Instructional model for teaching blended math-science sensemaking in undergraduate science, technology, engineering, and math courses using computer simulations

The ability to express scientific concepts in mathematical terms and integrate scientific and mathematical reasoning about a phenomenon is a foundational cognitive process involved in scientific thinking. This process called “blended math-science sensemaking” (MSS) is a desired skill for all science, technology, engineering, and math (STEM) students, but few students are learning it, and there is little research on how to teach it. In this work we introduce the development and testing of a novel instructional method for teaching MSS that is suitable for use in STEM courses in undergraduate and K-12 educational settings. This study builds on our past work on developing and validating a framework for characterizing in detail the cognitive levels involved in such sensemaking. This work uses the unique power of interactive simulations for assessing and developing MSS. We designed instructional activities to help students use MSS in the contexts of heat capacity and Coulomb’s law. The heat capacity activity was piloted in a freshmen chemistry course and the Coulomb’s law activity was piloted in a freshmen physics course. The results indicate that for students who came in with no knowledge of the relevant equation the activity supported the development of both the equation, and their understanding of the mathematical relationships of the equation. These results indicate that the teaching approach helps students engage in MSS at higher levels of cognitive complexity.

Figure 1

Instructional model for blended math-science sensemaking.

Figure 2

Screenshot of Coulomb’s law simulation.

Figure 3

Screenshot of Energy Forms and Changes simulation.

Figure 4

Number of students and their sublevel placement before and after physics activity.

Figure 5

Student learning path in physics activity.

Figure 6

Number of student groups and their sublevel placement before and after activity. Note that two groups did not provide justification for the formula or answers to other assessment questions which makes it impossible to determine their postactivity level.

Figure 7

Student learning path in chemistry activity.