Ayesha Delpish, Ph.D.
Elon University
Department of Mathematics
Introduction
Statistics as a discipline demands to be taught in an applied context. One way to accomplish this is through the use of inquiry-based techniques, such as case studies, that help students more critically consider the relationship between theory and application. The need for new approaches to teaching mathematics has become more evident as both the student and the Statistics landscape has changed. In recent years, new movements in Statistics education have been motivated by the American Statistical Association (ASA).
The ASA endorsed report entitled The Guidelines for Assessment and Instruction in Statistics Education (GAISE)[1] gives six recommendations for teachers of college-level statistics:
1. Emphasize statistical literacy and develop statistical thinking.
2. Use real data.
3. Stress conceptual understanding rather than mere knowledge of procedures.
4. Foster active learning in the classroom.
5. Use technology for developing concepts and analyzing data.
6. Use assessments to improve and evaluate student learning.
But literacy, thinking and learning are all truly complex ideas, so how can I “foster” them with my students? Is “understanding” mastery? How do students come to know the material? Am I facilitating learning in my classroom? How do students learn? These questions, and many others, led me to this project.
Statement of Problem
My overall goal for the project was to arrive at a useful understanding of the developmental stages involved in solving authentic problems involving statistics. The purpose of the research was thus to investigate critical thinking/problem solving development skills among statistics students with secondary focus on the effectiveness of the case-method approach as a teaching and learning tool.
At the beginning of the ETLP project, my primary research questions were:
1. Does teaching using the case method give evidence of student learning?
2. Does this method lead to more authentic problem solving?
3. What skills do students use when faced with a problem?
With the knowledge gained through the program, my research questions evolved to include the following:
1. How do students in statistics solve problems?
- How do they sort information?
- How do they start the problem?
2. How do students approach critical thinking situations within an inquiry-based context?
- What does effective problem-solving look like in the case method?
- How do students develop “statistical thinking”?
These questions are of interest not only to the statistics education community, but to all communities of learners who may consider approaches such as the case study method as means of strengthening student content knowledge and their own understanding of learning.
Previous Research
While research into problem-solving techniques has been conducted for many years, the statistics community has only recently begun exploring the idea of “statistical thinking” (not to be confused with the often researched “mathematical thinking”). The most relevant work to this project is that of Wild & Pfannkuch [3] who define statistical thinking as “the incarnation of ‘common sense’…we know it when we see it…its absence is often glaringly obvious” (p. 223). In investigating the thought processes involved in solving real world statistics problems, the authors propose a framework for statistical thinking that involves four-dimensions:
a. The investigative cycle—problem specification, planning, collection, analysis, conclusions
b. The types of thinking—strategic planning, seeking explanations, modeling, applying techniques, need for data, variation, integration of statistics and context
c. The interrogative cycle—generating, seeking, interpreting, criticizing, judging
d. Dispositions—skepticism, imagination, curiosity, a propensity to seek deeper meaning
References
[1] Guidelines for Assessment and Instruction in Statistics Education (GAISE) College Report.
[2] Naumes, W., & Nuames, M. J. (2006). The Art and Craft of Case Writing. Thousand Oaks: Sage Publications.
[3] Wild, C. J., & Pfannkuch, M. (1999). Statitsical Thinking in Empirical Enquiry. International Statistical Review, 67(3), pp. 223-248.
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