At the Intersection of Computer Science and Mathematics: Ideas and Strategies for Conceptual Growth

California State University-Long Beach Foundation, Long Beach CA

Investigators

Abstract

This project seeks to address a significant research gap at the intersection of computer science and mathematics education, focusing on the content area of discrete mathematics. Discrete mathematics encompasses topics such as logic, set theory, number theory, combinatorics, iteration, recursion, and graph theory. The objective of this project is to gain deeper insights into how undergraduate students in computer science and mathematics approach and comprehend these fundamental concepts, which are prominent in both domains. The project aims to identify productive strategies used by both groups of students and understand how and why students in each of the domains exhibit cognitively divergent or convergent approaches when solving these problems. Furthermore, by characterizing the approaches taken by mathematics and computer science students, and presenting these strategies to their respective counterparts, the project seeks to explore which strategies each group of students find to be the most beneficial for their understanding. By sharing this study's findings with both the computer science and mathematics education research fields, this project carries significant potential to benefit society by contributing to more effective mathematics education at the undergraduate level. Improved understanding and communication of concepts at the intersection of computer science and mathematics can lead to more skilled graduates who are well-equipped to tackle real-world challenges. This project aligns with broader societal goals of fostering interdisciplinary learning and preparing students for careers that demand proficiency in both computer science and mathematics. In summary, this work will inform fundamental research, and, eventually, evidence-based practices that can ultimately enhance the quality of mathematics education. The objective of this project is to gain deeper insights into how undergraduate students in computer science and mathematics approach and comprehend fundamental concepts which are prominent in both domains. The study will span one academic year and comprise of two phases, commencing with data collection and preliminary analysis in the fall semester of 2024 (Phase 1). The first phase will consist of research participants engaging in a think-aloud procedure, being asked to vocalize their thought processes as they work through the survey instrument containing questions related to logic, set theory, combinatorics, number theory, iteration, recursion, and graph theory. Analysis of this first round of interviews will focus on the cognitive activity of the two groups of students. To analyze the students' cognitive activity, the project will utilize a novel analytical approach which entails combining the analytical frameworks of process/object duality with the Instrumental Approach. By integrating both frameworks, the project adopts the theoretical stance that learning is theorized as the cognitive work the learner does at the individual level, as they move between process and object conceptualizations, in collaboration with any work they do to instrumentalize computational reasoning tools to solve a mathematical problem. In Phase 2, during the second round of interviews, the project will focus on the various approaches taken by computer science students with their mathematics counterparts, and vice versa. The interviews will serve as an opportunity to member-check with the research participants about their cognitive approaches, as well as to understand the cognitive approaches that they find to be most helpful for their own reasoning. Dissemination efforts of this study will include publishing asset-based narratives of the students' cognitive approaches, as well as the creation of in-class activities that may be used in Introduction to Proofs courses. By identifying, characterizing, and sharing strategies utilized by students in both domains, we can further the field's theoretical understanding of the relationship between computational and mathematical reasoning. Ultimately, this will lead to pedagogical improvements and reveal opportunities requiring further study. This project is supported by NSF's EDU Core Research (ECR) program. The ECR program emphasizes fundamental STEM education research that generates foundational knowledge in the field. Investments are made in critical areas that are essential, broad and enduring: STEM learning and STEM learning environments, broadening participation in STEM, and STEM workforce development. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.