RUME 14 (Volume 4)
2011
Portland, Oregon
THE IMPACT OF INSTRUCTION DESIGNED TO SUPPORT DEVELOPMENT OF STOCHASTIC UNDERSTANDING OF PROBABILITY DISTRIBUTION
Page: 49
Large numbers of college students study probability and statistics, but research indicates many are not learning with understanding. The concept of probability distribution undergirds development of conceptual connections between probability and statistics and a principled understanding of statistical inference. Using a control-treatment design, this study employed differing technology-based lab assignments and investigated the impact of instruction aimed at fostering development of stochastic reasoning on students' understanding of probability distribution. Participants were approximately 200 undergraduate students enrolled in a lecture/recitation, calculus-based, introductory probability and statistics course. This preliminary research report will discuss the framework used to develop the stochastic lab materials and preliminary results of an assessment of students' understandings. Key words: Probability distribution, stochastic reasoning, technology-based instruction, instructional intervention. Statement of research issue: Large numbers of university students study probability and statistics (Moore & Cobb, 2000), but research indicates that many of these students exhibit difficulties in learning and applying probabilistic and statistical concepts (Garfield & Ben-Zvi, 2007; Shaughnessy, 1992, 2007). Inappropriate reasoning in probability and statistics is widespread and persistent across all age levels. After probability instruction, many post-calculus students demonstrate merely instrumental understanding (Skemp, 1976) and present notions about probability that are not aligned with formal probabilistic concepts (Barragues, Guisasola, & Morais, 2007). This study draws on constructivist and situated learning perspectives and assumes understandings are built through learning experiences, which are impacted by the learner, teachers, and the instructional material. The study assumes that: (1) teaching impacts learning and can facilitate learning with understanding; (2) effective teaching elicits students' pre-existing understandings and builds on that understanding; (3) effective teaching helps students develop deep knowledge connections in the context of a conceptual frame for the content domain (Bransford, Brown, & Cocking, 2000). This research was designed to evaluate the effectiveness of an instructional intervention that builds on students' initial understandings of probability and statistics and facilitates student understanding of content within a connected conceptual framework. The study seeks to measure and describe individual understandings of probability distribution. The concept of probability distribution is a powerful springboard for the development of stochastic reasoning as it may facilitate making deep conceptual connections around probabilistic understandings related to variability, independence, sample space, and distribution (Liu & Thompson, 2007). Principled knowledge (Spillane, 2000) refers to an understanding of the ideas and concepts that support mathematical procedures. Principled knowledge of probability