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Ferrara, Francesca; Sinclair, Nathalie – Educational Studies in Mathematics, 2016

This paper focuses on pattern generalisation as a way to introduce young students to early algebra. We build on research on patterning activities that feature, in their work with algebraic thinking, both looking for sameness recursively in a pattern (especially figural patterns, but also numerical ones) and conjecturing about function-based…

Descriptors: Algebra, Mathematics, Mathematics Instruction, Generalization

Castro-Rodríguez, Elena; Pitta-Pantazi, Demetra; Rico, Luis; Gómez, Pedro – Educational Studies in Mathematics, 2016

The part-whole multiplicative relationship, as a topic that gives rise to the concept of fraction, is fundamental in education at the primary school level, and must therefore be included in training courses for prospective primary school teachers (PSTs). In this paper, we introduce a first study of a larger project, which aims to understand the…

Descriptors: Elementary School Teachers, Fractions, Preservice Teachers, Multiplication

Brown, Tony – Educational Studies in Mathematics, 2016

This paper argues that rationality and belief are mutually formative dimensions of school mathematics, where each term is more politically embedded than often depicted in the field of mathematics education research. School mathematics then presents not so much rational mathematical thought distorted by irrational beliefs but rather a particular…

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

Presmeg, Norma – Educational Studies in Mathematics, 2016

This paper is a commentary on the theoretical formulations of the five empirical papers in this special issue. All five papers use aspects of the theory of commognition as presented by Anna Sfard; however, even when the same notions (e.g., rituals or explorations) are incorporated into theoretical frameworks undergirding the research, these…

Descriptors: Journal Articles, Educational Theories, Cognitive Processes, Connected Discourse

Ng, Oi-Lam – Educational Studies in Mathematics, 2016

This paper discusses the importance of considering bilingual learners' non-linguistic forms of communication for understanding their mathematical thinking. In particular, I provide a detailed analysis of communication involving a pair of high school bilingual learners during an exploratory activity where a touchscreen-based dynamic geometry…

Descriptors: Nonverbal Communication, Mathematics Instruction, Mathematical Logic, Geometry

Wood, Marcy B. – Educational Studies in Mathematics, 2016

Student autonomy has been an important object of study for mathematics educators for many years. Over time, framings of autonomy have moved from a focus on the individual to considerations of how an individual's autonomy is entangled in classroom-level interactions. What has been less closely studied is how classroom interactions provide uneven…

Descriptors: Barriers, Mathematics Education, Personal Autonomy, Interaction

Güçler, Beste – Educational Studies in Mathematics, 2016

Despite the existence of extensive literature on functions, fewer studies used sociocultural views to explore the development of student learning about the concept. This study uses a discursive lens to examine whether an instructional approach that specifically attends to particular metalevel rules in the mathematical discourse on functions…

Descriptors: Reflection, Academic Achievement, Mathematics, Mathematics Instruction

Park, Jungeun – Educational Studies in Mathematics, 2016

This paper investigates how three widely used calculus textbooks in the U.S. realize the derivative as a point-specific object and as a function using Sfard's communicational approach. For this purpose, the study analyzed word-use and visual mediators for the "limit process" through which the derivative at a point was objectified, and…

Descriptors: Textbook Content, Textbooks, Calculus, Mathematics Education

Tabach, Michal; Nachlieli, Talli – Educational Studies in Mathematics, 2016

This special issue comprises five studies which vary in their focus and mathematical content, yet they all share an underlying communicational theoretical framework--commognition. Within this framework, learning mathematics is defined as a change in one's mathematical discourse, that is, in the form of communication known as mathematical. Teaching…

Descriptors: Mathematics Instruction, Mathematics, Models, Language Usage

Ekdahl, Anna-Lena; Venkat, Hamsa; Runesson, Ulla – Educational Studies in Mathematics, 2016

In this article, we present a coding framework based on simultaneity and connections. The coding focuses on microlevel attention to three aspects of simultaneity and connections: between representations, within examples, and between examples. Criteria for coding that we viewed as mathematically important within part-whole additive relations…

Descriptors: Coding, Mathematical Concepts, Mathematical Applications, Demonstrations (Educational)

da Ponte, João Pedro; Quaresma, Marisa – Educational Studies in Mathematics, 2016

This paper seeks to identify actions that can be regarded as building elements of teachers' classroom practice in mathematical discussion and how these actions may be combined to provide fruitful learning opportunities for students. It stands on a framework that focuses on two key elements of teaching practice: the tasks that teachers propose to…

Descriptors: Teaching Methods, Mathematics Education, Qualitative Research, Video Technology

Samper, Carmen; Perry, Patricia; Camargo, Leonor; Sáenz-Ludlow, Adalira; Molina, Óscar – Educational Studies in Mathematics, 2016

Proving an existence theorem is less intuitive than proving other theorems. This article presents a semiotic analysis of significant fragments of classroom meaning-making which took place during the class-session in which the existence of the midpoint of a line-segment was proven. The purpose of the analysis is twofold. First follow the evolution…

Descriptors: Theories, Geometric Concepts, Validity, Concept Formation

Chow, Alan F.; Van Haneghan, James P. – Educational Studies in Mathematics, 2016

This study reports the results of a study examining how easily students are able to transfer frequency solutions to conditional probability problems to novel situations. University students studied either a problem solved using the traditional Bayes formula format or using a natural frequency (tree diagram) format. In addition, the example problem…

Descriptors: Probability, College Students, Mathematical Formulas, Bayesian Statistics

Son, Ji-Won – Educational Studies in Mathematics, 2016

Although students' invented strategies typically prove to be meaningful and effective in improving the students' mathematical understanding, much remains unexplored in the current literature. This study examined, through a teaching-scenario task, the nature of 80 preservice teachers' reasoning and responses to students' informal and formal…

Descriptors: Subtraction, Mathematics, Numbers, Preservice Teachers

Roth, Wolff-Michael – Educational Studies in Mathematics, 2016

Recent theoretical advances on learning (mathematics) emphasize the fact that what results from engagement with curriculum materials is not entirely in the control of the students in the way classical theories of knowing and learning suggest. These new theories distinguish themselves by either invoking distributed agency, some of which is…

Descriptors: Mathematics Education, Theories, Mathematics Curriculum, Females