The relationship of cognitive learning styles, mathematics attitude, and achievement in a problem posing classroom

This study investigated relationships of cognitive learning styles, mathematics attitude, and mathematics achievement for students instructed with problem posing activities. It was conducted with pre-algebra students at Walters State Community College in Morristown, Tennessee. For one semester, three control classes (45 students) were taught in a traditional manner; and three treatment classes (46 students) were taught in a traditional manner plus one-third of the class time devoted to problem posing activities. Hypothesis one claimed there would be no significant difference in the mathematics achievement of control versus treatment students based on learning style and initial mathematics attitude. Hypothesis two claimed there would be no significant difference in attitude change during the study for students in the control versus treatment groups.

Pre-tests and post-tests of mathematics achievement, using the final examination of the course, and mathematics attitudes, using Fennema-Sherman Mathematics Attitudes Scales, were given. Teaming styles were evaluated with Kolb's Learning- Style Inventory (LSI-IIa). Due to the low number of converger learners, students were grouped for analyses in two ways: 1) concrete experience versus abstract conceptualization learners and 2) reflective observational versus active experimentation learners.

Achievement gain, for hypothesis one, was analyzed by ANOVA with factors of teaming style and treatment group membership; pre-attitude was tested as a covariate. Abstract conceptualization learners in the treatment group showed a significantly lower achievement gain than did abstract learners in the control group. No significant difference in achievement gain was seen between concrete learners in control and treatment groups. Mathematics pre-attitudes of students showed no significant effect on mathematics achievement gain. Analysis of students as reflective observational versus active experimentation learners showed no interactions.

Changes in mathematics attitudes were analyzed by repeated measures ANOVA with factors of learning style and treatment group membership; attitude tests were repeated over time. For attitude domains of anxiety and confidence in doing mathematics, abstract learners in the treatment group showed significantly lower attitude improvements than abstract learners in the control group. Abstract learners in general found mathematics more useful than did concrete learners.