Paul Drijvers, S. 139 in: DERIVE in the Dutch classroom, S. 133--146 in: Josef Böhm (Hg.), Teaching Mathematics with DERIVE (Proc. Intern. School on the Didactics of Computer Algebra, Krems 1992), Chartwell-Bratt, 1992; ISBN 91-44-37891-2:
Teachers on the other hand are fascinated by the power of the programme. So they tend to jump to abstactions that are made too fast while the handwork phase of simple examples is skipped. Students will not understand what they are doing and miss the experience to follow the abstaction. This will make mathematics very hard to do for them. In my opinion this is the main risk of the use of computer algebra: neglect of the handwork phase and abstraction made too fast and to a level that is too high.
Reinhard Schmidt, S. 89 in:
Einsatzmöglichkeiten des CAS Mathcad im
Mathematikunterricht am Gymnasium (Erfahrungen aus dem
Schulversuch CuMaU),
Tagungsband "Computeralgebra
in Lehre, Ausbildung und Weiterbildung III (Bildungshaus Kloster
Schöntal, 2. - 5. April 2002)", Fachgruppe Computeralgebra
der DMV, GAMM und GI, 2002.
Beim Einsatz eines CAS zur Lösung von Anwendungsaufgaben zeigt sich wiederum sehr deutlich, dass die Modellierung eines mathematischen Problems per Kopf und auf dem Papier vor dem "Eingeben" in den PC erfolgen muss. Sonst verselbständigt sich das Werkzeug Mathcad.
Paul Drijvers, S. 139 in: DERIVE in the Dutch classroom, S. 133--146 in: Josef Böhm (Hg.), Teaching Mathematics with DERIVE (Proc. Intern. School on the Didactics of Computer Algebra, Krems 1992), Chartwell-Bratt, 1992; ISBN 91-44-37891-2:
The students generally have a hard job to do during Derive
lessons: they have to think about mathematical problems
and at the same time about the handling of Derive, a
programme that is often not really familiar to them. So they
focus on the PC, and little energy is left for reflections.
They do not lean back to say: let us see what we are doing and
why. So here we have an important task for the teacher: to
stimulate the students to reflect, asking them questions such
as `What are you doing?', `Why do you do it?', `What are the
conclusions so far?', `What will be the next step?',
`Can you foresee the result of the next step?' and so on.
To make it more easy for students to recognize the
theme in the Derive session, it is important for the
teacher to introduce the session, to work out an example
(by hand?) and to reactivate some preliminary knowledge before the
students start to work on their own. After the session, an
overview by the teacher will be of great value.
You see that the teacher has a tough job as well: a
teaching task, a Derive trouble shooting task, an organisation
task ... .
Paul Drijvers, S. 139 in: DERIVE in the Dutch classroom, S. 133--146 in: Josef Böhm (Hg.), Teaching Mathematics with DERIVE (Proc. Intern. School on the Didactics of Computer Algebra, Krems 1992), Chartwell-Bratt, 1992; ISBN 91-44-37891-2:
Ad 1: If a problem is not relevant in the context of the
preceeding lessons, students will not be motivated.
Ad 2: If it doesn't you will loose time translating.
Ad 3: You can stimulate them to work seriously by
evaluating their written reports.
Josef Lechner, S. 159 und S. 173 in: Einsatz von Derive von der 4. - 7. Klasse AHS, S. 159--174 in: Josef Böhm (Hg.), Teaching Mathematics with DERIVE (Proc. Intern. School on the Didactics of Computer Algebra, Krems 1992), Chartwell-Bratt, 1992; ISBN 91-44-37891-2:
Die 7. Schulstufe - also 3. Klasse - dient der Einführung in den Unterrichtgegestand und dem Erwerb der notwendigen Grundkenntnisse in Maschinenschreiben und Textverarbeitung.
Das Computeralgebra-System kann aber nur dann eine wirksame Hilfe beim Operieren sein, wenn es wirklich beherrscht und bis zu einem gewissen Grad auch automatisiert wird. .. Überlegungen sind anzustellen, wie die Einführung eines solchen Systems vorbereitet werden kann und wann sie am besten erfolgt.