International Journal for Mathematics Teaching and Learning <p><span style="font-size: small;">This journal&nbsp;is published&nbsp;only in electronic form. It focuses on&nbsp;mathematics teaching and learning for all ages up to university through relevant articles and&nbsp;reviews&nbsp;from around the world.<br> It is aimed at researchers, practitioners and teacher educators providing a medium for stimulating and challenging ideas, offering innovation and practice in all aspects of mathematics teaching and learning.</span></p> <p>&nbsp;</p> en-US International Journal for Mathematics Teaching and Learning 1473-0111 Understanding Students' Computational Fluency: Synechistically Using Test Scores and Interviews for a Richer Picture <p>Mathematics education researchers are tasked with solving practical research problems involving complex constructs in complex settings. The effective integration of quantitative and qualitative data allows researchers to draw more nuanced conclusions about these complex phenomena. This article describes the use of a convergent parallel mixed methods design to integrate two seemingly conflicting data sources that measured six second-grade students’ development of computational fluency. The mixed methods analysis of students’ computational fluency assessments and interviews showed that there was variation in students’ assessment scores, strategy use, and engagement of number sense. Within these variations, the quantitative and qualitative data converged or diverged at various measurement points, and the results highlight the importance of merging the two data sets to capture a richer picture of students’ computational fluency. Implications for using mixed methods in understanding how mathematics learning occurs in classrooms are discussed.</p> Jessica F. Shumway Kerry E. Jordan ##submission.copyrightStatement## 2018-09-01 2018-09-01 19 2 159 175 Describing Lesson Study Designed for Improvement of Mathematics Teachers’ Knowledge of Student Thinking <p class="CONFAbstract"><span lang="EN-AU">The aim of this study is to explain the process of lesson study designed for improving the mathematics teachers’ knowledge of student thinking and to examine its effectiveness in terms of the teaching process and the teachers’ professional development.  The lesson study composed of three cycles was carried out with three mathematics teachers. Each cycle comprised of five stages. The data were collected from the interviews, the lesson observations, the field notes and the reflective diaries. The interviews were conducted with teachers, the teachers’ lessons were observed by the researchers, the field notes were taken by the researchers and the reflective diaries were written by the teachers after each cycles. The data were examined by considering knowledge of student thinking in a detailed way. The teachers’ awareness of knowledge of student thinking got increased by means of the lesson study model. They came to consider the students’ thinking in their lessons and to question the underlying reasons of their ideas. </span></p> Aytuğ ÖZALTUN ÇELİK Esra BUKOVA GÜZEL ##submission.copyrightStatement## 2018-08-23 2018-08-23 19 2 176 204 Elementary School Students’ and Prospective Teachers’ Proportional Reasoning Skills <p class="CONFAbstract"><span lang="EN-AU">The purpose of this study is to investigate prospective elementary school mathematics teachers and elementary school students’ ability to distinguish proportional situations from non-proportional situations. Participants of the study were 319 prospective elementary teachers and 320 elementary school students. Four problems consisting of two proportional and two non-proportional situations were used as a data collection tool. Participants’ strategies were coded as multiplicative, additive, and other. Findings indicated that while elementary school students were dominantly additive reasoners, prospective teachers were multiplicative reasoners. While prospective teachers tended to display multiplicative errors, elementary school students inclined to make additive errors in choice of strategy. It was striking that less than half of the prospective elementary mathematics teachers and only one-third of the prospective primary teachers was able to apply appropriate strategies.</span></p> Zulbiye Toluk Ucar Figen Bozkus ##submission.copyrightStatement## 2018-12-23 2018-12-23 19 2 205 222 Acquiring Math: Connecting Math Learning and Second Language Acquisition <p>Research in second language acquisition and the learning of mathematics has matured through long, albeit disconnected, histories. This study examines how theories and models of second language acquisition can be applied to the learning of mathematics. Herein we investigate the intersection of second language acquisition theories and hierarchical models of mathematical learning and mastery. This comparison and analysis of seemingly disparate fields of study allows us to develop of a novel framework that helps to better define mathematical learning.</p> Michael J. Bosse, Dr. Marjorie Ringler, Dr. Anass Bayaga, Prof. Catherine Fountain, Dr. Erica Slate Young, Dr. ##submission.copyrightStatement## 2018-12-23 2018-12-23 19 2 223 252 Pedagogical entrepreneurship in school mathematics: an approach for students’ development of mathematical literacy Emphasis on the development of the inner qualities thought to make up pedagogical entrepreneurship and use of such entrepreneurship as a strategy in mathematics teaching and learning could be expected to strengthen students’ development of mathematical literacy. This is because problem solving, local cultures and resources, authenticity and action competence are key elements in the development of mathematical literacy and in pedagogical entrepreneurship in mathematics. A foundation for research on an alternative mathematics teaching approach for future decades is suggested based on the relationship between pedagogical entrepreneurship in mathematics and mathematical literacy in the literature and on the description of the contexts and teacher experiences of two best practice examples from the mathematics classroom. Emphasis on pedagogical entrepreneurship in school mathematics through problem solving and authenticity in a learning environment that applauds such approaches to learning of mathematics should be recognized as giving priority to the development of disciplinary literacy in mathematics. Frode Olav Haara ##submission.copyrightStatement## 2018-09-04 2018-09-04 19 2 253 268 Working with the Dynamic Perpendicular Quadrilateral in a Whole Class Setting <p><em>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 class discussion and an animation of the dynamic figure. The findings from this study, essentially the final iteration of a larger Design Based Research study, show how the task can be effectively used in a whole class context. The dynamic nature of the figure together with the narrative descriptions of what happens to the figure under dragging can be shown to be valuable in the development of geometrical concepts and in particular the inclusion of the rhombus as a subset of the kites.</em></p> Susan Kathleen Forsythe ##submission.copyrightStatement## 2018-12-23 2018-12-23 19 2 269 286 The Development of Secondary Mathematics Teachers’ Pedagogical Identities in the Social Context of Classroom Interactions Research demonstrates a disjuncture between the practices encouraged by teacher education programs and what teachers actually do in the classroom. It also informs us that the cognitive and social characteristics of individual teachers such as their attitudes, beliefs and knowledge contribute to their classroom practices. This qualitative study investigates how the teacher identity of mathematics teachers – the person’s sense of who he/she is as a mathematics teacher – is related to the disjuncture between encouraged and actual classroom practices. Specifically, the study looks into how mathematics teachers form their teaching practices in the social context of their classroom interactions, and tries to understand the nature of the discomfort that teachers sometimes experience in the process of shaping their classroom role and teaching practices. The study takes a dialogical approach to identity, seeing the self as something that an individual develops through interactions between his or her core “substantial self” and context-dependent “situational selves.” The qualitative data were collected from four in-service high school teachers in the United States. The study sheds light on the variability of the process of shaping teaching practices; it discusses factors in this variability, and explores how teachers develop and settle into their practices through negotiation between the substantial self and situational selves in the classroom context. Hyung Won Kim ##submission.copyrightStatement## 2018-12-23 2018-12-23 19 2 287 305