Building and Enhancing Mathematical Reasoning (24w5212)

The Banff International Research Station will host the “Building and Enhancing Mathematical Reasoning” workshop in Banff from April 28 - May 3, 2024.

For the context of this five-day BIRS workshop, we conceptualize mathematical reasoning (MR) as reasoning that is required to solve mathematical tasks, and which includes: understanding how to write and use definitions and theorems; applying inductive and deductive thinking; working with elements of mathematical logic, mathematical language and symbols; creating and communicating clear, and precise mathematical narratives; and making connections between mathematical ideas. In spite of a general agreement that MR is an absolutely essential skill without which it is impossible to succeed in mathematics, the teaching of MR is inadequate. In high school, students are mostly exposed to algorithmic and computational routines; they rarely engage in MR, and end up with very little, or no, experience with it. The major conflict for these students arises when their university mathematics instructors assume that they are somewhat familiar with the structure of a theorem, and concepts such as counterexamples and quantifiers.

The main objective of the five-day BIRS workshop is to generate specific suggestions for possible larger-scale modifications in enhancing the teaching and learning of MR in universities, and in the transition from the secondary to post-secondary mathematics. These modifications will aim to move us onward toward the creation of a modern mathematics curriculum which will challenge the traditional organization into subject boxes (courses); it will be built around big ideas, one of which is the development or MR skills through a vertical integration into undergraduate math curriculum.

Borrowing from successful strategies employed at the Canadian Mathematics Education Study Group annual meetings, and at the recent (August 2022) BIRS UBCO workshop in Kelowna, a significant part of the workshop will be based on working groups, tasked with specific objectives. To inform our work and assist us in reaching the workshop objectives, we will invite international colleagues, researchers in mathematics education, and cognitive psychologists.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada’s Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), and Alberta Technology and Innovation.