Course Title:

  • AI for Assured Autonomy, EP
  • Computational Methods of Analysis, EP


Students are often better able to visualize and comprehend complex or abstract concepts when multiple sources of information or representations are provided. Learners then have the option to choose the sources that work best for their own path toward becoming an expert learner. The structure of fields such as physics and engineering are well suited to providing multiple formats to support knowledge construction (Opfermann et al., 2017).

Areas of Focus:

  • Represent content in a variety of formats 

“Learn the theory – have the coding explained – then practice coding. I want to give them job and life skills, not just theories.”

 Cecil Bowe, instructor

“Providing the theory, commentary, equations, and Python code all in one place, a Jupyter Notebook, provides multiple modalities and enables students to apply their learning beyond the classroom immediately.”

 Christopher Stiles, instructor

  • Barrier to Student Success

    Many complex concepts or processes can be more readily understood through multiple means of representation than through words or lengthy explanations.

  • Solution

    The use of multiple representations has been widely studied in adult learning theory and instructional design research focusing on the sight structure of learning scenarios and external representations or visualizations (Schnotz, 2021; Mayer, 2021; Ainsworth, 2021). Multiple formats support learners in developing the deep connections and structure inherent in fields like science and engineering by using both external and internal representations. External representations include text, graphs, pictures, models, and symbols such as equations or formulas, while internal representations are mentals models that the learners build in constructing knowledge (Opfermann et al., 2017). In chemistry, for example, external representations might be a description of the empirical properties of a compound, a visual depiction of the molecular model, or symbolic or chemical formulas (Gilbert & Treagust, 2009). In physics, mathematical models, idealized behaviors, equations, graphs, tables, and images combine to support sense making of complex phenomena.

    Similar examples can be found in Cecil Bowe’s course AI for Assured Autonomy and Christopher Stiles’ course Computational Methods of Analysis, both taught in the Engineering for Professionals Program. Professors Bowe and Stiles utilize multiple representations through the use of Jupyter Notebooks, a mixed media tool to provide theory, commentary, equations, and Python code all in one place. These living notebooks enable students to view lectures, expand upon the concepts, and easily add new information and their own interpretations to the notebook. Students have 4 means of learning that can be leveraged individually or all at once – video lectures, text-based captions and transcripts, coding, and the dynamic notebook that can be edited to test and extend the students’ knowledge. This approach allows the students to test their understanding directly, by modifying the code used in class without the need for transcription to an external tool. Walking through code and graphical output empowers students to understand the interactions between representations in a way that verbal explanations alone fall short (Grout, 2022). The students also have a powerful open-source toolset that they can take with them anywhere!

  • Alignment with UDL
  • Additional Information

    Division/Department: Engineering for Professionals (EP)
    HUDL Ambassador: Sara Shunkwiler 
    Faculty Name:
    AI for Assured Autonomy: Cecil Bowe
    Computational Methods of Analysis:
    Christopher Stiles


    Ainsworth, S. E. (2021). The multiple representations principle in multimedia learning. In R. E. Mayer (Ed.), The Cambridge handbook of multimedia learning (3rd ed., pp. 158-170). Cambridge University Press.

    Gilbert, J. K., & Treagust, D. F. (2009). Introduction: macro, submicro and symbolic representations and the relationship between them, key models in chemical education. In J. K. Gilbert & D. Treagust (Eds.), Multiple representations in chemical education. Springer.

    Grout, I. (2022). Considering universal design principles and guidelines in a laboratory based module providing an introduction to microcontroller based embedded sensor systems design. 31st Annual Conference of the European Association for Education in Electrical and Information Engineering (EAEEIE), 1-6.

    Mayer, R. E. (2021). Cognitive theory of multimedia learning. In R. E. Mayer & L. Fiorella, Cambridge handbook of multimedia learning (3rd ed., pp. 57-72). Cambridge University Press.

    Opfermann, M., Schmeck, A., & Fischer, H. E. (2017). Multiple representations in physics and science education: Why should we use them? In D. F. Treagust, R. Duit, & H. E. Fischer (Eds.) Multiple representations in physics education: Models and modeling in science education (Vol. 10). Springer, Cham.

    Schnotz, W. (2021). Integrated model of text and picture comprehension. In R. E. Mayer, Cambridge handbook of multimedia learning (3rd ed., pp. 82-99). Cambridge University Press.