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Sebastian Holt; David Barner – Cognitive Science, 2025
Humans count to indefinitely large numbers by recycling words from a finite list, and combining them using rules--for example, combining sixty with unit labels to generate sixty-one, sixty-two, and so on. Past experimental research has focused on children learning base-10 systems, and has reported that this rule learning process is highly…
Descriptors: Computation, Numbers, Adult Students, Number Concepts
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Erik Tillema; Joseph Antonides – Investigations in Mathematics Learning, 2024
The multiplication principle (MP) is foundational for combinatorial problem-solving. From a units-coordination perspective, applying the MP with justification entails establishing unit relationships between the number of options at each independent stage of a counting process and the total number of combinatorial outcomes. Existing research…
Descriptors: Multiplication, Mathematical Logic, Mathematics Instruction, Problem Solving
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Grabner, Roland H.; Brunner, Clemens; Lorenz, Valerie; Vogel, Stephan E.; De Smedt, Bert – Journal of Experimental Psychology: Learning, Memory, and Cognition, 2022
There is broad consensus on the assumption that adults solve single-digit multiplication problems almost exclusively by fact retrieval from memory. In contrast, there has been a long-standing debate on the cognitive processes involved in solving single-digit addition problems. This debate has evolved around two theoretical accounts. Proponents of…
Descriptors: Cognitive Processes, Addition, Computation, Arithmetic
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Vanluydt, Elien; Verschaffel, Lieven; Van Dooren, Wim – Educational Studies in Mathematics, 2022
Several studies have shown that children do not only erroneously use additive reasoning in proportional word problems, but also erroneously use proportional reasoning in additive word problems. Traditionally, these errors were contributed to a lack of calculation and discrimination skills. Recent research evidence puts forward an additional…
Descriptors: Preferences, Word Problems (Mathematics), Problem Solving, Error Patterns
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Kim, Sun A.; Bryant, Diane P.; Bryant, Brian R.; Shin, Mikyung; Ok, Min Wook – Remedial and Special Education, 2023
The effects of whole number computation interventions among school students with learning disabilities in Grades K to 5 were examined using a multilevel meta-analysis. Applying a correlated and hierarchical effect model of robust variance estimation, we examined the intervention effects among 15 peer-reviewed articles and dissertations (two…
Descriptors: Computation, Intervention, Elementary School Students, Students with Disabilities
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Van den Heuvel-Panhuizen, Marja; Elia, Iliada – ZDM: The International Journal on Mathematics Education, 2020
In this study we investigated the structure of quantitative competence of kindergartners by testing a hypothesized four-factor model of quantitative competence consisting of the components counting, subitizing, additive reasoning and multiplicative reasoning. Data were collected from kindergartners in the Netherlands (n = 334) and in Cyprus (n =…
Descriptors: Kindergarten, Numeracy, Foreign Countries, Mathematics Skills
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Tzur, Ron; Johnson, Heather Lynn; Norton, Anderson; Davis, Alan; Wang, Xin; Ferrara, Michael; Harrington, Cody; Hodkowski, Nicola Mercedes – Cognition and Instruction, 2021
We examine a hypothesis implied by Steffe's constructivist model of children's numerical reasoning: a child's "spontaneous" additive strategy may relate to a foundational form of multiplicative reasoning, termed multiplicative double counting (mDC). To this end, we mix quantitative and qualitative analyses of 31 fourth graders' responses…
Descriptors: Constructivism (Learning), Mathematics Skills, Elementary School Students, Grade 4
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Hurst, Chris; Huntley, Ray – Journal of Research and Advances in Mathematics Education, 2020
Multiplicative thinking underpins much of the mathematics learned beyond the middle primary years. As such, it needs to be understood conceptually to highlight the connections between its many aspects. This paper focuses on one such connection; that is how the array, place value partitioning and the distributive property of multiplication are…
Descriptors: Multiplication, Mathematics Instruction, Teaching Methods, Concept Formation
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Lockwood, Elise; Purdy, Branwen – Journal for Research in Mathematics Education, 2019
The multiplication principle (MP) is a fundamental aspect of combinatorial enumeration, serving as an effective tool for solving counting problems and underlying many key combinatorial formulas. In this study, we used guided reinvention to investigate 2 undergraduate students' reasoning about the MP, and we sought to answer the following research…
Descriptors: Undergraduate Students, Multiplication, Mathematical Concepts, Mathematical Logic
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Aylar-Çankaya, Ebru – Journal of Theoretical Educational Science, 2020
Four operations algorithm is among the major topics occupying a significant position in primary school schedule. Moreover, utilizing alternative strategies during the education process and improving operation flexibility of students also considered important in teaching of mathematics. Flexibility in computing is the ability of solving any…
Descriptors: Mathematics Instruction, Computation, Elementary School Mathematics, Elementary School Teachers
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McMullen, Jake; Hannula-Sormunen, Minna M.; Lehtinen, Erno; Siegler, Robert S. – British Journal of Educational Psychology, 2022
Background: Adaptive expertise is a highly valued outcome of mathematics curricula. One aspect of adaptive expertise with rational numbers is adaptive rational number knowledge, which refers to the ability to integrate knowledge of numerical characteristics and relations in solving novel tasks. Even among students with strong conceptual and…
Descriptors: Elementary School Students, Middle School Students, Grade 6, Grade 7
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Günes, Canan – Digital Experiences in Mathematics Education, 2021
When two third-graders collaboratively manipulated a multi-modal, digital learning device called TouchTimes (hereafter, TT), that introduces multiplication through visual, tangible and symbolic means, their thinking about quantity shifted from being additive to being multiplicative. In this study, I examine the children's interactions around/with…
Descriptors: Multiplication, Thinking Skills, Mathematics Instruction, Teaching Methods
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Mulligan, Joanne; Oslington, Gabrielle; English, Lyn – ZDM: The International Journal on Mathematics Education, 2020
An Australian longitudinal study of 319 Kindergartners developed, implemented and evaluated an intervention, the Pattern and Structure Mathematics Awareness Program (PASMAP). It comprised of repetitions and growing patterns, structured counting and grouping, grids and shapes, partitioning, additive and multiplicative structures, measurement and…
Descriptors: Foreign Countries, Kindergarten, Mathematical Concepts, Repetition
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Zhang, Shu; Cao, Yiming; Wang, Lidong; Li, Xinlian – ZDM: The International Journal on Mathematics Education, 2019
This study investigates the teaching and learning of single-digit whole number multiplication in China. Analysis of data from documents, classroom teaching, and semi-structured interviews revealed three salient characteristics of emphasizing "oral calculation," "calculation speed," and "understanding" across…
Descriptors: Teaching Styles, Numbers, Mathematics Instruction, Foreign Countries
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Lockwood, Elise; Reed, Zackery; Caughman, John S. – International Journal of Research in Undergraduate Mathematics Education, 2017
The multiplication principle serves as a cornerstone in enumerative combinatorics. The principle underpins many basic counting formulas and provides students with a critical element of combinatorial justification. Given its importance, the way in which it is presented in textbooks is surprisingly varied. In this paper, we analyze a number of…
Descriptors: Multiplication, Textbooks, Mathematics Instruction, Mathematical Concepts
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