The Roles of Text Domain and Learner Characteristics in Undergraduate Students' Mathematics Comprehension

• In Event: Exploring Processes That Underlie College Students' Motivational Challenges

Abstract

Objectives
Mathematics, and working with mathematics text, is essential for work in STEM disciplines. It is also a site of struggle for many undergraduates. This study was undertaken to examine how text domain (whether framed in everyday language and contexts versus esoteric symbols) combines with learner characteristics (e.g., prior coursework, mathematics interest) to identify sources of students’ struggle as they work to identify metamathematical concepts and comprehend argument.

Theoretical Significance
Whereas most research in undergraduate mathematics has been undertaken with mathematics majors, the study included both majors and nonmajors to understand the struggles with mathematical text for students more generally. The research jointly analyzes learner characteristics, including level of prior coursework, level of mathematics interest [Renninger & Hidi, 2016]), development of proof scheme (analytically-based mathematics justification [Harel & Sowder 1998), reflecting more advanced knowledge), and gender. Because these factors may naturally covary, this approach allowed us to consider their combined influence in predicting responses to mathematical texts conveyed via esoteric symbols (commonly used in mathematics instruction) versus everyday language and contexts (public domain text) (see Dowling 1998, 2001).

Methods
A total of 64 (32 male, 32 female) undergraduates were randomly selected for participation and sorted into one of two groups: those with more prior coursework (16 males, 16 females) and those with less prior coursework (16 males and 16 females). They all completed (a) a survey assessing prior course work in mathematics, interest in mathematics [frequency of engagement, depth, voluntary reengagement, reengagement independently], and demographic information, (b) an interactive online assessment of participants’ abilities to identify metamathematical concepts and comprehend argumentation structures that explained the mathematical topic of Fibonacci numbers in both esoteric (symbolic) and public (words and everyday context) domain texts, and (c) a short survey asking about their work with sections of the assessment.

Results
Cluster analysis revealed two groups based on prior course work, proof scheme, and interest: more mathematically developed (MMD) and less mathematically developed (LMD). Gender did not cluster. Findings indicate that MMD participants perform comparably across the two types of text domain, whereas LMD participants improve performance and increase interest only when working with public domain text.

Significance
Differences between the clusters suggest the potential of leveraging text domain as a method to support the development of mathematical comprehension. Furthermore, given that the variables that clustered are malleable (e.g., coursework, interest), it appears that text domain (and instructional conditions more generally) can be adjusted to support LMD students. We wonder whether the text domain of resources that are typically available to students (e.g., esoteric) may unintentionally be constraining the possibility that LMD students will develop interest and learning. We suggest the need to examine whether resources matched to students’ readiness to engage metamathematics and argumentation structures would increase the likelihood that students will elect to take mathematics courses, and develop into learners who are MMD.

Authors

• K. Ann Renninger, Swarthmore College

• Allison Gantt, University of Delaware

• Abram Lipman, Swarthmore College