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Dixon, Juli K. – Solution Tree, 2023
How can students achieve an understanding of multiplication that allows them to go beyond recall to explain their thinking? Author and mathematics education professor Juli Dixon introduces a program that teachers can seamlessly integrate into existing mathematics instruction. Learn six tactics to help you shift from an anxiety-producing,…
Descriptors: Multiplication, Grade 3, Grade 4, Grade 5
Tzur, Ron; Johnson, Heather Lynn; Norton, Anderson; Davis, Alan; Wang, Xin; Ferrara, Michael; Harrington, Cody; Hodkowski, Nicola Mercedes – Cognition and Instruction, 2021
We examine a hypothesis implied by Steffe's constructivist model of children's numerical reasoning: a child's "spontaneous" additive strategy may relate to a foundational form of multiplicative reasoning, termed multiplicative double counting (mDC). To this end, we mix quantitative and qualitative analyses of 31 fourth graders' responses…
Descriptors: Constructivism (Learning), Mathematics Skills, Elementary School Students, Grade 4
Lorraine Day; Dianne Siemon; Rosemary Callingham; Rebecca Seah – Research in Mathematics Education, 2024
Making connections within and between different aspects of mathematics is recognised as fundamental to learning mathematics with understanding. However, exactly what these connections are and how they serve the goal of learning mathematics is rarely made explicit in curriculum documents with the result that mathematics tends to be presented as a…
Descriptors: Mathematics Instruction, Evidence Based Practice, Multiplication, Mathematical Logic
Catherine A. Kaduk – ProQuest LLC, 2020
Unitizing, a cognitive support for number sense, describes how students conceptualize quantities in terms of units. Given the importance of this skill, a formative assessment tool was developed for array multiplication problems, including arrays that model the distributive property found in typical classroom curricula. Video of 77 fourth grade…
Descriptors: Elementary School Mathematics, Multiplication, Grade 4, Visual Aids
Jorgensen, Cody; Smith, Amy; Tzur, Ron; Johnson, Heather L. – North American Chapter of the International Group for the Psychology of Mathematics Education, 2019
We address the question: How can a student's conceptual transition, from attending only to singleton units (1s) given in multiplicative situations to distinguishing composite units made of such 1s, be explained? We analyze a case study of one fourth grader (Adam, a pseudonym) during the course of a video recorded cognitive interview. Adam's case…
Descriptors: Multiplication, Thinking Skills, Mathematics Instruction, Mathematical Concepts
Hurst, Chris; Huntley, Ray – International Journal for Mathematics Teaching and Learning, 2018
Multiplicative thinking is a critical component of mathematics which largely determines the extent to which people develop mathematical understanding beyond middle primary years. We contend that there are several major issues, one being that much teaching about multiplicative ideas is focussed on algorithms and procedures. An associated issue is…
Descriptors: Mathematics, Multiplication, Mathematical Logic, Mathematics Instruction
Degrande, Tine; Verschaffel, Lieven; Van Dooren, Wim – European Journal of Psychology of Education, 2018
While previous studies mainly focused on children's additive and multiplicative reasoning abilities, we studied third to sixth graders' "preference" for additive or multiplicative relations. This was investigated by means of schematic problems that were "open" to both types of relations, namely arrow schemes containing three…
Descriptors: Addition, Multiplication, Mathematical Logic, Student Attitudes
Risley, Rachael Ann – ProQuest LLC, 2016
This study explored the impact of numbers used in instructional tasks on the construction and generalization of multiplicative reasoning by fourth grade students designated as having learning difficulties or disabilities in mathematics (SLDs). In particular, this study addressed the following research questions: (1) In what ways do SLDs'…
Descriptors: Numbers, Teaching Methods, Generalization, Mathematical Logic
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
Fielding-Wells, Jill; Dole, Shelley; Makar, Katie – Mathematics Education Research Journal, 2014
Proportional reasoning as the capacity to compare situations in relative (multiplicative) rather than absolute (additive) terms is an important outcome of primary school mathematics. Research suggests that students tend to see comparative situations in additive rather than multiplicative terms and this thinking can influence their capacity for…
Descriptors: Mathematical Logic, Mathematics Instruction, Elementary School Mathematics, 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
Hodkowski, Nicola; Tzur, Ron; Johnson, Heather Lynn; McClintock, Evan – North American Chapter of the International Group for the Psychology of Mathematics Education, 2014
We examine a 4th grade teacher's development of a constructivist-based, adaptive pedagogy (AP) approach--and its contribution to student multiplicative reasoning and outcomes, mixing qualitative analysis of segments from her interviews with quantitative analysis of her student outcomes on the state-mandated test. Her reflections indicate a shift…
Descriptors: Grade 4, Elementary School Teachers, Constructivism (Learning), Teaching Methods
Pagni, David, Ed. – 1991
The National Science Foundation funded Calculators and Mathematics Project, Los Angeles (CAMP-LA) developed curriculum materials focused solely on the use of calculators. The project was developed in three stages. The first stage studied the mathematics curriculums from different states and identified topics that are not included but should be if…
Descriptors: Addition, Algebra, Arithmetic, Calculators