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Jones, Steven R. – Educational Studies in Mathematics, 2018

Many mathematical concepts may have prototypical images associated with them. While prototypes can be beneficial for efficient thinking or reasoning, they may also have self-attributes that may impact reasoning about the concept. It is essential that mathematics educators understand these prototype images in order to fully recognize their benefits…

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

Paoletti, Teo; Stevens, Irma E.; Hobson, Natalie L. F.; Moore, Kevin C.; LaForest, Kevin R. – Educational Studies in Mathematics, 2018

Researchers have argued teachers and students are not developing connected meanings for function inverse, thus calling for a closer examination of teachers' and students' inverse function meanings. Responding to this call, we characterize 25 pre-service teachers' inverse function meanings as inferred from our analysis of clinical interviews. After…

Descriptors: Preservice Teachers, Mathematical Concepts, Interviews, Knowledge Level

Zazkis, Rina; Rouleau, Annette – Educational Studies in Mathematics, 2018

In our exploration of the order of operations we focus on the following claim: "In the conventional order of operations, division should be performed before multiplication." This initially surprising claim is based on the acronym BEDMAS, a popular mnemonic used in Canada to assist students in remembering the order of operations. The…

Descriptors: Mathematics Instruction, Mathematical Concepts, Teaching Methods, Mnemonics

Chambris, Christine – Educational Studies in Mathematics, 2018

This paper examines the existence and impact of theoretical mathematical foundations on the teaching and learning of whole numbers in elementary school in France. It shows that the study of the New Math reform--which was eventually itself replaced in the longer term--provides some keys to understanding the influence of mathematical theories on…

Descriptors: Mathematics Instruction, Elementary School Mathematics, Elementary Education, Teaching Methods

Glade, Matthias; Prediger, Susanne – Educational Studies in Mathematics, 2017

According to the design principle of progressive schematization, learning trajectories towards procedural rules can be organized as independent discoveries when the learning arrangement invites the students first to develop models for mathematical concepts and model-based informal strategies; then to explore the strategies and to discover pattern…

Descriptors: Grade 6, Video Technology, Fractions, Mathematics Instruction

Simon, Martin A. – Educational Studies in Mathematics, 2017

Mathematical understanding continues to be one of the major goals of mathematics education. However, what is meant by "mathematical understanding" is underspecified. How can we operationalize the idea of mathematical understanding in research? In this article, I propose particular specifications of the terms "mathematical…

Descriptors: Mathematics Education, Mathematical Concepts, Concept Formation, Educational Research

Schüler-Meyer, Alexander – Educational Studies in Mathematics, 2017

After being introduced to the distributive law in meaningful contexts, students need to extend its scope of application to unfamiliar expressions. In this article, a process model for the development of structure sense is developed. Building on this model, this article reports on a design research project in which exercise tasks support students…

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

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

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

Moore, Kevin C.; LaForest, Kevin R.; Kim, Hee Jung – Educational Studies in Mathematics, 2016

We discuss a teaching experiment that explored two pre-service secondary teachers' meanings for the unit circle. Our analyses suggest that the participants' initial unit circle meanings predominantly consisted of calculational strategies for relating a given circle to what they called "the unit circle." These strategies did not entail…

Descriptors: Preservice Teachers, Secondary School Teachers, Secondary School Mathematics, Mathematics Instruction

Casey, Stephanie A.; Nagle, Courtney – Educational Studies in Mathematics, 2016

Learning experiences regarding the line of best fit are typically students' first encounters with the fundamental topic of statistical association. Students bring with them into these learning experiences prior knowledge and experiences about mathematical lines and their properties, namely slope. This study investigated the role students'…

Descriptors: Mathematics Instruction, Grade 8, Interviews, Mathematical Concepts

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

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