8e rencontre "Les mathématiques en action"

 

 

 

10h30 - 12h30 : David Landy (Indiana University), Algebraic Reasoning

 

Abstract. Reasoning about abstract relational structures is hard. Even such a simple task as computing the value of arithmetic expressions (e.g., 2x3+8) requires the ability to combine symbols according to formal syntactic rules to generate ever more complex representations—but how can concrete, body-bound agents such as ourselves instantiate formal syntactic computations? External formal notations can play a central role in this instantiation by providing stable physical environments that are easily interpreted by powerful but domain-limited perceptual and motor processes—that is, by serving as diagrams of abstract structures. Compositional reasoning processes that may appear to result from abstract internal symbol systems can instead arise from a relatively simple embodied agent perceiving, acting in and learning about an environment rich with structured symbolic expressions.  I will present several experiments and models demonstrating the influence of these experiences on intentionally formal reasoning. Recognizing the importance of the physical structure of symbolic environments urges the construction of a mathematics pedagogy that puts perceptual-motor interactions with dynamic notations at the heart of syntactic understanding.  I will present design work and initial pilot experiments illustrating the form such an approach could take.

 

12h30 - 14h30 Lunch

 

14h30-15h Introduction to the discussion: Dirk Schlimm (McGill University and MCMP), Remarks on Logical Notations

 

15h-16h30 General discussion

 

 

 

Salle 313

 

10h30 - 12h30 : David Landy (Indiana University), Large Numbers, Large Populations: How the mind copes with large values and wide scales

 

Abstract. Most psychological research has focused on the understanding of ‘everyday’ numbers and magnitudes.  Here, I will initiate a psychological exploration of how people process and work with large quantities. The first part of this talk will focus on ‘ arge' numerical quantities.  Despite their importance in public discourse, numbers in the range of 1 million to 1 trillion are notoriously difficult to understand. I will present research exploring the variety of common methods people use when interpreting these ‘big’ numbers in laboratory, classroom, and political contexts.  I will argue that culturally developed representations enable precise, fluid reasoning about quantities that seem to be otherwise conceptually inaccessible, but that these same representations lead to systematic errors. The second part of the talk will focus instead on large proportional magnitudes, particularly analyzing extant data on the estimation of demographic proportions: Previous international surveys assert that people are 'ignorant' of basic demographic facts: for example, US residents vastly overestimate LGBT and immigrant populations, but underestimate the proportion of people who are white or high-school educated. This pattern is regularly presented in major media outlets and the academic literature as caused by issue-specific biases such as racism and homophobia. We demonstrate that these biases are nearly entirely explained by domain-general cognitive mechanisms governing the perception of proportions, regardless of topic, domain, and time. We conclude that there is little evidence for widespread voter misinformation regarding specific, hot-topic demographic issues.  Across these topics, I will suggest that people cope with unimaginable mathematical concepts by instead directing their attention to representations of those quantities which can be conceived.

 

12h30 - 14h30 Lunch

 

14h30-15h Introduction to the discussion: Yacin Hamami (Vrije Universiteit Brussel), The Epistemology of Symbolic Reasoning

 

15h-16h30 General discussion