Extending the Theoretical Framework of Numeracy to Engineers

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Engineering students typically are capable of the procedural aspects of applying math to their discipline, but may lack conceptual insight into what the math "says". A common example involves students' abilities to solve problems that involve translating a given scenario into its corresponding mathematical representation. In general, numeracy is the ability to translate math into different representations or state what the math says. Many concepts in engineering are difficult for students to understand or are built upon misconceptions regarding how the world works. Mathematical misconceptions compound this misunderstanding when the engineering concept relies upon high-level math. Mathematical misconceptions have been studied, particularly for early childhood, but never under the lens of numeracy for high-level math like derivatives, which have direct application to engineering concepts. The ultimate goal of the numeracy field is to prevent numeracy misconceptions (e.g., understanding what derivatives represent) from compounding engineering misconceptions (e.g. the difference between heat and temperature). As such, this work will formally define the most common numeracy misconceptions and provide a means for educators to identify these misconceptions among their students. By knowing what the root misconception is, steps can be taken so it no longer hinders understanding other discipline-specific concepts.A major limitation in the current field of numeracy is a lack of insight into engineering and calculus-based numeracy. Specifically, engineering education lacks a formal theoretical framework related to engineering numeracy. One objective of this project is to conduct a comprehensive review of the literature associated with mathematical misconceptions in engineering fields. What is learned from summarizing the literature will guide a Delphi Study of experts. The Delphi Study will obtain consensus from experts on what constitute the core competencies of engineering numeracy. Prompts to the Delphi surveys will be influenced by the literature search, and the Delphi Study will provide insight on how to expand the literature search on engineering numeracy. The resulting framework will allow researchers to make connections between related works associated with numeracy in addition to laying the foundation for building understanding of engineering numeracy misconceptions. Once the theoretical framework and lexicon are formalized for engineering numeracy, a concept inventory will be developed to measure and assess numeracy. This concept inventory will identify strengths and weaknesses of an individual's numeracy skills to guide strategies on how to improve those skills. The process of developing this concept inventory will mimic the process used in developing other concept inventories like the Thermal and Transport Concept Inventory. Ultimately, creation of an engineering numeracy concept inventory will open up new areas of research in engineering education.