skip to main content


This content will become publicly available on July 8, 2025

Title: Reasoning students employed when mathematizing during a predator-prey modelling task
In this chapter, we address the problem of why blockages occur during mathematization by introducing a method for studying mathematizing based in quantitative reasoning. We report on interview data with six tertiary STEM majors as they developed models of the population dynamics of cats and birds in a backyard habitat. Our analysis focused on real-world relationships participants tried to express when using a given arithmetic operation in a predator-prey modelling task. Our results reveal the conceptions of × participants used to justify their models when constructing an expression for the decrease in the bird population. We conclude by discussing the method’s utility for studying mathematization and with conjectures on how instructors might leverage participants’ justifications to scaffold their emergent models towards a conventionally correct model.  more » « less
Award ID(s):
1750813
NSF-PAR ID:
10511002
Author(s) / Creator(s):
;
Publisher / Repository:
Springer
Date Published:
Journal Name:
International perspectives on the teaching and learning of mathematical modelling
ISSN:
2211-4939
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. User adoption of security and privacy (S&P) best practices remains low, despite sustained efforts by researchers and practitioners. Social influence is a proven method for guiding user S&P behavior, though most work has focused on studying peer influence, which is only possible with a known social graph. In a study of 104 Facebook users, we instead demonstrate that crowdsourced S&P suggestions are significantly influential. We also tested how reflective writing affected participants’ S&P decisions, with and without suggestions. With reflective writing, participants were less likely to accept suggestions — both social and Facebook default suggestions. Of particular note, when reflective writing participants were shown the Facebook default suggestion, they not only rejected it but also (unknowingly) configured their settings in accordance with expert recommendations. Our work suggests that both non-personal social influence and reflective writing can positively influence users’ S&P decisions, but have negative interactions. 
    more » « less
  2. We consider age-structured models with an imposed refractory period between births. These models can be used to formulate alternative population control strategies to China’s one-child policy. By allowing any number of births, but with an imposed delay between births, we show how the total population can be decreased and how a relatively older age distribution can be generated. This delay represents a more ‘continuous’ form of population management for which the strict one-child policy is a limiting case. Such a policy approach could be more easily accepted by society. Our analyses provide an initial framework for studying demographics and how social constraints influence population structure. 
    more » « less
  3. This paper reports on how 10 middle and high school preservice teachers (PSTs) designed a social justice focused lesson using the culturally responsive mathematics teaching (CRMT) tool. Results from our analysis indicate that most of the PSTs were able to select appropriate social justice topics, though not all the PSTs integrated mathematics and social justice throughout their lessons. The results show that most of the PSTs need more experience with mathematization, handling controversial discussions, and developing transformative student action. Our work also led to a modification of the tool (CRMT-M). We discuss the implications of the study for mathematics teacher preparation. 
    more » « less
  4. Students frequently struggled with the mathematizing process – forging connections between implicit and explicit mathematical thinking – when solving a context-rich applied problem. The current research investigated how students interact with and leverage purposively designed ‘mathematizing’ supports when solving applied math problems in a game-based, inquiry-oriented math learning environment. We conducted a naturalistic observation case study and a mixed-method study to investigate middle school students’ usage of mathematizing supports in relation to their math problem-solving performance. The findings indicated a positive and predictive impact of using mathematizing supports on the logged and observed practice of mathematization as well as the performance of applied math problem solving by the students during and after gaming. However, not all students leverage in-game mathematizing supports or engage in problem mathematizing processes. The grounds of students’ constructive interaction with a mathematizing support include their productive persistence in problem solving, their exercise of agency in gauging the utility of mathematizing, and their engagement with deductive reasoning from concrete to abstract. We also observed an interplay between internal and external mathematizing supports, which is moderated by the modality of learning settings.

     
    more » « less
  5. Some people exhibit impressive memory for a wide array of semantic knowledge. What makes these trivia experts better able to learn and retain novel facts? We hypothesized that new semantic knowledge may be more strongly linked to its episodic context in trivia experts. We designed a novel online task in which 132 participants varying in trivia expertise encoded “exhibits” of naturalistic facts with related photos in one of two “museums.” Afterward, participants were tested on cued recall of facts and recognition of the associated photo and museum. Greater trivia expertise predicted higher cued recall for novel facts. Critically, trivia experts but not non-experts showed superior fact recall when they remembered both features (photo and museum) of the encoding context. These findings illustrate enhanced links between episodic memory and new semantic learning in trivia experts, and show the value of studying trivia experts as a special population that can shed light on the mechanisms of memory. 
    more » « less