An investigation of the heuristics used by selected grade eleven academic algebra students in the solution of mathematical problems

This normative survey investigated the question, "What general heuristics are used by selected grade eleven academic algebra students in the solution of mathematical problems?" The investigator was interested in determining if students who had either A or B mathematics eleven grades used any heuristics. Forty-two students, who were enrolled in nine schools, were interviewed. Each student was given two mathematical problems to solve. These problems could be solved using two of nine general heuristics namely, cases, deduction, inverse deduction, invariation, analogy, symmetry, preservation of rules, variation, and extension. The researcher requested the students to think aloud. The student was encouraged to attempt the problems any way he chose. They were asked to be more concerned with revealing as much of their thought processes as possible, as with the accuracy of their solution. All the interviews were taped. The investigator found evidence that eight of the nine heuristics were used. The heuristics were cases, deduction, inverse deduction, invariation, analogy, preservation of rules, variation, and extension. Thirty-eight of the forty-two students interviewed showed evidence of using one or more of the heuristics. Eighteen of the students used cases, seven used deduction, three used invariation, two used inverse deduction, seven used analogy, two used preservation of rules, three used variation, and seven used extension. The investigator also found evidence that a heuristic which was not mentioned previously was used by eleven of the students. For the purpose of this investigation the heuristic was called "successive variation." When the heuristic of successive variation is used a possible resolution to the given problem is chosen at random. If the answer is not correct, the student determines what changes must be made. Then the possible solution is varied successively until the correct answer is found. The students’ command of the heuristics was not developed and therefore they could not use these techniques efficiently and effectively to solve the problems they were given.Education, Faculty ofCurriculum and Pedagogy (EDCP), Department ofGraduat