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Chimoni, Maria; Pitta-Pantazi, Demetra; Christou, Constantinos – Educational Studies in Mathematics, 2023
Little is known about the cognitive effort associated with algebraic activity in the elementary and middle school grades. However, this investigation is significant for sensitizing teachers and researchers to the mental demands of algebra learning. In this paper, we focus on the relationship between algebraic thinking and domain-general cognitive…
Descriptors: Algebra, Mathematics Skills, Cognitive Processes, Cognitive Ability
Thanheiser, Eva; Melhuish, Kathleen; Sugimoto, Amanda; Rosencrans, Brenda; Heaton, Ruth – Educational Studies in Mathematics, 2021
In this paper, we network five frameworks (cognitive demand, lesson cohesion, cognitive engagement, collective argumentation, and student contribution) for an analytic approach that allows us to present a more holistic picture of classrooms which engage students in justifying. We network these frameworks around the edges of the instructional…
Descriptors: Networks, Classroom Environment, Mathematics Instruction, Learner Engagement
Kidron, Ivy – Educational Studies in Mathematics, 2011
We explore conditions for productive synthesis between formal reasoning and intuitive representations through analysis of college students' understanding of the limit concept in the definition of the derivative. In particular, we compare and contrast cognitive processes that accompany different manifestations of persistence of intuitions and tacit…
Descriptors: College Students, Mathematical Concepts, Logical Thinking, Intuition

Jansson, Lars C. – Educational Studies in Mathematics, 1974
Regression analysis was used to investigate which selected structural and linguistic variables strongly influenced the relative difficulty of preservice elementary school teachers in judging simple deductive arguments. (JP)
Descriptors: Cognitive Processes, Critical Thinking, Deduction, Logic
Which Notion of Implication Is the Right One? From Logical Considerations to a Didactic Perspective.

Durand-Guerrier, Viviane – Educational Studies in Mathematics, 2003
Summarizes Tarski's semantic truth theory to clarify different aspects of implication. Extends the classical definition of implication as a relationship between propositions to a relationship between open sentences with at least one free variable. Analyzes two problematic situations and the presentation of some experimental results from research…
Descriptors: Cognitive Processes, Higher Education, Logical Thinking, Mathematics Education
Dubinsky, Ed; Weller, Kirk; Mcdonald, Michael A.; Brown, Anne – Educational Studies in Mathematics, 2005
This paper applies APOS Theory to suggest a new explanation of how people might think about the concept of infinity. We propose cognitive explanations, and in some cases resolutions, of various dichotomies, paradoxes, and mathematical problems involving the concept of infinity. These explanations are expressed in terms of the mental mechanisms of…
Descriptors: Mathematical Concepts, Mathematics, Logical Thinking, Mathematics Education
Dubinsky, Ed; Weller, Kirk; McDonald, Michael A.; Brown, Anne – Educational Studies in Mathematics, 2005
This is Part 2 of a two-part study of how APOS theory may be used to provide cognitive explanations of how students and mathematicians might think about the concept of infinity. We discuss infinite processes, describe how the mental mechanisms of interiorization and encapsulation can be used to conceive of an infinite process as a completed…
Descriptors: Logical Thinking, Philosophy, Mathematical Concepts, History

O'Brien, Thomas C.; And Others – Educational Studies in Mathematics, 1971
An experimental study of children's confusion between if" and if and only if" statements when phrased in different language and used in different contexts (grades 4, 6, 8, and 10). (MM)
Descriptors: Abstract Reasoning, Cognitive Processes, Context Clues, Elementary School Mathematics

Duval, Raymond – Educational Studies in Mathematics, 1991
Beginning geometry students misunderstand the requirements of formal proof because of confusion between deductive reasoning and argumentation. Presented is a cognitive analysis of deductive organization versus argumentative organization of reasoning and the applications of this analysis to learning. Implications of a study analyzing students'…
Descriptors: Abstract Reasoning, Cognitive Processes, Deduction, French