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Swidan, Osama; Sabena, Cristina; Arzarello, Ferdinando – Educational Studies in Mathematics, 2020

This paper examines mathematical meaning-making from a phenomenological perspective and considers how a specific dynamic digital tool can prompt students to disclose the relationships between a function and its antiderivatives. Drawing on case study methodology, we focus on a pair of grade 11 students and analyze how the tool's affordances and the…

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

Understanding and Promoting Students' Mathematical Thinking: A Review of Research Published in "ESM"

Goos, Merrilyn; Kaya, Sila – Educational Studies in Mathematics, 2020

In this paper, we offer a comparative review of research on understanding and promoting students' mathematical thinking. The sources for the review are papers that were published in "Educational Studies in Mathematics" ("ESM") during two windows of time: 1994-1998 and 2014-2018. Selection of these two time periods enables us to…

Descriptors: Educational Research, Mathematical Logic, Research Reports, Mathematics Education

Lew, Kristen; Mejía Ramos, Juan Pablo – Educational Studies in Mathematics, 2020

This paper presents the findings from a survey used to investigate how mathematicians perceive the genre of mathematical proof writing at the undergraduate level. Mathematicians were asked whether various proof excerpts highlighted in four partial proofs were unconventional in each one of three pedagogical contexts: undergraduate mathematics…

Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Undergraduate Students

Melhuish, Kathleen; Ellis, Brittney; Hicks, Michael D. – Educational Studies in Mathematics, 2020

Binary operations are one of the fundamental structures underlying our number and algebraic systems. Yet, researchers have often left their role implicit as they model student understanding of abstract structures. In this paper, we directly analyze students' perceptions of the general binary operation via a two-phase study consisting of task-based…

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

Supply, Anne-Sophie; Van Dooren, Wim; Lem, Stephanie; Onghena, Patrick – Educational Studies in Mathematics, 2020

Comparing probabilities is a useful skill in life. Binary choice tasks are popular means in research on probabilistic reasoning. Falk, Yudilevich-Assouline, and Elstein ("Educational Studies in Mathematics," 81(2), 207-233 2012) noted that many of these tasks contain design flaws. We designed and evaluated an extended and improved binary…

Descriptors: Young Children, Mathematics Skills, Probability, Age Differences

Papadopoulos, Ioannis; Gunnarsson, Robert – Educational Studies in Mathematics, 2020

When a number sentence includes more than one operation, students are taught to follow the rules for the order of operations to get the correct result. In this context, brackets are used to determine the operations that should be calculated first. However, it seems that the written format of an arithmetical expression has an impact on the way…

Descriptors: Mathematics Instruction, Elementary School Mathematics, Arithmetic, Foreign Countries

Hankeln, Corinna – Educational Studies in Mathematics, 2020

The study presented in this article takes a closer look at how French and German high-school students deal with a mathematical modeling problem, what blockages they encounter and how differences in the modeling processes between students from both nations can be explained by differences between the teaching and learning of mathematical modeling in…

Descriptors: Foreign Countries, Comparative Education, Mathematical Models, High School Students

Tabach, Michal; Rasmussen, Chris; Dreyfus, Tommy; Apkarian, Naneh – Educational Studies in Mathematics, 2020

The networking of theories is an increasingly common and powerful approach to analyzing complex phenomena such as learning processes in classrooms. In this paper, we aim to advance the theoretical coordination of two approaches that we have previously combined to analyze individual, small group, and whole class mathematical progress. The…

Descriptors: Learning Theories, Mathematics Achievement, Coordination, Evaluation Methods

Lockwood, Elise; Caughman, John S.; Weber, Keith – Educational Studies in Mathematics, 2020

There is a longstanding conversation in the mathematics education literature about proofs that explain versus proofs that only convince. In this essay, we offer a characterization of explanatory proofs with three goals in mind. We first propose a theory of explanatory proofs for mathematics education in terms of representation systems. Then, we…

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

Kullberg, Angelika; Björklund, Camilla; Brkovic, Irma; Runesson Kempe, Ulla – Educational Studies in Mathematics, 2020

In this paper, we report how 5-year-olds' arithmetic skills developed through participation in an 8-month-long intervention. The intervention program aimed to enhance the children's ways of experiencing numbers' part-part-whole relations as a basis for arithmetic skills and was built on principles from the variation theory of learning. The report…

Descriptors: Preschool Children, Mathematics Skills, Arithmetic, Learning Strategies

Soldano, Carlotta; Luz, Yael; Arzarello, Ferdinando; Yerushalmy, Michal – Educational Studies in Mathematics, 2019

The paper describes two versions of an inquiry-based activity in geometry, designed as a game between two players. The game is inspired by Hintikka's semantic game, which is a familiar tool in the field of logic to define truth. The activity is designed in a dynamic geometry environment (DGE). The inquiry is initially guided by the game itself and…

Descriptors: Geometry, Semantics, Mathematics Instruction, Inquiry

Schukajlow, Stanislaw; Achmetli, Kay; Rakoczy, Katrin – Educational Studies in Mathematics, 2019

The development of multiple solutions for a given problem is important for learning mathematics. In the present intervention study, we analyzed whether prompting students to construct multiple solutions (more precisely: prompting them to apply multiple mathematical procedures to real-world problems) and prior self-efficacy influenced students'…

Descriptors: Mathematics Instruction, Self Efficacy, Teaching Methods, Student Attitudes

Roos, Helena – Educational Studies in Mathematics, 2019

This literature review focuses on the definitions and roles of "inclusion" in the field of mathematics education to help promote the sustainable development of inclusion in the discipline. Discourse analysis was used to analyse 76 studies published between 2010 and 2016. The results show that the term "inclusion" is used both…

Descriptors: Mathematics Instruction, Inclusion, Teaching Methods, Intervention

Sánchez-Matamoros, Gloria; Fernández, Ceneida; Llinares, Salvador – Educational Studies in Mathematics, 2019

This study explores relationships among prospective secondary teachers' skills of attending to relevant mathematics elements in students' answers, interpreting students' mathematical understanding, and proposing instructional actions. Thirty prospective secondary mathematics teachers analyzed three high school students' answers to three problems…

Descriptors: Mathematics Instruction, Teaching Methods, Teacher Education Programs, High School Students

Weixler, Simon; Sommerhoff, Daniel; Ufer, Stefan – Educational Studies in Mathematics, 2019

The empirical law of large numbers is an important content in secondary school mathematics. Tasks used to analyze students' understanding of this law are often based on the hospital problem, but vary in various features, leading to mixed and conflicting empirical results. To identify task features that support students when approaching this type…

Descriptors: Numbers, Mathematics Instruction, Problem Solving, Secondary School Mathematics