Whole number computations are a critical skill that serves as a foundation upon which higher-order concepts in mathematics are taught to children. To facilitate their instruction, educators often use multiple representations to support a child's cognition. Representations with physical manipulatives are widely studied through a graduated…

In undergraduate engineering education, students are often overexposed to problem-solving methods that are unrepresentative of how engineers solve problems in practice. For decision-making problems, in particular, students are commonly taught to compare alternative solutions using known and provided information. However, many real-world…

The Applied and Industrial Mathematics program partners applied mathematics students with businesses, governments, laboratories, and agencies to solve real problems. We will discuss the logistics of the program and give advice on starting and running similar programs. We also give a detailed example of a specific project, namely our work with the…

The Teaching Teamwork Project is using an online simulated electronic circuit, running on multiple computers, to assess students' abilities to work together as a team. We pose problems that must be tackled collaboratively, and log students' actions as they attempt to solve them. Team members are isolated from one another and can communicate only…