Literature Index

Displaying 2851 - 2860 of 3326
  • Author(s):
    Lesser, L. M.
    Year:
    1994
    Abstract:
    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.
  • Author(s):
    Borovcnik, M. G.
    Editors:
    Bell, A., Low, B., & Kilpatrick, J.
    Year:
    1984
    Abstract:
    Descriptive statistics plays a subsidiary role in the stochastics curriculum, it is used to introduce notions in probability theory by analogy to corresponding notions in descriptive statistics and to motivate problems in inferential statistics. New ideas are to be developed and discussed in this paper which might enrich teaching descriptive statistics and change its status, namely exploratory data analysis, "open mathematics", and the idea of visualization. Descriptive statistics can and should be taught as interesting subject of its own right. Furthermore the new ideas have consequences on the view on statistics as a whole.
  • Author(s):
    Bannan-Ritland, B.
    Year:
    2003
    Abstract:
    In this article, a general model is proposed for design research in education that grows out of the author's research and work in related design fields. The model emphasizes the stage sensitivity of (a) research questions, (b) data and methods, and (c) the need for researchers to design artifacts, processes, and analyses at earlier stages in their research that can then be profitably used (perhaps by different researchers) in later stages.
  • Author(s):
    Meganck, B.
    Editors:
    Phillips, B.
    Year:
    2002
    Abstract:
    This paper focuses on the learning, rather than the teaching, of statistics in the context of Eurostat's role in developing statistical programmes and the transfer of statistical knowledge for the implementation of monetary union in Europe. It was against this background that the Committee for Monetary, Financial and Balance of Payments Statistics (CMFB) was established, bringing together senior officials responsible for statistics at central banks, senior statisticians at statistical offices, Eurostat and the European Central Bank statistics directorate in order to foster consultation and cooperation in areas of common interest. One of the important milestones achieved in the CMFB concerns work on new statistical methods, harmonisation, exchange of experience in the use of statistical techniques, and the general exchange of new statistical knowledge. Such knowledge transfer has not been restricted to members of the European Union but has also influenced statistical programmes of other countries, in particular candidate countries for accession to the European Union. They have a major interest in exchanging knowledge and learning more.
  • Author(s):
    Myers, J. L., Hansen, R. S., Robson, R. C., & McCann, J.
    Year:
    1983
    Abstract:
    In this study, 48 subjects who had no previous exposure to probability or statistics read one of three texts that varied in the degree of explanation of basic concepts of elementary probability. All texts contained six formulas, each accompanied by an example as well as definitions and information logically required to solve all problems. The high-explanatory test differed from the low-explanatory and standard texts in that it emphasized the logical basis underlying the construction of the formulas, the relations among formulas, and the relations of variables to real-world objects and events. On both immediate and delayed performance tests, subjects in the low-explanatory and standard-text conditions performed better on formula than on story problems, whereas the subjects in the high-explanatory text condition did equally well on both types of problems. It was concluded that explanation did not improve the learning of formulas but rather facilitated the application of what was learned to story problems.
  • Author(s):
    Myers, J. L.
    Editors:
    Grey, D. R., Holmes, P., Barnett, V., & Constable, G. M.
    Year:
    1983
    Abstract:
    We view understanding of mathematical material as a function of (1) connections of text concepts and formulas to real-world referents; (2) integration of concepts and formulas within the text; and (3) explanation of formulas. This view has provided a basis for constructing three written treatments of elementary probability, presumably varying in the degree to which they convey understanding. Our view of the processes involved in solving problems has led us to use both formula and story problems, and to emphasize analyses of error protocols. A research study is described involving 48 undergraduate students, randomly assigned to three text conditions. Results indicated that very different patterns of knowledge appear to be present in subjects in the non-explanatory (standard and low-explanatory texts) and explanatory conditions. Subjects in the two non-explanatory groups performed considerably less well on story than on formula problems, and often used the correct formula for a problem (that is, met the lenient criterion) but failed to solve it. A closer look at answers to story problems revealed that subjects in the non-explanatory conditions often required the explicit presence of key words which unambiguously pointed to certain operations, tended to misclassify problems in the presence of irrelevant or redundant information, and made many errors when the values in the story required modification before insertion into the formula. In contrast, subjects in the highly explanatory condition performed equally well on story and formula problems, tended to solve whenever they showed evidence of knowing the appropriate formula, and were considerably less hindered by absence of key words, the presence of irrelevant information, and the need to translate values in the story.
  • Author(s):
    Gil, E., & Ben-Zvi, D.
    Editors:
    K. Makar
    Year:
    2009
    Abstract:
    Explanations in statistics education are an uncommon research subject. Explanations however play an important role in the study of learning as documented in other disciplines, such as, science education, mathematics education, philosophy of science, and psychology. Explanations in these fields are considered a key and significant aid to promoting understanding and learning processes. This pre-SRTL6 paper will consider the role of explanations and context in learning to reason about Informal Statistical Inference (ISI) among sixth graders (age 12). This is a case study of several small groups of students, within an inquiry-based and technology-rich learning environment that was designed to promote Informal Inferential Reasoning (IIR). 
  • Author(s):
    BURRILL, Gail
    Year:
    2007
    Abstract:
    Providing tasks that enable teachers to understand how students are processing concepts allows teachers to shape instruction, plan, adapt, and differentiate, depending on what students need to learn. What does this look like when teaching statistics? This paper presents background on formative assessment and describes a framework for thinking about how it can be enacted in practice. The framework is illustrated by focusing on the nature of statistical tasks that can elicit information about student thinking and on instructional strategies that deliberately provoke such information. The discussion is grounded in work with students in middle school, pre-service mathematics education, and in-service elementary teachers, describing the challenges and dilemmas that arose and the strategies employed to overcome these challenges.
  • Author(s):
    Adair Mendes Nacarato and Regina Célia Grando
    Year:
    2014
    Abstract:
    This paper is based on research that investigated the development of probabilistic language and thinking by students 10–12 years old. The focus was on the adequate use of probabilistic terms in social practice. A series of tasks was developed for the investigation and completed by the students working in groups. The discussions were video recorded and complemented by the students’ written notes. The analysis was carried out under a historical-cultural perspective. We have identified how some notions about frequency, chances, possibility and probability are intuitive and how others are mistaken. Subjectivist probabilistic thinking is present in students’ ideas, and this indicates the need to develop teaching approaches that confront and overcome these ideas.
  • Author(s):
    Dvir, M., & Ben-Zvi, D.
    Year:
    2017

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The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education

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