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Real World Applications on Student Understanding in an AP Calculus Class: An Action Research Project 

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Indian River Schools 


Brian McMahon 




Indian River Schools 




Vero Beach, FL 


To assess the effectiveness of the use of GDCs though real world examples I designed a pre- and post- test to be given before and after a mini-unit involving three real world labs. The pre-test was administered after the normal discourse of the curricular unit on the applications of the derivative. However, shortly after administering the assessment, I had doubts regarding the validity of the scores. Because of the nature of the study and not wanting to penalize students unnecessarily, I did not factor the grade of this assessment into their nine weeks grade. Because of this, students did not prepare themselves as well as they would have had this test counted. Regardless, increases in scores from the pre-test to the post-test should not be summarily dismissed as the increases in scores were not totally due to a lack of preparation and an increased time in studying the content. In fact, an examination of the test scores found in Table 1 shows the class average increasing 34.5 percentage points. Further, not one student decreased scores from the pre-test to the post-test.
50% of the students surveyed responded that they understood little of the content assessed before the mini unit on GDCs. However, after the mini unit, 100% of those surveyed said they understood at least a good amount of the material with 38% stating they felt very comfortable with the content assessed.




TI-89, TI-Nspire CAS, AP, Advanced Placement, Calculus, Florida, Case Study 

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One of the most surprising results from this survey ran counter to what some researchers considered a limitation of GDCs. In Doerr and Zangor’s qualitative study on the use of GDCs in a math classroom, they summarized these limitations by stating “the graphing calculator emerged as a constraint and limitation in two ways: (1) students’ attempted uses of the device as a ‘black box’ without attending to meaningful interpretations of the problem situation; and (2) the personal (or private) use of the tool,” (2000). However, student responses from the survey showed that relying on the calculator to do complex mathematical operations allowed them to focus on the overall problem at hand. For example, one student responded, “The graphing calculator didn't increase my understanding on the applications of derivatives, but it made it easier to do the problems.” Another student stated “being able to use a calculator to reduce human errors” contributed to a greater understanding of the material. Finally, one student stated “the calculator can easily take care of the tedious algebraic simplifying that is so prone to mistake by hand. The use of the calculator boosted my confidence on the second test date, which helped me a lot.” While students did not address in the survey the personal use of the GDC, through informal observations and discussions, students expressed the use of the GDC actually increased the group learning dynamic leading to increased individual understanding. When one member of the group did not get the same answer as the others, it forced the group to examine the key strokes to locate the error. This error analysis performed as a group led to a greater student understanding of the material.
The benefit to student understanding of the multi-representational function of GDCs previously cited in this paper was also confirmed through the survey. One student summarized this thought stating, “I feel since I'm more of a visual type of person, at least when it comes to math, that the ability to see the graphs I’m working on helped substantially.” Further informal discussion in class further confirmed this sentiment. Students cited several “Aha” moments when looking at graphs, tables, and algebraic results of functions and their derivatives.
The survey did reveal one limitation in that the continued study of the content also led to a greater understanding during the post-test. A student summarized this thought by stating in the survey, “The extra time helped the material sink in better.” However, this limitation was tempered by the vast amount of comments touting the benefits of the GDC unit. Additionally, of the 8 students who took the survey, 2 stated they mostly agree and 4 stated they totally agree with the statement “The use of graphing calculators greatly contributed to my understanding applications of the derivative.” While there is truth in the thought continued study will result in higher scores, there is a point of diminishing returns where continued study utilizing the same methods will not return the same rate of improvement. That is why it is incumbent on teachers to integrate the use of graphing technology throughout their curriculum.
Student Understanding in AP Calculus - McMahon 2011.pdf    
Created at 8/22/2012 8:27 AM  by SP017\rfoshay 
Last modified at 8/22/2012 8:27 AM  by SP017\rfoshay