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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
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Herbert, Sandra; Pierce, Robyn – Educational Studies in Mathematics, 2012
Rate (of change) is an important but complicated mathematical concept describing a ratio comparing two different numeric, measurable quantities. Research referring to students' difficulties with this concept spans more than 20 years. It suggests that problems experienced by some calculus students are likely a result of pre-existing limited or…
Descriptors: Concept Formation, Mathematical Concepts, Calculus, Comparative Analysis
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Bingolbali, Erhan; Monaghan, John – Educational Studies in Mathematics, 2008
Concept image and concept definition is an important construct in mathematics education. Its use, however, has been limited to cognitive studies. This article revisits concept image in the context of research on undergraduate students' understanding of the derivative which regards the context of learning as paramount. The literature, mainly on…
Descriptors: Undergraduate Students, Mathematics Education, Calculus, Transformations (Mathematics)
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Kleiner, Israel – Educational Studies in Mathematics, 2001
Considers examples of aspects of the infinitely small and large as they unfolded in the history of calculus from the 17th through the 20th centuries. Presents didactic observations at relevant places in the historical account. (Author/MM)
Descriptors: Calculus, Cognitive Processes, Concept Formation, Higher Education
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Benbachir, Amina; Zaki, Moncef – Educational Studies in Mathematics, 2001
Reports on a study on the construction of examples and counter-examples in a college-level calculus course. Verbal and written productions of the students were classified as one of activity, expression, content, and correctness. Finds two types of strategies, global and local. Analysis also distinguishes between "winning" and…
Descriptors: Calculus, Concept Formation, Educational Strategies, Functions (Mathematics)
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Raman, Manya – Educational Studies in Mathematics, 2003
Examines the views of proof held by university-level mathematics students and teachers. Develops a framework for characterizing people's views of proof based on a distinction between public and private aspects of proof and the key ideas that link these two domains. (Author/KHR)
Descriptors: Calculus, Cognitive Processes, Concept Formation, Epistemology
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Thompson, Patrick W. – Educational Studies in Mathematics, 1994
Discusses a teaching experiment with (n=19) senior and graduate mathematics students. Analysis suggests that students' difficulties with the Fundamental Theorem of Calculus stem from impoverished concepts of rate of change and from poorly developed and coordinated images of functional covariation and multiplicatively constructed quantities.…
Descriptors: Calculus, Cognitive Development, College Students, Concept Formation
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Tall, David; Vinner, Shlomo – Educational Studies in Mathematics, 1981
A number of general ideas intended to be helpful in analyzing differences in concept images among individuals are formulated. These ideas are applied to the specific concepts of continuity and limits, as taught in the secondary school and university. (MP)
Descriptors: Calculus, Cognitive Processes, College Mathematics, Concept Formation
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Schneider, Maggy – Educational Studies in Mathematics, 1992
Divided into two parts, this article analyzes why some pupils feel reserve about instantaneous velocities and instantaneous flows. The second part relates reactions of pupils facing a problem that implicates the instantaneous rate of change. Describes some characteristics of this problem that enables the authors to explain its instructional…
Descriptors: Calculus, Cognitive Processes, Concept Formation, Foreign Countries