References biggs j b collis k f 1982 evaluating the

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REFERENCES Biggs, J. B. & Collis, K. F. (1982). Evaluating the quality of learning: The SOLO taxonomy . New York: Academic Press. Case, R. (1985 ). Intellectual development: birth to adulthood . Orlando: Academic Press. Case, R., Okamoto, Y. & Griffin, S. (1996). The role of central conceptual structures in the development of children's thought (with discussion ). Monographs of the Society for Research in Child Development , 61(2), 1- 295. Jones, G. A., Langrall, C. W &Thornton, C. A. (1997). A framework for assessing and nurturing young children's thinking in probability. Educational Studies in Mathematics , 32 (3), 101-125. ROBERT DELMAS 109 Appleby Hall University of Minnesota 128 Pleasant Street S.E. Minneapolis, MN 55455 USA
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45 15. CONCEPTUAL ISSUES IN UNDERSTANDING SAMPLING DISTRIBUTIONS AND MARGIN OF ERROR PAT THOMPSON Vanderbilt University, USA [email protected] This study presented at SRTL-2 employed two teaching experiments to probe essential difficulties in students' constructions of schemes and imagery that might underlie their ability to reason powerfully about distributions of sample statistics. The study's methodology involved analyzing the idea in terms of conceptual operations it might entail, designing objects and situations with the intent of bringing those operations into play within conversations around them, and employing those objects and situations within the teaching experiments. Analysis of the teaching experiment data entailed using the conceptual analysis to guide initial explanations of students' successes and difficulties and feedback into the conceptual analysis in those instances where it failed to provide satisfactory explanations of critical events. The first teaching experiment comprised 9 instructional days with 27 junior and senior high school students followed by 60-minute interviews of 10 students. Instruction in the teaching experiment focused on having students build multi-level images of repetitively sampling from a population and tracking the sample statistics to form distributions generated there from, and determining invariant properties of those distributions. Videos from Teaching Experiment 1 revealed several, possible essential, difficulties students encountered. The first was their disposition to participate in lessons unproductively. The conversations that actually took place sometimes confused students who anticipated that the instructor would demonstrate procedures that they would then commit to memory. The conversations most often focused on how to understand important issues and on reasonable ways to conceive of them so that people might develop reasonable ways to approach problems entailing them (such as, what does it mean that a particular event is "unusual" and how to determine whether it is). The second difficulty, grounded more in conceptual operations, was some students' predilection to conceive of samples as "some of" a population, instead of as a proportional mini-version of the population. The third difficulty, also
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