Modelling and Applications in Mathematics Education: The 14th ICMI Study

Peter L. Galbraith, Hans-Wolfgang Henn, Mogens Niss
Springer Science & Business Media, 5. des. 2007 - 523 sider
Among the themes that have been central to mathematics education dur ing the last 30 years are those of mathematical modelling and applications of mathematics to extra-mathematical fields. More generally we refer to these as relations between mathematics and the extra-mathematical world (some times also called the "real world") or preferably, according to Henry PoUak, the "rest of the world". That applications and modelling have been important themes in mathematics education can be inferred from the wealth of litera ture on these topics, including material generated from a multitude of na tional and international conferences. In particular let us mention firstly the ICMEs (the International Congresses on Mathematical Education), with their regular working or topic groups and lectures on applications and modelling; and secondly the series of ICTMAs (the International Conferences on the Teaching of Mathematical Modelling and Applications) which have been held biennially since 1983. Their Proceedings and Survey Lectures, have addressed the state-of-the-art at the relevant time, and contain many exam ples, studies, conceptual contributions and resources involving relations between the real world and mathematics, for all levels of the educational system. In curricula and textbooks we find today many more references to real world phenomena and problems than, say, twenty years ago.

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Modelling pedagogy overview
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Side 58 - Inquiry is the controlled or directed transformation of an indeterminate situation into one that is so determinate in its constituent distinctions and relations as to convert the elements of the original situation into a unified whole.
Side 378 - For many parts of nature can neither be invented with sufficient subtilty, nor demonstrated with sufficient perspicuity, nor accommodated unto use with sufficient dexterity, without the aid and intervening of the Mathematics; of which sort are perspective, music, astronomy, cosmography, archite^ture, enginery, and divers others.
Side 378 - Mathematics nrr cither pure or mixed. To the pure mathematics are those sciences belonging which handle quantity determinate, merely severed from any axioms of natural philosophy ; and these are two, Geometry, and Arithmetic j the one handling quantity continued, and the other dissevered.
Side xii - mathematical literacy" as an individual's capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgments, and to use and engage with mathematics in ways that meet the needs of that individual's life as a constructive, concerned, and reflective citizen.
Side 98 - Realistic considerations in mathematical modelling of school arithmetic word problems. Learning and Instruction, 4, 273-294. Verschaffel, L., De Corte, E., Lasure, S., Van Vaerenbergh, G., Bogaerts, H., & Ratinckx, E. (1999). Learning to solve mathematical application problems: A design experiment with fifth graders. Mathematical Thinking and Learning, I, 195-229.
Side 94 - When a teacher discovers that he or she is a politician, too, the teacher has to ask, What kind of politics am I doing in the classroom?
Side 91 - Schoenfeld (1991, p. 340): . . . such behavior is sense-making of the deepest kind. In the context of schooling, such behavior represents the construction of a set of behaviors that results in praise for good performance, minimal conflict, fitting in socially etc. What could be more sensible than that? Students...
Side 91 - This flask is being filled from a tap at a constant rate. If the depth of the water is 4 cm after 10 seconds, how deep will it be after 30 seconds?
Side 135 - Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work.
Side 98 - Verschaffel, L, De Corte, E., & Borghart, I. (1997). Pre-service teachers' conceptions and beliefs about the role of real-world knowledge in mathematical modelling of school word problems. Learning and Instruction, 4, 339-359.

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