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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
Månsson, Anders – Acta Didactica Napocensia, 2023
It is investigated if the mental computation strategies in the research literature are enough to satisfactorily categorize the mental computation strategy use by preservice elementary teachers in multiplication on one- and two-digit natural numbers. The preservice elementary teachers use of mental computation strategies is measured operationally…
Descriptors: Preservice Teachers, Elementary School Teachers, Mental Computation, Multiplication
Guez, Ava; Piazza, Manuela; Pinheiro-Chagas, Pedro; Peyre, Hugo; Heude, Barbara; Ramus, Franck – Developmental Science, 2023
A converging body of evidence from neuroimaging, behavioral, and neuropsychology studies suggests that different arithmetic operations rely on distinct neuro-cognitive processes: while addition and subtraction may rely more on visuospatial reasoning, multiplication would depend more on verbal abilities. In this paper, we tested this hypothesis in…
Descriptors: Language Skills, Spatial Ability, Preschool Children, Prediction
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
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
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
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
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
Chen, Edward H.; Bailey, Drew H.; Jaeggi, Susanne M. – Journal of Numerical Cognition, 2022
Several working memory processes have been hypothesized to influence different arithmetic operations. Working memory has been compartmentalized into a number of different sub-processes, such as phonological memory and visuospatial memory that are believed to have unique contributions to the performance of two distinct arithmetic operations:…
Descriptors: Mathematics Skills, Arithmetic, Mental Computation, Learning Processes
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
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
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
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
Sahin, Ömer; Danaci, Dönsel – International Journal of Mathematical Education in Science and Technology, 2022
This study aims to investigate the effect of history-of-mathematics activities on the development of mental computation of middle-grade students and to determine the students' views on the history of mathematics. This study was carried out as an action research project. The participants of the study consisted of 19 seventh-grade students studying…
Descriptors: Mathematics Education, History, Mathematics Activities, Middle School Students
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