Bridging Mathematics and Computer Science Through Threshold Concepts

Abstract

Contribution: Using threshold concepts as the framework for curriculum design, a project on neural network methods for solving differential equations is presented, with a rich set of transformative concepts from mathematics and computer science. Projects of this kind complement a typical curriculum with expertise that is crucial for critique and fundamental development of modern machine learning. Background: The curricula of many schools of mathematics and computer science present a relatively shallow introduction to the other subject. Student projects, on the other hand, provide an effective environment for interdisciplinary research between the two disciplines. Intended Outcomes: Providing students from computer science and mathematics the opportunity to obtain a deeper understanding and appreciation of the other subject, beyond the confines of the school curriculum. Application Design: The project contains tasks that require acquisition, not just of knowledge, but also of effective strategies and mental models, relevant to a set of transformative concepts from both disciplines. The tasks require a spectrum of activities, ranging from rigorous theoretical work to coding. Findings: Although the theory of threshold concepts needs further development, the existing paradigms provide a helpful framework for curriculum design. The continuous formative assessment proved effective in monitoring the participants’ journeys through the liminal state.