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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
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
Foundations of Mathematics: Unsolvable Problems
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Steen, Lynn Arthur – Science, 1975
Reports on two types of unsolvability in mathematics. One is an instance of impossibility and the second is a judgment of undecidability. Presents a number of examples of undecidable propositions. (GS)
Descriptors: Algorithms, Mathematical Concepts, Mathematical Logic, Mathematics Education
Dehn's Algorithm and the Complexity of Word Problems.
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Book, Ronald V. – American Mathematical Monthly, 1988
The "word problem" is stated for a given collection. Facts regarding Dehn's Algorithm, definition of Thue systems, a rewriting system, lemmas and corollaries are provided. The situation is examined where the monoid presented by a finite Thue system is a group. (DC)
Descriptors: Abstract Reasoning, Algebra, Algorithms, College Mathematics
Numerical Algorithms.
Engel, Arthur – Mathematics Teaching, 1981
The need for incorporating algorithmics into mathematics instruction is presented. The proliferation of computers is seen to have made the designing of algorithms an essential skill. Examples are given, and the view that mathematics will lose much prestige and importance if algorithmics is not integrated into it is presented. (MP)
Descriptors: Algorithms, Computers, Elementary Secondary Education, Higher Education
Math That Adults Need.
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Burke, Paul – Journal of College Admissions, 1990
Argues that the vast majority of adults have no use for the specialized mathematics taught in high schools and required by colleges--algebra, geometry, or calculus. Suggests that colleges should accept applicants who have studied percents, formulas, logic, computer commands, and basic statistics. (TE)
Descriptors: Algebra, Algorithms, Arithmetic, Calculus
The Programmable Calculator in the Classroom.
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Stolarz, Theodore J. – 1979
The uses of programable calculators in the mathematics classroom are presented. A discussion of the "microelectronics revolution" that has brought programable calculators into our society is also included. Pointed out is that the logical or mental processes used to program the programable calculator are identical to those used to program…
Descriptors: Algorithms, Calculators, Cognitive Processes, Computer Programs