Participatory approach to introduce computational modeling at the undergraduate level, extending existing curricula and practices: Augmenting derivations

Recent educational policies advocate a radical revision of science curricula and pedagogy, to support interdisciplinary practices, a distinguishing feature of contemporary science. Computational modeling (CM) is a core methodology of interdisciplinary science, as such models allow intertwining of data and theoretical perspectives from multiple domains, to address complex problems such as climate change and pandemics. This integrative nature of CM could support the pedagogical transition to interdisciplinary science as well. Most approaches to introduce CM in science curricula are based on learning new practices, such as VPython programming or agent-based modeling. These approaches do not integrate CM with existing content, media, and teaching practices. To facilitate this integration, we present a more gradualist design, starting from derivation models in physics. This design was implemented as a set of teacher professional development modules, and presented to a group of physics teachers interested in introducing CM to undergraduate students. The analysis of their responses indicates that even this gradual transition to CM requires teachers to significantly revise their ideas about the nature of physics and physics learning (their personal epistemologies). We discuss how the teacher professional development modules were redesigned based on this finding.

Figure 1

A schematic of the design of our teacher professional development program and an outline of the key stages, components, and processes involved in this design.

Figure 2

Outline of the projected design sequence of the workshop for teachers.

Figure 3

Four general steps underlying many derivations in physics. The derivation of the equation of motion of a simple pendulum (analyzed in the lab frame) is deconstructed along the four steps, as an illustrative example.

Figure 4

A snapshot of the bridge simulation based on the simple pendulum (for access, see, Pendulum Ref. [61]). The schematic and the equation can be manipulated interactively, and the simultaneous changes in the graph can be observed.

Figure 5

A snapshot of the bridge simulation based on the spring-oscillator system (to access the system, please see piecewise oscillator [61]). The parameters can be manipulated interactively, to study the motion of damped, forced, and piecewise oscillators. The simulation has a tab that illustrates in detail the processes involved in the numerical solutions of differential equations.

Figure 6

An initial (pre-analysis) schematic representation of the dynamics of the meaning making process. Further analysis was conducted to reveal the specific dynamics of the meaning-making process, and to determine its implications for the redesign of the modules.

Figure 7

Overview of the steps involved in our data analysis.

Figure 8

An overview of teacher participants’ and researchers’ conflicting and accordant opinions about the modules.

Figure 9

A taxonomy of the codes developed using an inductive approach to data coding. As is evident from the diagram, we labeled our first cluster “discourse objects.” Here, we define discourse objects as operative procedures that embed within them psychological processes such as inference, deduction, categorization, generalization, learning, and decision-making. Next, we labeled our second cluster “processes.” By processes, we mean any mental or cognitive function that is involved in the acquisition, use, interpretation, manipulation, and transformation of knowledge. Finally, we labeled our third cluster “science learning.” The codes contained within this cluster conveyed beliefs and assumptions about science teaching and learning.

Figure 10

Overview of coding procedures used to study connotative and interpretive variations in discussants’ use of technical terms or concepts.

Figure 11

The two circular structures capture the teachers’ and researchers’ epistemological frames in an integrated way—textbook problem solving as modeling, and modeling as a process of loading reality into equations, respectively. The spirals signify stability and local coherence in the activation of their respective epistemic resources. Note that this integration is driven by design considerations, and does not follow directly from the qualitative analysis results.

Figure 12

Students are taught topics like mechanics, optics, thermodynamics, etc., as sequential modules, before moving to advanced topics like quantum mechanics (trajectory shown at the bottom of the figure). Introducing computational modeling (top right) in the senior undergraduate years introduces a whole set of new and unfamiliar practice elements, which makes physics difficult for most students. A dominant approach at this level is to teach CM using-agent based modeling (in green), which is disconnected from the core physics courses, and thus lacks pedagogical continuity and coherence. This problem is mitigated in our approach (the diagonal ovals), based on bridge simulations and numerical solutions as boundary crossing spaces. This structure creates a smoother transition.