Problem solving heuristics and mathematical abilities of heterogeneous learners

Abstract

Descriptive design was utilized to identify the problem-solving heuristics and mathematical abilities of students in solving non-routine problems in terms of conceptual understanding, procedural knowledge, and problem-solving skill. Both quantitative and qualitative data were gathered from students' mathematical solutions, journals, and interviews. Six non-routine problems were given to thirty Grade 10 students. Each level of mathematical achievement includes ten students who were randomly selected using their averages in the first two quarters. "Compute or Simplify"and "Model or Diagram"were the usual strategies employed by the Proficient respondents. On the other hand, Compute or Simplify is the most frequent strategy used by Apprentice Problem Solvers. The first strategy includes straightforward application of rules in mathematics, correctly sequencing the operations and using other mathematical procedures, while the second includes the use of concrete representations and figures, acting out and formulation of algebraic statements. All the strategies were considered in solving the six non-routine problems. Most students under the three levels solved the problem by combining two or more strategies in getting the answer. Three students who belong to above-average mathematical achievement are considered proficient problem solvers while twenty-seven students who belong to average and below average are regarded as Apprentice Problem Solvers. No student among the thirty was considered Novice. Students performed best in conceptual understanding and least in problem- solving skills. The results revealed that there are no significant differences in the levels of each of the three components of mathematical abilities of students when they are grouped according to mathematical achievement.