LEARNING DIFFICULTIES AND MISCONCEPTIONS OF STUDENTS’ ON THE CONCEPT OF FUNCTIONS IN PREPARATORY SCHOOLS OF ARSI NEGELE TOWN, OROMIA NATIONAL REGIONAL STATE, ETHIOPIA

Abstract

The purpose of this study was to investigate the learning difficulties (LD) and misconceptions that preparatory school students’ have on the concept of function and their possible causes. In the study mixed research approach were employed. The major data collection tools were diagnostic test (DT); interview, and document analysis. The DT was administered to 178 grade 12 students enrolled in government (n=98) and private (n=80) preparatory schools during semester one of the academic year 2016/17. To conduct more detailed analysis of their responses to the DT, 20 students’ were interviewed. Four mathematics teachers were also interviewed. The DT used to determine students’ level of understanding (LU) in to five categories and explore students’ LD and misconceptions on the concept of function. The quantitative data obtained from DT was analyzed by SPSS version 20. The descriptive statistics and statistics inference t-test was used for analyzing the students LU. Narration was used for the different students written texts, interview and document analysis. Accordingly, students’ LD and misconceptions, and their possible sources were surveyed. The study results confirmed that the overall mean of students’ LU was partial understanding with specific misconception (PM). A t-test failed to reveal a statistically reliable difference between the means of LU on the concept of function private preparatory students ( = 3.188, s=1.310) and that of government preparatory school students ( = 3.00, s=1.422), p =0.362, p>0.05, however, study stream differences were observed (p=0.01, p<0.05). The finding reveal that students have several LD and misconceptions on concepts of function, mainly, on the definition of function, relationships function and equation, relationships between function and graph of equation, on piecewise function, composite function and in interpreting the components of function. The students written texts and interview results indicate that, their lack of skills and background, the existence many definitions of function, lack knowledge of associating function and equation as well as function and graph of equation and insufficient comprehension were some of sources of the problem. The finding of students LD and misconceptions and their nature held by students indicated a general failure of textbook prepared by MoE to teach a reasonable understanding of the concept of function. In addition, students’ interest and prior knowledge; lack of application and fun problems in the textbook and mathematics teachers burden of large period were the major sources of the problem suggested by preparatory school mathematics teachers. These results suggest that more work must be done in developing students’ understanding of the concept of function in the secondary school mathematics curriculum, and greater measure should be taken to ensure that students entering introductory calculus and advanced mathematics which directly need the concept of function as a prerequisite have a sufficient understanding, further, presents some suggestions for teachers, curriculum developers, and textbook authors to make students understand the subjects easier and to remediate their LD and misconceptions.