# 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

Shen, Che (2012) 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. Doctoral thesis, University of East Anglia.

## Abstract

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.

Item Type: Thesis (Doctoral) Faculty of Social Sciences > School of Education and Lifelong Learning Users 2259 not found. 12 Mar 2014 17:40 12 Mar 2014 17:40 https://ueaeprints.uea.ac.uk/id/eprint/48142