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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
Daugulis, Peteris; Sondore, Anita – PRIMUS, 2018
Efficient visualizations of computational algorithms are important tools for students, educators, and researchers. In this article, we point out an innovative visualization technique for matrix multiplication. This method differs from the standard, formal approach by using block matrices to make computations more visual. We find this method a…
Descriptors: Mathematics Instruction, Matrices, Visualization, Multiplication
What Works Clearinghouse, 2021
This document includes instructional tips on: (1) Building on students' informal understanding of sharing and proportionality to develop initial fraction concepts; (2) Helping students recognize that fractions are numbers that expand the number system beyond whole numbers, and using number lines to teach this and other fraction concepts; (3)…
Descriptors: Mathematics Instruction, Instructional Effectiveness, Fractions, Elementary School Students
Quane, Kate; Brown, Leni – Australian Primary Mathematics Classroom, 2022
Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…
Descriptors: Mathematics Instruction, Toys, Manipulative Materials, Foreign Countries
Hurst, Chris; Hurrell, Derek – Australian Primary Mathematics Classroom, 2017
A journey into multiplicative thinking by three teachers in a primary school is reported. A description of how the teachers learned to identify gaps in student knowledge is described along with how the teachers assisted students to connect multiplicative ideas in ways that make sense.
Descriptors: Elementary School Teachers, Elementary School Mathematics, Mathematics Instruction, Multiplication
Ura, Suzana Kaori; Stein-Barana, Alzira C. M.; Munhoz, Deisy P. – Mathematics Teaching, 2011
The multiplicative principle is the tool allowing the counting of groups that can be described by a sequence of events. An event is a subset of sample space, i.e. a collection of possible outcomes, which may be equal to or smaller than the sample space as a whole. It is important that students understand this basic principle early on and know how…
Descriptors: Mathematical Concepts, Probability, Mathematics Instruction, Multiplication
Otto, Albert; Caldwell, Janet; Hancock, Sarah Wallus; Zbiek, Rose Mary – National Council of Teachers of Mathematics, 2011
This book identifies and examines two big ideas and related essential understandings for teaching multiplication and division in grades 3-5. Big Idea 1 captures the notion that multiplication is usefully defined as a scalar operation. Problem situations modeled by multiplication have an element that represents the scalar and an element that…
Descriptors: Mathematics Education, Problem Solving, Mathematics Instruction, Elementary School Mathematics
Dixon, Juli K.; Tobias, Jennifer M. – Mathematics Teaching in the Middle School, 2013
What does it look like to "understand" operations with fractions? The Common Core State Standards for Mathematics (CCSSM) uses the term "understand" when describing expectations for students' knowledge related to each of the fraction operations within grades 4 through 6 (CCSSI 2010). Furthermore, CCSSM elaborates that…
Descriptors: Computation, Arithmetic, Preservice Teacher Education, Preservice Teachers
Mead, Katie; Maxwell, Tom W. – Australian Primary Mathematics Classroom, 2010
Action research (AR) is defined by Macintyre to be: "an investigation, where, as a result of rigorous self-appraisal of current practice, the researcher focuses on a problem,or a topic or an issue which needs to be explained, and on the basis of information, plans, implements, then evaluates an action then draws conclusions on the basis of…
Descriptors: Action Research, Number Concepts, Mathematics Instruction, Teaching Methods
Bobis, Janette – Australian Primary Mathematics Classroom, 2007
Drawing upon research, theory, classroom and personal experiences, this paper focuses on the development of primary-aged children's computational fluency. It emphasises the critical links between number sense and a child's ability to perform mental and written computation. The case of multi-digit multiplication is used to illustrate these…
Descriptors: Computation, Mathematics Education, Primary Education, Mental Computation

Reys, Robert E., Ed.; Reys, Barbara J., Ed. – Arithmetic Teacher, 1986
Using factoring as an aid to mental multiplication is illustrated. Other suggestions for teaching mental computation are also included. (MNS)
Descriptors: Computation, Elementary Education, Elementary School Mathematics, Mathematics Instruction

Moore, Theodore F. – Mathematics Teacher, 1986
Presents a technique for multiplying two-digit numbers whose tens digits are equal and whose units digits have a sum of 10. Then various mental calculations with other types of two-digit and larger numbers are discussed. (MNS)
Descriptors: Computation, Learning Activities, Mathematics Instruction, Mental Computation

Hope, John A. – Journal for Research in Mathematics Education, 1987
This case study examined the performance of a 13-year-old highly skilled mental calculator on mental multiplication tasks. She solved difficult tasks by using various ingenious calculation methods, including distributing, factoring, and recalling the product directly. Implications for instruction are reported. (Author/RH)
Descriptors: Academically Gifted, Adolescents, Computation, Elementary Education

Fielker, David S. – For the Learning of Mathematics, 1986
How children perceive doubling and halving numbers is discussed, with many examples. The use of calculators is integrated. The tendency to avoid division if other ways of solving a problem can be found was noted. (MNS)
Descriptors: Calculators, Cognitive Processes, Computation, Division

Hopkins, Martha H. – Arithmetic Teacher, 1992
Presents five activities focusing on mental computation and estimation for the K-3, 3-5, 4-6, and 6-8 grade levels that require the student, acting as a judge, to review solutions to problems and to pronounce and justify a verdict. Provides suggested materials, questions, possible extensions, answers, and worksheets for each activity. (MDH)
Descriptors: Addition, Computation, Elementary Education, Error Correction