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The Role of the Partitioning and Coset Algorithm Quotient Group Partial Meanings in Comprehending the First Isomorphism Theorem and Its Proof
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Melhuish, Kathleen; Guajardo, Lino; Dawkins, Paul C.; Zolt, Holly; Lew, Kristen – Educational Studies in Mathematics, 2023
In many advanced mathematics courses, comprehending theorems and proofs is an essential activity for both students and mathematicians. Such activity requires readers to draw on relevant meanings for the concepts involved; however, the ways that concept meaning may shape comprehension activity is currently undertheorized. In this paper, we share a…
Descriptors: Algorithms, Comprehension, Mathematical Logic, Mathematical Concepts
Developing Mathematical Reasoning: Avoiding the Trap of Algorithms
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Pamela Weber Harris; Cameron Harris, Contributor – Corwin, 2025
Author Pam Harris argues that teaching real math--math that is free of distortions--will reach more students more effectively and result in deeper understanding and longer retention. This book is about teaching undistorted math using the kinds of mental reasoning that mathematicians do. Memorization tricks and algorithms meant to make math…
Descriptors: Mathematics Instruction, Mathematical Logic, Mathematics Skills, Addition
A Note on Matrix Multiplication Appearing as Element Concatenation or Coinciding with Matrix Addition
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Samuel B. Allan; Peter K. Dunn; Robert G. McDougall – International Journal of Mathematical Education in Science and Technology, 2024
In this note we demonstrate two instances where matrix multiplication can be easily verified. In the first setting, the matrix product appears as matrix element concatenation, and in the second, the product coincides with matrix addition. General proofs for some results are provided with a more complete description for 2×2 matrices. Suggested for…
Descriptors: Mathematics Instruction, Teaching Methods, Multiplication, Addition
What Challenges Emerge When Students Engage with Algorithmatizing Tasks?
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Tupouniua, John Griffith – Journal of Pedagogical Research, 2023
A critical part of supporting the development of students' algorithmic thinking is understanding the challenges that emerge when students engage with algorithmatizing tasks--tasks that require the creation of an algorithm. Knowledge of these challenges can serve as a basis upon which educators can build effective strategies for enhancing students'…
Descriptors: Algorithms, Thinking Skills, Mathematics Skills, Task Analysis
Computer-Supported Assessment of Geometric Exploration Using Variation Theory
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Luz, Yael; Yerushalmy, Michal – Journal for Research in Mathematics Education, 2023
We report on an innovative design of algorithmic analysis that supports automatic online assessment of students' exploration of geometry propositions in a dynamic geometry environment. We hypothesized that difficulties with and misuse of terms or logic in conjectures are rooted in the early exploration stages of inquiry. We developed a generic…
Descriptors: Algorithms, Computer Assisted Testing, Geometry, Mathematics Instruction
Handbook of Research on the Applications of Neutrosophic Sets Theory and Their Extensions in Education. Advances in Data Mining and Database Management (ADMDM) Book Series
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Broumi, Said, Ed. – IGI Global, 2023
Fuzzy sets have experienced multiple expansions since their conception to enhance their capacity to convey complex information. Intuitionistic fuzzy sets, image fuzzy sets, q-rung orthopair fuzzy sets, and neutrosophic sets are a few of these extensions. Researchers and academics have acquired a lot of information about their theories and methods…
Descriptors: Theories, Mathematical Logic, Intuition, Decision Making