Including School Mathematics Teaching Applications in an Undergraduate Discrete Mathematics Course

Fulton, Elizabeth W.; Arnold, Elizabeth; Burroughs, Elizabeth A.; Álvarez, James A. Mendoza; Kercher, Andrew; Turner, Kyle

doi:10.1080/10511970.2021.1905120

Cited by 2 publications

(3 citation statements)

References 9 publications

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“…As part of our study design, we stipulate that while approximations of practice situate mathematics in the realm of prospective teachers' future careers, they are equally beneficial for students who are not obtaining a teaching credential. Moreover, including approximations of practice as an application of mathematics to teaching does not detract from the mathematics learning goals of the content course (Fulton et al, 2022) just as it is generally accepted that including applications to engineering, say, does not detract from the learning of mathematics.…”

Section: Approximations Of Teaching Practice In Prospective Teacher C...mentioning

confidence: 99%

“…Our study uses mathematical tasks (Álvarez et al, 2020, 2022Fulton et al, 2022) that embed approximations of teaching practice in order to provide undergraduate students opportunities to encounter ideas about mathematics and ideas about teaching and learning mathematics. The tasks provide focused opportunities to engage in analyzing, anticipating, or guiding student thinking in the context of expanding or deepening undergraduate learning of mathematical ideas and concepts.…”

Section: Mathematical Tasksmentioning

confidence: 99%

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Encountering ideas about teaching and learning mathematics in undergraduate mathematics courses

Burroughs

Arnold

Álvarez

et al. 2023

ZDM Mathematics Education

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We study the ideas about teaching and learning mathematics that undergraduate students generate when they encounter tasks designed to embed approximations of teaching practice in mathematics courses taken by a general population of students. These tasks attend to the dual goals of developing an understanding of mathematics content and an understanding of how teachers provide classroom experiences that foster mathematics learning. The study employs a qualitative, multiple-case study methodology, with four cases bounded by the content areas of abstract algebra, single variable calculus, discrete mathematics, and introductory statistics. The data for the study come from undergraduate students’ written work on mathematical tasks, interviews with a subset of students from each course, and interviews with each instructor throughout the term during which they implemented the tasks. Our findings indicate that students identified the broad applicability of teaching skills (discussed by 32 of the 61 interviewed students), recognized the value of examining hypothetical learners’ mathematical work (discussed by 59 of the 61 interviewed students), and reported empathy for hypothetical learners (discussed by 38 of the 61 interviewed students). These findings persisted across the course content and course levels we studied, leading us to conclude that our findings can transfer to additional mathematics courses in secondary mathematics teacher preparation.

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Section: Approximations Of Teaching Practice In Prospective Teacher C...mentioning

confidence: 99%

Section: Mathematical Tasksmentioning

confidence: 99%

Encountering ideas about teaching and learning mathematics in undergraduate mathematics courses

Burroughs

Arnold

Álvarez

et al. 2023

ZDM Mathematics Education

Self Cite

View full text Add to dashboard Cite

show abstract

“…Greefrath et al (2022) have highlighted the value of modeling-based strategies, emphasizing application-oriented learning. Similarly,Fulton et al (2022) promote bridging connections with traditional school math practices. Our research concretely manifests these ideas by showcasing how leveraging real-world applications and examples can deepen students' understanding and retention of core concepts.…”

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confidence: 99%

Unveiling the Digital Equation Through Innovative Approaches for Teaching Discrete Mathematics to Future Computer Science Educators

Suranchiyeva,

Bostanov,

Kenesbayev

et al. 2023

JITE:IIP

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Aim/Purpose: This study seeks to present a learning model of discrete mathematics elements, elucidate the content of teaching, and validate the effectiveness of this learning in a digital education context. Background: Teaching discrete mathematics in the realm of digital education poses challenges, particularly in crafting the optimal model, content, tools, and methods tailored for aspiring computer science teachers. The study draws from both a comprehensive review of relevant literature and the synthesis of the authors’ pedagogical experiences. Methodology: The research utilized a system-activity approach and aligned with the State Educational Standard. It further integrated the theory of continuous education as its psychological and pedagogical foundation. Contribution: A unique model for instructing discrete mathematics elements to future computer science educators has been proposed. This model is underpinned by informative, technological, and personal competencies, intertwined with the mathematical bedrock of computer science. Findings: The study revealed the importance of holistic teaching of discrete mathematics elements for computer science teacher aspirants in line with the Informatics educational programs. An elective course, “Elements of Discrete Mathematics in Computer Science”, comprising three modules, was outlined. Practical examples spotlighting elements of mathematical logic and graph theory of discrete mathematics in programming and computer science were showcased. Recommendations for Practitioners: Future computer science educators should deeply integrate discrete mathematics elements in their teaching methodologies, especially when aligning with professional disciplines of the Informatics educational program. Recommendation for Researchers: Further exploration is recommended on the seamless integration of discrete mathematics elements in diverse computer science curricula, optimizing for varied learning outcomes and student profiles. Impact on Society: Enhancing the quality of teaching discrete mathematics to future computer science teachers can lead to better-educated professionals, driving advancements in the tech industry and contributing to societal progress. Future Research: There is scope to explore the wider applications of the discrete mathematics elements model in varied computer science sub-disciplines, and its adaptability across different educational frameworks.

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Including School Mathematics Teaching Applications in an Undergraduate Discrete Mathematics Course

Cited by 2 publications

References 9 publications

Encountering ideas about teaching and learning mathematics in undergraduate mathematics courses

Encountering ideas about teaching and learning mathematics in undergraduate mathematics courses

Unveiling the Digital Equation Through Innovative Approaches for Teaching Discrete Mathematics to Future Computer Science Educators

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