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Sigrid Iversen Klock – International Journal of Mathematical Education in Science and Technology, 2025
This article addresses argumentation in middle-school students' group work with conjectures in arithmetic with different epistemic states. Twenty-five episodes were analysed using G. J. Stylianides' framework for reasoning and proving, which comprised a mathematical, psychological, and pedagogical component. The mathematical component was studied…
Descriptors: Middle School Students, Persuasive Discourse, Mathematics Education, Arithmetic
Vincenzi, Giovanni – International Journal of Mathematical Education in Science and Technology, 2020
In this article, we will give a geometric interpretation of certain finite arithmetic progressions. For this purpose, we will introduce the concept of the "n-regular partition (P[subscript n]) of a quadrilateral.
Descriptors: Mathematical Concepts, Arithmetic, Equations (Mathematics), Geometry
Laudano, Francesco – International Journal of Mathematical Education in Science and Technology, 2022
We introduce the concept of the "sequence of the ratios of convex quadrilaterals," identify some properties of these sequences and use them to provide new characterizations for some classic quadrilateral families. The research involves aspects of geometry, arithmetic and mathematical analysis, which converge to produce the results.
Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Geometry
Padrón, Miguel A.; Plaza, Ángel – International Journal of Mathematical Education in Science and Technology, 2021
Many proofs of the arithmetic mean harmonic mean inequality have been proposed based on the rich connections between mathematics and physics. Sometimes the Arithmetic Mean Harmonic Mean inequality is proved by using electric networks. In this note, we use a simple set of two springs, instead of four springs which would be the equivalent set to…
Descriptors: Mathematics Instruction, Teaching Methods, Validity, Mathematical Logic
Oxman, Victor; Stupel, Moshe; Weissman, Shula – International Journal of Mathematical Education in Science and Technology, 2021
The present paper describes beautiful conservation relations between areas formed by different geometrical shapes and area relations formed by algebraic functions. The conservation properties were investigated by students at an academic college of education using a computerized technological tool and were subsequently accompanied by justified…
Descriptors: Mathematics Instruction, Teaching Methods, Computer Assisted Instruction, Geometry
Sprows, David – International Journal of Mathematical Education in Science and Technology, 2017
The fundamental theorem of arithmetic is one of those topics in mathematics that somehow "falls through the cracks" in a student's education. When asked to state this theorem, those few students who are willing to give it a try (most have no idea of its content) will say something like "every natural number can be broken down into a…
Descriptors: Arithmetic, Mathematical Logic, Number Concepts, Numeracy
Kosyvas, Georgios – International Journal of Mathematical Education in Science and Technology, 2016
This paper presents the results of an experimental teaching carried out on 12-year-old students. An open-ended task was given to them and they had not been taught the algorithmic process leading to the solution. The formal solution to the problem refers to a system of two linear equations with two unknown quantities. In this mathematical activity,…
Descriptors: Arithmetic, Mathematical Logic, Problem Solving, Equations (Mathematics)
Whitacre, Ian; Pierson Bishop, Jessica; Lamb, Lisa L.; Philipp, Randolph A.; Bagley, Spencer; Schappelle, Bonnie P. – International Journal of Mathematical Education in Science and Technology, 2015
We interviewed 40 students each in grades 7 and 11 to investigate their integer-related reasoning. In one task, the students were asked to write and interpret equations related to a story problem about borrowing money from a friend. All the students solved the story problem correctly. However, they reasoned about the problem in different ways.…
Descriptors: Grade 7, Grade 11, Interviews, Mathematical Logic
Lynch, Mark A. M. – International Journal of Mathematical Education in Science and Technology, 2011
A procedure for generating quasigroups from groups is described, and the properties of these derived quasigroups are investigated. Some practical examples of the procedure and related results are presented.
Descriptors: Algebra, Mathematics, Mathematics Instruction, Mathematics Education
Sugden, Steve – International Journal of Mathematical Education in Science and Technology, 2012
A newspaper numbers game based on simple arithmetic relationships is discussed. Its potential to give students of elementary algebra practice in semi-"ad hoc" reasoning and to build general arithmetic reasoning skills is explored. (Contains 3 figures, 7 tables and 3 notes.)
Descriptors: Arithmetic, Algebra, Mathematics Skills, Mathematical Logic
Herrera, Aurelia Noda; Bruno, Alicia; Gonzalez, Carina; Moreno, Lorenzo; Sanabria, Hilda – International Journal of Mathematical Education in Science and Technology, 2011
We present a research report on addition and subtraction conducted with Down syndrome students between the ages of 12 and 31. We interviewed a group of students with Down syndrome who executed algorithms and solved problems using specific materials and paper and pencil. The results show that students with Down syndrome progress through the same…
Descriptors: Number Systems, Down Syndrome, Subtraction, Mathematics Skills
Srinivasan, V. K. – International Journal of Mathematical Education in Science and Technology, 2011
This article presents different approaches to a problem, dubbed by the author as "the consecutive pages problem". The aim of this teaching-oriented article is to promote the teaching of abstract concepts in mathematics, by selecting a challenging amusement problem and then presenting various solutions in such a way that it can engage the attention…
Descriptors: Problem Sets, Problem Solving, Mathematical Applications, Mathematical Concepts
Kulkarni, Raghavendra G. – International Journal of Mathematical Education in Science and Technology, 2009
We describe a method to extract roots of a reducible quintic over the real field, which makes use of a simple division. A procedure to synthesize such quintics is given and a numerical example is solved to extract the roots of quintic with the proposed method.
Descriptors: Problem Solving, Equations (Mathematics), Mathematics Instruction, Mathematical Concepts
Abramovich, Sergei – International Journal of Mathematical Education in Science and Technology, 2012
This article explores the notion of collateral learning in the context of classic ideas about the summation of powers of the first "n" counting numbers. Proceeding from the well-known legend about young Gauss, this article demonstrates the value of reflection under the guidance of "the more knowledgeable other" as a pedagogical method of making…
Descriptors: Teaching Methods, Preservice Teacher Education, Learning Experience, Mathematics Education
Plaza, A.; Falcon, S. – International Journal of Mathematical Education in Science and Technology, 2008
This note shows a combinatorial approach to some identities for generalized Fibonacci numbers. While it is a straightforward task to prove these identities with induction, and also by arithmetical manipulations such as rearrangements, the approach used here is quite simple to follow and eventually reduces the proof to a counting problem. (Contains…
Descriptors: Arithmetic, Mathematics Instruction, Problem Solving, Validity
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