Past studies have documented some pre-service teachers' (PSTs) difficulties in reasoning about sampling variability. This study adds to the body of literature by investigating the ideas that PSTs employ in reasoning about sampling variability, and by conjecturing what is behind the difficulties especially during the contextuality episodes. This…

We present a view of knowledge construction processes, focusing on partially correct constructs. Motivated by unexpected and seemingly inconsistent quantitative data based on the written reports of students working on an elementary probability task, we analyze in detail the knowledge construction processes of a representative student. We show how…

Honors the contribution of Efraim Fischbein to the study and analysis of probabilistic thinking. Summarizes Fischbein's early work, then focuses on the role of intuition in mathematical and scientific thinking; the development of probabilistic thinking; and the influence of instruction on that development. (Author/MM)

Features and tools to outline and shape the long-term learning process for ratio are presented, with examples. Ratio-anticipating activity and creating visual models and schemes are stressed, with the basis for a theory of teaching and learning ratio presented. (MNS)

The effects of a teaching program in probability devised for students in grades five to seven were analyzed. Most of the notions were too difficult for fifth graders; 60-70 percent of the sixth graders and 80-90 percent of the seventh graders were able to understand and use correctly most of the concepts. (MNS)

Describes a study to determine middle school children's representational strategies to form part-whole or part-part relationships for relational numbers such as proportions, ratios, or fractions. Quantitative and qualitative analysis revealed that children prefer a part-part representation to solve relational quantity problems. (15 references)…

Reviews research indicating that students' cognitive models hold random events to be equiprobable Examined 87 students between the ages of 15 and 17 to determine whether masking a random event using geometric figures would affect the students' view of the event as equiprobable. Results indicated that masking overcame the equiprobable bias of the…