ALGEBRAIC THINKING OVERVIEW

Introduction

The Algebra Success Keys (ASK) guide is a compilation of research-based practices developed to help teach algebra to students with diverse learning needs. A foundation in algebraic thinking begins in grades K-5 and continues through the middle school grades to high school algebra. It is important to recognize that in the development of algebraic thinking, students should be able to understand abstract concepts, if the concepts are developed gradually from concrete to semi-concrete or representational to abstract over a period of time (Miller & Mercer, 1993).

The purpose of the Algebra Success Keys (ASK) is to provide algebra teachers of grades K-12 with research-based strategies in instruction, assessments, accommodations, and technology to help students learn algebraic thinking. Math teachers and special education teachers should use this guide to enhance their teaching of algebraic thinking skills to students with diverse learning needs. This guide should be used in conjunction with action research. Action research allows a teacher to understand and reflect what they are learning as well as how and what the students are learning.

The Algebra Success Keys (ASK) is not a curriculum. It is a resource available to teachers to improve student learning of algebra in grades K-12. ASK should be used to help teachers teach algebraic thinking using three levels of learning (Concrete-Representational-Abstract) as well as to meet the needs of individual students. It is based on selected "big ideas" taken from the NCTM Standards, Florida Sunshine State Standards, and research related to the teaching of algebraic thinking using the three levels of learning: Concrete, Representational (or Semi-Concrete), and Abstract (Miller & Mercer, 1993; Witzel, Mercer, & Miller, 2003).

The Algebra Success Keys (ASK) provides strategies for the teaching of algebra within the four standards:

• Understanding patterns, relations, and functions
• Representing and analyzing mathematical situations and structures using algebraic symbols
• Using mathematical models to represent and understand quantitative relationships
• Analyzing change in various contexts (NCTM, 2001)

This guide is divided into ten sections and includes topics such as the levels of learning, instructional strategies, assessments, accommodations and technology. ASK provides teachers with assistance, to enhance their teaching and their students learning environment, which enables them to reach diverse learners in algebraic thinking.

Fundamental Components of Algebraic Thinking
It is important to understand the "big ideas" taught in algebraic thinking at each grade level. These ideas are taught in order to build on the student's prior knowledge. High expectations are essential to helping students learn algebra at all grade levels. The NCTM Algebra Standards and the Florida Sunshine State Standards (SSS) provide a framework based on standards at each grade level in algebraic thinking. The following table aligns the four NCTM (2000) algebra standards to the SSS by grade level. Vertical understanding of benchmarks in algebraic thinking will help develop concepts and strategies used to expand each student's ability. Assessment strategies should help evaluate student's knowledge of algebraic thinking in order to differentiate instruction. The ability to identify student learning gains (combined with the benchmarks for learning algebra), provide a base for teachers to develop strategies, incorporate accommodations, and use technology to aid students in learning algebra.