Journal Article

  • Teachers can use variety of strategies to instruct students in stat literacy. One such stratedy is using articles that contatin statistics which display commonly held beliefs. These encourage students to seek weaknesses and di ** strengths of factual information. Using essay questions that appear to have a answer are another means to engage students in statistical learning.<br>University students are best taught statistical literacy through a general education course. The first step is to explore an issue that has been taken for granted and is incontrovertible in the students' minds, such as the safety and effectiveness of immunizations. Students begin by evaluating an article with a negative slant on immunizations and by examining their own preconceived ideas. Students then receive a comment sheet in which the teacher responds generally to their arguments, provides factual support for their beliefs, and mentions some of the strengths of the article. Students are then asked to consider how a study can be designed to examine a particular question and to discuss why such a definitive study cannot actually be performed. An example of how the student discussion can be translated to a consideration of immunizations for Hepatitis B is presented.

  • A sample of 134 sixth-grade students who were using the Connected Mathematics curriculum were administered an open-ended item entitled, Vet Club (Balanced Assessment, 2000). This paper explores the role of misconceptions and naive conceptions in the acquisition of statistical thinking for middle grades students. Students exhibited misconceptions and naive conceptions regarding representing data graphically, interpreting the meaning of typicality, and plotting 0 above the x-axis.

  • The influences on adult quantitative literacy were studied using information from the National Adult Literacy Survey, 1,800,000 individuals between 25 and 35 years of age and not in school. The major influences on quantitative literacy were educational background (t=123-; df=1; p[less than].0001), daily television usage (t=1538; df=1; p[less than].0001), and disability (t=713; df=a;p[less than].0001). Education impacted television usage (t=691; df=1;p[less than].0001) and personal yearly income (t=991; df=1;p[less than].0001). Ethnicity affected income levels (t=898; df=1 p[less than].0001), which in turn influenced television viewing (t=1514; df=1; p[less than].0001). The results indicated that education seemed the key to increasing adult levels of quantitative literacy. Library usage, parents' education, and gender did not exhibit any relationship with quantitative literacy

  • Describes the WISE (Web Interface for Statistics Education) that was developed to enhance student learning and understanding of core statistical concepts relevant in higher education. Discusses the use of Web technology; the impact on teaching; barriers to computer-based learning; and impact on student learning.

  • Attempts to teach statistical thinking using corrective feedback or a ``rule-training'' approach have been only moderately successful. A new training approach is proposed which relies on the assumption that the human mind is naturally equipped to solve many statistical tasks in which the relevant information is presented in terms of absolute f requencies instead of probabilities. In an investigation of this approach, people were rained to solve tasks involving conjunctive and conditional probabilities using a requency grid to represent probability information. It is suggested that learning by doing, whose mportance was largely neglected in prior training studies, has played a major role in the current training. Study 1 showed that training that combines external pictorial epresentations and learning by doing has a large and lasting effect on how well people an solve conjunctive probability tasks. A ceiling effect prevented comparison of the requency grid and a conventional pictorial representation (Venn diagrams) with respect o effectiveness. However, the grid representation was found to be more effective in Study 2, which dealt with the more difficult topic of conditional probabilities. These results uggest methods to optimize the teaching of statistical thinking and the presentation of statistical information in the media.

  • It is essential to base instruction on a foundation of understanding of children's thinking, but it is equally important to adopt the longer-term view that is needed to stretch these early competencies into forms of thinking that are complex, multifaceted, and subject to development over years, rather than weeks, or month. We pursue this topic through our studies of model-based reasoning. We have identified four forms of models and related modeling practices that show promise for developing model-based reasoning. Models have the fortuitous feature of making forms of student reasoning public and inspectable - not only among the community of modelers, but also to teachers. Modeling provides feedback about student thinking that can guide teaching decisions, an important dividend for improving professional practice.

  • After 4 decades of severe criticism, the ritual of null hypothesis significance testing - mechanical dichotomous decisions around a sacred .05 criterion - still persists. This article reviews the problems with this practice, including its near-universal misinterpretation of p as the probability that H 0 is false, the misinterpretation that its complement is the probability of successful replication, and the mistaken assumption that if one rejects H 0 one thereby affirms the theory that led to the test. Exploratory data analysis and the use of graphic methods, a steady improvement in and a movement toward standardization in measurement, an emphasis on estimating effect sizes using confidence intervals, and the informed use of available statistical methods is suggested. For generalization, psychologists must finally rely, as has been done in all the older sciences, on replication.

  • One hundred-eight students in Grades 3, 5, 6, 7, and 9 were asked about their beliefs concerning fairness of dice before being presented with a few dice (at least one of which was "loaded") and asked to determine whether each die was fair. Four levels of beliefs about fairness and four levels of strategies for determining fairness were identified. Although there were structural similarities in the levels of response, the association between beliefs and strategies was not strong. Three or four years later, we interviewed 44 of these students again using the same protocol. Changes and consistencies in levels of response were noted for beliefs and strategies. The association of beliefs and strategies was similar after three or four years. We discuss future research and educational implications in terms of assumptions that are often made about students' understanding of fairness of dice, both prior to and after experimentation.

  • It is claimed here that the confidence mathematics education researchers have in statistical significance testing (SST) as an inference tool par excellence for experimental research is misplaced. Five common myths about SST are discussed, namely that SST: (a) is a controversy-free, recipe-like method to allow decision making; (b) answers the question whether there is a low probability that the research results were due to chance; (c) logic parallels the logic of mathematical proof by contradiction; (d) addresses the reliability /replicability question; and (e) is a necessary but not sufficient condition for the credibility of results. It is argued that SST's contribution to educational research in genera, and mathematics education research in particular, as not beneficial, and that SST should be discontinued as a tool for such research. Some alternatives to SST are suggested, and a call is made for mathematics education researchers to take the lead in using these alternatives.

  • I have found writing this response to be a difficult task, as evidenced by my inability to resist the combination of clich&eacute;s in the title. As I read Menon's article I found myself agreeing with much of what he had written, although sometimes I wondered why it was considered to be worth stating. Then Menon would take a more extreme line which had not really been justified by what had preceded it, and I found myself frustrated by the lack of continuity as much as by the extreme view itself. I will give some examples of what I found to be problems with Menon's position, based around the themes of (a) was it worth saying anyway; (b) the function of over-statement; (c) methodology and the role of theory in educational research; and (d) the proposed ideal world of educational research. IN this response I have taken research in mathematics education to be entirely subsumed in educational research generally.

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