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Heather Lynn Johnson; Courtney Donovan; Robert Knurek; Kristin A. Whitmore; Livvia Bechtold – Educational Studies in Mathematics, 2024
Using a mixed methods approach, we explore a relationship between students' graph reasoning and graph selection via a fully online assessment. Our population includes 673 students enrolled in college algebra, an introductory undergraduate mathematics course, across four U.S. postsecondary institutions. The assessment is accessible on computers,…
Descriptors: Models, Graphs, Cognitive Processes, Abstract Reasoning
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
Blanton, Maria; Isler-Baykal, Isil; Stroud, Rena; Stephens, Ana; Knuth, Eric; Gardiner, Angela Murphy – Educational Studies in Mathematics, 2019
We share here results from a quasi-experimental study that examines growth in students' algebraic thinking practices of generalizing and representing generalizations, particularly with variable notation, as a result of an early algebra instructional sequence implemented across grades 3--5. Analyses showed that, while there were no significant…
Descriptors: Elementary School Students, Grade 3, Grade 4, Grade 5
Louie, Nicole L. – Educational Studies in Mathematics, 2018
This paper responds to the burgeoning literature on mathematics teacher noticing, arguing that its cognitive orientation misses the cultural and ideological dimensions of what and how teachers notice. The author highlights Goodwin's concept of "professional vision" as a way of bringing analyses of culture and power into studies of…
Descriptors: Mathematics Teachers, Mathematics Instruction, Teaching Methods, Perception
Hitt, Fernando; Saboya, Mireille; Zavala, Carlos Cortés – Educational Studies in Mathematics, 2017
Part of the research community that has followed the Early Algebra paradigm is currently delimiting the differences between arithmetic thinking and algebraic thinking. This trend could prevent new research approaches to the problem of learning algebra, hiding the importance of considering an arithmetico-algebraic thinking, a new approach which…
Descriptors: Arithmetic, Algebra, Educational Technology, Thinking Skills
Martínez-Sierra, Gustavo; García-González, María del Socorro – Educational Studies in Mathematics, 2016
Little is known about students' emotions in the field of Mathematics Education that go beyond students' emotions in problem solving. To start filling this gap this qualitative research has the aim to identify emotional experiences of undergraduate mathematics students in Linear Algebra courses. In order to obtain data, retrospective focus group…
Descriptors: Mathematics Education, Emotional Response, Algebra, College Mathematics
Magiera, Marta T.; van den Kieboom, Leigh A.; Moyer, John C. – Educational Studies in Mathematics, 2013
Using algebraic habits of mind as a framework, and focusing on thinking about functions and how they work, we examined the relationship between 18 pre-service middle school teachers' ability to use the features of the algebraic thinking (AT) habit of mind "Building Rules to Represent Functions" and their ability to recognize and…
Descriptors: Algebra, Mathematical Logic, Mathematics Instruction, Middle School Teachers
Leron, Uri; Hazzan, Orit – Educational Studies in Mathematics, 2009
This article is an attempt to place mathematical thinking in the context of more general theories of human cognition. We describe and compare four perspectives--mathematics, mathematics education, cognitive psychology, and evolutionary psychology--each offering a different view on mathematical thinking and learning and, in particular, on the…
Descriptors: Mathematics Education, Cognitive Psychology, Misconceptions, Mathematics Instruction
Nemirovsky, Ricardo; Ferrara, Francesca – Educational Studies in Mathematics, 2009
The goal of this paper is to explore qualities of mathematical imagination in light of a classroom episode. It is based on the analysis of a classroom interaction in a high school Algebra class. We examine a sequence of nine utterances enacted by one of the students whom we call Carlene. Through these utterances Carlene illustrates, in our view,…
Descriptors: Imagination, Interaction, Cognitive Processes, Algebra

Demby, Agnieszka – Educational Studies in Mathematics, 1997
Investigates different types of procedures used by students (N=108) to simplify certain algebraic expressions. Findings indicate seven types of procedures including automatization, formulas, guessing-substituting, preparatory modification, concretization, rules, and quasi-rules. Contains 30 references. (JRH)
Descriptors: Algebra, Cognitive Processes, Elementary Secondary Education, Foreign Countries

Graham, Alan T.; Thomas, Michael O. J. – Educational Studies in Mathematics, 2000
Presents a study using a module of work based on a graphing calculator that provided an environment where students could experience some aspects of variables and begin to build an understanding of them. Graphing calculators proved to be an instrument for achieving significant improvement in student understanding, which had often proved difficult…
Descriptors: Algebra, Cognitive Processes, Graphing Calculators, Mathematics Instruction

Gallardo, Aurora – Educational Studies in Mathematics, 2002
Analyzes from an historical perspective the extension of the natural-number domain to integers in students' transition from arithmetic to algebra in the context of word problems. Extracts four levels of acceptance of these numbers--subtrahend, relative number, isolated number and formal negative number--from historical texts. The first three…
Descriptors: Algebra, Arithmetic, Cognitive Processes, Concept Formation

Zaslavsky, Orit; Sela, Hagit; Leron, Uri – Educational Studies in Mathematics, 2002
Presents evidence that there exists much confusion regarding the connection between the algebraic and geometric aspects of slope, scale, and angle. Participants responded to a simple but non-standard task concerning the behavior of slope under a non-homogeneous change of scale. Analysis of the responses reveals two main approaches termed…
Descriptors: Algebra, Cognitive Processes, Cognitive Restructuring, Concept Formation

Noss, Richard – Educational Studies in Mathematics, 1986
This study, part of a longitudinal investigation, examined the kinds of thinking which children aged 10 and 11 could carry over from Logo instruction to an algebraic context. Interviews focused on their ability to construct meaningful symbolization for the concept of variable and to construct formalized algebraic rules. (MNS)
Descriptors: Algebra, Cognitive Processes, Computer Oriented Programs, Educational Research

Tall, David; Thomas, Michael – Educational Studies in Mathematics, 1991
Presents computer approach formulated within a framework of versatile thinking designed to overcome obstacles to understanding algebra. Results from related studies comparing the computer and traditional approaches taught to 11, 12, and 13 year olds showed that the computer approach significantly improved the understanding of higher order concepts…
Descriptors: Algebra, Cognitive Development, Cognitive Dissonance, Cognitive Processes