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Miyazaki, Mikio; Fujita, Taro; Jones, Keith – Educational Studies in Mathematics, 2017

While proof is central to mathematics, difficulties in the teaching and learning of proof are well-recognised internationally. Within the research literature, a number of theoretical frameworks relating to the teaching of different aspects of proof and proving are evident. In our work, we are focusing on secondary school students learning the…

Descriptors: Secondary School Students, Secondary School Mathematics, Mathematical Logic, Validity

Sangwin, Christopher J.; Jones, Ian – Educational Studies in Mathematics, 2017

In this paper we report the results of an experiment designed to test the hypothesis that when faced with a question involving the inverse direction of a reversible mathematical process, students solve a multiple-choice version by verifying the answers presented to them by the direct method, not by undertaking the actual inverse calculation.…

Descriptors: Mathematics Achievement, Mathematics Tests, Multiple Choice Tests, Computer Assisted Testing

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

Kaiser, Gabriele; Blömeke, Sigrid; König, Johannes; Busse, Andreas; Döhrmann, Martina; Hoth, Jessica – Educational Studies in Mathematics, 2017

Recent research on the professional competencies of mathematics teachers, which has been carried out during the last decade, is characterized by different theoretical approaches on the conceptualization and evaluation of teachers' professional competencies, namely cognitive versus situated approaches. Building on the international IEA Teacher…

Descriptors: Mathematics Teachers, Teacher Competencies, Teacher Attitudes, Evaluation Methods

Bruce, Catherine D.; Davis, Brent; Sinclair, Nathalie; McGarvey, Lynn; Hallowell, David; Drefs, Michelle; Francis, Krista; Hawes, Zachary; Moss, Joan; Mulligan, Joanne; Okamoto, Yukari; Whiteley, Walter; Woolcott, Geoff – Educational Studies in Mathematics, 2017

This paper finds its origins in a multidisciplinary research group's efforts to assemble a review of research in order to better appreciate how "spatial reasoning" is understood and investigated across academic disciplines. We first collaborated to create a historical map of the development of spatial reasoning across key disciplines…

Descriptors: Educational Research, Spatial Ability, Network Analysis, Intellectual Disciplines

Dawkins, Paul Christian; Weber, Keith – Educational Studies in Mathematics, 2017

In this theoretical paper, we present a framework for conceptualizing proof in terms of mathematical values, as well as the norms that uphold those values. In particular, proofs adhere to the values of establishing a priori truth, employing decontextualized reasoning, increasing mathematical understanding, and maintaining consistent standards for…

Descriptors: Values, Norms, Mathematical Logic, Validity

Kaspersen, Eivind; Pepin, Birgit; Sikko, Svein Arne – Educational Studies in Mathematics, 2017

Studies on identity in general and mathematical identity in particular have gained much interest over the last decades. However, although measurements have been proven to be potent tools in many scientific fields, a lack of consensus on ontological, epistemological, and methodological issues has complicated measurements of mathematical identities.…

Descriptors: STEM Education, Mathematics, Identification (Psychology), Professional Identity

Stouraitis, Konstantinos; Potari, Despina; Skott, Jeppe – Educational Studies in Mathematics, 2017

The study reported in this paper concerns the tensions and conflicts that teachers experience while they enact a new set of reform-oriented curricular materials into their classrooms. Our focus is ?n the interactions developed in two groups of teachers in two schools for a period of a school year. We use Activity Theory to study emerging…

Descriptors: Mathematics Instruction, Teaching Experience, Mathematics Teachers, Teaching Methods

Blanton, Maria; Brizuela, Bárbara M.; Gardiner, Angela Murphy; Sawrey, Katie; Newman-Owens, Ashley – Educational Studies in Mathematics, 2017

Recent research suggests that children in elementary grades have some facility with variable and variable notation in ways that warrant closer attention. We report here on an empirically developed progression in first-grade children's thinking about these concepts in functional relationships. Using learning trajectories research as a framework for…

Descriptors: Elementary School Mathematics, Grade 1, Mathematics Instruction, Thinking Skills

Palatnik, Alik; Koichu, Boris – Educational Studies in Mathematics, 2017

This article concerns student sense making in the context of algebraic activities. We present a case in which a pair of middle-school students attempts to make sense of a previously obtained by them position formula for a particular numerical sequence. The exploration of the sequence occurred in the context of two-month-long student research…

Descriptors: Mathematics Instruction, Algebra, Middle School Students, Problem Solving

Fernandes, Anthony; Kahn, Leslie H.; Civil, Marta – Educational Studies in Mathematics, 2017

In this article, we use multimodality to examine how bilingual students interact with an area task from the National Assessment of Educational Progress in task-based interviews. Using vignettes, we demonstrate how some of these students manipulate the concrete materials, and use gestures, as a primary form of structuring their explanations and…

Descriptors: Bilingual Students, Interviews, Vignettes, Nonverbal Communication

Foster, Colin; Inglis, Matthew – Educational Studies in Mathematics, 2017

Curricular implementations are unlikely to deliver the anticipated benefits for mathematics learners if written guidance to teachers is interpreted and enacted differently from the ways that policymakers and curriculum designers intend. One way in which this could happen is in relation to the mathematics tasks that teachers deploy in the…

Descriptors: Mathematics Instruction, Mathematics Teachers, Mathematics, Foreign Countries

Downton, Ann; Sullivan, Peter – Educational Studies in Mathematics, 2017

While the general planning advice offered to mathematics teachers seems to be to start with simple examples and build complexity progressively, the research reported in this article is a contribution to the body of literature that argues the reverse. That is, posing of appropriately complex tasks may actually prompt the use of more sophisticated…

Descriptors: Problem Solving, Mathematical Aptitude, Mathematics Skills, Difficulty Level

FitzSimons, Gail E.; Björklund Boistrup, Lisa – Educational Studies in Mathematics, 2017

Preparing students for their lives beyond schooling appears to be a universal goal of formal education. Much has been done to make mathematics education more "realistic," but such activities nevertheless generally remain within the institutional norms of education. In this article, we assume that pedagogic relations are also an integral…

Descriptors: Mathematics Education, Education Work Relationship, Mathematical Applications, Mathematics Skills

Bass, Hyman – Educational Studies in Mathematics, 2017

Mathematicians commonly distinguish two modes of work in the discipline: "Problem solving," and "theory building." Mathematics education offers many opportunities to learn problem solving. This paper explores the possibility, and value, of designing instructional activities that provide supported opportunities for students to…

Descriptors: Mathematics Education, Problem Solving, Instructional Design, Mathematics