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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
Watson, Steven – Mathematics Teaching Research Journal, 2020
George Spencer-Brown's Laws of Forms was first published in 1969. In the fifty years since its publication, it has influenced mathematicians, scientists, philosophers, and sociologists. Its influence on mathematics education has been negligible. In this paper, I present a brief introduction to the theory and its philosophical underpinnings. And I…
Descriptors: Mathematics Education, Educational Philosophy, Educational History, Arithmetic
Hußmann, Stephan; Schacht, Florian; Schindler, Maike – Mathematics Education Research Journal, 2019
The purpose of this article is to show how the philosophical theory of inferentialism can be used to understand students' conceptual development in the field of mathematics. Based on the works of philosophers such as Robert Brandom, an epistemological theory in mathematics education is presented that offers the opportunity to trace students'…
Descriptors: Inferences, Epistemology, Mathematics Skills, Mathematical Logic
Hickendorff, Marian – European Journal of Psychology of Education, 2018
Strategy flexibility, adaptivity, and the use of clever shortcut strategies are of major importance in current primary school mathematics education worldwide. However, empirical results show that primary school students use such shortcut strategies rather infrequently. The aims of the present study were to analyze the extent to which Dutch sixth…
Descriptors: Foreign Countries, Grade 6, Problem Solving, Mathematics Skills
Beckmann, Sybilla; Izsák, Andrew – Journal for Research in Mathematics Education, 2015
In this article, we present a mathematical analysis that distinguishes two distinct quantitative perspectives on ratios and proportional relationships: variable number of fixed quantities and fixed numbers of variable parts. This parallels the distinction between measurement and partitive meanings for division and between two meanings for…
Descriptors: Mathematics Education, Mathematical Concepts, Multiplication, Measurement
Tempier, Frédérick – Journal of Mathematics Teacher Education, 2016
Many studies have shown the difficulties of learning and teaching the decimal number system for whole numbers. In the case of numbers bigger than one hundred, complexity is partly due to the multitude of possible relationships between units. This study was aimed to develop conditions of a resource which can help teachers to enhance their teaching…
Descriptors: Mathematics, Mathematical Concepts, Mathematics Instruction, Mathematical Logic
Deliyianni, Eleni; Gagatsis, Athanasios; Elia, Iliada; Panaoura, Areti – International Journal of Science and Mathematics Education, 2016
The aim of this study was to propose and validate a structural model in fraction and decimal number addition, which is founded primarily on a synthesis of major theoretical approaches in the field of representations in Mathematics and also on previous research on the learning of fractions and decimals. The study was conducted among 1,701 primary…
Descriptors: Fractions, Problem Solving, Arithmetic, Numbers
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
Liljedahl, Peter, Ed.; Allan, Darien, Ed.; Chapman, Olive, Ed.; Gourdeau, Frédéric, Ed.; Lajoie, Caroline, Ed.; Oesterle, Susan, Ed.; Simmt, Elaine, Ed.; Taylor, Peter, Ed. – Canadian Mathematics Education Study Group, 2016
This special issue of the Canadian Mathematics Education Study Group/Groupe Canadien d'Étude en Didactique des Mathématiques (CMESG/GCEDM) Proceedings looks at CMESG/GCEDM's collective history, reflects on where the group has been, and who the members have become as an organization. Through a selection of excerpts from past proceedings, the…
Descriptors: Mathematics Education, History, Educational Research, Foreign Countries
Lee, Jae Ki; Licwinko, Susan; Taylor-Buckner, Nicole – Journal of Mathematics Education at Teachers College, 2013
PEMDAS is a mnemonic device to memorize the order in which to calculate an expression that contains more than one operation. However, students frequently make calculation errors with expressions, which have either multiplication and division or addition and subtraction next to each other. This article explores the mathematical reasoning of the…
Descriptors: Case Studies, Mathematics, Mathematics Instruction, Mathematical Logic
Godino, Juan D.; Font, Vicenc; Wilhelmi, Miguel R.; Lurduy, Orlando – Educational Studies in Mathematics, 2011
The semiotic approach to mathematics education introduces the notion of "semiotic system" as a tool to describe mathematical activity. The semiotic system is formed by the set of signs, the production rules of signs and the underlying meaning structures. In this paper, we present the notions of system of practices and configuration of objects and…
Descriptors: Semiotics, Mathematics Education, Arithmetic, Mathematical Formulas
Banerjee, Rakhi; Subramaniam, K. – Educational Studies in Mathematics, 2012
The article reports aspects of the evolution of a teaching approach over repeated trials for beginning symbolic algebra. The teaching approach emphasized the structural similarity between arithmetic and algebraic expressions and aimed at supporting students in making a transition from arithmetic to beginning algebra. The study was conducted with…
Descriptors: Grade 6, Arithmetic, Algebra, Teaching Methods
Somchaipeng, Tongta; Kruatong, Tussatrin; Panijpan, Bhinyo – Mathematics Teacher, 2012
Exploring and deriving proofs of closed-form expressions for series can be fun for students. However, for some students, a physical representation of such problems is more meaningful. Various approaches have been designed to help students visualize squares of sums and sums of squares; these approaches may be arithmetic-algebraic or combinatorial…
Descriptors: Mathematical Logic, Validity, Arithmetic, Mathematics
Tsankova, Jenny K.; Pjanic, Karmen – Mathematics Teaching in the Middle School, 2009
Teaching students how to multiply fractions is challenging, not so much from a computational point of view but from a conceptual one. The algorithm for multiplying fractions is much easier to learn than many other algorithms, such as subtraction with regrouping, long division, and certainly addition of fractions with unlike denominators. However,…
Descriptors: Prior Learning, Multiplication, Arithmetic, Mathematical Logic
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