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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

Metaxas, N.; Potari, D.; Zachariades, T. – Educational Studies in Mathematics, 2016

In this article, we elaborate methodologies to study the argumentation speech of a teacher involved in argumentative activities. The standard tool of analysis of teachers' argumentation concerning pedagogical matters is Toulmin's model. The theory of argumentation schemes offers an alternative perspective on the analysis of arguments. We propose…

Descriptors: Persuasive Discourse, Discourse Analysis, Graduate Students, Hypothesis Testing

Lee, Ji-Eun; Kim, Kyoung-Tae – Educational Studies in Mathematics, 2016

This study aimed to explore pre-service elementary teachers' (PSTs') conceptions of effective teacher talk in mathematics instruction, which were interpreted primarily based on the concept of communicative approach. This was accomplished through a task that involves analyzing and evaluating a sample teacher-student dialogue. This study…

Descriptors: Preservice Teachers, Teacher Attitudes, Teacher Student Relationship, Teacher Effectiveness

Fernández-Plaza, José Antonio; Simpson, Adrian – Educational Studies in Mathematics, 2016

In many mathematics curricula, the notion of limit is introduced three times: the limit of a sequence, the limit of a function at a point and the limit of a function at infinity. Despite the use of very similar symbols, few connections between these notions are made explicitly and few papers in the large literature on student understanding of…

Descriptors: Concept Teaching, Mathematical Concepts, Mathematics Curriculum, Symbols (Mathematics)

Peck, Frederick; Matassa, Michael – Educational Studies in Mathematics, 2016

In this paper, we explore algebra students' mathematical realities around fractions and division, and the ways in which students reinvented mathematical productions involving fractions and division. We find that algebra students' initial realities do not include the fraction-as-quotient sub-construct. This can be problematic because in algebra,…

Descriptors: Algebra, Mathematics Instruction, Fractions, Mathematical Concepts

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

Komatsu, Kotaro – Educational Studies in Mathematics, 2016

The process of proofs and refutations described by Lakatos is essential in school mathematics to provide students with an opportunity to experience how mathematical knowledge develops dynamically within the discipline of mathematics. In this paper, a framework for describing student processes of proofs and refutations is constructed using a set of…

Descriptors: Mathematical Logic, Validity, Mathematics Instruction, Knowledge Level

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

Ernest, Paul – Educational Studies in Mathematics, 2016

Two questions about certainty in mathematics are asked. First, is mathematical knowledge known with certainty? Second, why is the belief in the certainty of mathematical knowledge so widespread and where does it come from? This question is little addressed in the literature. In explaining the reasons for these beliefs, both cultural-historical and…

Descriptors: Mathematics Education, Mathematical Concepts, Mathematical Logic, Epistemology

Boylan, Mark – Educational Studies in Mathematics, 2016

The relationships between mathematics, mathematics education and issues such as social justice and equity have been addressed by the sociopolitical tradition in mathematics education. Others have introduced explicit discussion of ethics, advocating for its centrality. However, this is an area that is still under developed. There is a need for an…

Descriptors: Ethics, Mathematics Education, Ambiguity (Context), Heuristics

Pais, Alexandre – Educational Studies in Mathematics, 2016

The issue of subjectivity has recently occasioned a lively discussion in this journal opposing socioculturalism and Lacanian psychoanalysis. By confronting Luis Radford's cultural theory with Jacques Lacan's psychoanalysis, Tony Brown sought to show the limitations of socioculturalism. This article takes advantage of that discussion to develop a…

Descriptors: Sociocultural Patterns, Social Influences, Cultural Influences, Mathematics Instruction