Mathematics--Study and teaching

The purpose of this study was to determine if urban high school mathematics teachers' attitudes toward the algebra mandate could be predicted by the variables: years of teaching mathematics, college major, highest college degree, gender, and ethnicity. Toward this end, the Attitude Toward the Algebra Mandate Survey (TATAMS) was administered to 98 high school mathematics teachers drawn from a total population of 493 who were employed by the School Board of Miami-Dade County, Florida, during the 1998--1999 School Year. The study was carried out in June 1999, roughly 20 months after the mandate became effect in Florida. Multiple linear regression analysis was used to test each hypothesis and to provide a model that was. predict of teacher attitudes. Five null hypotheses were formed to determine if there were significant relationships between teacher attitudes toward the algebra mandate and the aforementioned variables. The results of the tests of five null hypotheses showed that the hypotheses that involved years of teaching mathematics and ethnicity was rejected. These five predictor variables accounted for 27% of the variance in teacher attitudes. The inference drawn from the study was that the negative attitudes of veteran White teachers and the positive attitudes of Hispanic teachers toward the mandate appear to have their roots in political and social considerations. Black teachers, on the other hand, have never challenged for the power in the district and are moderate in their attitudes toward the mandate.

The purpose of this study was to investigate which of two different instructional formats of a geometric construction activity was best suited to enhance student task performance. The subjects (N=50) were selected from community college students enrolled in introductory college mathematics courses and randomly assigned to one of two treatment groups. The groups differed in that group A received a different format of the procedural steps to reconstruct a given angle than that of group B. Form A consisted of adjoining text and diagrams where a diagram for each of the five steps of the task was pictured. Form B consisted of only two diagrams for the five-step process where it was necessary for subjects to determine which of the two diagrams was being referred to while proceeding through the steps. Both formats are representative of instructional materials currently in use in classrooms from the middle school level to the post-secondary level. During a personal interview session, each subject received one of two sets of directions describing the procedure of reproducing a given angle using a compass and straightedge. Each subject was asked to study the assigned set of directions with materials provided to practice the task. With the directions removed, each subject was then asked to reconstruct another, slightly different angle. Students given Form B, the reduced diagram format, significantly outperformed those students given Form A, x^2 (1, $N=50)=5.19, with no significant differences in the two groups with respect to the time spent studying the directions, t(48)=0.04, or completing the testing phase, t(48)=1.58. Other than use of the assigned form, mathematics ability was a significant factor in the subjects' ability to successfully complete the construction task, F(1,46)=7.79, p<.01. Verbal ability was not a significant factor, F(1,46)=1.81, p=.19, in the subjects' ability to successfully complete the construction task. Gender alone was not a significant factor, F1,46 =0.31, p = .58; however, when examined in combination with mathematics ability a significant interaction resulted, F1,46)=6.41, p=.02. Overall, success was significantly related to format, mathematics ability, and gender relative to mathematics ability.