Scaffolding Moves for Constructing Cognitively Meaningful Models of a Predator-Prey Scenario

Abstract

We studied aspects of undergraduate STEM majors’ mathematical reasoning as they engaged in mathematically modeling a predator-prey scenario. The study used theoretical viewpoints on quantitative reasoning to inform scaffolding moves that would assist modelers in overcoming blockages to their mathematization of real-world problems. Our contribution is a set of four scaffolding moves contingent upon and responsive to participants’ in-the-moment quantitative reasoning that guided them toward a meaningful model for a predator-prey scenario.

KEYWORDS:

• Mathematical modeling
• scaffolding
• differential equations
• STEM majors

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the author(s).

COMPLIANCE WITH ETHICAL STANDARDS

Informed consent was obtained from all human subject participants. The study was approved by the Texas State University IRB.

DATA AVAILABILITY STATEMENT

The datasets generated and/or analyzed during the current study are not publicly available due to the fact that participants have not consented to the public release of data.

Notes

1 We use the term non-normative to mean reasoning or solutions that are sensible to students but do not comport with mathematical norms or conventions endorsed by mathematicians or textbook solutions.

2 This problem is based on an article written by Lauerman (2016) [5].

3 Peet was using tau ($\tau$) to refer to time, $t$.

Additional information

Funding

This work was supported by the National Science Foundation (Grant Number 1750813). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Notes on contributors

Jennifer Czocher

Jennifer A. Czocher is an Associate Professor of Mathematics Education at Texas State University. Her main research interests concern how individuals learn to use mathematics as a representational system. She uses mixed-methods to study the role teacher scaffolding may play in supporting students’ growth of modeling skills. She also enjoys thinking about epistemological, methodological and philosophical issues in mathematics education, students’ mathematical thinking and cognition, and research in undergraduate mathematics education (RUME).

Elizabeth Roan

Elizabeth Roan is a Mathematics Education PhD candidate at Texas State University. Her primary research interests are in undergraduate mathematics education focusing on students reasoning while mathematical modeling. After graduation, she plans to pursue a career in academia.

Sindura Subanemy Kularajan

Sindura (Suby) Kularajan is an Assistant Professor of Mathematics Education at Utah State University. She studies the interplay between quantitative reasoning and students’ creation of mathematical models from first principles from a cognitive constructivist perspective.