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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

Kapon, Shulamit; Ron, Gila; Hershkowitz, Rina; Dreyfus, Tommy – Educational Studies in Mathematics, 2015

There is ample evidence that reasoning about stochastic phenomena is often subject to systematic bias even after instruction. Few studies have examined the detailed learning processes involved in learning probability. This paper examines a case study drawn from a large corpus of data collected as part of a research project that dealt with the…

Descriptors: Probability, Learning Processes, Junior High School Students, Case Studies

Kidron, Ivy; Dreyfus, Tommy – Educational Studies in Mathematics, 2014

The emergence of a proof image is often an important stage in a learner's construction of a proof. In this paper, we introduce, characterize, and exemplify the notion of proof image. We also investigate how proof images emerge. Our approach starts from the learner's efforts to construct a justification without (or before) attempting any…

Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Persuasive Discourse

Grounded Blends and Mathematical Gesture Spaces: Developing Mathematical Understandings via Gestures

Yoon, Caroline; Thomas, Michael O. J.; Dreyfus, Tommy – Educational Studies in Mathematics, 2011

This paper examines how a person's gesture space can become endowed with mathematical meaning associated with mathematical spaces and how the resulting mathematical gesture space can be used to communicate and interpret mathematical features of gestures. We use the theory of grounded blends to analyse a case study of two teachers who used gestures…

Descriptors: Nonverbal Communication, Calculus, Motion, Teaching Methods

Ron, Gila; Dreyfus, Tommy; Hershkowitz, Rina – Educational Studies in Mathematics, 2010

We present a view of knowledge construction processes, focusing on partially correct constructs. Motivated by unexpected and seemingly inconsistent quantitative data based on the written reports of students working on an elementary probability task, we analyze in detail the knowledge construction processes of a representative student. We show how…

Descriptors: Probability, Students, Thinking Skills, Evaluation

Kidron, Ivy; Dreyfus, Tommy – Educational Studies in Mathematics, 2010

This case study deals with a solitary learner's process of mathematical justification during her investigation of bifurcation points in dynamic systems. Her motivation to justify the bifurcation points drove the learning process. Methodologically, our analysis used the nested epistemic actions model for abstraction in context. In previous work, we…

Descriptors: Constructivism (Learning), Case Studies, Learning Processes, Mathematics Instruction

Peer reviewed

Dreyfus, Tommy – Educational Studies in Mathematics, 1999

One sentence answer to the question in the title is that the ability to prove depends on forms of knowledge to which most student are rarely, if ever, exposed. Presents more detailed analysis, drawing on research in mathematics education and classroom experiences. (Contains 44 references.) (Author/ASK)

Descriptors: Cognitive Structures, Elementary Secondary Education, Mathematics Instruction, Proof (Mathematics)

Peer reviewed

Schwarz, Baruch; Dreyfus, Tommy – Educational Studies in Mathematics, 1995

A computer microworld called Triple Representation Model uses graphical, tabular, and algebraic representations to influence conceptions of function. A majority of students were able to cope with partial data, recognize invariants while coordinating actions among representations, and recognize invariants while creating and comparing different…

Descriptors: Cognitive Development, College Students, Computer Uses in Education, Functions (Mathematics)

Peer reviewed

Shama, Gilli; Dreyfus, Tommy – Educational Studies in Mathematics, 1994

Identified and classified solution strategies of (n=49) 10th-grade students who were presented with linear programming problems in a predominantly visual setting in the form of a computerized game. Visual strategies were developed more frequently than either algebraic or mixed strategies. Appendix includes questionnaires. (Contains 11 references.)…

Descriptors: Algebra, Cognitive Style, Computer Assisted Instruction, Functions (Mathematics)