Journal Article

  • Gigerenzer has argued that it may be inappropriate to characterize some of the biases identified by Kahneman and Tversky as errors or fallacies, for three reasons: (a) according to frequentists, no norms are appropriate for single-case judgments because single-case probabilities are meaningless; (b) even if single-case probabilities make sense, they need not be governed by statistical norms because such norms are content-blind and can conflict with conversational norms; (c) conflicting statistical norms exist. I try to clear up certain misunderstandings that may have hindered progress in this debate. Gigerenzer's main point turns out to be far less extreme than the position of normative agnosticism attributed to him by Kahneman and Tversky: Gigerenzer is not denying that norms appropriate for single-case judgments exist, but is rather complaining that the existence and the nature of such norms have been dogmatically assumed by the heuristics and biases literature. In response to this complaint I argue that single-case probabilities (a) make sense and (b) are governed by probabilistic norms, and that (c) the existence of conflicting statistical norms may be less widespread and less damaging than Gigerenzer thinks.

  • A solid understanding of inferential statistics is of major importance for designing and interpreting empirical results in any<br>scientific discipline. However, students are prone to many misconceptions regarding this topic. This article structurally summarizes<br>and describes these misconceptions by presenting a systematic review of publications that provide empirical evidence of them. This<br>group of publications was found to be dispersed over a wide range of specialized journals and proceedings, and the methodology<br>used in the empirical studies was very diverse. Three research needs rise from this review: (1) further empirical studies that identify<br>the sources and possible solutions for misconceptions in order to complement the abundant theoretical and statistical discussion<br>about them; (2) new insights into effective research designs and methodologies to perform this type of research; and (3) structured<br>and systematic summaries of findings like the one presented here, concerning misconceptions in other areas of statistics, that might<br>be of interest both for educational researchers and teachers of statistics.<br>&copy; 2007 Elsevier Ltd. All rights reserved.

  • This paper discusses the role of mathematics teachers' beliefs and their impact on<br>curriculum reform. It is argued that teachers' beliefs about the teaching and<br>learning mathematics are critical in determining the pace of curriculum reform.<br>Educational change is a complex process in which teachers hold strong beliefs<br>about the quality and the process of innovation. Curriculum implementation may<br>only occur through sufferance as many teachers are suspicious of reform in<br>mathematics education given its equivocal success over the past decades. It is not<br>surprising then that many teachers, when they come to enact the curriculum in<br>their classes, rely more on their own beliefs than on current trends in pedagogy.<br>These beliefs, conservative as they might be, have their own rationality in the<br>practical and daily nature of the teaching profession, and in the compelling<br>influence of educational systems from which these teachers are paradoxically the<br>social product. The literature indicates that many of these teachers hold<br>behaviourist beliefs, a fact that has strong implications for the success of<br>constructivist-oriented curriculum reform. In general, studies of teachers'<br>pedagogical beliefs reveal the extreme complexity of bringing about educational<br>change, and largely explains the failure of many past reform endeavours.

  • To investigate the origins and nature of intuitive obstacles affecting the learning of elementary probability theory, 618 Italian elementary and middle school students were interviewed about their methods of solution for several problems dealing with probability. The discussion focuses on four varieties of obstacles to learning prevalent within the findings of this study.

  • This paper outlines developments in statistical education in the period preceding the formation of the<br>International Association for Statistical Education (IASE) 1991, and takes a tentative look at the future.<br>The first section reviews the history of the ISI's Statistical Education Committee from its setting up in<br>1948 to the birth of the IASE in 1991. The second section attempts to identify some of the underlying<br>factors contributing to the rapid growth of interest in statistical education during the last two decades or<br>so. The third section gives a personal view of some of the issues the IASE may have to confront during its<br>first few years of existence.

  • This article presents bootstrap methods for estimation, using simple arguments. minitab macros for implementing these methods are given

  • We investigated a theoretical model including an instructional intervention and systematic processing to account for change in preservice teachers' epistemological beliefs about teaching and learning in mathematics. General and subject-specific epistemological beliefs and systematic processing were assessed in 161 preservice teachers, randomly assigned to an experimental group whose epistemological beliefs about mathematics were activated and challenged through augmented activation and refutational text or to a control group who read a traditional expository text. The model was partially supported. The treatment group receiving the instructional intervention demonstrated greater change in implicit epistemological beliefs than the control group, and partial support for systematic processing as a mediator of the relationship between general epistemological beliefs and change in specific epistemological beliefs was obtained.

  • We developed measures of current statistics self-efficacy (CSSE) and self-efficacy to learn statistics (SELS) to address whether statistics self-efficacy is related to statistics performance, and whether self-efficacy for statistics increases during an introductory statistics course. Both instruments yielded reliable, one-factor solutions that were related positively to each other and to two measures of statistics performance (i.e., specific statistics problems and overall course performance). The CSSE and SELS also were related positively to math self-efficacy and attitudes towards statistics, but related negatively to anxiety. Changes between two different testing occasions using the CSSE indicated that statistics self-efficacy increased almost two standard deviations over a 12-week instructional period.

  • This study explored whether and how teachers' mathematical knowledge for teaching contributes to gains in students' mathematics achievement. The authors used a linear mixed-model methodology in which first and third graders' mathematical achievement gains over a year were nested within teachers, who in turn were nested within schools. They found that teachers' mathematical knowledge was significantly related to student achievement gains in both first and third grades after controlling for key student- and teacher-level covariates. This result, while consonant with findings from the educational production function literature, was obtained via a measure focusing on the specialized mathematical knowledge and skills used in teaching mathematics. This finding provides support for policy initiatives designed to improve students' mathematics achievement by improving teachers' mathematical knowledge.

  • Th e long-term impact of studies of statistical power is investigated using Cohen's (1962) pioneering work as<br>an example. We argue that the impact is nil; the power of studies in the same journal that Cohen reviewed<br>(now the Journal of Abnormal Psychology) has not increased over the past 24 years. In 1960 the median power<br>(i.e., the probability that a signifi cant result will be obtained if there is a true eff ect) was .46 for a medium<br>size eff ect, whereas in 1984 it was only .37. Th e decline of power is a result of alpha-adjusted procedures.<br>Low power seems to go unnoticed: only 2 out of 64 experiments mentioned power, and it was never estimated.<br>Nonsignifi cance was generally interpreted as confi rmation of the null hypothesis (if this was the<br>research hypothesis), although the median power was as low as .25 in these cases. We discuss reasons for<br>the ongoing neglect of power.

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