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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

Miyakawa, Takeshi – Educational Studies in Mathematics, 2017

This paper reports the results of an international comparative study on the nature of proof to be taught in geometry. Proofs in French and Japanese lower secondary schools were explored by analyzing curricular documents: mathematics textbooks and national curricula. Analyses on the three aspects of proof--statement, proof, and theory--suggested by…

Descriptors: Comparative Analysis, Mathematical Logic, Geometry, Teaching Methods

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

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

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

Dawkins, Paul Christian; Cook, John Paul – Educational Studies in Mathematics, 2017

Motivated by the observation that formal logic answers questions students have not yet asked, we conducted exploratory teaching experiments with undergraduate students intended to guide their reinvention of truth-functional definitions for basic logical connectives. We intend to reframe the relationship between reasoning and logic by showing how…

Descriptors: Mathematical Logic, Thinking Skills, Undergraduate Students, College Mathematics

Komatsu, Kotaro – Educational Studies in Mathematics, 2017

In contrast to existing research that has typically addressed the process from example generation to proof construction, this study aims at enhancing empirical examination after proof construction leading to revision of statements and proofs in secondary school geometry. The term "empirical examination" refers to the use of examples or…

Descriptors: Secondary School Mathematics, Mathematics Instruction, Geometry, Mathematical Logic

Stylianides, Gabriel J.; Stylianides, Andreas J. – Educational Studies in Mathematics, 2017

The concept of "proof" has attracted considerable research attention over the past decades in part due to its indisputable importance to the discipline of mathematics and to students' learning of mathematics. Yet, the teaching and learning of proof is an instructionally arduous territory, with proof being recognized as a hard-to-teach…

Descriptors: Validity, Mathematical Logic, Intervention, Mathematics Instruction

Mata-Pereira, Joana; da Ponte, João-Pedro – Educational Studies in Mathematics, 2017

A proof is a connected sequence of assertions that includes a set of accepted statements, forms of reasoning and modes of representing arguments. Assuming reasoning to be central to proving and aiming to develop knowledge about how teacher actions may promote students' mathematical reasoning, we conduct design research where whole-class…

Descriptors: Mathematics Instruction, Mathematical Logic, Generalization, Validity

Gabel, Mika; Dreyfus, Tommy – Educational Studies in Mathematics, 2017

The notion of flow of a proof encapsulates mathematical, didactical, and contextual aspects of proof presentation. A proof may have different flows, depending on the lecturer's choices regarding its presentation. Adopting Perelman's New Rhetoric (PNR) as a theoretical framework, we designed methods to assess aspects of the flow of a proof. We…

Descriptors: Mathematics Instruction, Validity, Mathematical Logic, Theories

Roy, Somali; Inglis, Matthew; Alcock, Lara – Educational Studies in Mathematics, 2017

This paper presents two studies of an intervention designed to help undergraduates comprehend mathematical proofs. The intervention used multimedia resources that presented proofs with audio commentary and visual animations designed to focus attention on logical relationships. In study 1, students studied an e-Proof or a standard written proof and…

Descriptors: Intervention, Undergraduate Students, Multimedia Instruction, Eye Movements

Fiallo, Jorge; Gutiérrez, Angel – Educational Studies in Mathematics, 2017

We present results from a classroom-based intervention designed to help a class of grade 10 students (14-15 years old) learn proof while studying trigonometry in a dynamic geometry software environment. We analysed some students' solutions to conjecture-and-proof problems that let them gain experience in stating conjectures and developing proofs.…

Descriptors: Mathematical Logic, Validity, Mathematics Instruction, Grade 10

Guala, Elda; Boero, Paolo – Educational Studies in Mathematics, 2017

This paper deals with the competence of Cultural (epistemological, historical and anthropological) Analysis of the Content (CAC), which is important for teachers' awareness and autonomy when dealing with educational choices in a changing cultural and institutional context. We report on an 18-hour intervention in a teacher education course at the…

Descriptors: Mathematics Instruction, Teacher Education Programs, Undergraduate Study, Intervention

Fan, Lianghuo; Qi, Chunxia; Liu, Xiaomei; Wang, Yi; Lin, Mengwei – Educational Studies in Mathematics, 2017

We conducted an intervention-based study in secondary classrooms to explore whether the use of geometric transformations can help improve students' ability in constructing auxiliary lines to solve geometric proof problems, especially high-level cognitive problems. A pre- and post-test quasi-experimental design was employed. The participants were…

Descriptors: Intervention, Secondary School Mathematics, Geometry, Validity

Nardi, Elena; Knuth, Eric – Educational Studies in Mathematics, 2017

This paper is a commentary on the classroom interventions on the teaching and learning of proof reported in the seven empirical papers in this special issue. The seven papers show potential to enhance student learning in an area of mathematics that is not only notoriously difficult for students to learn and for teachers to teach, but also…

Descriptors: Mathematical Logic, Validity, Mathematics Instruction, Integrated Curriculum