Academic journal article Research & Teaching in Developmental Education

Investigating Algebraic Procedures Using Discussion and Writing

Academic journal article Research & Teaching in Developmental Education

Investigating Algebraic Procedures Using Discussion and Writing

Article excerpt

Abstract

This study reports on the implementation of an intermediate algebra curriculum centered on a framework of student-centered questions designed to investigate algebraic procedures. Instructional activities were designed to build discourse in the small-group discussion meetings of the course. Students were assigned writing prompts to emphasize the importance of understanding different aspects of a procedure beyond simple execution of the procedure. Skills-based pre- and post-tests were administered as well as a researcher developed procedural understanding instrument. No significant differences were observed between the treatment and control groups on posttest performance; however the treatment group showed a significant difference in gains from the pretest to the posttest. The treatment group did score significantly higher on the procedural understanding exam suggesting that the treatment was effective without hindering basic skill development.

This research study evaluates the effectiveness of using classroom discussion and student journaling to focus lessons on a series of investigative questions to help students gain a deep, well-connected understanding of algebraic procedures.

Research has been conducted over the last several years that has focused on students' algebraic deficiencies and the development of strategies to combat the problems of skill development and retention. Implementing a practical, instructional framework has yielded some promising results. Hasenbank (2006) developed and implemented a Framework for Procedural Understanding (hereafter referred to as the "Framework") in a college algebra course. This Framework was developed through observations, student interviews, and reflection on available learning research. The goal of this Framework is to enhance student performance and retention by deepening their understanding of algebraic procedures.

This article reports on results of a curriculum and instructional treatment that incorporated the Framework in a developmental intermediate algebra course. This Framework is based upon guidelines that were proposed by National Council of Teachers of Mathematics (NCTM). The teaching and learning of mathematics should strive for the following goals:

1. The student understands the overall goal of the algebraic process and knows how to predict or estimate the outcome.

2. The student understands how to carry out an algebraic process and knows alternative methods and representations of the process.

3. The student understands and can communicate to others why the process is effective and leads to valid results.

4. The student understands how to evaluate the results of an algebraic process by invoking connections with a context or with other mathematics the student knows.

5. The student understands and uses mathematical reasoning to assess the relative efficiency and accuracy of an algebraic process compared with alternative methods that might have been used.

6. The student understands why an algebraic process empowers her or him as a mathematical problem solver (NCTM, 2001, p. 3 1, emphasis in original).

Hasenbank re-expressed these guidelines as eight student-centered questions for application in the classroom setting:

1. (a) What is the goal of the procedure, and (b) what sort of answer should I expect?

2. (a) How do I execute the procedure, and (b) what are some other procedures I could use instead?

3. Why is the procedure effective and valid?

4. What connections or contextual features could I use to verify my answer?

5. When is this the "best" procedure to use?

6. What can I use this procedure to do? (Hasenbank, 2006, p. 7-8)

The focus of many developmental algebra courses and students is on 2a of the Framework, "How do I execute the procedure?" A brief review of mathematics education suggests that algebraic expertise does not result from extensive practice alone. …

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