Literature Index

Our analysis identified problems both with the subject matter of statistics (e.g. multiple levels of abstraction, difficulty mapping statistical representations to real-world situations) and with its pedagogy (which typically does little to help concertize abstract concepts or illuminate the mapping process). Drawing on research in education, cognitive psychology and statistical computing, we designed, implemented, and pilot-tested software (ELASTIC) and a curriculum (Reasoning Under Uncertainty) to address these problems. Our approach was successful in many of the problem areas identified above; in addition, our experiences in classrooms helped us better understand the difficulties students have in understanding and applying statistical reasoning.

While other research has begun to contribute to our understanding of how pre-college students reason about variation, little has been published regarding pre-service teachers' statistical conceptions. This paper summarizes a framework useful in examining elementary pre-service teachers' conceptions of variation, and investigates the question of how a class of pre-service teachers' responses concerning variation in a probability context compare from before to after class interventions. The interventions comprised hands-on activities, computer simulations, and discussions that provided multiple opportunities to attend to variation. Results showed that there was overall class improvement regarding what subjects expected and why, in that more responses after the interventions included appropriate balancing of proportional thinking along with an appreciation of variation in expressing what was likely or probable.

This research focuses on fourth-grade (9-year-old) students' informal and intuitive<br>conceptions of probability and distribution revealed as they worked through a sequence of tasks. These<br>tasks were designed to study students' spontaneous reasoning about distributions in different settings and<br>their understanding of probability of various binomial random events that they explored with a set of<br>physical chance mechanisms. The data were gathered from a pilot study with four students. We analyzed<br>the interplay of reasoning about distribution and understanding of probability. The findings suggest that<br>students' qualitative descriptions of distributions could be developed into the quantification of probabilities<br>through reasoning about data in chance situations.

This paper presents results from a case study that explored elementary school teachers' understanding of essential topics in statistics. Teachers' understanding of the mean and median is presented in light of the suggestions by the GAISE document at Level A. It is important to consider where inservice teachers' understanding currently lies as we explore issues related to improving the sophistication of teaching and learning statistics in elementary schools.