NIU Department of Mathematical Sciences
Upcoming Colloquia and Seminars
October 20-24, 2014
Math Department Colloquium
Friday, October 24, 4:00-5:00 p.m. in DU 348
Speaker: Paul Dawkins, NIU
Title: Semantic and Logical Negation: the initial emergence of thinking about the logic of mathematical statements
Abstract: As Toulmin (1957) famously argued there is an ambiguity about the relation between logic as the form of reasoning and logic as a formal system. While psychological studies of "deductive reasoning" continue to move away from using formal logic as a model for people?s untrained reasoning, proof-oriented mathematics education requires that students learn to adopt the norms of linguistic interpretation and argumentation entailed in mathematical logic. To explore how and why students' untrained reasoning tends to diverge from mathematical norms (e.g. Durand-Guerrier, 2003, 2008; Epp, 2003), we conducted several teaching experiments with undergraduates intended to guide them to reinvent standards truth-functional interpretations of mathematical disjunctions and conditionals. Our findings strongly suggest that the students did have any single or systematized meaning for such linguistic forms (what one might call a "logic" for such statements) at the outset, but the experiment activities clearly engendered students reasoning about logic in several key ways. Students began attending to the role of logical connectives, trying to systematize their interpretations across mathematical statements, and trying to generalize patterns they noticed in the semantic structure. However, students also displayed some unforeseen patterns of interpreting negative properties that are incompatible with logical norms. This tendency toward semantic negation stymied their progress toward the standard tools for interpreting quantified disjunctions. The talk will provide examples of reasoning about logic, semantic negation, and discuss the implications of these reasoning phenomena for proof-oriented mathematics instruction.
Speaker: Paul Dawkins, NIU
Title: Semantic and Logical Negation: the initial emergence of thinking about the logic of mathematical statements
Abstract: As Toulmin (1957) famously argued there is an ambiguity about the relation between logic as the form of reasoning and logic as a formal system. While psychological studies of "deductive reasoning" continue to move away from using formal logic as a model for people?s untrained reasoning, proof-oriented mathematics education requires that students learn to adopt the norms of linguistic interpretation and argumentation entailed in mathematical logic. To explore how and why students' untrained reasoning tends to diverge from mathematical norms (e.g. Durand-Guerrier, 2003, 2008; Epp, 2003), we conducted several teaching experiments with undergraduates intended to guide them to reinvent standards truth-functional interpretations of mathematical disjunctions and conditionals. Our findings strongly suggest that the students did have any single or systematized meaning for such linguistic forms (what one might call a "logic" for such statements) at the outset, but the experiment activities clearly engendered students reasoning about logic in several key ways. Students began attending to the role of logical connectives, trying to systematize their interpretations across mathematical statements, and trying to generalize patterns they noticed in the semantic structure. However, students also displayed some unforeseen patterns of interpreting negative properties that are incompatible with logical norms. This tendency toward semantic negation stymied their progress toward the standard tools for interpreting quantified disjunctions. The talk will provide examples of reasoning about logic, semantic negation, and discuss the implications of these reasoning phenomena for proof-oriented mathematics instruction.
Coffee and refreshments at 3:30 in Watson 322
Seminars
Algebra Seminar: | Thursday, Oct. 16, 3:00-4:00 p.m. in DU 412 | |
Speaker: | Andrew Wang | |
Topic: | Constrained Table Algebras and the Exchange Condition |
Complex Analysis Seminar: | Tuesday, Oct. 14, 12:00-12:50 p.m. in DU 310 | |
Speaker: | Doug Macclure | |
Topic: | Classification of Quasiregular Poincare Linearizers (part 2) |