RELATIONSHIP BETWEEN MATHEMATICAL THINKING AND ACHIEVEMENT IN MATHEMATICS AMONG SECONDARY SCHOOL STUDENTS OF NORTH WEST FRONTIER PROVINCE, PAKISTAN

Abstract

This study aimed to investigate the relationships between mathematical thinking and achievement in mathematics in the 9th grade scientific stream students in North West Frontier Province, Pakistan which was renamed as Khyber Pakhtunkhwa by the parliament of Pakistan through 18 th constitutional amendment in 2009. In addition, this study also investigated the gender, school sector, and school location differences in mathematical thinking and mathematics achievement. Besides, this study also investigated the interaction between gender and school location, gender and sector, sector and location, in relation to mathematical thinking and achievement. Further, this study examined conceptions of teachers about mathematical thinking and any inconsistencies between the teachers’ opinions about the aspects of mathematical thinking in terms of level of importance, level of difficulty and the results derived from the quantitative analyses of the student answers to the mathematical thinking test. In relation to the student interviews, the study also aimed to identify popular strategies used by students to arrive at solutions, question understanding, their perceptions about difficulty level of aspects of mathematical thinking and to differentiate between the thinking skills they used and to ascertain their attitude towards optimal solutions like checking their solutions. To achieve the above mentioned objectives, a model of mathematical thinking was first developed representing the best possible six aspects of mathematical thinking relevant to the curriculum of grade 9 in Pakistan with the help of experts and practising teachers. A test of mathematical thinking was developed based on this model to measure viimathematical thinking of the students. Besides a test of mathematics achievement with items taken from textbook of grade 9 and two interviews (one for teachers and one for students) were also conducted for data collection. Quantitative data was analyzed using t-test, Anova and regression analysis. Similarly qualitative data from interviews was analyzed using qualitative data analysis techniques. Main findings of the study showed that mathematical thinking was moderately related to mathematics achievement with proofs as the most correlated aspect. The study further showed that male students outperformed their female counterparts. In the same way, the students of the private schools scored significantly better than the students of public schools in all aspects of mathematical thinking and mathematics achievement. Teachers’ interview revealed that problem solving, induction, deduction, logical thinking, proofs and optimal solution were the most important aspects of mathematical thinking with proofs as the most difficult and generalization as the easiest aspects. Teachers expressed their opinions that student-centered teaching was the effective way in teaching of mathematics.