Determining Effectiveness

We tried to align each question in the calculus readiness test to specific standards. After giving the tests in our classes we met and organized our results to see if any obvious patterns emerged. It seemed initially that students struggled with representing functions in multiple forms in particular it seemed that students had difficult recognizing the relationship between function notation and graphs. It was also clear that they had limited ability to deal with functions described numerically. We decided we wanted more information so we each gave our students some “free-response” questions from previous AP Calculus courses  and met together to examine the student work. We again noticed that students struggled when dealing with functions in numerical, verbal or graphical form more than they did when the problem just asked for a symbolic representation. It was here that we decided to develop the pre-calculus tasks and try them in our classrooms. Each of implemented the pre-calculus tasks in our pre-calculus courses. We used a “Pre-test” and “Post-test” to measure significant learning that was designed for each task. A paired t-test was done on the data to measure the effectiveness. In the community college class the students seems to have a good knowledge of numerical presentations (they did quite well on the pre-test) so this left little room for improvement. The students did really seem to struggle with the questions that asked for detailed descriptions of function notation and this was not measured on the pre and post test. The community college students did show some improvement on both the graphical and verbal presentations, although neither level of improvement was statistically significant. This was not too surprising as students had limited exposure to this type of thinking prior to the administration of the task.  A general struggle we had with this project is that we just ran out of time. We would have liked to do an additional iteration of these tasks, give them to more classes and maybe develop them further.