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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
Bofferding, Laura – Research in Mathematics Education, 2019
This chapter focuses on the development of concepts that children draw on as they work toward understanding negative numbers. Framed from a conceptual change lens, I discuss different interpretations children have of minus signs, numerical order, numerical values, and addition and subtraction operations and how children draw on these varied…
Descriptors: Numbers, Mathematics Skills, Concept Formation, Teaching Methods
Wessman-Enzinger, Nicole M.; Mooney, Edward S. – International Journal of Mathematical Education in Science and Technology, 2021
In this article, we report the findings of a study conducted with 6 Grade 8 students in the United States. The students posed stories for open number sentences involving addition and subtraction of integers. We analysed the stories posed by the students to build models that describe the conceptual structures behind these posed stories -- the…
Descriptors: Addition, Subtraction, Mathematics Instruction, Numbers
Putra, Zetra Hainul – International Electronic Journal of Mathematics Education, 2019
The aim of this study is to investigate Danish pre-service teachers' (PSTs) mathematical and didactical knowledge of operations with rational numbers. This knowledge is studied through their collaborative activities to certain tasks related to the teaching of operations with rational numbers. An explicit model of the teachers' mathematical and…
Descriptors: Foreign Countries, Preservice Teachers, Mathematics Education, Numbers
Fouryza, Darin; Amin, Siti Maghfirotun; Ekawati, Rooselyna – International Journal of Evaluation and Research in Education, 2019
This paper dealt with the design of learning tools, that was the development of learning implementation plan or Rencana Pelaksanaan Pembelajaran (RPP) based on Fun and Easy Math (FEM) approach in the form of a number line model. FEM was an approach in order to teach mathematics effectively to students in a fun and easy way according to the…
Descriptors: Lesson Plans, Numbers, Mathematics Instruction, Teaching Methods
Bofferding, Laura; Wessman-Enzinger, Nicole M. – Research in Mathematics Education, 2018
This chapter identifies the ways in which 15 prospective teachers engage the strands of mathematical proficiency as they solve word problems involving integer addition and subtraction. The prospective teachers, through think-aloud interviews, demonstrated a strong focus on solving problems using procedures, which some did not explain and others…
Descriptors: Preservice Teachers, Mathematics Skills, Word Problems (Mathematics), Numbers
Lee, Ji-Eun; Hornburg, Caroline Byrd; Chan, Jenny Yun-Chen; Ottmar, Erin – Grantee Submission, 2021
We investigated the effects of proximal grouping of numbers, problem-solving goals to make 100, and prior knowledge on students' solution strategies in an online mathematics game. Logistic regression on 857 problem-level data points from 227 middle-school students showed that students were more likely to use productive solution strategies on…
Descriptors: Mathematics Instruction, Teaching Methods, Middle School Students, Computer Games
Khalid, Madihah; Embong, Zulmaryan – International Electronic Journal of Mathematics Education, 2020
This research investigated students' sources and causes of errors and misconception in solving routine problems involving addition, subtraction, multiplication, and division of integers. This qualitative study involved observation of eight Year 7 classes and interviews with the respective classroom teachers. Sixteen Year 7 students who exhibit…
Descriptors: Error Patterns, Misconceptions, Problem Solving, Addition
Lamb, Lisa A.; Bishop, Jessica Pierson; Philipp, Randolph A.; Whitacre, Ian; Schappelle, Bonnie P. – Journal for Research in Mathematics Education, 2018
In a cross-sectional study, 160 students in Grades 2, 4, 7, and 11 were interviewed about their reasoning when solving integer addition and subtraction open-number-sentence problems. We applied our previously developed framework for 5 Ways of Reasoning (WoRs) to our data set to describe patterns within and across participant groups. Our analysis…
Descriptors: Problem Solving, Grade 2, Grade 4, Grade 7
Bofferding, Laura – Research in Mathematics Education, 2018
This chapter focuses on the interaction of two first graders as they attempt to make sense of a particular instructional context for learning negative numbers. The context is one where they move an elevator to a building's floors above and below ground in order to model integer addition and subtraction problems. In particular, the focus of the…
Descriptors: Numbers, Number Concepts, Concept Formation, Mathematics Instruction
Aqazade, Mahtob; Bofferding, Laura; Farmer, Sherri – North American Chapter of the International Group for the Psychology of Mathematics Education, 2017
We investigate thirty-three second and fifth-grade students' solution strategies on integer addition problems before and after analyzing contrasting cases with integer addition and participating in a lesson on integers. The students took a pretest, participated in two small group sessions and a short lesson, and took a posttest. Even though the…
Descriptors: Numbers, Grade 2, Grade 5, Addition
Bofferding, Laura; Aqazade, Mahtob; Farmer, Sherri – North American Chapter of the International Group for the Psychology of Mathematics Education, 2017
In this study, we explore thirty-two second graders' performance on integer addition problems before and after analyzing contrasting cases involving integers. The students, as part of a larger study, completed a pretest, were randomly assigned to one of three intervention groups, and participated in two small-group sessions, one short whole-class…
Descriptors: Grade 2, Elementary School Students, Addition, Numbers
Xin, Yan Ping – ZDM: The International Journal on Mathematics Education, 2019
Whole number arithmetic is the foundation of higher mathematics and a core part of elementary mathematics. Awareness of pattern and underlying problem structure promote the learning of whole number arithmetic. A growing consensus has emerged on the necessity to provide students with the opportunity to engage in algebraic reasoning earlier in their…
Descriptors: Addition, Mathematics Instruction, Word Problems (Mathematics), Problem Solving
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
Bofferding, Laura, Ed.; Wessman-Enzinger, Nicole, Ed. – Research in Mathematics Education, 2018
Over the past few decades there has been increased interest in how students and teachers think and learn about negative numbers from a variety of perspectives. In particular, there has been debate about when integers should be taught and how to teach them to best support students' learning. This book brings together recent work from researchers to…
Descriptors: Addition, Subtraction, Numeracy, Thinking Skills