Interactions between instructional approaches, students' reasoning processes, and their understanding of elementary algebra

This research explored the effectiveness of various teaching strategies used for introducing early algebraic concepts. The research focused on investigating three approaches commonly used for introducing the concept of a variable, namely, generalising from tables of data, generalising from visual patterns, and establishing the links between algebra the structural aspects of the number system. The research also identified specific reasoning processes that interact with these strategies.

The research incorporated two investigations, an introductory and main study. One hundred and sixteen students participated in the introductory study and 379 students participated in the main study. The age of the students ranged from 12 years 6 months to 15 years and 10 months. The introductory study incorporated the development and trialing tests used for measuring students' reasoning processes, their preference for a visual or symbolic approach to solution, and their understanding of pre-algebra and early algebra ideas. These tests were reformulated for the main study. An analysis of the students' responses indicated a number of areas where more in-depth information would help identify the ways in which students reflected on basic algebraic concepts. Forty one students were selected for a semi-structured interview.

The research employed a multiple measurement approach. The first stage consisted of a correlational analysis. This analysis teased out the relationships among the three written test. The next stage in the study entailed the use of a semi-structured interview. This phase was considered an important part of the methodology as it provided insights into the ways students think, and enabled clarification, extension, and interpretations of the information recorded in the written responses. Implications for further research, for classroom teaching, and for curriculum development for introducing the concept of a variable are discussed.