Multiple choice questions are traditionally expensive to produce. Recent advances in large language models (LLMs) have led to fine-tuned LLMs that generate questions competitive with human-authored questions. However, the relative capabilities of ChatGPT-family models have not yet been established for this task. We present a carefully-controlled…

This study investigates how utilizing student-invented strategies in the classroom can inform teachers' pedagogical content knowledge. Two elementary school teachers participated in professional development discussing the benefits of invented strategies. Data was then gathered as the participants implemented this practice in their classrooms. Data…

Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…