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Jungic, Veselin; Yan, Xiaoheng – For the Learning of Mathematics, 2020
The aim of this article is to advise readers that natural numbers may be introduced as ordinal numbers or cardinal numbers and that there is an ongoing discussion about which come first. In addition, through several examples, the authors demonstrate that in the process of answering the question "How many?" one may, if convenient, use…
Descriptors: Number Concepts, Mathematics Instruction, Cognitive Processes, Numbers
Norton, Anderson; Flanagan, Kyle – North American Chapter of the International Group for the Psychology of Mathematics Education, 2022
This paper frames children's mathematics as mathematics. Specifically, it draws upon our knowledge of children's mathematics and applies it to understanding the prime number theorem. Elementary school arithmetic emphasizes two principal operations: addition and multiplication. Through their units coordination activity, children construct two…
Descriptors: Mathematics Instruction, Arithmetic, Elementary School Students, Addition
Matthews, Percival G.; Ziols, Ryan – Research in Mathematics Education, 2019
Rational number knowledge is critical for mathematical literacy and academic success. However, despite considerable research efforts, rational numbers present perennial difficulties for a large number of learners. These difficulties have led some to posit that rational numbers are not a natural fit for human cognition. In this chapter, we…
Descriptors: Number Concepts, Cognitive Processes, Mathematics Instruction, Instructional Design
Roy, George J.; Harbour, Kristin E.; Martin, Christie; Cunningham, Matthew – Mathematics Teacher: Learning and Teaching PK-12, 2022
One way to emphasize students' strengths when reasoning verbally is through number talks. During a number talk, a teacher facilitates a 5- to 15-minute conversation during which students have the opportunity to engage in mental mathematics and verbally explain and justify their reasoning regarding how they make sense of numerical computations.…
Descriptors: Teaching Methods, Mathematics Instruction, Fractions, Cognitive Processes
Tzur, Ron – Research in Mathematics Education, 2019
In this chapter, I propose a stance on learning fractions as multiplicative relations through reorganizing knowledge of whole numbers as a viable alternative to the Natural Number Bias (NNB) stance. Such an alternative, rooted in the constructivist theory of knowing and learning, provides a way forward in thinking about and carrying out…
Descriptors: Fractions, Mathematics Instruction, Guidelines, Multiplication
Alibali, Martha W.; Norton, Anderson – Research in Mathematics Education, 2019
The overarching theme of this book can be simply stated: Building on a foundation of biologically based abilities, children construct number via sensorimotor and mental activity. In this chapter, we return to this theme, and we connect it to three additional themes that emerge across chapters: comparing competing models for conceptual change;…
Descriptors: Mathematics Instruction, Interdisciplinary Approach, Teaching Methods, Numbers
Bofferding, Laura – Teaching Children Mathematics, 2014
As students progress from working with whole numbers to working with integers, they must wrestle with the big ideas of number values and order. Using objects to show positive quantities is easy, but no physical negative quantities exist. Therefore, when talking about integers, the author refers to number values instead of number quantities. The…
Descriptors: Mathematics Instruction, Teaching Methods, Grade 1, Elementary School Mathematics
Erb, Christopher D. – Journal of Cognition and Development, 2018
Developmental theory has long emphasized the importance of linking perception, cognition, and action. Techniques designed to record the spatial and temporal characteristics of hand movements (i.e., "manual dynamics") present new opportunities to study the nature of these links across development by providing a window into how perceptual,…
Descriptors: Motor Reactions, Children, Measurement Techniques, Adults
Davis, Zain – African Journal of Research in Mathematics, Science and Technology Education, 2016
Anthropological approaches to studying the contextual specificity of mathematical thought and practice in schools can productively inform descriptions and analyses of mathematical practices within and across different teaching and learning contexts. In this paper I argue for an anthropological methodological orientation that takes into…
Descriptors: Anthropology, Elementary School Mathematics, Mathematics Instruction, Teaching Methods
Geary, David C. – Mathematical Thinking and Learning: An International Journal, 2015
The collection of studies in this special issue make an important contribution to our understanding and measurement of the core cognitive and noncognitive factors that influence children's emerging quantitative competencies. The studies also illustrate how the field has matured, from a time when the quantitative competencies of infants and young…
Descriptors: Preschool Children, Statistical Analysis, Knowledge Level, Competence
Ngu, Bing – Mathematics Education Research Group of Australasia, 2014
An analysis of one-step equations from a cognitive load theory perspective uncovers variation within one-step equations. The complexity of one-step equations arises from the element interactivity across the operational and relational lines. The higher the number of operational and relational lines, the greater the complexity of the equations.…
Descriptors: Algebra, Equations (Mathematics), Cognitive Processes, Difficulty Level
Lee, Ji Un – Mathematics Teaching, 2010
Unlike old perceptions of algebra as a subject that needs to be taught in the upper grade levels of schooling, much of the recent research reports that young students are capable of reasoning algebraically. It is important to note that the recommendation to include algebraic experiences in the early grades is not made simply to introduce typical…
Descriptors: Algebra, Mathematical Logic, Mathematics Instruction, Elementary School Mathematics
Piantadosi, Steven T.; Tenenbaum, Joshua B.; Goodman, Noah D. – Cognition, 2012
In acquiring number words, children exhibit a qualitative leap in which they transition from understanding a few number words, to possessing a rich system of interrelated numerical concepts. We present a computational framework for understanding this inductive leap as the consequence of statistical inference over a sufficiently powerful…
Descriptors: Statistical Inference, Number Concepts, Models, Computation
Champagne, Zachary M.; Schoen, Robert; Riddell, Claire M. – Teaching Children Mathematics, 2014
Early elementary school students are expected to solve twelve distinct types of word problems. A math researcher and two teachers pose a structure for thinking about one problem type that has not been studied as closely as the other eleven. In this article, the authors share some of their discoveries with regard to the variety of…
Descriptors: Elementary School Students, Word Problems (Mathematics), Problem Solving, Teaching Methods
Slusser, Emily B.; Sarnecka, Barbara W. – Journal of Experimental Child Psychology, 2011
An essential part of understanding number words (e.g., "eight") is understanding that all number words refer to the dimension of experience we call numerosity. Knowledge of this general principle may be separable from knowledge of individual number word meanings. That is, children may learn the meanings of at least a few individual number words…
Descriptors: Evidence, Semantics, Number Concepts, Numeracy