The Nature of Misconceptions and Cognitive Obstacles Faced by Secondary School Mathematics Students in Understanding Probability: A Case Study of Selected Polokwane Secondary Schools

Abstract

The study investigated the probabilistic misconceptions of South African students. A questionnaire was administered to a group of 74 students from grades 10, 11 and 12 selected randomly from 5 schools around Polokwane and analysed using SPSS version 22. Five groups of misconceptions were identified. The Structure of the Observed Learning Outcome (SOLO) taxonomy was used in this study to describe students’ hierarchical understanding levels on the concept of probability. It was found that, generally there was no significant improvement in developmental level from grades 10 to 12. Overally, the mean of correct responses on the test problems was 2, 1411. The modal cognitive level on the individual test items was 2 which indicate that participants had some evidence of the use of probability principles and appropriate quantitative information is evident, but they may be incomplete or are incorrectly used. All participants had the basic understanding of the concept of probability and could carry out simple probability calculations. Participants of all levels showed evidence of the equiprobability bias (miscounting of outcomes in questions concerning theoretical probability), exhibited ignorance of the effect of sample size and were seldom successful on counter intuitive conditional probability problems. Gender differences were observed. The overall correct response rate of males (56.3%) was significantly greater than that of females (51.6%). Males and females also tended to answer differently, based on the type of question; many of these differences were statistically significant.

DOI: 10.5901/mjss.2014.v5n8p446