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Project Background and Impetus Introductory statistics is one of the few ways in which the core mathematics literacy of liberal arts education is taken from the theoretical to the applied. Yet, as found in my own experience and as documented in literature from such sources as the Journal of Statistics Education, required courses in statistical analysis are generally unsuccessful in conveying the necessary concepts for students to apply or understand statistics. The limited degree of student learning is a disappointing outcome and the resulting dissatisfaction is common among faculty who teach in this area. This outcome arises from the unfamiliar nature of statistical concepts and the need to stack multiple levels of abstract thought one upon another to achieve critical insights and understanding. The levels of abstractions involved, the "dryness" of many foundation topics, and the math anxiety and inexperience with mathematical reasoning common to many students create a difficult learning environment. Several solutions to these problems have been proposed. These include the use of active learning methods; collaborative learning focused on a data analysis project; and use of computer tools for illustrating and visualizing abstract concepts. But there is still no systematic evaluation of any of these elements to determine what best addresses the pedagogical dilemma of introductory statistics. In order to address these issues, I have experimented with the use of digital video interviews with former students from my statistics classes, who have utilized statistical analysis to solve major problems in a professional context. The bottleneck here is twofold -- the difficulty that students have in relating what they are doing in the classroom to actual problem-solving in the real world, and motivating students to spend the time and energy required to learn the critical concepts and analytical techniques necessary to become proficient with statistics.
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Interpretation of Evidence and Results Overall, the survey results affirm the efficacy of the digitized video case study as the focus of a group exercise to enhance motivation and improve student learning. Moreover, the unexpected outcome of students revealing heightened critical thinking in the middle of the exercise further supports the finding that this video-based, digitized, case study technique is a successful active and collaborative learning method. However, additional research is needed to be able to generalize these results beyond the single case study utilized here. I anticipate having an opportunity to incorporate at least one additional video into the class prior to June 12th, thus supplementing these conclusions with additional evidence.
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The Video-Based, Digitized Case Study and Preliminary Signs of Student Learning My first video-based case study involved a former student who was an assistant to New York City Mayor Giuliani in the spring of 1996. The Mayor's Office was contacted by an elderly woman who had received a monthly water bill in excess of $50,000. This call was soon followed by a deluge of additional calls to the Mayor's Office. The problem went unresolved for a year, with numerous critical articles periodically appearing in the City's newspapers. Sitting in a staff meeting where no one could offer an explanation, this former student suggested a random sample of the millions of utility customers and an analysis that would include variables that might be related to such specious billings. She then utilized a multivariate regression that uncovered a strong statistical relationship between the erroneous bills and a specific manufacturer's water meter read with another (i.e., incorrect) manufacturers sensing device. The problem was resolved through the application of statistics and the former student was promoted. Capturing the description of this experience on fifteen minutes of digitized video provided a fascinating case that, in the context of the active learning, collaborative exercise, was the focus of small group and full class discussions. The learning outcome of this digitized video exercise first became apparent in the full-class discussion prior to the students seeing the second-half of the video. Even though none of the individual groups came up with the actual solution that was used, collectively the class touched upon all of the major elements that were incorporated into the statistical analysis. This was surprising, since I did not expect the students to be able to articulate the logic behind the outcome until after the second half of the video was shown. I now believe that this was an indication of the impact that a truly motivational exercise can have on stimulating students critical thinking and interaction via the small group process.
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Challenges, Pitfalls, and Implications for Student Learning In addition to the specific results derived from the digital video case study, there are several additional generalizations that can be made based on my experience with this project. First, because statistical analysis courses generally focus on developing a conceptual understanding of various methods and then applying that understanding to address real world problems, the development and application of these concepts is not a linear learning process. A major challenge in teaching statistics is the necessity to move back and forth between concepts and applications, such that one continuously reinforces the other. The digitized-video case assists in this endeavor by inherently incorporating these elements. Second, this project involves overcoming bottlenecks caused by students' misconceptions coming from an over-reliance on their own experience. With respect to introductory statistics, students have great difficulty in seeing how the techniques covered in the class can be applied in a professional setting. Moreover, the learning environment that is the focus of this research involves a conceptual leap to a higher level of analytical thinking. Thus, a critical element of the active learning exercise is the motivational component that gives students the impetus and confidence to make this conceptual leap. Third, one potential pitfall is the finding that it was necessary to reinforce the major concepts addressed by the exercise immediately after its completion. This was achieved by summarizing and reviewing the outcome of the exercise and directly relating that outcome back to critical concepts. Given my experience with this project, it is apparent that the lack of such a reinforcing capstone element would greatly reduce the learning outcome. Finally, another challenge and implication for both my teaching and student learning is the necessity to work iteratively toward a successful implementation of such new teaching and learning methods. Just as our students learn from these exercises, so do we, but our learning is focused on how to better achieve the desired outcome for the exercise. I was fortunate enough to have had previous experience that led to the realization that successfully implementing such learning exercises often takes two, three, or more iterations. It is clear that one must be willing to experiment with these learning methods, iterating towards success.
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Quantitative Evidence of Student Learning The motivational and learning outcomes of this digitized video exercise were formally evaluated using a survey that I gave to the students during the class meeting immediately following the exercise. The survey responses indicated overwhelmingly that: - the large majority of students found the video to be interesting and helpful in understanding how regression and general statistical analysis can be applied to real world problems;
- students thought that the small group and full class discussions were critical to their understanding of how statistical analysis can be applied;
- the video increased students' enthusiasm toward using statistical analysis in their professional careers; and
- the video and the active learning exercise were perceived as "fun."
The survey also produced some weaker but still significant results that demonstrated that the video: - increased students' desire to take additional statistical analysis classes; and
- enhanced their ability to communicate the results of statistical analysis to decision-makers.
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Bibliography Thomas Angelo and K. Patricia Cross (1993). Classroom Assessment Techniques: A Handbook for College Teachers, 2nd ed. (Josey-Bass: San Francisco). Paul Gardner and Ingrid Hudson (1999). University Students Ability to Apply Statistical Procedures. Journal of Statistics Education (1999), Vol. 7 (1), on-line Rhonda Magel (1998). Using Cooperative Learning in a Large Introductory Statistics Class. Journal of Statistics Education, Vol 6 (3), on-line. Leah Savion (April, 2003). Pet theories and nave misconceptions: What students bring to class. The Successful Professor, Vol 1(4), 4-6.
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