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Showing 1 to 15 of 33 results Save | Export
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Simon, Martin A.; Della Volpe, Daniela; Velamur, Arundhati – Mathematical Thinking and Learning: An International Journal, 2023
Development of the cardinality principle, an understanding that the last number-word recited in counting a collection of items specifies the number of items in that collection, is a critical milestone in developing a concept of number. Researchers in early number development have endeavored to theorize its development. Here we critique two widely…
Descriptors: Mathematics Instruction, Teaching Methods, Numbers, Number Concepts
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Mellone, Maria; Ramploud, Alessandro; Di Paola, Benedetto; Martignone, Francesca – ZDM: The International Journal on Mathematics Education, 2019
The paper presents some reflections and activities developed by researchers and teachers involved in teacher education programs on cultural transposition. The construct of cultural transposition is presented as a condition for decentralizing the didactic practice of a specific cultural context through contact with other didactic practices of…
Descriptors: Foreign Countries, Arithmetic, Number Concepts, Algebra
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MacDonald, Beth L. – North American Chapter of the International Group for the Psychology of Mathematics Education, 2018
This proposal explores relationships between young children's unit development/coordination and young children's subitizing. In particular, this theoretical commentary considers students' degrees of abstraction, students' development of actions on units, and students' operations with units when subitizing. As a result of this commentary, this…
Descriptors: Young Children, Early Childhood Education, Number Concepts, Numeracy
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Rumbelow, Michael – For the Learning of Mathematics, 2021
"Where Mathematics Comes From" (Lakoff & Núñez 2000) proposed that mathematical concepts such as arithmetic and counting are constructed cognitively from embodied metaphors of actions on physical objects, and four actions, or 'grounding metaphors' in particular: collecting, stepping, constructing and measuring. This article argues…
Descriptors: Arithmetic, Mathematics Instruction, Mathematical Concepts, Figurative Language
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Spelke, Elizabeth S. – Language Learning and Development, 2017
The natural numbers may be our simplest, most useful, and best-studied abstract concepts, but their origins are debated. I consider this debate in the context of the proposal, by Gallistel and Gelman, that natural number system is a product of cognitive evolution and the proposal, by Carey, that it is a product of human cultural history. I offer a…
Descriptors: Computation, Number Systems, Number Concepts, Language Usage
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Ervin, Heather K. – International Journal of Research in Education and Science, 2017
It is well documented in literature that rational number is an important area of understanding in mathematics. Therefore, it follows that teachers and students need to have an understanding of rational number and related concepts such as fraction multiplication and division. This practitioner reference paper examines models that are important to…
Descriptors: Mathematics Education, Fractions, Multiplication, Arithmetic
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Polotskaia, Elena – International Journal for Mathematics Teaching and Learning, 2017
The main goal of this paper is to show how Vasily Davydov's powerful ideas about the nature of mathematical thinking and learning can transform the teaching and learning of additive word problem solving. The name Vasily Davydov is well known in the field of mathematics education in Russia. However, the transformative value of Davydov's theoretical…
Descriptors: Models, Mathematics Instruction, Foreign Countries, Problem Solving
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Cipora, Krzysztof; Patro, Katarzyna; Nuerk, Hans-Christoph – Mind, Brain, and Education, 2015
The mental number line metaphor describes how numbers are associated with space. These spatial-numerical associations (SNA) are subserved by parietal structures (mainly intraparietal sulcus [IPS] and posterior superior parietal lobule [PSPL]). Generally, it is assumed that this association is a basic cornerstone for arithmetic skills. In this…
Descriptors: Arithmetic, Spatial Ability, Mathematical Concepts, Mathematics Skills
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Lamberg, Teruni; Wiest, Lynda R. – Teaching Children Mathematics, 2012
"What do you do with the remainder when you divide?" Mrs. Thompson asked her third-grade students. They replied with such comments as, "You can't share that, because they won't be equal!" and "It's not going to come out even because you can't do that!" These answers were consistent with third- and fourth-grade student performance in a pretest and…
Descriptors: Problem Solving, Grade 3, Arithmetic, Number Concepts
Young-Loveridge, Jenny; Bicknell, Brenda – Mathematics Education Research Group of Australasia, 2014
This paper focuses on children's number fact knowledge from a study that explored the impact of using multiplication and division contexts for developing number understanding with 34 five- and six-year-old children from diverse cultural and linguistic backgrounds. After a series of focused lessons, children's knowledge of number facts, including…
Descriptors: Numbers, Number Concepts, Elementary School Students, Elementary School Mathematics
Siegler, Robert S.; Fazio, Lisa K.; Bailey, Drew H.; Zhou, Xinlin – Grantee Submission, 2013
Recent research on fractions has broadened and deepened theories of numerical development. Learning about fractions requires children to recognize that many properties of whole numbers are not true of numbers in general and also to recognize that the one property that unites all real numbers is that they possess magnitudes that can be ordered on…
Descriptors: Number Concepts, Numeracy, Cognitive Processes, Arithmetic
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Almeida, Rut; Bruno, Alicia – International Journal of Mathematical Education in Science and Technology, 2014
This paper analyses the strategies used by pre-service primary school teachers for solving simple addition problems involving negative numbers. The findings reveal six different strategies that depend on the difficulty of the problem and, in particular, on the unknown quantity. We note that students use negative numbers in those problems they find…
Descriptors: Preservice Teachers, Elementary School Teachers, Problem Solving, Elementary School Mathematics
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Klein, Elise; Nuerk, Hans-Christoph; Wood, Guilherme; Knops, Andre; Willmes, Klaus – Brain and Cognition, 2009
Two types of calculation processes have been distinguished in the literature: approximate processes are supposed to rely heavily on the non-verbal quantity system, whereas exact processes are assumed to crucially involve the verbal system. These two calculation processes were commonly distinguished by manipulation of two factors in addition…
Descriptors: Number Concepts, Computation, Cognitive Processes, Arithmetic
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Mussolin, Christophe; Mejias, Sandrine; Noel, Marie-Pascale – Cognition, 2010
Developmental dyscalculia (DD) is a pervasive difficulty affecting number processing and arithmetic. It is encountered in around 6% of school-aged children. While previous studies have mainly focused on general cognitive functions, the present paper aims to further investigate the hypothesis of a specific numerical deficit in dyscalculia. The…
Descriptors: Number Concepts, Arithmetic, Cognitive Processes, Children
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Navi, K.; Molahosseini, A. S.; Esmaeildoust, M. – IEEE Transactions on Education, 2011
The residue number system (RNS) has been an important research field in computer arithmetic for many decades, mainly because of its carry-free nature, which can provide high-performance computing architectures with superior delay specifications. Recently, research on RNS has found new directions that have resulted in the introduction of efficient…
Descriptors: Number Systems, Teaching Methods, Computer System Design, Computer Science Education
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