Though engaging in mathematical proof is a central part of an undergraduate mathematics course of study, and the body of research on student learning in this arena is burgeoning, we have no constructivist models of how students understand or come to learn the logic of mathematical proof. As a result, we do not have research-based learning goals for the Transition to Proof courses being offered by many mathematics departments. In this EHR: Core, Tier 2 project in the STEM Learning and Learning Environments strand, we seek to build upon some promising teaching experiments to address this gap. We propose an initial model of students Reflection and Abstraction of Proof Structures (RAPS) based on findings from our initial studies and propose how we will develop and extend this model through a series of teaching experiments. This work builds upon the success of our earlier work (Dawkins 2017b, 2019; Dawkins & Cook 2016; Dawkins & Roh 2016, 2019; Hub & Dawkins 2018) modeling students learning of the logic of mathematical reference, meaning the conditions for when mathematical statements are true and false. At the heart of this approach is helping students apprehend the questions of logic as they abstract their own mathematical activity to address those questions. In this way, we organically develop insights into students content-general learning (of logical relations) as it emerges from within their content-specific reasoning (about the specific mathematical relations they reason about).
|Effective start/end date||10/1/20 → 9/30/23|
- National Science Foundation (NSF): $369,473.00