University students' problem posing abilities and attitudes towards mathematics

Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, Jun 2002 by Grundmeier, Todd A

ABSTRACT: This study explored the problem posing abilities and attitudes towards mathematics of students in a university pre-calculus class and a university mathematical proof class. A measure of attitude towards mathematics and corresponding two sample t-test revealed a significant (p = .001) difference in the attitude levels of students in the two classes. A measure of problem posing ability explored students problem posing abilities in both numeric and non- numeric contexts. Two sample t-tests showed no significant difference in the problem posing ability (numeric or non-numeric) of students in the two classes. A matched pairs t-test showed a significant difference in numeric posing versus non-numeric posing ability in both classes. Lastly there was no correlation between students attitudes towards mathematics and problem posing abilities.

KEYWORDS: Problem posing, attitudes, undergraduate mathematics.

INTRODUCTION

Problem posing is becoming recognized in the United States as a necessary component of mathematics teaching and learning [5,8,9,10]. Allowing students to pose their own mathematics problems can influence, among other things, attitudes towards mathematics, ownership of mathematics and mathematics achievement [3,10]. As stated by Silver, "contemporary constructivist theories of teaching and learning require that we acknowledge the importance of student-generated problem posing as a component of instructional activity [10, p. 19]." Researchers and educators have begun to incorporate problem posing into mathematics teaching and learning [3,4,14]. English and Grove studied the implementation of a problem posing program in third, fifth and seventh grade classrooms and showed that it is feasible to incorporate problem posing into instruction at these grades [4]. Winograd and Higgins have utilized problem posing as a tool for interdisciplinary English and mathematics classes [14].

Research has also examined problem posing abilities ranging from elementary school students to middle school teachers [6,11,12]. Winograd has shown that elementary school students are both willing and able to pose mathematical problems that challenge themselves and classmates [12,13]. Leung and Silver showed that prospective elementary school teachers were able to pose mathematical problems but in many cases their problems lacked mathematical complexity [6]. As problem posing is beginning to be incorporated into mathematics classrooms it is important to continue to document students capabilities as problem posers.

Research has also examined the relationship between students mathematics achievement and mathematics anxiety and between mathematics achievement and attitudes towards mathematics [2,7]. These results combined with past research on problem posing have lead to the question, "Is there a relationship between students' problem posing ability and attitudes towards mathematics?"

The research presented here documents and analyzes the problem posing abilities and attitudes towards mathematics of students in two university mathematics classrooms. The following aims motivated this research,

1. To record the problem posing abilities and attitudes towards mathematics for both Pre-calculus and Mathematical Proof students and try to identify quantitative differences in problem posing abilities and attitudes.

2. Make conclusions related to how problem posing ability and attitude towards mathematics differ between students in introductory and advanced mathematics classes.

The remainder of this paper will focus on the research methods undertaken in this project, results, implications of these results, and suggestions for future research.

RESEARCH METHODS

This was an observational study with the intention of examining problem posing abilities and attitudes towards mathematics of university students. The research was undertaken at a medium sized state university in the northeast and was done with approval from the institutions review board for the use of human subjects. Data was collected in both a pre-calculus and mathematical proof class and the students responded to measures of their attitude towards mathematics and problem posing ability.

Figure 1. Sample statements (from the complete set of 21 statements) from the measure of attitude towards mathematics.

Directions: Respond to the statements on a scale from 1 to 5, 1 being strongly disagree, 3 being neutral and 5 being strongly agree. Do not spend time thinking about each question in detail, please answer with your initial instinct [1].

1. I enjoy going beyond the assigned work and trying to solve new problems in mathematics.

2. Mathematics is enjoyable and stimulating to me.

3. Mathematics makes me feel uneasy and confused.

4. I am interested and willing to use mathematics outside of school and on the job.

5. I have never liked mathematics, and it is my most dreaded subject.

6. I have always enjoyed studying mathematics in school.

7. I would like to develop my mathematical skills and study this subject more.