On the Teaching of Linear AlgebraJ.-L. Dorier Springer Science & Business Media, 30 sep 2000 - 290 pagina's To a large extent, it lies, no doubt, in what is presented in this work under the title of ‘meta lever‘, a method which it is certainly interesting to develop and further refine. There exists in mathematics courses a strange prudery which forbids one to ask questions such as, ‹‹ Why are we doing this? », ‹‹ At what is the objective aimed? », whereas it is usually easy to reply to such questions, to keep them in mind, and to show that one can challenge these questions and modify the objectives to be more productive or more useful. If we don‘t do this we give a false impression of a gratuitous or arbitrary interpretation of a discipline whose rules are far from being unmotivated or unfounded. One must also consider the time aspect. Simple ideas take a long time to be conceived. Should we not therefore allow the students time to familiarize themselves with new notions? And must we not also recognize that this length of time is generally longer than that ofthe official length of time accorded to this teaching and that we should be counting in years? When the rudiments of linear algebra were taught at the level of the lycée (college level), the task of first year university teachers was certainly easier : for sure the student's knowledge was not very deep, however it was not negligible and it allowed them to reach a deeper understanding more quickly. |
Inhoudsopgave
vi | 3 |
THE OBSTACLE OF FORMALISM | 83 |
90 | 125 |
THE TEACHING EXPERIMENTED IN LILLE | 133 |
AN IMPORTANT METHODOLOGICAL PROBLEM | 173 |
THE CONCRETENESS PRINCIPLE | 180 |
GENERALIZIBILITY PRINCIPLE | 187 |
Language | 197 |
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abstract activity analysis analytic geometry analytic-arithmetic answer aspect Ausdehnungslehre axiomatic approach axioms basis Cabri calculation Cartesian chapter cognitive concepts context coordinate vector coordinates David Hilbert defined determinants didactical difficulties dimension Dorier elementary elements epistemological example exercises explicit Figure formula functions Gaussian method given Grassmann Hilbert idea independent intersection introduced IREM knowledge language linéaire linear algebra linear algebra course linear combination linear equations linear independence linear operator linear systems linear transformation mathematicians mathematics education matrix meaning meta Moreover n-tuples notion objects obstacle of formalism parametric equations parametric representation Paris plane point of view polynomials presented problem proof properties question rank reflection relation scalar semiosis semiotic set theory shows Sierpinska solution solving structural subspaces synthetic-geometric system of equations systems of linear teacher teaching linear algebra teaching of linear theory of vector understanding variables vector space viewpoint