Application of Linear Programming Knowledge and Skills to Real Life Contexts by Secondary School Students in Kenya

Abstract

Linear programming is a specific class of mathematical problems, in which a linear function is maximized (or minimized) subject to given linear constraints. Linear programming can be used in a variety of business problems including: transportation and distribution, production scheduling, financial and tax plan, human resource planning, facility planning and fleet scheduling [1,2]. Yet many Kenyan secondary schools hardly teach this topic. The purpose of this study was to investigate whether using the origin test and extreme points technique can encourage and improve students’ learning of linear programming. Students’ performance on an achievement test, and application of linear programming skills were monitored. The study adopted the pre-test, post-test non-equivalent groups experimental design. The experimental group was taught the topic using the origin test and extreme points technique, a version of Problem Based Learning. The control group was taught using conventional methods. A mathematics achievement pre-test and a post-test were given to both groups to ascertain their respective entry and final performance abilities. In the pre-test, the experimental group had a mean score of 63.05%, while the control group had a mean score of 65.73%. An independent samples t-test gave a significance of 0.280 which is greater than 0.05, and a t value of 1.103 which is less than the table value of 2.37. This implied that the two groups had statistically similar entry behavior. Analysis of the post-test results gave a mean score of 58.07% for the experimental group, and 34.97% for the control group. A paired samples t-test gave a significance of 0.000 and a t value 20.13, implying a significant difference in performance between the two groups. In addition, the marks scored in item 3, and item 5 of the post-test, were used to determine the level of students’ application of linear programming skills. The mean score for these two items was 60.80 for the experimental group and 34.53 for the control group. A paired samples t-test gave a significance of 0.000 and a t value of 22.456, implying the experimental group was able to apply the linear programming skills significantly better than the control group. Two schools in Kakamega County were used to pilot the study. The face and content validity of the research instruments were determined with the help of mathematics educators and experienced secondary school mathematics teachers. The split half method was utilized in determining the instruments’ reliability. Pearson's coefficient (r) obtained for MAT 1 and MAT 2 in the two schools was above 0.88. Stratified Random Sampling was used to select ten each of form four boys, girls, and co-educational schools for the study. In total 1,502 form four respondents participated in the study.