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Paoletti, Teo; Gantt, Allison L.; Vishnubhotla, Madhavi – Educational Studies in Mathematics, 2022
Although there is much research exploring students' covariational reasoning, there is less research exploring the ways students can leverage such reasoning to coordinate more than two quantities. In this paper, we describe a system of covariational relationships as a comprehensive image of how two varying quantities, having the same attribute…
Descriptors: Mathematics Skills, Thinking Skills, Mathematical Concepts, Middle School Students
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
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
Clarke, Doug M.; Roche, Anne – Educational Studies in Mathematics, 2009
As part of individual interviews incorporating whole number and rational number tasks, 323 grade 6 children in Victoria, Australia were asked to nominate the larger of two fractions for eight pairs, giving reasons for their choice. All tasks were expected to be undertaken mentally. The relative difficulty of the pairs was found to be close to that…
Descriptors: Numbers, Foreign Countries, Grade 6, Teaching Methods
Radford, Luis – Educational Studies in Mathematics, 2009
The goal of this article is to present a sketch of what, following the German social theorist Arnold Gehlen, may be termed "sensuous cognition." The starting point of this alternative approach to classical mental-oriented views of cognition is a multimodal "material" conception of thinking. The very texture of thinking, it is suggested, cannot be…
Descriptors: Symbols (Mathematics), Grade 10, Nonverbal Communication, Classroom Communication
Watson, Anne; Shipman, Steve – Educational Studies in Mathematics, 2008
In this paper we describe learners being asked to generate examples of new mathematical concepts, thus developing and exploring example spaces. First we elaborate the theoretical background for learner generated examples (LGEs) in learning new concepts. The data we then present provides evidence of the possibility of learning new concepts through…
Descriptors: Mathematical Concepts, Mathematics Instruction, Teaching Methods, Learning Theories
Lithner, Johan – Educational Studies in Mathematics, 2008
This conceptual research framework addresses the problem of rote learning by characterising key aspects of the dominating imitative reasoning and the lack of creative mathematical reasoning found in empirical data. By relating reasoning to thinking processes, student competencies, and the learning milieu it explains origins and consequences of…
Descriptors: Rote Learning, Cognitive Processes, Models, Learning Strategies
Brown, Laurinda; Reid, David A. – Educational Studies in Mathematics, 2006
We describe the "somatic marker hypothesis" proposed by Damasio (1996) to account for the ability of most people to make decisions quickly and continually in the course of their lives. We relate this hypothesis to two other theoretical constructs, emotional orientations and purposes, which we have used in our research on students' reasoning and…
Descriptors: Decision Making Skills, Thinking Skills, Mathematics Activities, Emotional Intelligence
Peer reviewed
Herbst, Patricio G. – Educational Studies in Mathematics, 2002
Provides an historical account of how proving evolved in school geometry. Explains how the two-column proof format brought stability to the course of studies in geometry. Uncovers what the nature of school geometry came to be as a result of the emphasis on student learning. Draws connections between that century-old reform and current reform…
Descriptors: Curriculum Development, Educational History, Geometry, Mathematics Instruction
Peer reviewed
Lithner, Johan – Educational Studies in Mathematics, 2000
Describes an earlier study on the main characteristics and background of undergraduate students' difficulties when trying to solve mathematical tasks. Focuses on and extends part of an earlier study that concerned task solving strategies. Indicates that focusing on what is familiar and remembered at a superficial level is dominant over reasoning…
Descriptors: Abstract Reasoning, Higher Education, Learning Strategies, Mathematics Education
Peer reviewed
McClain, Kay; Cobb, Paul – Educational Studies in Mathematics, 2001
Describes the role of an instructional sequence and two accompanying computer-based tools in supporting students' developing understandings of statistical data analysis. Documents the emergence of the sociomathematical norm of what counts as a mathematical argument in the context of data analysis. (Author/MM)
Descriptors: Computer Uses in Education, Data Analysis, Mathematics Education, Middle Schools