Conference Paper

  • 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.

  • August has come and a lotof you have joined ICOTS II, the Second International Conference on Teaching Statistics. Some may attribute credit to "Footie", but we are indebed to the ISI Task Force for Conferences on the Teaching of Statistis and to the conference Organizing and Program Committees.<br><br>ICOTS I and this conference have been preceded and interlocked iwth various other conferences, workshops, and meeting sessions ont he teaching of statistics and statistical consulting. This attests to our concerns with the teaching of statistics and the training of statisticians, concerns healthy for the discipline and suggestive of a continuing search for excellence. One may wonder what remains to be said, but reminders and reappraisals are helpful and the nature of our discipline and its setting continue to evolve.

  • Now that you have heard about the evolution of GAPS, as well as a description of the content and the instruction al approach, I would like to discuss at a more theoretical level an instructional model which underlies the GAPS course. In addition, I will touch on implications for teaching at the high school and university levels.

  • As teachers, most of us enourage the students in our classes to come to us during special office hours if they wish to receive extra help. Many students feel that they should not "waste" the teachers' time with their questions. Others may feel embarrassed to ask questions in a one-to-one setting. Whatever the reason a student may have, we have felt that students who really need help frequently do not get help through the office-hour channel. We have tried to provide a variety of sources of extra help for students. In this paper we will describe the sources of help and summarize how students utilized these sources over the course of the semester.

  • When solvers have more than one strategy available for a given problem, they must make a selection. As they select and use different strategies, solvers can learn the strengths and weaknesses of each. We study how solvers learn about the relative success rates of two strategies in the Building Sticks Task and what influence this learning has on later strategy selections. A theory of how people learn from and make such selections in an adaptive way is part of the ACT-R architecture (Anderson, 1993). We develop a computational model within ACT-R that predicts individual subjects' selections based on their histories of success and failure. The model fits the selection behavior of two subgroups of subjects: those who select each strategy according to its probability of success and those who select the more successful strategy exclusively. We relate these results to probability matching, a robust finding in the probability-learning literature that occurs when people select a response (e.g., guess heads vs. tails) a proportion of the time equal to the probability that the corresponding event occurs (e.g., the coin comes up heads vs. tails).

  • 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.

  • 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.

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