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Karen S. Karp; Sarah B. Bush; Barbara J. Dougherty – Mathematics Teacher: Learning and Teaching PK-12, 2025
Even though there is a great temptation as teachers to share what is known, many are aware of an idea called "rules that expire" (RTE) and have realized the importance of avoiding them. There is evidence that students need to understand mathematical concepts and that merely presenting rules to carry out in a procedural and disconnected…
Descriptors: Teaching Methods, Mathematics Instruction, Arithmetic, Mathematical Concepts
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Marah Sutherland; David Furjanic; Joanna Hermida; Ben Clarke – Intervention in School and Clinic, 2024
This article illustrates how teachers can use number lines to support students with or at risk for learning disabilities (LD) in mathematics. Number lines can be strategically used to help students understand relations among numbers, approach number combinations (i.e., basic facts), as well as represent and solve addition and subtraction problems.…
Descriptors: Number Concepts, Arithmetic, Mathematics Instruction, Teaching Methods
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Chang Xu; Hongxia Li; Sabrina Di Lonardo Burr; Jiwei Si; Jo-Anne LeFevre; Xinfeng Zhuo – Journal of Cognition and Development, 2024
Students' understanding of the meaning of the equal sign develops slowly over the primary grades. In addition to updating their representations of equations to recognize that the equal sign represents an equivalence relation rather than signaling an operation, students need to move beyond full computation to efficiently solve equivalence problems.…
Descriptors: Mathematics Achievement, Grade 3, Grade 4, Elementary School Students
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Castillo, Jorge Rincón; Hurtado, Orlando García; Parra, Edinson Caicedo – Journal of Language and Linguistic Studies, 2022
This article aims to show some activities based on non-routine problems with different levels of difficulty and from different classes that are integrated into the curriculum, additionally two spaces were opened for students to interact with recreational mathematics activities with the purpose of providing opportunities to all students access the…
Descriptors: Learning Activities, Mathematics Activities, Mathematical Concepts, Concept Formation
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Braithwaite, David W.; Sprague, Lauren – Cognitive Science, 2021
When, how, and why students use conceptual knowledge during math problem solving is not well understood. We propose that when solving routine problems, students are more likely to recruit conceptual knowledge if their procedural knowledge is weak than if it is strong, and that in this context, metacognitive processes, specifically feelings of…
Descriptors: Concept Formation, Mathematical Concepts, Metacognition, Knowledge Level
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Oh Hoon Kwon – North American Chapter of the International Group for the Psychology of Mathematics Education, 2023
A new classification for semantic structures of one-step word problems is proposed in this paper. The classification is based on illustrations of word problem situations in Common Core State Standards (CCSSM, 2010) and related historical studies (e.g. Weaver, 1973, 1979, 1982), as well as conceptual elaborations of embodied and grounded nature in…
Descriptors: Semantics, Word Problems (Mathematics), Mathematics Instruction, Classification
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She, Xiaobo; Harrington, Timothy – Mathematics Teacher: Learning and Teaching PK-12, 2022
Problem solving has been the focus of the Common Core State Standards for Mathematical Practice. Helping students acquire critical-thinking and problem-solving skills has become the primary goal of mathematics education across all grade levels. However, research has found that many students struggle with word problems because of poor text…
Descriptors: Word Problems (Mathematics), Problem Solving, Mathematics Instruction, Visual Aids
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Marcruz, Ong Yew Lee; Carrie, Ho Ka Lee; Manabu, Kawata; Mayumi, Takahashi; Kumpei, Mizuno – International Journal of Early Years Education, 2022
It has become increasingly clear that the early use of decomposition for addition is associated with later mathematical achievement. This study examined how younger children execute a base-10 decomposition strategy to solve complex arithmetic (e.g. two-digit addition). 24 addition problems in two modalities (WA: Written Arithmetic; OA: Oral…
Descriptors: Cross Cultural Studies, Arithmetic, Foreign Countries, Correlation
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Simsek, Emine; Xenidou-Dervou, Iro; Hunter, Jodie; Dowens, Margaret Gillon; Pang, JeongSuk; Lee, Yujin; McNeil, Nicole M.; Kirkland, Patrick K.; Jones, Ian – Journal of Educational Psychology, 2022
Many primary school students have difficulties understanding mathematical equivalence with considerably poorer performance in some countries than in others. However, students' formal understanding of equivalence has significant and long-lasting effects, as it predicts arithmetic and algebra achievement throughout school years. Currently, little is…
Descriptors: Mathematics Instruction, Elementary School Students, Mathematical Concepts, Concept Formation
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Jing Tian; David W. Braithwaite; Robert S. Siegler – Journal of Educational Psychology, 2021
This study investigated relations between the distribution of practice problems in textbooks and students' learning of decimal arithmetic. In Study 1, we analyzed the distributions of decimal arithmetic practice problems that appeared in 3 leading math textbook series in the United States. Similar imbalances in the relative frequencies of decimal…
Descriptors: Textbooks, Mathematics Instruction, Arithmetic, Problem Solving
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Passarella, Simone – International Journal of Mathematical Education in Science and Technology, 2022
Introducing the distributivity property of multiplication over addition is a well-known challenge in mathematics education, especially in primary school. As a contribution, this paper presents the results of a cycle of design research that focuses on the design, implementation and evaluation of a modelling activity in which 2nd-grade students are…
Descriptors: Multiplication, Mathematics Instruction, Elementary School Students, Mathematical Concepts
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Schiller, Lauren K.; Fan, Ao; Siegler, Robert S. – Journal of Numerical Cognition, 2022
The number one plays a special role in mathematics because it is the identity element in multiplication and division. The present findings, however, indicate that many middle school students do not demonstrate mathematical flexibility representing one as a fraction. Despite possessing explicit knowledge of fraction forms of one (e.g., 95% of…
Descriptors: Numbers, Mathematics Instruction, Multiplication, Division
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
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Nur, Andi Saparuddin; Kartono, Kartono; Zaenuri, Zaenuri; Rochmad, Rochmad – Participatory Educational Research, 2022
The integer is a basic concept in studying arithmetic and algebra. However, students still frequently experience misconceptions, especially in negative integer, count operations. Traditional games are activities that are often carried out by students in coastal areas so that they are relevant to be used as a tool to construct learning trajectories…
Descriptors: Learning Processes, Elementary School Students, Grade 6, Preadolescents
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Scheibling-Sève, Calliste; Pasquinelli, Elena; Sander, Emmanuel – Educational Studies in Mathematics, 2020
We propose to assess conceptual knowledge of mathematical notions by having recourse to isomorphic word problems. We assumed that failing to solve isomorphic problems is an indicator of lack of conceptual knowledge. To reach these conclusions, two experiments were conducted among 4th and 5th grade students. In experiment 1, each student had to…
Descriptors: Arithmetic, Word Problems (Mathematics), Problem Solving, Mathematical Concepts
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