of attention due to concerns about students' weak mathematics skills and their effects on the United States' ability to compete globally. In the spring of 2008, the National Mathematics Advisory Panel (NMAP) recommended policies and practices necessary for the improvement of mathematical proficiency of American students. The NMAP chose to focus those recommendations on the implications for the preschool through middle school curriculum in preparing students for Algebra.

Although those recommendations may help future generations of American students, they do little to help the students who are currently taking Algebra and lack proficiency with prerequisite skills. The goal of this supplementary curriculum is to improve Algebra students' conceptual understanding of number and quantity and to use that improved understanding to enrich students' learning of basic Algebra concepts. The backbone of the curriculum is the careful design and sequencing of mental mathematics problems to foster rich discussions. The problem solving and subsequent discussions in the classroom promote the development of number and operations sense, conceptual knowledge, executive control and algebraic thinking skills. All of this skill development is possible when undertaken in a safe and equitable learning environment favoring process over result and requiring sound mathematical justification while providing plentiful opportunities for assessment of teaching and learning.

This project report has two main components: (1) a companion paper providing research support for each of the key aspects of the supplementary curriculum, and (2) curriculum materials including an instructor's guide for the curriculum, sample problem sets, and other teacher support materials.