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Download full textTall, David – Mathematics Education Research Journal, 2008
This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…
Descriptors: Mathematical Logic, Mathematics Instruction, Mathematical Concepts, College Mathematics
Peer reviewedTall, David – Educational Studies in Mathematics, 1980
A concept of infinity is described which extrapolates the measuring rather than counting aspects of number. Various theorems are proved in detail to show that "false" properties of infinity in a cardinal sense are "true" in a measuring sense. (MP)
Descriptors: College Mathematics, Learning Theories, Mathematical Concepts, Mathematics Education
Peer reviewedTall, David – Mathematics in School, 1981
Cardinal infinities, the superrational numbers, and intuitions of infinity in limiting processes are discussed. (MP)
Descriptors: College Mathematics, Higher Education, Mathematical Concepts, Mathematical Enrichment
Peer reviewedTall, 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
Existence Statements and Constructions in Mathematics and Some Consequences to Mathematics Teaching.
Peer reviewedVinner, Shlomo; Tall, David – American Mathematical Monthly, 1982
Discussed are the: (1) Notion of Mathematical Objects and the Realist Approach; (2) Psychological Need for Mathematical Realities, A Psychological Point of View; (3) Formalist Approach; (4) Meaning of Mathematical Existence; (5) Relative versus Absolute Existence; (6) Psychological Need for Mathematical Realities and the Offer of Mathematics; and…
Descriptors: College Mathematics, Higher Education, Mathematical Concepts, Mathematics Curriculum
Giraldo, Victor; Carvalho, Luiz Mariano; Tall, David – International Group for the Psychology of Mathematics Education, 2003
In this paper, we discuss the (potentially positive) pedagogical role of intrinsic limitations of computational descriptions for mathematical concepts, with special focus on the concept of derivative. Our claim is that, in a suitable approach, those limitations can act for the enrichment of learners' concept images. We report a case study with a…
Descriptors: Undergraduate Students, Foreign Countries, Educational Technology, Mathematical Concepts
