Research

  • Pfannkuch (1997) contends that variation is a critical issue throughout the statistical inquiry process, from posing a question to drawing conclusions. This is particularly true for K-6 teachers when they attempt to use the process of statistical investigation as a means of teaching and learning across the spectrum of the K-6 curricula. In this context statistical concepts and ideas are taught and learned in conjunction with the important content area ideas and concepts. For a K-6 teacher, this means that the investigation must not only be planned in advance, but also aimed at being responsive to students. The potential for surprise questions, unanticipated responses and unintended outcomes is high, and teachers need to "think on their feet" statistically and react immediately in ways that accomplish content objectives, as well as convey correct statistical principles and reasoning. The intellectual demands in this context are no different than in other instances where teachers are trying to teach for understanding (i.e., Cohen, McLaughlin, &amp; Talbert, 1993; Ma, 1999).<br>In this line of research, we explore the role variability plays in this form of teaching and learning. Simultaneously, we analyze what teachers need to know about variability and be able to do with variability in data so that purposeful investigations into topics of the curriculum can be successful in teaching both statistical concepts and process and the important ideas associated with content. We work from a situative perspective (Greeno, 1997) and analyze the degree to which the statistical knowledge needed for teaching appears to have been learned for understanding (Hiebert &amp; Carpenter, 1992) and leads to generative understanding (Franke, Carpenter, Levi &amp; Fennema, 2001). The findings of this study point toward the situated nature of knowledge about variability needed for and used in teaching and leads to significant implications for the growth of teachers' statistical knowledge.

  • Recently, Nathan (1986) criticized Bar-Hillel and Falk's (1982) analysis of some classical probability puzzles on the grounds that they wrongheadedly applied mathematics to the solving of problems suffering from "ambiguous informalities". Nathan's prescription for solving such problems boils down to assuring in advance that they are uniquely and formally soluble--though he says little about how this is to be done. Unfortunately, in real life problems seldom show concern as to whether their naturally occurring formulation is or is not ambigous, does or does not allow for unique formalization, etc. One step towards dealing with such problems intelligently is to recognize certain common cognitive pitfalls to which solvers seem vulnerable. This is discussed in the context of some examples, along with some empirical results.

  • Relationships among student motivational orientation, self-regulated learning, and classroom academic performance were examined for 173 seventh graders. Results provide empirical evidence for considering motivational and self-regulated learning components in models of academic performance. Involvement in self-regulated learning is tied closely to student efficacy beliefs.

  • StatPlay, our mulimedia for introductory statistics, aims to promote understanding of fundamental concepts. We describe assessment of students' use of StatPlay's Sampling Playground for learning about sampling variability, standard error and sampling distributuions. Students worked with StatPlay's interactive simulations, and undertook a range of prediction, estimation, labelling and explanation tasks. Results suggest that variability, and that confrontation with prior misconceptions and experience with the results of repated sampling can be valuable, in particular for understanding standard error.

  • Responding to world wide recommendations that recognize the importance of having younger students develop a greater understanding of probability, this study designed and evaluated a third-grade instructional program in probability. The instructional program was informed by a cognitive framework that describes students' probabilistic thinking and also adopted a socio-constructivist orientation. Two classes participated in the instructional program, one in the fall (early) and the other in the spring (delayed). Following instruction, both groups displayed significant growth in probabilistic thinking that was not simply due to maturation. There was also evidence, based on four target students, that children's readiness to list the outcomes of the sample space, their ability to connect sample space and probability, and their predisposition to use valid number representations in describing probabilities, were key factors in fostering learning.

  • In the past decade, various countries have produced national mathematics eudcation reform documents that recommend that students learn to produce, explore and interpert disctributions of data meaningfully. The purpose of this study is to expand on what has been learned about student notions of the average as a represeentation of a distribution. For this paper we report interview data with Jim, a middle school student. We followed the investigation of Mokros and Russell (1995) and their framework for understanding how children develop an understanding of the concept of mean. Jim did not seem to fall clearly into any one of the strategy types identified by Mokros and Russell. His problem solving strategies for finding the mean seem to vary, but at the same time he maintains a consistent interest in making sense of the results of his computations. Jim did not appear to make sense of the mean as a statistical measure of a distribution.

  • Research on misconceptions of probability indicates that students' conceptions are difficult to change. A recent review of concept learning in science points to the role of contradiction in achieving conceptual change. A software program and evaluation activity were developed to challenge students' misconceptions of probability. Support was found for the effectiveness of the intervention, but results also indicate that some misconceptions are highly resistant to change.

  • In this study I look at university students' orientations to learning statistics--how they feel about learning it, their conceptions of the subject matter and their approaches to learning it. I use complementary methods of anlysis to understand the relationships among students' appraisals and attainments on assessments. The findings reveal underlying dimensions of the variables and present dramatically different profiles of students' experiences. Students' learning is linked to a complex web of personal, social and contextual factors.

  • This study was concerned with finding what characteristics of data, such as direction of skewness, degree of skewness and degree of kurtosis, affected students' ability to use histograms and boxplots for detecting non-symmetry in the parent population. The study found that while there was no consistent difference between boxplots and histograms in the proportion of students detecting skewness when the data was displayed in a left-skewed orientation, the direction of skewness did have a significant effect, with more students detecting skewness when the same data was displayed in a right-skewed orientation. This results is consistent with research reported in the psychological literature where many, but not all, studies have shown an over emphasis on the left hand field of view for normal subjects. Other findings of the study are given and suggestions for further research made.

  • This paper addressed the broad issue of relating research findings with pedagogical practices by analysing the responses to questions set in an undergraduate statistics examination using Eisner's connoisseurship and crticism approach, supported by general pedagagical and psychological principles. Comparisons are made between responses to the same course given in two different countries to assess similarities, differences, and weaknesses in order to indicate possible ways in which future courses might be modified to improve student learning.

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