An Investigation of the Relationship Between Fifth-Grade Student and Teacher Performance on Selected Tasks Involving Nonmetric Geometry
Publication or External Link
Statement of the Problem: This study investigated the relationship between teacher and student performance on selected mathematical tasks. A measure of teacher effectiveness was obtained by comparing teacher and student performance on identical geometric tasks. Procedure: Teachers and their students from nineteen fifth-grade classes were designated as either control or experimental subjects. The six control treatment classes were presented topics in nonmetric geometry by means of self-instructional reading materials. The thirteen experimental treatment classes were presented the same topics by their teachers without the use of the reading materials. The duration of the instructional period consisted of four, fifty minute class periods. A criterion test, consisting of selected geometric tasks, was administered as a pre-test and post - test to the students of the control and experimental classes. The same test was administered to the teachers of the experimental classes at the conclusion of the instructional period. The hypothesis that students who read instructional materials in mathematics on their own will perform as well on selected tasks as those who have teachers explain and interpret the content for them was tested by comparing class mean scores. A second hypothesis questioned the relationship between the level of teacher performance on selected tasks and the level of performance exhibited by his students on these tasks. This hypothesis was examined by correlating the teacher scores on the criterion test with the mean scores of the classes in the experimental treatment. The relationship between teacher and student performance on individual tasks appearing on the criterion test was examined by comparing correct and incorrect item responses selected by teachers and students. A comparison of the proportion of student incorrect responses for classes whose teachers missed an item, with the proportion of student incorrect responses for classes whose teachers correctly responded to a particular item, was made by applying the chi square statistic to response frequencies. A similar procedure investigated the relationship between particular incorrect teacher response and student response. This aspect of the study investigated the effect of the teacher on student performance by comparing teacher and student behavior on individual tasks. Results: The reliability coefficient obtained for the criterion test was 0.72 as determined by the Kuder-Richardson formula 20. An estimate of item reliability was obtained and sixteen of the twenty-five test items exhibited acceptable reliability measures. The results of the analyses are summarized as follows: (1) An analysis of variance revealed that the mean score for the experimental classes was significantly higher than for the control classes at the 0.01 level; (2) there was a significant positive correlation between teacher test scores and class mean scores on the criterion test at the 0.02 level; (3) upon testing for independence of student and teacher selection of correct and incorrect responses to a particular item on the criterion test, ten of twenty-two items revealed a significant chi square at less than the 0.01 level. Items which exhibited a relationship between student and teacher performance either required a direct recall or application of a single definition presented in the materials; and (4) all but three of sixteen chi squares, which were not significant at less than the 0.10 level, supported the independence of teacher and student selection of a particular incorrect response to an item on the criterion test. Conclusions: It was concluded that:(l) There is no support for the hypothesis that students who read materials in mathematics on their own will perform as well on selected tasks as those who have teachers explain and interpret the content for them; (2) there is support for the hypothesis that if a teacher performs at a certain level of success on selected mathematical tasks, then his students, following instruction, will perform at the same level on these tasks; (3) there is a relationship between student and teacher correct and incorrect performance on selected tasks involving the direct identification and application of a single definition. No evidence was found of a relationship for tasks which require a combination of the application of two or more definitions; and (4) there is no relationship between teacher and student selection of a particular incorrect response to a task on the criterion test.