HIGH SCHOOL STUDENTS’ LEVELS OF THINKING IN REGARD TO ANALYZING
UNIVARIATE DATA SETS
Randall E. Groth
Salisbury University
## email not listed ##
This study investigated levels of thinking about the analysis of univariate data sets. The two
primary research questions addressed were: (1) What are some of the levels of thinking among
high school students in regard to comparing univariate data sets?; (2) What are some of the levels
of thinking among high school students in regard to analyzing the impact of a linear
transformation upon the center and spread of a univariate data set? Three levels of thinking were
identified for each research question.
Theoretical Perspective on Levels of Thinking
The study used the Structure of the Observed Learning Outcome (SOLO) Taxonomy of
Biggs and Collis (1991) in order to differentiate among levels of thinking. The unistructural,
multistructural, and relational levels of SOLO were of the greatest relevance to the present study.
The same theoretical perspective has previously been employed in describing levels of statistical
thinking for elementary and middle school students (Jones et al, 2000; Mooney, 2002).
Methodology
Participants
Purposeful sampling (Patton, 1990) was used in the selection of study participants. Fifteen
students representing a range of experiences with high school mathematics were recruited and
volunteered to be interviewed for the study. Since participants were selected in this manner, this
study did not attempt to statistically generalize findings across a large population. Instead, it
described the levels of thinking exhibited by students within the diverse sample chosen.
Procedure and instruments
An interview protocol (Groth, 2003) designed to elicit statistical thinking was administered
to each of the study participants. This paper reports upon the levels of thinking that were evident
in the responses to three questions on the interview protocol. The first two questions of interest
asked students to compare two sets of univariate data. They were given the opportunity to
compare data sets presented in both graphical and tabular form. The last question of interest
asked students to determine what would happen to the center and spread of a specific univariate
data set if each of the values in the data set was increased by a constant.
Data gathering and analysis
As students were interviewed, their responses were audiotaped, and the interviewer took
observational notes. The audiotapes were later transcribed for analysis. Written work completed
by the students during the interviews was also kept for analysis. Coding of students’ responses
was influenced by the SOLO Taxonomy, since interview responses were grouped into categories
on the basis of the number of relevant attributes included in each response and whether or not
connections were made among the relevant attributes incorporated.
Results
Levels of Thinking in Regard to Comparing Univariate Data Sets
The patterns of response for comparing univariate data sets represented one complete
unistructural-multistructural-relational (UMR) cycle. The cycle progressively built to the point
that it became evident that students perceived each of the data sets being compared as
Page 1 of 2 
Convention