The Relationship between Knowledge of Mathematical Concepts and Problems-Solving Ability in School in School Mathematics
The purpose of this study is twofold. Firstly, it seeks to investigate the relationship between students’ knowledge of mathematical concepts and their problem-solving ability with due consideration of their computational ability and comprehension of mathematics language. Secondly, it intends to find out whether teachers’ methods of teaching mathematical concepts would have any positive effect on the improvement of problem-solving ability of students. The study was carried out in Lagos State, using form four students of selected schools as subjects. For the first part of the study, five hundred and eighty eight (588) form four students in selected schools’ Management committees were used as subjects while new group of students numbering two hundred and forty (240) participated in the second part. Four tests were constructed to measure the performance of students in problem-solving in mathematics. The tests included knowledge of concepts, comprehension of mathematical language; computation and mathematics problem-solving. A matrix of bivariate correlations was obtained among the four variables. Multiple regressions analysis technique was applied in testing the significance of the F-ratio and the beta weighs. Problem solving was the dependent variable and the remaining three variables formed the independent variables. Significant positive correlations were found between problem –solving performance and each of the three variables. A significant positive bivariate correlation of 0.91 was obtained between knowledge of concepts and problem-solving ability. The F-ratio in the multiple regression analysis was significant at p<.05. Thus, knowledge of concepts contributed significantly to the prediction of students’ problem-solving performance in the presence of computational ability and mathematical language. The three independent variables had significant correlation coefficients and accounted for about 83% of the variation in problem-solving scores. For the second part of the study, that is experiencing with teaching methods, a concept-teaching approach combined with practice in problem-solving was used in teaching one experimental group for the five weeks. The students in the control group were not divided into three ability groups and administered the pre-test, treatment and post-test. The control group was also divided into three ability groups and were given the same pre-test and post-test. A concept-teaching approach combined with practice in problem-solving was significantly more effective than just asking students to practice on their own at the three ability groups. However, a concepts teaching approach with practice in problem-solving was found to be more effective with lower achievers. There was no significant difference between the higher and average achievers of the two experimental groups. The study highlighted some of the implications of these findings on mathematics instruction in Nigerian Secondary Schools. It also suggested various activities which the teacher might provide in order to improve the concept acquisition and problem-solving ability of secondary school students.