Modeling in the Quantitative Reasoning Pathway

Modeling is a powerful tool for analyzing real-life phenomena. Modeling is the process of using mathematics to describe, analyze, and gain insight into real life phenomena. It entails identifying and representing quantities and determining relationships among relevant quantities. Modeling requires careful recognition of, and attention to, the relevant quantities involved in the situation.

Faculty at the MIP Quantitative Reasoning Initiation Workshop in May, 2021 recommended that instructional resources developed by CoRDs and ARCs addressing Modeling for success in the Oklahoma Quantitative Reasoning Pathway should:

1. Base modeling problems in contextual problems, affording students an opportunity to address the social context of the data (e.g. including multiple values/perspectives/needs, attending to implicit biases)

2. Encourage students to develop clear (mental and physical) images of a problem scenario to identify relevant quantities and relationships among them

3. Support students in understanding the meaning of model parameters, how those parameters impact important outcomes, and how the parameters are developed (e.g., a qualitative understanding of how one arrives at the slope in a regression calculation)

4. Give students experience in modeling with technology (e.g., spreadsheets, interactive mathematical software, graphing calculators), and leverage technology to give students experience with modeling messy, complicated, real-life data

5. Give students experience with both constructing models and analyzing given models

Addressing Components of Inquiry

Participants of the MIP Workshop on Quantitative Reasoning suggested the following ways resources about Modeling could address the three MIP components of mathematical inquiry:

Active Learning: Modeling provides an opportunity for students to reason with complex data. As such, it engages students in problematic situations, as well as selecting, performing, and evaluating the type of model to use.

Meaningful Applications: Models support students in identifying mathematical relationships and making and justifying claims. In particular, using technology for calculations affords a focus on relationships, exploration, and making and justifying claims.

Academic Success Skills: A key component of modeling is imposing a structure on a situation in order to identify patterns and draw implications from a situation. Modeling can therefore elicit students’ creativity in ways that are not commonly afforded by other mathematics topics or courses (thereby increasing confidence and potentially positively influencing their identities as mathematics learners). The use of technology, which reduces the focus on students’ computations in favor of other skills, might help lessen students’ mathematics anxiety.

References

Gaze, E. (2019). Thinking quantitatively: Creating and Teaching a Quantitative Reasoning Course. In Tunstall, L., Karaali, G., and Piercey, V. (Eds.), Shifting Contexts, Stable Core: Advancing Quantitative Literacy in Higher Education. (p. 89-106). MAA Press.

Thompson, P. W. (2011). Quantitative reasoning and mathematical modeling. In L. L. Hatfield, S. Chamberlain & S. Belbase (Eds.), New perspectives and directions for collaborative research in mathematics education. WISDOMe Mongraphs (Vol. 1, pp. 33- 57). Laramie, WY: University of Wyoming.