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Gulkilik, Hilal; Kaplan, Hatice Aydan; Emul, Nida – International Journal for Mathematics Teaching and Learning, 2019

The purpose of this qualitative study was to analyze the relationship between argumentation and proof in terms of verbal, visual, and algebraic representations of mathematical concepts. We conducted task-based interviews based on geometric locus problems with six undergraduate mathematics teachers while they were working in pairs. We identified…

Descriptors: Persuasive Discourse, Mathematical Logic, Algebra, Public Colleges

Uygun, Tugba – International Journal for Mathematics Teaching and Learning, 2019

The purpose of the current article is to test and revise the hypothetical learning trajectory designed for teaching quadrilaterals by reporting the classroom mathematical practices emerged in a social learning environment developing preservice middle school mathematics teachers' understanding of quadrilaterals. Ten preservice teachers participated…

Descriptors: Mathematics Instruction, Classroom Techniques, Preservice Teachers, Middle School Mathematics

Krajcevski, Milé; Sears, Ruthmae – International Journal for Mathematics Teaching and Learning, 2019

In this paper, we demonstrate how atypical visual representations of a triangle, square or a parallelogram may hinder students' understanding of a median and altitude. We analyze responses and reasoning given by 16 preservice middle school teachers in a Geometry Connection class. Particularly, the data were garnered from three specific questions…

Descriptors: Preservice Teachers, Mathematics Education, Visualization, Misconceptions

Forsythe, Susan K. – International Journal for Mathematics Teaching and Learning, 2018

This paper describes how a dynamic figure was used as the basis for a task designed to support students in developing the hierarchical classification of the kites and their subsets. Following on from a previous study using the task with pairs of students, I describe how I embedded the task into a pedagogical sequence of activities, which included…

Descriptors: Mathematics Instruction, Teaching Methods, Concept Formation, Geometric 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

Cullen, Amanda L.; Tobias, Jennifer M.; Safak, Elif; Kirwan, J. Vince; Wessman-Enzinger, Nicole M.; Wickstrom, Megan H.; Baek, Jae M. – International Journal for Mathematics Teaching and Learning, 2017

Previous research on preservice teachers' understanding of fractions and algebra has focused on one or the other. To extend this research, we examined 85 undergraduate elementary education majors and middle school mathematics education majors' solutions and solution paths (i.e., the ways or methods in which preservice teachers solve word problems)…

Descriptors: Preservice Teachers, Student Teacher Attitudes, Undergraduate Students, Elementary School Teachers

Polotskaia, Elena – International Journal for Mathematics Teaching and Learning, 2017

The main goal of this paper is to show how Vasily Davydov's powerful ideas about the nature of mathematical thinking and learning can transform the teaching and learning of additive word problem solving. The name Vasily Davydov is well known in the field of mathematics education in Russia. However, the transformative value of Davydov's theoretical…

Descriptors: Models, Mathematics Instruction, Foreign Countries, Problem Solving

Eriksson, Inger; Jansson, Anders – International Journal for Mathematics Teaching and Learning, 2017

The issue of this article is to identify and discuss what conditions may be necessary to build into tasks to make it likely for students to be involved in an algebraic Learning Activity inspired by Davydov. Data from a pilot study was used in which a group of students (N = 28) in grade 1 (7-year-olds) were invited to participate in discussions and…

Descriptors: Algebra, Mathematics Instruction, Young Children, Pilot Projects

Nivera, Gladys C. – International Journal for Mathematics Teaching and Learning, 2017

A mathematical investigation (MI) encapsulates the reform movement in mathematics education by addressing content and process simultaneously and providing a novel opportunity for students to develop thinking skills and good mental habits. However, introducing MI to teachers and students who are used to routinised teaching approaches and…

Descriptors: Mathematics Instruction, Teaching Methods, Thinking Skills, High School Students

Zeybek, Zulfiye – International Journal for Mathematics Teaching and Learning, 2016

This study aimed to document pre-service elementary teachers' (PSTs'), who are going to teach K-5, ability to construct as well as evaluate justifications varied in terms of levels of sophistication. Additionally, this study aimed to investigate how PSTs' knowledge of content in which they were being asked to prove influenced their ability to…

Descriptors: Preservice Teachers, Elementary School Teachers, Mathematics Skills, Mathematical Logic

Poon, Kin-Keung; Leung, Chi-Keung – International Journal for Mathematics Teaching and Learning, 2016

The purposes of the study reported herein were to identify the common mistakes in geometry made by junior secondary school students in Hong Kong, and to compare the students' performance in geometry with their results in a logic test. A geometry test and a logic test were developed and administered to a sample of 554 students aged between 13 and…

Descriptors: Foreign Countries, Geometry, Secondary School Students, Mathematics Instruction

Shumway, Jessica F.; Westenskow, Arla; Moyer-Packenham, Patricia S. – International Journal for Mathematics Teaching and Learning, 2016

The purpose of this study was to identify and describe students' use of number sense as they solved story problem tasks. Three 8- and 9-year-old students participated in clinical interviews. Through a process of holistic and qualitative coding, researchers used the number sense view as a theoretical framework for exploring how students' number…

Descriptors: Numbers, Mathematics Instruction, Mathematics Education, Problem Solving

Lesseig, Kristin – International Journal for Mathematics Teaching and Learning, 2016

The purpose of this study was to detail teachers' proving activity and contribute to a framework of Mathematical Knowledge for Teaching Proof (MKT for Proof). While working to justify claims about sums of consecutive numbers, teachers searched for key ideas and productively used examples to make, test and refine conjectures. Analysis of teachers'…

Descriptors: Mathematics Instruction, Validity, Mathematical Logic, Knowledge Level

Brendefur, Jonathan L.; Hughes, Gwyneth; Ely, Robert – International Journal for Mathematics Teaching and Learning, 2015

In this article we examine how secondary school students think about functional relationships. More specifically, we examined seven students' intuitive knowledge in regards to representing two real-world situations with functions. We found students do not tend to represent functional relationships with coordinate graphs even though they are able…

Descriptors: Secondary School Students, Knowledge Level, Mathematics Instruction, Mathematical Concepts

Tobias, Jennifer M.; Roy, George J.; Safi, Farshid – International Journal for Mathematics Teaching and Learning, 2015

This article examines prospective elementary teachers' conceptions of unitizing with whole numbers and fraction concepts and operations throughout a semester-long mathematics content course. Student work samples and classroom conversations are used to illustrate the types of unitizing understandings that prospective teachers bring to teacher…

Descriptors: Preservice Teachers, Elementary School Teachers, Mathematical Concepts, Concept Formation

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