Revisiting the Medical Diagnosis Problem: Reconciling Intuitive and Analytical Thinking
A recurrent concern in mathematics education—both theory and practice—is a family of mathematical tasks which elicit from most people strong immediate (“intuitive”) responses, which on further reflection turn out to clash with the normative analytical sol
- PDF / 379,959 Bytes
- 23 Pages / 441 x 666 pts Page_size
- 57 Downloads / 189 Views
Abstract A recurrent concern in mathematics education—both theory and practice—is a family of mathematical tasks which elicit from most people strong immediate (“intuitive”) responses, which on further reflection turn out to clash with the normative analytical solution. We call such tasks cognitive challenges because they challenge cognitive psychologists to postulate mechanisms of the mind which could account for these phenomena. For the educational community, these cognitive challenges raise a corresponding educational challenge: What can we as mathematics educators do in the face of such cognitive challenges? In our view, pointing out the clash is not enough; we’d like to help students build bridges between the intuitive and analytical ways of seeing the problem, thus hopefully creating a peaceful co-existence between these two modes of thought. In this article, we investigate this question in the context of probability, with special focus on one case study— the Medical Diagnosis Problem—which figures prominently in the cognitive psychology research literature and in the so-called rationality debate. Our case study involves a combination of theory, design and experiment: Using the extensive psychological research as a theoretical base, we design a new “bridging” task, which is, on the one hand, formally equivalent to the given “difficult” task, but, on the other hand, is much more accessible to students’ intuitions. Furthermore, this new task would serve as a “stepping stone”, enabling students to solve the original difficult task without any further explicit instruction. These design requirements are operationalized and put to empirical test.
L.R. Ejersbo (B) DPU, Aarhus University, Copenhagen, Denmark e-mail: [email protected] U. Leron Israel Institute of Technology, Haifa, Israel e-mail: [email protected] E.J. Chernoff, B. Sriraman (eds.), Probabilistic Thinking, Advances in Mathematics Education, DOI 10.1007/978-94-007-7155-0_12, © Springer Science+Business Media Dordrecht 2014
215
216
L.R. Ejersbo and U. Leron
1 Introduction: Cognitive and Educational Challenges A recurrent concern in mathematics education—both theory and practice—is a family of mathematical tasks which elicit from most people strong immediate responses, which on further reflection, however, turn out to clash with the normative analytical solution. We will call such tasks cognitive challenges1 because they challenge cognitive psychologists to postulate mechanisms of our mind which could account for these phenomena. Indeed, an extensive empirical and theoretical research program on cognitive challenges (or cognitive biases) has been going on in cognitive psychology since the second half of the last century, culminating in the 2002 Nobel prize in economy to Daniel Kahneman for his work with Amos Tversky on “intuitive judgment and choice” (Kahneman 2002). For the educational community, these cognitive challenges raise a corresponding educational challenge, which will be the focus of this article: What can we as mathematics educators do in the
Data Loading...
