A comparative study of the performance of high school Regular and Honors level students in geometry.

摘要

The main purpose of this study is to investigate the commonalities and the differences in the performance of Regular and Honors high school students in geometry. Students' achievement in geometry and students' geometric thinking were explored. The work of students in Regular and Honors geometry classes of one large high school were investigated. As part of the Regular classroom instruction and assessment, students were given a paper-and-pencil geometry pretest and a paper-and-pencil geometry posttest. Students' written work was analyzed, and then seven students were selected to be interviewed. During the interviews students were asked to explain their reasoning and to reflect on the solutions they provided on selected items of the written geometry posttest. Results were analyzed to answer the following major research questions:;Are there any significant differences between the pretest and the posttest geometry achievement scores of the Regular geometry and the Honors geometry students?;How does algebraic knowledge relate to high school students' geometry achievement scores in Regular and Honors geometry classes?;How do the justifications used in geometry solutions given by the Honors high school students compare to Regular high school students? What factors may be identified that may influence students' explanations of their reasoning?;Based on the statistical analysis performed in this study the results showed that: (a) There are significant differences between the Honors group and the Regular group with respect to students' achievement test scores for both pretest and posttest considered collectively. (b) There are no significant differences between the mean scores for the pretest and posttest scores of the Honors and Regular groups considered separately. (c) There are no significant differences between the mean scores of the boys and girls on the pretest and posttest within the Honors and Regular groups considered separately. (d) There are no significant differences between the mean scores of the pretest and posttest among the ethnic groups within the Honors and Regular groups considered separately.;This study shows that Honors students have a stronger algebraic knowledge than Regular students, and because of their algebraic background, for both the pretest and the posttest there is a higher significant difference between the score variances of the Regular and Honors groups.;This study shows that Honors students are able to explain their reasoning in a better educated manner than Regular students when solving geometry problems. Some of the factors that may influence students' explanations of their reasoning would be students not understanding fully the concepts, students having difficulties translating their thought processes into words because of a poor mathematical vocabulary, students' experience with their previous instruction and required type of work, and laziness in writing down their thoughts.