EXPLORING GRADE 11 LEARNERS’ ALGEBRAIC THINKING IN THE FORMULATION OF QUADRATIC EQUATIONS FROM GRAPHS

Abstract

Algebraic thinking enables learners to devise algebra generalization when configuring quadratic equations from their graphical representations. Noticeable, learners grapple with this topic and there are some silent issues in the literature that should be explored in this discourse. Consequently, this prompted the current study, aimed to explore Grade 11 learners’ algebraic thinking when formulating quadratic equations from drawn graphs. The study adopted three tenets of the Lesh’s Translational model, pictorial and symbolic representations. An exploratory case study was used with 22 purposively sampled learners to explore algebraic thinking exhibited in learners’ responses to the graphical questions and transcripts from unstructured interviews. The algebraic thinking came from the exploration documents and interviews analysed through thematic analysis. The findings revealed that 17 learners lacked basic knowledge of algebra concepts which prevented the formulation of equations from graphs. This resulted from learners exploiting improper properties of algebra which were the requirement for the formulation of equations. The implication is that teaching, and learning should focus on the establishment of skills that permit exploiting appropriate prior knowledge relevant to this topic. Last, we suggest that empirical studies be conducted to focus on improving the instruction for the crafting of equations from graphs.

Keywords

• algebraic thinking, equation representation, graph, quadratic functions