A Practitional Perspective on Probabilistic Thinking Models and Frameworks
Our goal in this chapter is to showcase the various theories and cognitive models that have been developed by mathematics and statistics educators regarding the development of probabilistic thinking from a “practitional” perspective. This perspective juxt
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Abstract Our goal in this chapter is to showcase the various theories and cognitive models that have been developed by mathematics and statistics educators regarding the development of probabilistic thinking from a “practitional” perspective. This perspective juxtaposes the work of mathematics and statistics educators with research on probability from the field of psychology. Next, we synthesize theories and models that have been developed for specific probability concepts and processes. These models suggest different levels or patterns of growth in probabilistic reasoning. Finally, we examine the role these models have had on instruction and curriculum recommendations.
Mathematics education should identify its specific problems and should try to build its own concepts and its own research strategies. Psychology certainly may be very helpful but only as a general theoretical framework. Fischbein (1999, p. 53)
More than any other topic in mathematics education, the study of probability has been rooted in the field of psychology. The previous chapter showcased some of the prominent psychological contributions to the research literature and presented recent developments in psychology that appear promising to future probability research. In this chapter, we shift the focus to the theories and cognitive frameworks characterizing the development of probabilistic thinking from the perspective of mathematics education. First, we describe what we have coined the practitional perspective, as a means to juxtapose the work of mathematics and statistics educators studying probability with that of psychologists. Next we summarize the research literature on probabilistic thinking frameworks, which suggest different levels or patterns of growth in probabilistic reasoning that result from maturational or interactionist effects in both structured and unstructured learning environments. Finally, we discuss the potential and influence of these frameworks from a practitional perspective.
E.S. Mooney (B) · C.W. Langrall · J.T. Hertel Normal, IL, USA e-mail: [email protected] E.J. Chernoff, B. Sriraman (eds.), Probabilistic Thinking, Advances in Mathematics Education, DOI 10.1007/978-94-007-7155-0_27, © Springer Science+Business Media Dordrecht 2014
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Fig. 1 Facets of a practitional perspective
1 What Is a “Practitional” Perspective? We use the word practitional to distinguish the general interests and concerns of mathematics educators from those of psychologists. Following Shaughnessy (1992), we consider the psychological perspective as one of observing and describing, whereas the practitional perspective is aimed at intervening. The lens of a psychologist is broadly directed at human learning and thought; the practitional lens of a mathematics educator takes a sharper focus on improving teaching practice and increasing student learning. Moreover, the practitional lens is multifaceted; it is centered on instructional practice and informed by findings from mathematics education research and theoretical po
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