The effectiveness of the concrete / semi-concrete / abstract (CSA) appoach and drill- practice on grade 10 learners' ability to simplify addition and subtraction algebraic fractions

Abstract

This study was conducted in one of the education districts in the Eastern Cape Province of South Africa. The purpose was to analyse the effectiveness of the concrete/semi-concrete/abstract (CSA) approach and drill-practice instructional strategies on Grade 10 learners’ ability to simplify addition and subtraction of algebraic fractions. The following two objectives were set. First, to identify the learners’ challenges in studying addition and subtraction of algebraic fractions in grade 10; and second to analyse the effectiveness of the CSA approach and drill-practice instructional strategies on Grade 10 learners’ ability to simplify addition and subtraction of algebraic fractions. Both threshold concepts and troublesome knowledge, Polya’s problem-solving techniques, CSA Approach theory and Drill-practice theory were all pertinent as a theoretical framework for the study. Positivism research paradigm was adopted for the study and it afforded the researcher opportunity to employ quantitative research approach. Based on the research question of this study, an experimental design was chosen as a suitable descriptive design. Purposive sampling method was used to select three schools which involved 135 grade 10 mathematics learners. Stratified random sampling method was thereafter employed to select 45 learners from each school for the study. The learners were grouped in each school as top, average and weak based on their performance in Algebra in term one. Pre-questionnaire and post-questionnaire were used to obtain data regarding challenges learners experience in simplifying addition and subtraction of algebraic fractions. Ethical clearance from the relevant school and university authorities were obtained. On the first two days, the researcher briefed the school authorities and learners and explained to them the purpose and details of the study. Day three was used to administer the pre-questionnaire test, thereafter, the next ten days were used to teach addition and subtraction of both numeric and algebraic fractions with same and different numerators and denominators. The next two days were used for revision and the last day was used to administer the postquestionnaire test out 25 marks. The respondent rate was 98.5%. The data collected were analysed by using SPSS version 16.10. Both descriptive and inferential statistics were used to analyse the data. The pre-questionnaire scores revealed that majority of the learners’ perceived fractions as two separate entities and as a result add or subtract numerator to numerator and denominator to denominator. It was also discovered that learners had a challenge in finding LCM of algebraic fractions. A t-Test for independent means was used to test the following hypotheses at = 0.05: : The CSA approach and drill-practice intervention has no significant effect on Grade 10 learners’ ability to simplify addition and subtraction of algebraic fractions; : The CSA approach and drill-practice will significantly enhance Grade 10 learners’ ability to simplify addition and subtraction of algebraic fractions. The t-Test revealed a p-value of 0.139 which was statistically significant at = 0.05. Therefore, the researcher rejected the null hypothesis and concluded that the CSA approach and drill-practice have significantly enhanced the Grade 10 learners’ ability to simplify algebraic fractions