Beyond Theorem–Proof–Example: Differentiating College Math to Spark Creativity and Motivation

College mathematics often provides the students polished results while hindering the creative and flexible work of mathematical discovery. In this talk, we will report our exploratory mixed methods study in an R1 first-year seminar that made the creative core of mathematics visible through differentiated instruction: weekly small-group “games” grounded in advanced ideas (e.g., Königsberg bridges and Euler characteristic, Hilbert’s Hotel and injectivity, group theory, finite fields, and a glimpse of -adic distance), followed by short post-class videos that formalized the underlying theory. Twenty-five freshmen completed a pre/post “How I Feel About Math” survey and produced 225 weekly response logs. A Wilcoxon signed-rank analysis showed a significant gain on effectance/motivation; other subscales trended upward. Content analysis of logs revealed rising frequencies of creativity codes (using metaphors and analogies, interdisciplinary thinking, making associations, selective thinking, unique/unorthodox problem solving, metacognitive thinking, appreciation of simplicity and aesthetics, and using different representations) and motivational codes (emotions and enjoyment, curiosity and meaningful questioning, and meta-mathematical thinking) over three successive course periods. Furthermore, we will discuss our class design playbook which includes (1) partition abstract theory into accessible steps that culminate in a “big theorem,” (2) pair collaborative activity with just-in-time micro-lectures, and (3) assess for question-asking, representation-shifting, and explanation quality rather than only answer correctness.