Towards a validation and refinement of dual process frameworks of reasoning: A process-oriented study of proportional reasoning and of the use of intuitive rules

In this doctoral project we will interpret some reasoning errors in mathematics and science from a dual process account and we will evaluate the scientific value of this alternative paradigmatic perspective. The phenomena under investigation are the over-use of proportional reasoning (e.g., Van Dooren, De Bock, Hessels, Janssens, & Verschaffel, 2005) and the use of intuitive rules, more specifically the ‘More A - more B’ rule (e.g., Stavy & Tirosh, 2003). Proportional reasoning is useful in many everyday life situations. Research, however, demonstrated that students often over-use proportional solution methods. For example, people often answer “90” to the non-proportional problem ‘Ellen and Kim are running around a track. They run equally fast but Ellen started later. When Ellen has run 5 rounds, Kim has run 15 rounds. When Ellen has run 30 rounds, how many has Kim run?’. The ‘More A - more B’ rule refers to students’ tendency to argue, when comparing two objects which differ with respect to a salient quantity A (A1 > A2), that for another quantity B it holds that B1 > B2. While often correct, in some situations this reasoning is incorrect. For example when comparing two geometrical figures, a larger area does not always implicate a larger perimeter. First, we will demonstrate that also for these tasks the dual process framework can account for the gap between people’s performances and the normative correct response, by focusing on two main processing claims of dual process theories, namely the differential involvement of cognitive resources in heuristic and analytic processing, and their different processing speed. We have already demonstrated that for word problem solving, as expected, proportional reasoning to non-proportional problems (like the one above) increases (and accuracy decreases) both under time pressure and under working memory load, while little or no impact was found for problems where proportional reasoning is appropriate. We plan to extend these findings to proportional and non-proportional probability problems (e.g., ‘The likelihood of getting heads at least 2 times when tossing a coin 3 times is smaller than / equal to / greater than the likelihood of getting heads at least 200 times out of 300 times.’). Also for the ‘More A - more B’ rule the first step will be to investigate whether both processing claims of the dual process framework hold. We plan to demonstrate this for two comparison tasks: a polygon task (comparing the perimeter of to polygons) and a probability task (comparing two boxes filled with black and white balls with regard to the probability of picking a black ball). Second, we shall refine the cognitive model underlying performance on these tasks by determining how the heuristic and analytic processes interact (Do the two processes operate in a serial or a parallel mode? ) and specifying the nature of the reasoning error (Do people fail to detect a conflict between the heuristic and analytic responses, or do they detect this conflict, but are they unable to inhibit the dominant heuristic response?), both for proportional reasoning and the ‘More A - more B’ intuitive rule. This shall be done by means of a thinking aloud methodology, but also by more implicit measures like, moving windows methodology or a speeded response task with variable cut off time. As Evans (in press b) argues, it could be that different models are needed to account for different types of implicit processing, but possibly a default-interventionist model wherein several routes are possible to arrive at the heuristic or analytic outcome, can account for performance on several types of tasks (like for example, for proportional reasoning tasks and ‘More A - more B’ tasks).status: publishe