On the Teaching of Linear Algebra

Voorkant
J.-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.
 

Wat mensen zeggen - Een review schrijven

We hebben geen reviews gevonden op de gebruikelijke plaatsen.

Inhoudsopgave

vi
19
TOWARDS A FORMAL AXIOMATIC THEORY
30
viii
36
CONCLUSION
59
REFERENCES PART I
73
TEACHING AND LEARNING ISSUES
79
THE OBSTACLE STILL
103
Equation ofa Geometric Object
111
NOTES
149
AN EXAMPLE OF THE USE OF META FOR TEACHING
163
THREE PRINCIPLES OF LEARNING AND TEACHING
177
THE NECESSITYPRINCIPLE
185
THE PROBLEM OFREPRESENTATIONS
199
APPLICABLITY OF THE GENERAL THEORY
205
NOTES
246
PRESENTATION OF OTHER RESEARCH WORKS
247

ANNEX MATHEMATICAL SOLUTION OF THE HYPERPLANES
123
CONCEPTUALIZATION
131
Primary Importance
135
Linear Algebra
143
NOTES
264
CONCLUSION
273
INDEX
281
Copyright

Overige edities - Alles weergeven

Veelvoorkomende woorden en zinsdelen

Bibliografische gegevens