An investigation into students' understanding of statistics

Abstract

This thesis is an investigation, both qualitative and quantitative, of students' understanding of statistics. Early investigations into the study of levels of understanding were directed at course content, but more recently the search has focused on student responses. This present study describes and analyses levels of statistical understanding identified in secondary students' responses. Students were given open-format questions concerning four basic areas of statistics, namely, data collection, data tabulation and representation, data reduction, and interpretation and inference. Their responses were grouped according to the degree of statistical sophistication exhibited and these groupings were further refined to develop an hierarchy of levels of understanding in each of the four areas. The framework of the SOLO Taxonomy (Biggs and Collis, 1991) was used to describe the hierarchy. The responses fell into two modes, the ikonic and the concrete-symbolic and features of each level within these modes were described. The influence of a number cf factors on these levels was investigated, quantitatively. The codings were found to increase in level with increasing academic year. Mathematical ability was also found to be an influencing factor on the level but gender had far less influence. By presenting data in raw form and as graphs, it was determined that in some instances the form of presentation of the data influences the level of understanding. During coding, responses were found to diverge into two distinct paths and a students' tendency to process simultaneously (Luria, 1966) was found to have some influence on this tendency. QUEST software was used to apply the Rasch model to the data to estimate overall statistical understanding for each student. From this analysis, tau and threshold values were used to provide quantitative evidence that the coding of the responses fell into two distinct cycles in the concrete-symbolic mode. The longitudinal aspect was also investigated by retesting the same students twelve months later. The identified hierarchy proved sufficient to code the responses and analysis of the results substantiated most results observed in the previous year. The increase in understanding was not significant over the twelve months. This supported the earlier findings of little significant difference in understanding between successive academic years. Interviewing of a small sample of students showed that prompting usually provided more information in the response but often at the same level. Probing allowed some students to increase their level but if pressured some students reverted to lower levels for support, thus exhibiting mutli-modal functioning. Level descriptions and the cycles identified in this study are consistent with recent findings by other researchers in the field of statistical understanding.