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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
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
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
Downton, Ann; Russo, James; Hopkins, Sarah – Mathematics Education Research Group of Australasia, 2019
We report on 25 Year 5-6 students' written responses to two items taken from an assessment of mental computation fluency with multiplication, alongside their reasoning of the strategy they had employed, which may or may not have made use of the associative property. Coding of this interview data revealed four distinct levels of conceptual…
Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Elementary School Mathematics
Day, Lorraine; Hurrell, Derek – Australian Primary Mathematics Classroom, 2015
Lorraine Day and Derek Hurrell provide a convincing argument for using arrays to promote students' understandings of mental computation strategies for multiplication. They also provide a range of different examples that illustrate the benefits of arrays in the primary classroom.
Descriptors: Mathematics Instruction, Elementary School Mathematics, Mathematical Concepts, Computation
Kusuma, Josephine; Sulistiawati – Indonesian Mathematical Society Journal on Mathematics Education, 2014
Multiplication of numbers from 1 to 10 is very important as it provides the basis for learning multiplication of other larger numbers as well as other related mathematical operations. How do students learn multiplication? Usually students just memorize the results of multiplication. This is often performed without a complete comprehension of the…
Descriptors: Mathematics Instruction, Multiplication, Teaching Methods, Manipulative Materials
Flores, Margaret M.; Hinton, Vanessa; Strozier, Shaunita D. – Learning Disabilities Research & Practice, 2014
Based on Common Core Standards (2010), mathematics interventions should emphasize conceptual understanding of numbers and operations as well as fluency. For students at risk for failure, the concrete-representational-abstract (CRA) sequence and the Strategic Instruction Model (SIM) have been shown effective in teaching computation with an emphasis…
Descriptors: Mathematics Instruction, Teaching Methods, Mathematical Concepts, Addition
Ikhwanudin, Trisno; Suryadi, Didi – International Journal of Instruction, 2018
This research aims to analyze ways of understanding of students with mathematics learning disabilities when learning fraction. The research was conducted in an Inclusive Junior High School in the West Java Province, Indonesia. This study is qualitative, with the single-case (holistic) designs. The case will focus on three students who suspected of…
Descriptors: Foreign Countries, Junior High School Students, Learning Disabilities, Mathematics Education
Devin's Construction of a Multiplicative Double Counting Scheme: Dual Anticipation of Start and Stop
Risley, Rachael; Hodkowski, Nicola M.; Tzur, Ron – North American Chapter of the International Group for the Psychology of Mathematics Education, 2016
In this case study with Devin (pseudonym), which was part of a larger, constructivist teaching experiment with students identified as having learning difficulties in mathematics, we examine how a fourth grader constructed a dual anticipation involved in monitoring when to start and when to stop the simultaneous count of composite units (numbers…
Descriptors: Case Studies, Constructivism (Learning), Teaching Methods, Grade 4
Risley, Rachael; Hodkowski, Nicola M.; Tzur, Ron – North American Chapter of the International Group for the Psychology of Mathematics Education, 2015
This case study examined how a teacher's choice of numbers used in tasks designed to foster students' construction of a scheme for reasoning in multiplicative situations may afford or constrain their progression. This scheme, multiplicative double counting (mDC) is considered a significant conceptual leap from reasoning additively with units of…
Descriptors: Case Studies, Mathematics Instruction, Mathematics Teachers, Concept Formation
Flores, Margaret M.; Hinton, Vanessa M.; Schweck, Kelly B. – Learning Disabilities Research & Practice, 2014
The Common Core Standards require demonstration of conceptual knowledge of numbers, operations, and relations between mathematical concepts. Supplemental instruction should explicitly guide students with specific learning disabilities (SLD) in these skills. In this article, we illustrate implementation of the concrete-representational-abstract…
Descriptors: Mathematics Instruction, Multiplication, Teaching Methods, Academic Standards

Fuson, Karen C. – Teaching Children Mathematics, 2003
Provides an alternative to traditional instruction in multiplication and division to develop computational fluency in students. (Author/NB)
Descriptors: Arithmetic, Computation, Concept Formation, Division

Wickett, Maryann S. – Teaching Children Mathematics, 2003
Focuses on children making sense of multiplication. In an activity called "Silent Multiplication," students use what they know about easier multiplication problems to solve increasingly difficult, related problems mentally. (Author/NB)
Descriptors: Arithmetic, Computation, Concept Formation, Elementary Education

Spitler, Gail – Arithmetic Teacher, 1979
Allowing students to examine different ways of performing an operation is suggested as a means of increasing their understanding. (MP)
Descriptors: Addition, Algorithms, Computation, Concept Formation

Kouba, Vicky L.; Franklin, Kathy – Teaching Children Mathematics, 1995
Discusses mathematics education research on multiplication and division which implies that instruction should emphasize development of a sound conceptual basis for multiplication and division rather than memorization of tables and rules. Presents action research ideas. (10 references) (MKR)
Descriptors: Action Research, Algorithms, Arithmetic, Computation
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