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3 results on '"Antonio Estevan Martinez"'

1. Using Python to Reason about Logic and Set Theory: Three Instrumented Action Schemes

Author

Antonio Estevan Martinez IV

Abstract

Many areas of mathematics naturally lend themselves to machine-based computing environments, which suggests that computational environments may serve as useful mediating tools for the teaching and learning of mathematical content. While some mathematics classes are leveraging the use of computational tools, the implementation of computer programming to teach and learn mathematics is not widespread. In this study, I highlight the mathematical activity of four undergraduate students who used Python to solve mathematical tasks in the context of set theory and logic. To understand how the students leveraged the computer programming environment, I use the analytical framework known as the instrumental approach, which can be utilized to investigate the confluence of an artifact (often a piece of technology) and the human mind to solve a mathematical problem. Results indicate that the students were able to use Python and its computational capabilities such as For Loops, If Statements, and Functions as artifacts to reason about propositional statements, set intersection, and subsets. Specifically, three instrumented action schemes emerged from their work on three different tasks. These schemes describe the use of Python in creative ways to solve mathematical tasks, which suggests various implications for teaching and research.

Published
2024
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2. Bridging the Gap between Set Theory and Logic: Leveraging Computing as a Mediating Tool for Learning

Author

Antonio Estevan Martinez

Abstract

Undergraduate mathematics education research focused on Introduction to Proofs courses has gained traction as more students are experiencing challenges in their proof-based courses. While studies have analyzed the teaching and learning of proofs, there is a growing need for research in students' understanding of mathematical logic and set theory because of the foundational nature of these topics in more advanced mathematics courses. In this dissertation, I present a teaching experiment that explores how computing/programming can be leveraged to facilitate and strengthen the connection between set theory and logic. Programming is a focus of this work due to the growing need for undergraduate Science, Technology, Engineering and Mathematics majors to be prepared for their future careers, which will likely entail the utilization of computing in some form. The purpose of this study is to take a step in the direction of where undergraduate education is headed and better understand how the use of computing can potentially fit into the mathematics curriculum. There are three main dimensions of this study. The first is a look at how programming can influence students' in-the-moment ways of reasoning about mathematical set theory and logic. The second takes a step back to consider the students' advancing mathematical activity and growth over the course of a multi-session long teaching experiment. The third is a focus on the students' affective experiences, as non-cognitive factors such as confidence, interest and self-efficacy are analyzed to characterize the shifting nature of the students' mathematical identities. The results of this study indicate that the students in my study were able to leverage computing as an accessible onramp to the fundamental ideas related to set theory and logic. Moreover, my findings show that computing can have a positive effect on one's sense of confidence and interest in relation to mathematics and programming. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

Published
2022

3. Course Coordinator Orientations Toward their Work and Opportunities for Professional Development

Author

Kristen Vroom, Talia Latona-Tequida, Chris Rasmussen, Jessica Gehrtz, and Antonio Estevan Martinez

Subjects
Higher education, business.industry, 4. Education, 05 social sciences, Professional development, 050301 education, Education, Course (navigation), Community of practice, Leverage (negotiation), Work (electrical), 0502 economics and business, ComputingMilieux_COMPUTERSANDEDUCATION, Mathematics education, business, 0503 education, 050203 business & management
Abstract

One way that university mathematics departments across the United States are making efforts to improve their introductory mathematics courses is by implementing or increasing the level of course coordination. This can entail creating uniform course elements for multi-section courses and efforts to build a community of practice among the instructors teaching these courses. In this paper we explore coordinator orientations that implicitly (and in some cases explicitly) guide their work. In particular, we identified two orientations toward coordination, a Humanistic-Growth orientation and a Resource-Managerial orientation. Data analyzed in this manuscript consists of interviews with 19 course coordinators and 53 instructors from seven different higher education institutions across the United States. We introduce a framework that aligns two approaches to professional development with these two coordinator orientations and conclude with a discussion on how department chairs and others looking to implement or improve coordination may leverage this framework provided in this paper.

Published
2021
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