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Stacy K. Boote; Terrie M. Galanti; Danielle Felicien; Tara Kelly – Mathematics Teacher: Learning and Teaching PK-12, 2025
Teachers and teacher educators have been sharing strategies and resources for implementing mathematics routines in National Council of Teachers of Mathematics (NCTM) journals for years. A less commonly shared mathematics routine, especially with young learners, is "Clothesline Math" (Shore, 2017, 2018). In this routine, teachers create…
Descriptors: Mathematics Instruction, Visual Aids, Early Childhood Education, Mathematics Skills
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
Goffin, Celia; Ansari, Daniel – Mind, Brain, and Education, 2019
What is the nature of the relationship between different lower-level numerical skills and their role in developing arithmetic skills? We consider the hypothesis of a reciprocal relationship between the development of symbolic (e.g., Arabic numerals) and nonsymbolic (e.g., arrays of objects) numerical magnitude processing. Evidence for…
Descriptors: Numeracy, Young Children, Numbers, Arithmetic
Papadopoulos, Ioannis; Gunnarsson, Robert – Educational Studies in Mathematics, 2020
When a number sentence includes more than one operation, students are taught to follow the rules for the order of operations to get the correct result. In this context, brackets are used to determine the operations that should be calculated first. However, it seems that the written format of an arithmetical expression has an impact on the way…
Descriptors: Mathematics Instruction, Elementary School Mathematics, Arithmetic, Foreign Countries
Wessman-Enzinger, Nicole M. – Research in Mathematics Education, 2019
Mathematics education researchers have long pursued--and many still pursue--an ideal instructional model for operations on integers. In this chapter, I argue that such a pursuit may be futile. Additionally, I highlight that ideas of relativity have been overlooked; and, I contend that current uses of translation within current integer…
Descriptors: Numbers, Mathematics Education, Educational Research, Mathematics Instruction
Sidney, Pooja; Thompson, Clarissa G.; Opfer, John E. – Grantee Submission, 2019
Children's understanding of fractions, including their symbols, concepts, and arithmetic procedures, is an important facet of both developmental research on mathematics cognition and mathematics education. Research on infants', children's, and adults' fraction and ratio reasoning allows us to test a range of proposals about the development of…
Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Fractions
Bishop, Jessica P.; Lamb, Lisa L.; Philipp, Randolph A.; Whitacre, Ian; Schappelle, Bonnie P. – Research in Mathematics Education, 2018
We share a subset of the 41 underlying strategies that comprise five ways of reasoning about integer addition and subtraction: formal, order-based, analogy-based, computational, and emergent. The examples of the strategies are designed to provide clear comparisons and contrasts to support both teachers and researchers in understanding specific…
Descriptors: Thinking Skills, Numbers, Numeracy, Comparative Analysis
Murray, Eileen – Research in Mathematics Education, 2018
Mathematics educators advocate for the use of models as an instructional practice that can potentially aid in building students' understanding of difficult topics. Integers and integer operations are historically problematic for students and are critically important in both arithmetic and the future study of algebra. In this chapter, I explore one…
Descriptors: Mathematical Models, Numbers, Mathematics Instruction, Problem Solving
Askew, Mike – ZDM: The International Journal on Mathematics Education, 2019
This paper is centred around a framework for studying teaching--Mediating Primary Mathematics (MPM)--developed in the context of the teaching of Whole Number Arithmetic (WNA) in South Africa. Findings from the analysis of four WNA lessons are used to illustrate how the application of the MPM framework can measure nuanced differences in the…
Descriptors: Elementary School Mathematics, Mathematics Instruction, Numbers, Arithmetic
Takker, Shikha; Subramaniam, K. – Journal of Mathematics Teacher Education, 2019
Existing frameworks of teachers' knowledge required to teach mathematics do not adequately capture the dynamic aspects of knowledge manifested in teaching practice. In this paper, we examine the knowledge demands that arise in situ, in the course of a teacher listening and responding to students' thinking, while teaching the topic of decimal…
Descriptors: Mathematics Instruction, Arithmetic, Teaching Methods, Knowledge Level
Siegler, Robert S.; Im, Soo-hyun; Schiller, Lauren K.; Tian, Jing; Braithwaite, David W. – Grantee Submission, 2020
Children's failure to reason often leads to their mathematical performance being shaped by spurious associations from problem input and overgeneralization of inapplicable procedures rather than by whether answers and procedures make sense. In particular, imbalanced distributions of problems, particularly in textbooks, lead children to create…
Descriptors: Logical Thinking, Arithmetic, Numbers, Fractions
Cooper, Jason – ZDM: The International Journal on Mathematics Education, 2019
Teachers and mathematicians hold different perspectives on the teaching and learning of whole number arithmetic. Though these perspectives may be complementary, sharing them across communities is challenging. An unusual professional development course for primary school teachers, initiated and taught by research mathematicians, provided a setting…
Descriptors: Professional Personnel, Elementary School Mathematics, Elementary School Teachers, Numbers
Siegler, Robert S.; Braithwaite, David W. – Grantee Submission, 2016
In this review, we attempt to integrate two crucial aspects of numerical development: learning the magnitudes of individual numbers and learning arithmetic. Numerical magnitude development involves gaining increasingly precise knowledge of increasing ranges and types of numbers: from non-symbolic to small symbolic numbers, from smaller to larger…
Descriptors: Numeracy, Numbers, Arithmetic, Fractions
Khosroshahi, Leyla G.; Asghari, Amir H. – Australian Primary Mathematics Classroom, 2016
There is a call for enabling students to use a range of efficient mental and written strategies when solving addition and subtraction problems. To do so, students should recognise numerical structures and be able to change a problem to an equivalent problem. The purpose of this article is to suggest an activity to facilitate such understanding in…
Descriptors: Arithmetic, Addition, Subtraction, Problem Solving
Siegler, Robert S. – Developmental Science, 2016
The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: (1) representing increasingly precisely the magnitudes of non-symbolic…
Descriptors: Numbers, Theories, Individual Development, Symbols (Mathematics)