Building on Students’ Prior Mathematical Thinking: Exploring Students’ Reasoning Interpretation of Preconceptions in Learning Mathematics

Abstract

The present study explored 285 11th-grade students’ preconceptions, misconceptions, and errors in solving mathematics tasks by graphical method. A descriptive-explorative study design was adopted. Cluster sampling was used to select students from sampled secondary schools in eastern and central Uganda. Students’ paper and pen solution sketches together with the task based interviews were used to identify students’ preconceptions, misconceptions, and errors in linear programming (LP). Students’ responses were analyzed thematically and interpreted as students’ learning gaps. The results indicated that students lacked proficiency in relating basic algebraic concepts and procedures to the mathematical language with which LP is conveyed. Generally, most students could not adequately use their previous knowledge and connect it to the learning and solving of LP tasks. Besides applying wrong mathematical algebraic concepts, students had difficulties interpreting and writing correct models (inequalities) from LP word problems. Misconceptions and errors were common and peculiar to and in individual student’s solution sketches especially in applying the concepts of equations and inequalities to graphically solve and optimize LP tasks. Students held extremely weak concept images of graphing equations, and inequalities and their linkage to optimizing feasible regions. This research provides insight into the learning of mathematics word problems (LP) and recommends that mathematics educators should effectively apply students’ preconceptions, misconceptions, and errors as opportunities for enhancing students’ LP conceptual changes. For mathematical proficiency, suitable learning approaches, methods, and strategies should be adapted to address specific individual student’s flawed conceptual and procedural knowledge and understanding. These approaches may guide educators in helping students to construct the connections between the old and the new knowledge.