Each instructor presented the calculus readiness test in their courses. The test was given in two different college classrooms in a high stakes situation (they were both given as parts of exams). In particular this test was given to a pre-calculus course at the end of the course as part of the final and to a calculus I course as a quiz early in the course. Because of the high stakes nature of these activities, the students did take this seriously and we felt the results could be trusted as a good indicator of their understanding. The pre-calculus assessment was presented in the high schools in a more low stakes environment. This was due to the fact that there was significant testing pressure already in the high schools as they had just finished rounds of state wide and national testing. These made giving another test seem excessive. Both Terra and Linda felt that their results were not as reliable as students were exhausted from the testing regime and may not have taken tests as seriously as those in the college environment.
The reaction to the particular pre-calculus activities was good in both environments. The students in all the classes were engaged and seemed interested in the tasks. All three instructors gave the activities during class time, although at the time of this writing they have only been completed in the college classrooms. The numerical function activity was given to a college pre-calculus classroom and as noted earlier in this report the students did quite well on the pre-test (average score of 8 out of nine points on the pre-assessment). This left little room for improvement. The students naturally did quite well on the numerical activity, but their scores on the post assessment were basically the same with many students seeing no improvement from the pre-assessment. Based on these results, we decided to add more questions on the activity that focused on the use of undefined constants in functions. This is the form of the activity that is attached. Unfortunately we have yet been able to test this modified form of the activity with a classroom.
The graphical functions task was also given in the college pre-calculus classroom and students did not do as well on the pre-assessment (average score of 2.8 out of 4) as they had with the numerical task. Again the students really enjoyed the task and were engaged during the class time it was given. The students did achieve some improvement on the task (average score of 3.1 on the post assessment) and overall the group of instructors felt this showed promise. We plan on giving this task to additional classrooms both in the college environment and the high school environment to analyze it further.
The verbal functions task was also given in the college pre-calculus classroom and students really did struggle on the pre-assessment (average score of 1.5 out of 5, where the problems were weighted with 1 point for the first problem and 2 for the second and third) The students were quite engaged with the activity during class especially with the problems that asked them to model the height of water in a bottle over time. Nearly all the students commented that they had rarely seen problems that asked them to draw graphs from verbal descriptions before and most commented that they found them interesting. The students did show some improvements on the post assessment (average score of 2.6 out of 5). Again we are planning on giving this task to more students in additional settings to analyze its effectiveness further.
