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Lee, Jiyoung; Pang, JeongSuk – International Journal of Science and Mathematics Education, 2023
It is important for students to develop a relational understanding of the equal sign, but students often have simultaneous operational and relational conceptions (i.e., SOR conceptions). This case study carefully explored how a student's conception of the equal sign changed during a classroom teaching experiment and analyzed the possibilities and…
Descriptors: Students, Mathematical Concepts, Symbols (Mathematics), Concept Formation
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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
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Prather, Richard – Journal of Numerical Cognition, 2023
Mastery of mathematics depends on the people's ability to manipulate and abstract values such as negative numbers. Knowledge of arithmetic principles does not necessarily generalize from positive number arithmetic to arithmetic involving negative numbers (Prather & Alibali, 2008, https://doi.org/10.1080/03640210701864147). In this study, we…
Descriptors: Prediction, Mastery Learning, Mathematics Instruction, Cognitive Processes
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Jost, Patrick; Rangger, Sebastian; Künz, Andreas – International Association for Development of the Information Society, 2023
With the growing prevalence of mobile apps for self-directed learning, educational games increasingly find their place in everyday routines, becoming accessible to a broad audience. Despite the growing ease of content creation by artificial intelligence computing, the challenge of designing effective and engaging Serious Games remains,…
Descriptors: Telecommunications, Handheld Devices, Mathematics Instruction, Educational Games
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Thomas, Jonathan Norris; Harkness, Shelly Sheats – Mathematics Education Research Journal, 2019
Differing research worldviews have typically resulted in interpretations at odds with one another. Yet, leveraging distinct perspectives can lead to novel interpretations and theoretical construction. Via an empirically grounded research commentary, we describe the value of such activity through the lens of previously reported findings. This…
Descriptors: Arithmetic, Mathematics Instruction, Teaching Methods, Numeracy
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Kaskens, Jarise; Goei, Sui Lin; Van Luit, Johannes E. H.; Verhoeven, Ludo; Segers, Eliane – Elementary School Journal, 2022
This study is conducted to further understand the direct and indirect contributions of executive functioning (visuospatial updating, verbal updating, inhibition, shifting) and arithmetic fluency to mathematical problem-solving in 458 fourth-grade students. Arithmetic fluency along with visuospatial and verbal updating were significant predictors…
Descriptors: Mathematics Instruction, Elementary School Mathematics, Arithmetic, Mathematics Skills
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Gros, Hippolyte; Thibaut, Jean-Pierre; Sander, Emmanuel – Educational Psychologist, 2020
Arithmetic problem solving is a crucial part of mathematics education. However, existing problem solving theories do not fully account for the semantic constraints partaking in the encoding and recoding of arithmetic word problems. In this respect, the limitations of the main existing models in the literature are discussed. We then introduce the…
Descriptors: Semantics, Arithmetic, Models, Word Problems (Mathematics)
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Melody García-Moya; Rocío Blanco – Education and Training in Autism and Developmental Disabilities, 2024
Mathematical problem-solving is a core content of primary school education. Therefore, it is necessary to provide all students with a meaningful way of acquisition of problem-solving skills. The objective of this research was to verify the effectiveness of a problem-solving routine based on the Pólya's model and the use of cognitive strategies…
Descriptors: Arithmetic, Problem Solving, Elementary School Students, Autism Spectrum Disorders
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Darius Endlich; Wolfgang Lenhard; Peter Marx; Tobias Richter – Journal of Learning Disabilities, 2024
Children with mathematical difficulties need to spend more time than typically achieving children on solving even simple equations. Since these tasks already require a larger share of their cognitive resources, additional demands imposed by the need to switch between tasks may lead to a greater decline of performance in children with mathematical…
Descriptors: Mathematics Instruction, Learning Problems, Arithmetic, Mathematics Achievement
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Ying, Yufeng – North American Chapter of the International Group for the Psychology of Mathematics Education, 2020
Mathematics education scholars have generally classified students' conception of the equal sign as either operational or relational. Adding to these conceptions, Jones (2008) introduced the idea of substitutional conception. Building off these scholars, I introduce a form of understanding the equal sign that includes a transformative equivalence…
Descriptors: Symbols (Mathematics), Equations (Mathematics), Mathematical Concepts, Cognitive Processes
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Somasundram, Piriya – EURASIA Journal of Mathematics, Science and Technology Education, 2021
Algebraic thinking in children can bridge the cognitive gap between arithmetic and algebra. This quantitative study aimed to develop and test a cognitive model that examines the cognitive factors influencing algebraic thinking among Year Five pupils. A total of 720 Year Five pupils from randomly selected national schools in Malaysia participated…
Descriptors: Foreign Countries, Elementary School Students, Elementary School Mathematics, Mathematics Skills
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Bye, Jeffrey K.; Harsch, Rina M.; Varma, Sashank – Journal of Numerical Cognition, 2022
Algebraic thinking and strategy flexibility are essential to advanced mathematical thinking. Early algebra instruction uses 'missing-operand' problems (e.g., x - 7 = 2) solvable via two typical strategies: (1) direct retrieval of arithmetic facts (e.g., 9 - 7 = 2) and (2) performance of the inverse operation (e.g., 2 + 7 = 9). The current study…
Descriptors: Algebra, Problem Solving, Mathematics Instruction, Arithmetic
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Ross, Wendy; Vallée-Tourangeau, Frédéric; Van Herwegen, Jo – International Journal of Science and Mathematics Education, 2020
Manipulative artefacts are considered useful scaffolds of arithmetic during early years education, but their use is considered less important as children get older. Yet adult arithmetic performance often recruits artefacts to improve accuracy and efficiency, and so the same benefits should accrue to children beyond early years. We propose that…
Descriptors: Mathematics Instruction, Manipulative Materials, Teaching Methods, Short Term Memory
Prayekti, N.; Nusantara, T.; Sudirman; Susanto, H. – Online Submission, 2019
Mental models are representations of students' minds concepts to explain a situation or an on-going process. The purpose of this study is to describe students' mental model in solving mathematical patterns of generalization problem. Subjects in this study were the VII grade students of junior high school in Situbondo, East Java, Indonesia. This…
Descriptors: Junior High School Students, Foreign Countries, Generalization, Algebra
Supianto, Ahmad Afif; Hayashi, Yusuke; Hirashima, Tsukasa – Research and Practice in Technology Enhanced Learning, 2016
Problem-posing is well known as an effective activity to learn problem-solving methods. Although the activity is considered in contributing to the understanding of the problem's structure, it is not clear how learners could understand it through the activity. This study proposes a method to offer a visual representation for analyzing the…
Descriptors: Problem Solving, Visual Aids, Sequential Approach, Cognitive Processes
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