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Research

  • Anchoring probability situations which are conceptually analogous to misconception-prone/target probability situations were generated and tested with secondary mathematics students. The testing showed that probability misconceptions were common but also that anchors for overcoming these misconceptions could be generated. Anchoring situations were effectively utilized in overcoming students' probability misconceptions in the short term. A follow-up study showed that short term effects were retained at the rate of 0.65 over a six month period thereby establishing the long term effectiveness of the approach.

  • This study is aimed at the investigation of the non-cognitive factors related to students' beliefs and attitude before and after taking an introductory statistics course using an interview methodology. Of particular interest is to compare students' beliefs and attitude between students from a technology-rich class and from a traditional class. The purposes are (a) to investigate if students' attitude has changed after taking a technology-rich statistics class and their experience about technology, and (b) to compare if there is a dramatic difference between the technology-rich class and a traditional class before and after taking the course.

  • This qualitative study examined students' experiences with the constructivist approach to learning in an introductory statistics university course. An overview of students' difficulties and frustrations were addressed for three pedagogical aspects. Findings suggested that students' difficulties were related to their epistemological beliefs of the nature of statistical knowledge, the simplicity of knowledge, and the source of knowledge. Therefore, students' frustrations seems to be connected to the agreement between their epistemological beliefs and those of the professor.

  • This paper compares the learning experiences of students from a technology based introductory statistics course with that of a group of students with non-technology based instruction.

  • The Sampling Distributions program and ancillary instructional materials were developed to guide student exploration and discovery. The program provides graphical, visual feedback which allows students to construct their own understanding of sampling distribution behavior. Diagnostic, graphics-based test items were developed to capture students' conceptual understanding before and after use of the program. Several versions of the activity have been used to date with mixed results. Our findings demonstrate that while software can provide the means for a rich classroom experience, computer simulations alone do not guarantee conceptual change.

  • In this paper we present the results from a theoretical and experimental study concerning university students' conceptions (Artigue, 1990) about the logic of statistical testing.

  • We asked active psychological researchers to answer a survey regarding the following data-analytic issues: (a) the effect of reliability on Type I and Type II errors, (b) the interpretation of interaction, (c) contrast analysis, and (d) the role of power and effect size in successful replications. Our 551 participants (a 60% response rate) answered 59% of the questions correctly; 46% accuracy would be expected according to participants' response preferences alone. Accuracy was higher for respondents with higher academic ranks and for questions with "no" as the right answer. It is suggested that although experienced researchers are able to answer difficult but basic data-analytic questions at better than chance levels, there is also a high degree of misunderstanding of some fundamental issues of data analysis.

  • Four experiments tested how well students in a college algebra class could use the solution of a distance, mixture, or work problem to solve other problems in the same category. The solution could either be applied directly to solve equivalent problems or had to be slightly modified to solve similar problems. Students in Experiment 1 could not use the solution to produce more correct solutions on either equivalent or similar problems. Experiments 2 and 3 demonstrated that either allowing students to consult the solution as they worked on the test problems or providing more elaborate solutions improved transfer to equivalent problems but did not improve transfer to similar problems. In Experiment 4 there was some transfer to similar problems that differed in complexity, but students relied too much on a syntactic approach in which they filled in the "slots" of an equation.

  • Continuous Quality Improvement (CQI) better known in industry as Total Quality Management (TQM), is a management philosophy which has transformed many businesses and corporations internally and is now beginning to make strong inroads into universities, predominantly on the administrative side. This paper raises the question of whether the conceptual framework provided by CQI/TQM is a fertile one for addressing the problems involved in university teaching. It translates basic tenets of CQI/TQM into the univeristy teaching context and outlines how these ideas have been implemented in a large, multisection, introductory statistics course. Particular attention is given to the problems of fostering steady year-to-year improvements in a course that can survive changes of personnel, and in making improvements by stimulating group creativity and then capturing the results for the future.

  • The purpose of this study was to develop a theoretical model for the use of counterintuitive examples in the introductory non-calculus-based statistics course at the college level. While intuition and misconceptions continue to be of great interest to mathematics and science educators, there has been little research, much less consensus or even internal consistency, in statistics curriculum development concerning the role of examples with counterintuitive results. Because the study intended to provide educators with useful connections to content, instructional methods (e.g., cooperative learning) and learning theory constructs that have been successfully used in mathematics or science education, the model that emerged was organized around a typical syllabus of topics. The study critiqued and the reconciled "Traditional" and "Alternative" perspectives. The Traditional Position attempts to minimize possible confusion and frustration by avoiding such examples, while the Alternative Position uses them to motivate and engage students in critical thinking, active learning, metacognition, communication of their ideas, real-world problem solving and exploration, reflection on the nature and process of statistics, and other types of activities encouraged by current reform movements. The study delineated specific criteria and conditions for selecting and using counterintuitive examples to achieve numerous cognitive and affective objectives. Examples explored include the Monty Hall problem, Simpson's Paradox, the birthday problem, de Mere's Paradox, The Classification Paradox, the Inspection Paradox, and required sample size. The study connected many of these examples (especially Simpson's Paradox) with other conterintuitive examples, with known probability or statistics misconceptions many students have, with representations from other branches of mathematics, and with the constructivist paradigm. Problematic issues addressed include difficulty in constructing assessment instruments and a multiplicity of terminologies and typologies. Additional directions for research were suggested, including several empirical investigations of various facets of the model. The connections, examples, and representations presented should be extremely useful for teachers of statistics, but should also enrich the pedagogy of teachers of other courses.

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