An Exploration of Students’ Construction of Meaning through Symbolic Manipulation and Table / Graph Use in Statistical Inference Tasks: The Cases of Normal and t Distributions

This study investigates college students’ use of statistics tables when solving problems on normal distribution and t distribution. Particular attention is given to the way in which students use the graphical representation of the normal curve and the t-curve in their solutions. A review of the literature on the teaching and learning of statistics at undergraduate level reveals that not much work has been carried out to investigate how students use statistics tables. The data in this study was collected in a business school at a private institute of technology in the south of Taiwan. Ten students in the second year of their course and their teacher participated in the study. The students were interviewed three times during the course of one semester. The data collected include field notes, audio recording and photos of classroom observation; participants’ answer sheet in the mid-term and final examinations, and exercise questions and audio/video recordings in the interviews. The main body of data are the clinical interviews carried out with the students. In these interviews the students were asked to solve statistics problems using a talk-aloud technique. The interviews were audio recorded and fully transcribed. The interview data were analysed by decomposing the students’ answer into the solving steps used in the solution of each problem. Analysis of the participants’ solutions revealed that using the tables of distribution to find the solution to the given task was problematic. Their solution attempts can be categorised into six types, but the underlying difficulty appeared to be the symbolic manipulation of the data in the question. Students seem not to ascribe statistics meaning to the symbols and tend to perform symbolic manipulations without investigating the meaning of the symbols first. Moreover, most participants did not use graphs when they solved the problems, and only four participants actively used graphs in a few questions, perhaps to visualise the values in the questions or to create meaning. The students who consistently used graphs in their solutions on the whole performed better than the ones who didn’t across the topics. The study concludes with some recommendations for the teaching of statistics as a service subject.

Name dc:type.qualificationname

phd

Level dc:type.qualificationlevel

doctoral

Grantor dc:publisher.institution

University of East Anglia

Year dc:date.issued

2012

Author dc:creator

• Shen, Che

Language dc:language

en