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Margherita Piroi – Educational Studies in Mathematics, 2025
This study aims at elaborating a well-established theoretical framework that distinguishes three modes of thinking in linear algebra: the analytic-arithmetic, the synthetic-geometric, and the analytic-structural mode. It describes and analyzes the bundle of signs produced by an engineering student during an interview, where she was asked to recall…
Descriptors: Undergraduate Students, Engineering Education, Case Studies, Algebra
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Papadopoulos, Ioannis; Thoma, Athina – International Journal of Science and Mathematics Education, 2023
Mental brackets constitute an idiosyncratic use of brackets sometimes used to evaluate arithmetic expressions and are closely connected with students' structure sense. The relevant literature describes the use of mental brackets focusing on primary school students and in the context of arithmetic. Using 181 high school students' solutions to seven…
Descriptors: Secondary School Mathematics, Arithmetic, High School Students, Mathematical Concepts
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María D. Torres; Antonio Moreno; Rodolfo Vergel; María C. Cañadas – International Journal of Science and Mathematics Education, 2024
This paper is part of broader research being conducted in the area of algebraic thinking in primary education. Our general research objective was to identify and describe generalization of a 2nd grade student (aged 7-8). Specifically, we focused on the transition from arithmetic to algebraic generalization. The notion of structure and its…
Descriptors: Grade 2, Elementary School Mathematics, Arithmetic, Algebra
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Marios Pittalis – Mathematics Education Research Journal, 2025
A theoretical model describing Grade 7 students' rational number sense was formulated and validated empirically (n = 360), hypothesizing that rational number sense is a general construct consisting of three factors: basic rational number sense, arithmetic sense, and flexibility with rational numbers. Data analysis suggested that rational-number…
Descriptors: Middle School Mathematics, Middle School Students, Grade 7, Numbers
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Pittalis, Marios – International Journal of Science and Mathematics Education, 2023
A theoretical model describing young students' (Grade 3) arithmetic-algebraic structure sense was formulated and validated empirically (n = 130), hypothesizing that young students' arithmetic-algebraic structure sense consists of five distinct but correlated factors; structure in numerical equivalence and word-problem modeling, structure in…
Descriptors: Elementary School Students, Grade 3, Mathematics Skills, Arithmetic
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Dogan, Hamide; Shear, Edith; Contreras, Angel F. Garcia; Hoffman, Lion – International Journal of Mathematical Education in Science and Technology, 2022
We investigated understanding of the linear independence concept based on the type and nature of connections displayed in seven non-mathematics majors' interview responses to a set of open-ended questions. Through a qualitative analysis, we identified six categories of frequently displayed connections. There were also recognizable differences in…
Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Undergraduate Students
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Schifter, Deborah; Russell, Susan Jo – ZDM: Mathematics Education, 2022
This article addresses the nature of student-generated representations that support students' early algebraic reasoning in the realm of generalized arithmetic. We analyzed representations created by students for the following qualities: representations that distinguish the behavior of one operation from another, that support an explanation of a…
Descriptors: Mathematical Logic, Algebra, Arithmetic, Mathematics Skills
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Wong, Terry Tin-Yau; Kwan, Kam-Tai – Developmental Psychology, 2023
The relation to operands (RO) principles describe the relation between operands and answers in arithmetic problems (e.g., the sum is always larger than its positive addends). Despite being a fundamental property of arithmetic, its empirical relation with arithmetic/algebraic problem solving has seldom been investigated. The current longitudinal…
Descriptors: Mathematics Instruction, Arithmetic, Problem Solving, Algebra
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Thomaidis, Yannis; Tzanakis, Constantinos – ZDM: Mathematics Education, 2022
In the last two decades, studying the possible relations between the history of mathematics and mathematics education has revealed the importance of certain foundational issues concerning the nature, relevance and validity of historical knowledge vis-à-vis problems of teaching and learning, which call for deeper exploration. Reviewing aspects of…
Descriptors: Mathematics Education, Educational History, Algebra, Mathematical Concepts
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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
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Demattè, Adriano; Furinghetti, Fulvia – ZDM: Mathematics Education, 2022
In this paper, we describe an experiment in using history to work on problem-solving and the relationship between arithmetic and algebra. The students involved attended the first year of the Italian upper secondary school (grade 9). The original sources we used are problems from Italian treatises on arithmetic and algebra that appeared in the…
Descriptors: History, Problem Solving, Mathematics Instruction, Arithmetic
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Kieran, Carolyn; Martínez-Hernández, Cesar – ZDM: Mathematics Education, 2022
"They are the same" is a phrase that teachers often hear from their students in arithmetic and algebra. But what do students mean when they say this? The present paper researches the notion of sameness within algebraic thinking in the context of generating equivalent numerical equalities. A group of Grade 6 Mexican students (10- to…
Descriptors: Mathematical Concepts, Algebra, Equations (Mathematics), Arithmetic
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Marianna Bosch; Angel Gutierrez; Salvador Llinares – ZDM: Mathematics Education, 2024
This survey paper presents recent relevant research in mathematics education produced in Spain, which allows the identification of different broad lines of research developed by Spanish groups of scholars. First, we present and describe studies whose research objectives are related to student learning of specific curricular contents and…
Descriptors: Foreign Countries, Mathematics Education, Preservice Teacher Education, Mathematics Skills
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Kojic, Vedran; Krpan, Mira; Lukac, Zrinka – International Journal of Mathematical Education in Science and Technology, 2021
One of the fundamental topics taught in the microeconomics class is minimizing economic costs. It includes understanding the concept of derivatives and applying them. However, most of the first-year undergraduate students find calculus difficult to understand, which also results in poor knowledge of optimization. We use the method based on the…
Descriptors: Microeconomics, Mathematical Concepts, Costs, Mathematics Instruction
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Jahudin, Janet; Siew, Nyet Moi – Problems of Education in the 21st Century, 2023
Algebraic Thinking Skills (ATS) are one of the skills that students need to master in order to solve nonroutine problems. These skills are also necessary as a foundation for students preparing to enter university studies and fields of work that require logical and analytical thinking. However, Malaysian students' performance in solving algebraic…
Descriptors: Algebra, Thinking Skills, Mathematics Skills, Problem Solving
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