Transformations in high school geometry, an experimental study

The purpose of this study was to determine the feasibility of introducing a unit on transformations to the tenth-grade geometry program. To do this the experimenter considered five questions. -- 1. Can students attain competence with the mathematical concepts unique to the transformation approach? -- 2. How does student achievement on the transformation unit compare with student achievement on topics in the current geometry program? -- 3. What is the effect of the unit on student attitudes towards mathematics? -- 4. What are the attitudes of teachers towards the experimental materials? -- 5. Can the united be taught effectively without special teacher training? -- The study is essentially a non-comparative study in that no control group was used. The study consisted of presenting a fourteen lesson unit on transformations to 208 grade ten geometry students in six classes at Beaconsfield High School. The materials for the unit were taken from chapters four and five of a text by Coxford and Usiskin, Geometry: a Transformation Approach. -- To determine the students’ achievement on the unit, two tests were administered. The first was given at the end of the eighth lesson and the other was gtiven at the end of the fourteenth lesson. Both of these tests were constructed by the experimenter and was designed to test whether the behavioral objectives for the unit had been achieved. The Connelly Taxonomized Attitude Questionnaire was given as a pre-test, post-test to determine the effect of the experimental unit on student attitudes towards mathematics. To determine how the teachers felt towards the materials an experimenter-made questionnaire was given to each of the five teachers who taught the experimental materials. -- A dependent t-test for means was performed on the average score for the experimental unit and the average score computed to represent the students’ achievement on topics in the regular program of studies. A t-value of 10.717 indicated that there was a significant difference between the two sets of scores at the .05 level of significance. Since the mean for the experimental unit was higher than the mean for the regular topics it seemed reasonable to assume that students achieved considerably higher on the experimental unit. -- A dependent t-test for means was also performed on the pre-test, post-test attitude scores. A t-value of .772 indicated that there was no significant change in the attitudes of students towards mathematics at the .10 level of significance during the teaching of the experimental materials. -- The responses to the teacher questionnaire were analyzed and the results showed that teachers had favorable attitudes towards the materials. They recommended them highly to other teachers and they indicated that the materials were easy to read and most appropriate for the average student. They also indicated that the unit had value for both the terminating and continuing students in mathematics