Cluster analysis of Catholic high school mathematics classroom environments and attitudes toward mathematics.

摘要

The overall purpose of this study was to discover what types of mathematics classroom environments exist in private Catholic high schools, and how they relate to students' attitudes toward the subject of mathematics. Specifically, this study is a replication and extension of previous investigations by Fouts (1987) and Fouts and Meyers (1992). This investigation builds on the previous studies in three ways: (a) The research was conducted in a different subject area (mathematics versus social studies and science), (b) it took place in private Catholic high schools rather than public high schools, and (c) it provided data from coeducational schools as well as two single-gender schools (one all-female and one all-male).;This study contains a stratified random sample of 30 high school mathematics classrooms drawn from five Catholic high schools in and around a major West Coast city. The number of high school students was 602. Each student completed a Classroom Environment Scale (CES) and an Estes Attitude Scale (EAS).;A cluster analysis was performed on the data collected from the CES. Three dusters were chosen a priori and were formed by using k means cluster analyses using Euclidian distances over the mean scores of the nine CES scales for each classroom. The 30 classrooms clustered well into three specific types. The mean scores of the CES arranged the classroom environments into high (most desirable), medium (moderately desirable), and low (least desirable) clusters.;An initial principal component analysis (PCA) was performed to see which of the nine CES scales were most important in separating the groups. Two definite components emerged, teacher-centered and student-centered scales. Therefore, two separate discriminant function analyses (DFA) were performed. The results of the teacher-centered DFA indicated that 69.9% of original grouped cases were correctly classified, and 65.1% of the student-centered were correctly classified. The teacher-centered predictors were Task Orientation, Rule Clarity, Order & Organization, Teacher Control and Competition; student-centered predictors were Teacher Support, Innovation Involvement, and Affiliation. However, when a DFA was performed on the EAS data, only 52% of the original grouped cases were correctly classified. This finding indicated a small degree of consistency in the classification scheme, where there is an almost 50/50 chance of classifying any one case correctly based on students' attitudes. This was an unexpected result.;The results of the study answered research question 1: What types of mathematics classroom environments exist in Catholic high schools? There are many types of classroom environments that exist in Catholic high schools, and they clustered well into three specific types as mentioned above as did their public school counterparts in previous studies. Findings for research question 2: Do single-gender Catholic high schools produce different mathematics classroom environments than their coeducational counterparts? The study showed that 7 of the 15 classrooms in cluster 1 with the most desirable environment were from single-gender schools (5 from the all-girls school and 2 from the all-boys school). This finding speaks well of single-gender classrooms but does not mean that coeducational classrooms cannot create satisfactory and productive environments as well. After the results of the tests were evaluated, research question 3 (i.e., What classroom environment factors in Catholic high schools are most closely related to positive attitude towards mathematics?) could not be answered unequivocally. Significantly different classroom environments did not produce different student attitudes toward mathematics.;The results of this study suggest that there is in fact a difference between these five Catholic high schools and the public schools in previous research in the effect of classroom environment on students' attitude toward a subject. Because this study produced results that were not expected---and therefore raised more questions than it answered---it lays the groundwork for further research in this area.