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Lockwood, Elise; Purdy, Branwen – International Journal of Research in Undergraduate Mathematics Education, 2020
The multiplication principle (MP) is a fundamental aspect of combinatorial enumeration. In an effort to better understand students' reasoning about the MP, we had two undergraduate students reinvent a statement of the MP in a teaching experiment. In this paper, we adopt an actor-oriented perspective (Lobato, "Educational Researcher,"…
Descriptors: Multiplication, Mathematics Skills, Thinking Skills, Undergraduate Students
Günes, Canan – Digital Experiences in Mathematics Education, 2021
When two third-graders collaboratively manipulated a multi-modal, digital learning device called TouchTimes (hereafter, TT), that introduces multiplication through visual, tangible and symbolic means, their thinking about quantity shifted from being additive to being multiplicative. In this study, I examine the children's interactions around/with…
Descriptors: Multiplication, Thinking Skills, Mathematics Instruction, Teaching Methods
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
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
Schulz, Andreas – Mathematical Thinking and Learning: An International Journal, 2018
Theoretical analysis of whole number-based calculation strategies and digit-based algorithms for multi-digit multiplication and division reveals that strategy use includes two kinds of reasoning: reasoning about the relations between numbers and reasoning about the relations between operations. In contrast, algorithms aim to reduce the necessary…
Descriptors: Computation, Mathematics Instruction, Multiplication, Arithmetic
Jalan, Sukoriyanto; Nusantara, Toto; Subanji, Subanji; Chandra, Tjang Daniel – Educational Research and Reviews, 2016
This study aims to explain the thinking process of students in solving combination problems considered from assimilation and accommodation frameworks. This research used a case study approach by classifying students into three categories of capabilities namely high, medium and low capabilities. From each of the ability categories, one student was…
Descriptors: Thinking Skills, Problem Solving, Cognitive Processes, Models
Whitacre, Ian; Nickerson, Susan D. – Journal for Research in Mathematics Education, 2016
This study examines how collective activity related to multiplication evolved over several class sessions in an elementary mathematics content course that was designed to foster prospective elementary teachers' number-sense development. We document how the class drew on as-if-shared ideas to make sense of multidigit multiplication in terms of…
Descriptors: Preservice Teachers, Multiplication, Elementary School Teachers, Elementary School Mathematics
Tzur, Ron; Johnson, Heather L.; McClintock, Evan; Kenney, Rachael H.; Xin, Yan P.; Si, Luo; Woordward, Jerry; Hord, Casey; Jin, Xianyan – PNA, 2013
We present a synthesis of findings from constructivist teaching experiments regarding six schemes children construct for reasoning multiplicatively and tasks to promote them. We provide a task-generating platform game, depictions of each scheme, and supporting tasks. Tasks must be distinguished from children's thinking, and learning situations…
Descriptors: Multiplication, Constructivism (Learning), Child Development, Educational Experiments
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
Hoffman, Bobby; Spatariu, Alexandru – Journal of Interactive Learning Research, 2011
A grounded theory approach was employed to explore the variation in strategies used by students when solving mental multiplication problems. Metacognitive prompts, externally generated stimuli that activate thoughtful cognition, were automatically generated via computer during the solving of mental multiplication problems to elicit awareness,…
Descriptors: Grounded Theory, Prompting, Multiplication, Preservice Teachers
Arizona Department of Education, 2009
Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…
Descriptors: Numeracy, Number Concepts, Grade 3, Mathematics Education
Arizona Department of Education, 2009
Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…
Descriptors: Numeracy, Number Concepts, Grade 5, Mathematics Education

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
Young-Loveridge, Jenny – Australian Mathematics Teacher, 2005
If the goal is to promote mathematical thinking and help children become flexible problem solvers, then it is important to show students multiple representations of a problem. Because it is important to help students develop both counting-based and collections-based conceptions of number, teachers should be showing students both number line…
Descriptors: Arithmetic, Mathematical Models, Computation, Thinking Skills

Pesenti, Mauro; Seron, Xavier; Samson, Dana; Duroux, Bruno – Mathematical Cognition, 1999
Describes the basic and exceptional calculation abilities of a calculating prodigy whose performances were investigated in single- and multi-digit number multiplication, numerical comparison, raising of powers, and short-term memory tasks. Shows how his highly efficient long-term memory storage and retrieval processes, knowledge of calculation…
Descriptors: Case Studies, Cognitive Ability, Elementary Secondary Education, Mathematics Education
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