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Lou, Hongwei – International Journal of Mathematical Education in Science and Technology, 2023
In current teaching materials, when using Dedekind cuts to construct real numbers, the definition of a Dedekind cut is always involved in defining addition and multiplication. In this paper, as it is done in many current textbooks, Dedekind cuts are used to construct the set of real numbers. Then the order in it is defined, and the…
Descriptors: Mathematics Instruction, Addition, Multiplication, Arithmetic
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
Krátká, Magdalena; Eisenmann, Petr; Cihlár, Jirí – International Journal of Mathematical Education in Science and Technology, 2022
The paper is the result of extensive research carried out among Czech students and focuses on a conception of infinity. The questionnaire survey was taken by 861 students ranging from grades 7 to 13. The aim of the research was to describe the development of students' conceptions of infinity. These conceptions are built on the intuitive phenomenon…
Descriptors: Foreign Countries, Secondary School Students, Knowledge Level, Mathematical Concepts
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
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
Vondrová, Nada – International Journal of Mathematical Education in Science and Technology, 2022
The adverse influence of the presence of an irrelevant number and language inconsistency in a word problem is well known. Our study focused on the combination of these two variables and on the position of the irrelevant number in the word problem for Grade 6 pupils. The study has a mixed design. Item Response Theory was used to make equally able…
Descriptors: Grade 6, Mathematics Instruction, Word Problems (Mathematics), Difficulty Level
Johansson, B. Tomas – International Journal of Mathematical Education in Science and Technology, 2018
Evaluation of the cosine function is done via a simple Cordic-like algorithm, together with a package for handling arbitrary-precision arithmetic in the computer program Matlab. Approximations to the cosine function having hundreds of correct decimals are presented with a discussion around errors and implementation.
Descriptors: Mathematics, Computation, Mathematical Concepts, Arithmetic
Passarella, Simone – International Journal of Mathematical Education in Science and Technology, 2022
Introducing the distributivity property of multiplication over addition is a well-known challenge in mathematics education, especially in primary school. As a contribution, this paper presents the results of a cycle of design research that focuses on the design, implementation and evaluation of a modelling activity in which 2nd-grade students are…
Descriptors: Multiplication, Mathematics Instruction, Elementary School Students, Mathematical Concepts
Olteanu, Constanta – International Journal of Mathematical Education in Science and Technology, 2018
This paper uses a post-qualitative philosophical perspective to find new ways of understanding teaching and learning. The paper presents a series of examples that were used in a longitudinal study, with the aim of creating variation patterns that would make it possible for students to discern the use of the four basic arithmetic operations in…
Descriptors: Arithmetic, Mathematics Instruction, Mathematical Models, Problem Solving
Shahbari, Juhaina Awawdeh; Tabach, Michal – International Journal of Mathematical Education in Science and Technology, 2021
The modelling approach to teaching and learning mathematics emphasizes the usefulness of mathematics in the real-world. The aim of the current study is to examine whether engagement in modelling activities provides learners an opportunity to expand their knowledge of a specific concept -- the "average" concept. Our data include…
Descriptors: Mathematics Instruction, Teaching Methods, Benchmarking, Arithmetic
Firozzaman, Firoz; Firoz, Fahim – International Journal of Mathematical Education in Science and Technology, 2017
Understanding the solution of a problem may require the reader to have background knowledge on the subject. For instance, finding an integer which, when divided by a nonzero integer leaves a remainder; but when divided by another nonzero integer may leave a different remainder. To find a smallest positive integer or a set of integers following the…
Descriptors: Mathematics Instruction, Numbers, Mathematical Concepts, Equations (Mathematics)
Botetano, Cesar; Abrahamson, Dor – International Journal of Mathematical Education in Science and Technology, 2022
In Peru, national assessments repeatedly rank Indigenous mathematics students as the lowest performing across the entirety of Latin America and South America. Whereas lack of financial resources often predicts low measures, the history of educational practice teaches us that students' poverty need not predict their educational outcomes -- creative…
Descriptors: Mathematics Instruction, Teaching Methods, Creative Teaching, Concept Formation
Lim, Kien H. – International Journal of Mathematical Education in Science and Technology, 2019
An exploratory study was conducted to investigate the use of magic activities in a math course for prospective middle-school math teachers. This research report focuses on a lesson using two versions of math magic: (1) the "5-4-3-2-1-½ Magic" involves having students choose a secret number and apply six arithmetic operations in sequence…
Descriptors: Teaching Methods, Mathematics Instruction, Algebra, Mathematical Concepts
Dolores-Flores, Crisólogo; Rivera-López, Martha Iris; García-García, Javier – International Journal of Mathematical Education in Science and Technology, 2019
This paper reports the results of a research exploring the mathematical connections of pre-university students while they solving tasks which involving rates of change. We assume mathematical connections as a cognitive process through which a person finds real relationships between two or more ideas, concepts, definitions, theorems, procedures,…
Descriptors: Mathematics Instruction, Mathematical Concepts, Foreign Countries, Arithmetic
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