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Showing 1 to 15 of 106 results Save | Export
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Jaehong Shin; Soo Jin Lee – Investigations in Mathematics Learning, 2024
In the present study, we illuminate students' multiplicative reasoning in the context of their units-coordinating activity. Of particular interest is to investigate students' use of three levels of units as given material for problem-solving activity, which we regard as supporting a more advanced level of multiplicative reasoning. Among 13 middle…
Descriptors: Mathematics Instruction, Multiplication, Middle School Students, Mathematical Logic
Sarah Lord – ProQuest LLC, 2023
The algorithm for fraction multiplication is relatively easy to memorize and implement with accuracy. The simplicity of the algorithm masks the conceptual complexity involved in making sense of what fraction multiplication means in quantitative situations. One important interpretation of fraction multiplication involves fraction composition,…
Descriptors: Fractions, Multiplication, Mathematical Concepts, Learning Processes
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Foster, Colin – For the Learning of Mathematics, 2022
In this article, I argue that the common practice across many school mathematics curricula of using a variety of different representations of number may diminish the coherence of mathematics for students. Instead, I advocate prioritising a single representation of number (the number line) and applying this repeatedly across diverse content areas.…
Descriptors: Mathematics Instruction, Mathematics Curriculum, Numbers, Multiplication
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Norton, Anderson; Ulrich, Catherine; Kerrigan, Sarah – Journal for Research in Mathematics Education, 2023
This article introduces unit transformation graphs (UTGs) as a tool for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We report findings from a study in which we identified patterns in the ways preservice elementary school teachers relied on working memory to coordinate mental actions when operating in…
Descriptors: Graphs, Fractions, Short Term Memory, Preservice Teachers
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Shih, Shu-Chuan; Chang, Chih-Chia; Kuo, Bor-Chen; Huang, Yu-Han – Education and Information Technologies, 2023
A one-on-one dialogue-based mathematics intelligent tutoring system (ITS) for learning multiplication and division of fractions was developed and evaluated in this study. This system could identify students' error types and misconceptions in real-time by using a block-based matching method. The adaptive dialogue-based instruction was supported by…
Descriptors: Mathematics Instruction, Intelligent Tutoring Systems, Multiplication, Division
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Bima Sapkota; Liza Bondurant – International Journal of Technology in Education, 2024
In November 2022, ChatGPT, an Artificial Intelligence (AI) large language model (LLM) capable of generating human-like responses, was launched. ChatGPT has a variety of promising applications in education, such as using it as thought-partner in generating curricular resources. However, scholars also recognize that the use of ChatGPT raises…
Descriptors: Cognitive Processes, Difficulty Level, Artificial Intelligence, Natural Language Processing
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Kamberi, Saranda; Latifi, Ismet; Rexhepi, Shpetim; Iseni, Egzona – International Electronic Journal of Mathematics Education, 2022
In this paper, we have tried to clearly explain the meaning of fractions and operations with fractions. Also, we have tried to illustrate with some examples how to apply the rules of operations with fractional numbers, giving different practical techniques through different figures, visualization methods, and concretizing problems. The paper…
Descriptors: Illustrations, Fractions, Mathematics Instruction, Foreign Countries
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Erik Jacobson – Investigations in Mathematics Learning, 2024
This study used units coordination as a theoretical lens to investigate how whole number and fraction reasoning may be related for preservice teachers at the conclusion of a math methods class. The study contributes quantitative evidence that units coordination provides a common foundation for both mathematical knowledge for teaching whole number…
Descriptors: Preservice Teachers, Elementary School Teachers, Mathematics Instruction, Methods Courses
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Simon, Martin A. – Research in Mathematics Education, 2019
Promoting an understanding of multiplication of fractions has proved difficult for mathematics educators. I discuss a research study aimed at developing a concept of multiplication that supports both multiplication of whole numbers and multiplication of fractions. The study demonstrates how domain-specific theories grounded in two major…
Descriptors: Multiplication, Fractions, Mathematics Instruction, Mathematical Concepts
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Copur-Gencturk, Yasemin; Ölmez, Ibrahim Burak – International Journal of Science and Mathematics Education, 2022
Attending to the whole unit that a number refers to in a mathematical problem situation and showing flexibility in coordinating different units are foundational for mathematical understanding. In this study, we explored teachers' attention to and flexibility with referent units in situations involving fractions and fraction multiplication. Using…
Descriptors: Mathematics Teachers, Grade 3, Grade 4, Grade 5
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Morano, Stephanie; Riccomini, Paul J. – Teacher Education and Special Education, 2020
To provide effective fractions instruction, teachers need deep understanding of fraction concepts (i.e., content knowledge) and skill in using visual representations of fractions to support student learning (i.e., pedagogical content knowledge); yet, research indicates that many pre- and in-service teachers lack knowledge in both areas. The…
Descriptors: Preservice Teachers, Mathematics Instruction, Pedagogical Content Knowledge, Fractions
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McMullen, Jake; Siegler, Robert S. – Mathematical Thinking and Learning: An International Journal, 2020
To test the hypothesis that a higher tendency to "s"pontaneously "f"ocus "o"n "m"ultiplicative "r"elations (SFOR) leads to improvements in rational number knowledge via more exact estimation of fractional quantities, we presented sixth graders (n = 112) with fraction number line estimations and a…
Descriptors: Fractions, Multiplication, Grade 6, Hypothesis Testing
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Hackenberg, Amy J.; Creager, Mark; Eker, Ayfer – Mathematical Thinking and Learning: An International Journal, 2021
Three iterative, 18-episode design experiments were conducted after school with groups of 6-9 middle school students to understand how to differentiate mathematics instruction. Prior research on differentiating instruction (DI) and hypothetical learning trajectories guided the instruction. As the experiments proceeded, this definition of DI…
Descriptors: Mathematics Instruction, Teaching Methods, Individualized Instruction, Thinking Skills
Cody Harrington – ProQuest LLC, 2021
This dissertation case study examines how teachers' levels of units coordination afford their ability to reason multiplicatively and fractionally, as well as use their mathematics knowledge for teaching to analyze student multiplicative and fractional reasoning, when a two-year intervention is put into place to evoke new mathematical reasoning.…
Descriptors: Mathematics Instruction, Multiplication, Fractions, Mathematical Logic
McMillan, Brandon – ProQuest LLC, 2018
Even though algebraic ideas are addressed across a number of grades, algebra continues to serve as a gatekeeper to upper mathematics and degree attainment because of the high percentage of students that fail algebra classes and become halted in their educational progress. One reason for this is students not having the opportunity to build on their…
Descriptors: Mathematics Instruction, Mathematical Concepts, Mathematical Logic, Thinking Skills
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