Factors Supporting College Mathematics Sucess: Orientation, Voice, and Technological Pedagogical Content Knowledge

The purpose of this study was to examine factors supporting college mathematics success. First, effect of a brief high school orientation to mathematical technologies used for college placement testing was examined. Secondly, the voice of participants in this orientation was heard. Finally, bootstrapped orientation data were presented to teachers and instructors of introductory statistics courses as a scaffold to their technological pedagogical content knowledge (TPCK) as these teachers and instructors strive to actively engage students to achieve college mathematics success.

Many entering college students are placed into developmental mathematics classes based on scores from college placement assessments that allow extremely limited use of calculating technology and have various time constraints. Students in a rural central Texas 3A high school that were enrolled in Algebra II course were given pre- and post- tests in Arithmetic and Algebra. Each 20-minute test contained 15 mathematical content questions and one qualitative question. The post-test was given approximately a week after the pre-test. During the week, students were provided time to explore review material using only pencil and paper for the arithmetic review, and a four-function calculator on the algebra review questions. Effects of the orientation were analyzed using mean scores, confidence intervals, effect size, and GLM for whole-group and sub-groups. A paired samples t-test was calculated. These effects were discussed.

A case study involving participants of the orientation was conducted. Twelve participants were interviewed after each had entered college. Five themes emerged from these interviews: (1) Knowledge of College Mathematics, (2) Technology and Mathematics, (3) Mathematics Tests/Assessments, (4) Teaching and Learning Mathematics, and (5) Mathematical Experiences, Hopes and Dreams. Each theme is discussed.

Using Microsoft Excel, bootstrapping is presented to instructors of first year introductory statistics courses in support of student success as instructors? technological pedagogical content knowledge is developed. A course project demonstrating and developing application of computational technology by bootstrapping confidence intervals at the 95 % level using Microsoft Excel is presented. Data from the orientation were further analyzed in the bootstrapping project. Confidence intervals were empirically calculated from bootstrapped resamples of the mean. The number of resamples used was 250 at each of three levels: Over-sampling, at-sampling, and under-sampling. Graphs of bootstrapped confidence intervals, using the Rule of Eye 4, showed statistically significant differences between pre-test and post-test scores for all pairs of data sets.