Assessing and using students' probabilistic thinking to inform instruction

Curriculum recommendations in mathematics at international and national levels have advocated increased attention to probability instruction K-8 (Australian Education Curriculum Corporation, 1994; Department of Education and Science and the Welsh Office, 1991; National Council of Teachers of Mathematics, 1989). In response to these recommendations, current curriculum materials have placed increased emphasis on the teaching and learning of probability (Berle-Carman, Economopoulos, Rubin, Russell, & Corwin, 1995; Chandler & Brosnon, 1994). With respect to teaching and learning, numerous studies (Fennema, Franke, Carptenter, & Carey, 1993; Fuys, Geddes, & Tischler, 1988; Lamon, 1996; Mack, 1995), advocate the use of research-based knowledge of students' thinking to inform instruction. Although there has been considerable research on students' probabilistic reasoning (e.g., Falk, 1983; Fischbein, Nello, & Marino, 1991; Hawkins & Kapadia, 1984; Piaget & Inhelder, 1975; Shaughnessy, 1992), none of this research has generated a framework for systematically describing and predicting students thinking in probability. Moreover, research has not generated or evaluated instructional programs at the elementary and middle school levels that are guided by research-based knowledge of students probabilistic thinking (Shaughnessy, 1992). This paper reports on a program of four research studies on probability in the elementary and middle grades. In particular, it examines: a) a research-based framework for describing and predicting how elementary and middle grades' students think in probability; b) an instructional program in probability for the elementary level that was informed by the research-based framework on students probabilistic thinking; and c) two instructional programs in the middle grades, one emphasizing conditional probability and independence, the other focusing on probabilistic thinking and writing in the context of probability.