Effects of heuristic-based problem-solving instructional approach for learning algebra with conceptual understanding in grade 8

Abstract

In Ethiopia, the content domain in mathematics at elementary school level, covering grades 1-8, consists of four thematic areas. These are numbers, geometry, algebra, probability and data handling. However, learners have difficulty with algebra and solving algebraic problems when compared to other mathematical topics and problems. This study aimed to enhance the development of middle school learners’ skills in algebra when responding to mathematics Model-Eliciting Activities (MEAs) drawn from a real-life context. The Models and Modelling Perspective (MMP) and the APOS (Action, Process, Object, Schema) theory were two frames that supported teaching activities in the experimental group. Mainly, MMP informed the design of an effective model-eliciting activity. The latter was used as a guide in designing a heuristic-based instructional sequence conducted in this study explaining the mental structure of learners and the method through which they attain the conception of algebra. To analyse the impact of the heuristic-based problem-solving instruction, 205 learners in four different middle schools in the North Wollo district (in Ethiopia) were selected by means of convenience sampling. The study used both qualitative and quantitative research methods. The main instruments in this study were, 1) a classroom observation schedule; 2) model-eliciting activities; and, 3) an achievement test. The first and second instruments are qualitative components. The first was used to document teachers’ teaching processes in participating classrooms during lesson observations. The second instrument was used to, 1) serve as a medium of interaction between the researcher and learners during the implementation of the heuristic-based problem-solving instruction; 2) assess learners’ background knowledge on algebraic variables in their effort to solve the designed MEA; and, 3) assess the learning opportunities created by the designed MEA. The third instrument was the quantitative component used to measure the comparative effects of the heuristic-based instructional method. The findings from the classroom observations revealed that participating schools employed comparable conventional teaching methods. The implementation of the problem-solving approach of instruction gave insights into how a heuristic-based problem-solving approach of instruction can be developed and used in grade 8 algebra lessons, and the factors that could influence conceptual development of learners in algebra. The results from the qualitative data also revealed that, 1) learners did not build relevant background knowledge in their previous schooling on algebraic variables that enabled them to understand and interpret the situations of the designed MEAs; and, 2) engaging learners in MEAs supports the goals of Science Technology Engineering and Mathematics (STEM) education. The findings from the quantitative component supported the initial hypothesis that participation in the heuristic-based problem-solving instructional method results in improved test scores in algebra.