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Font Moll, Vicenç; Trigueros, María; Badillo, Edelmira; Rubio, Norma – Educational Studies in Mathematics, 2016

This paper presents a networking of two theories, the APOS Theory and the ontosemiotic approach (OSA), to compare and contrast how they conceptualize the notion of a mathematical object. As context of reflection, we designed an APOS genetic decomposition for the derivative and analyzed it from the point of view of OSA. Results of this study show…

Descriptors: Mathematics, Constructivism (Learning), Semiotics, Theories

Kollosche, David – Educational Studies in Mathematics, 2016

Socio-political studies in mathematics education often touch complex fields of interaction between education, mathematics and the political. In this paper I present a Foucault-based framework for socio-political studies in mathematics education which may guide research in that area. In order to show the potential of such a framework, I discuss the…

Descriptors: Mathematics Education, Marxian Analysis, Social Influences, Ideology

Solomon, Yvette; Radovic, Darinka; Black, Laura – Educational Studies in Mathematics, 2016

A common theme in accounts of choosing mathematics is that of persistence in the face of troubles or difficulties which are often associated with the structuring effects of gender, class, culture and ethnicity. Centring on an analysis of one woman's account of becoming a mathematician, we build on our understanding of multiple and developing…

Descriptors: Mathematics, Professional Personnel, Professional Identity, Females

Csíkos, Csaba – Educational Studies in Mathematics, 2016

The focus of this study is the relationship between students' performance in mental calculation and the strategies they use when solving three-digit mental addition problems. The sample comprises 78 4th grade students (40 boys and 38 girls). Their mean age was 10 years and 4 months. The main novelties of the current research include (1)…

Descriptors: Elementary School Mathematics, Elementary School Students, Addition, Mental Computation

Frejd, Peter; Bergsten, Christer – Educational Studies in Mathematics, 2016

Educational research literature on mathematical modelling is extensive. However, not much attention has been paid to empirical investigations of its scholarly knowledge from the perspective of didactic transposition processes. This paper reports from an interview study of mathematical modelling activities involving nine professional model…

Descriptors: Mathematical Models, Mathematics Activities, Interviews, Professional Personnel

de Freitas, Elizabeth – Educational Studies in Mathematics, 2016

This paper contributes to research on the material dimensions of teaching and learning mathematics, arguing that perception is not sensory integration or synthesis of multi-modal information, but rather a speculative investment in specific material encounters. This approach entails sociopolitical consequences for how we work with dis/ability in…

Descriptors: Mathematics Instruction, Visual Perception, Human Body, Visualization

Lockwood, Elise; Gibson, Bryan R. – Educational Studies in Mathematics, 2016

Although counting problems are easy to state and provide rich, accessible problem-solving situations, there is much evidence that students struggle with solving counting problems correctly. With combinatorics (and the study of counting problems) becoming increasingly prevalent in K-12 and undergraduate curricula, there is a need for researchers to…

Descriptors: Undergraduate Students, Mathematics Instruction, Problem Solving, Mathematics Skills

Weinberg, Aaron; Wiesner, Emilie; Fukawa-Connelly, Tim – Educational Studies in Mathematics, 2016

Although lecture is the traditional method of university mathematics instruction, there has been little empirical research that describes the general structure of lectures. In this paper, we adapt ideas from narrative analysis and apply them to an upper-level mathematics lecture. We develop a framework that enables us to conceptualize the lecture…

Descriptors: Mathematics Instruction, Lecture Method, Narration, Teaching Methods

Scheiner, Thorsten – Educational Studies in Mathematics, 2016

The initial assumption of this article is that there is an overemphasis on abstraction-from-actions theoretical approaches in research on knowing and learning mathematics. This article uses a critical reflection on research on students' ways of constructing mathematical concepts to distinguish between abstraction-from-actions theoretical…

Descriptors: Mathematical Concepts, Learning Processes, Mathematics Skills, Abstract Reasoning

Kidron, Ivy – Educational Studies in Mathematics, 2016

A theoretical reflection on epistemology is presented. The important role of epistemological analysis in research in mathematics education is discussed. I analyze the epistemological evolution as a consequence of the changes in the mathematical culture and demonstrate how the epistemological analysis is tightly linked to the cultural dimension.…

Descriptors: Epistemology, Mathematics Education, Educational Research, Cultural Influences

Voutsina, Chronoula – Educational Studies in Mathematics, 2016

Empirical research has documented how children's early counting develops into an increasingly abstract process, and initial counting procedures are reified as children develop and use more sophisticated counting. In this development, the learning of different oral counting sequences that allow children to count in steps bigger than one is seen as…

Descriptors: Computation, Young Children, Mathematics Instruction, Mathematics Education

Hackenberg, Amy J.; Lee, Mi Yeon – Educational Studies in Mathematics, 2016

To understand relationships between students' quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. The study included six students with each of three different multiplicative concepts, which are based on how students create and coordinate composite…

Descriptors: Mathematics Instruction, Mathematical Logic, Fractions, Algebra

Kontorovich, Igor'; Zazkis, Rina – Educational Studies in Mathematics, 2016

This study is concerned with tensions between the two different perspectives on the concept of angle: angle as a static shape and angle as a dynamic turn. The goal of the study is to explore how teachers cope with these tensions. We analyze scripts of 16 in-service secondary mathematics teachers, which feature a dialogue between a teacher and…

Descriptors: Mathematics Instruction, Mathematical Concepts, Secondary School Mathematics, Secondary School Teachers

Zazkis, Dov; Weber, Keith; Mejía-Ramos, Juan Pablo – Educational Studies in Mathematics, 2016

We examine a commonly suggested proof construction strategy from the mathematics education literature--that students first produce a graphical argument and then work to construct a verbal-symbolic proof based on that graphical argument. The work of students who produce such graphical arguments when solving proof construction tasks was analyzed to…

Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Persuasive Discourse

Simon, Martin A.; Kara, Melike; Placa, Nicora; Sandir, Hakan – Educational Studies in Mathematics, 2016

Reversibility of concepts, a key aspect of mathematical development, is often problematic for learners. In this theoretical paper, we present a typology we have developed for categorizing the different reverse concepts that can be related to a particular initial concept and explicate the relationship among these different reverse concepts. We…

Descriptors: Mathematical Concepts, Mathematics Instruction, Classification, Concept Formation