Session Overview
Session
CADG Tools I/II: CADG Tools, Teaching and Learning (working group)
Time:
Friday, 26/Sep/2014:
11:00am - 1:00pm

Session Chair: Matija Lokar
Location: VSP 1.03
Von-Seckendorff-Platz 1 Room 1.03

Presentations

Lessons Learned In Course »Computer Tools In Mathematics«

Matija Lokar

University of Ljubljana, Slovenia

In first cycle professional study program Practical Mathematics at Faculty of mathematics and physics, University of Ljubljana, we have a course entitled Computer tools in mathematics. The main aim of this course is to show the students the practical usage of various tools in solving mathematical problems. There were several decisions we had to make during lectures preparation. In the talk we will discuss some of them:

• One tool covering all aspects of teaching and learning mathematics, or many "smaller" tools

Some teachers claim it is best to stay in the same environment all the time. However, is that really the case? Aren’t smaller tools often more flexible and versatile?

• How powerful should tools be when they are considered teaching tools

Should tools capability be limited to the level of math knowledge of the students? On the other hand, should the students be exposed to “real life” tools without limitations?

• Support materials development and usage

We will discuss our approach producing GeoGebra Wiki (http://lokar.fmf.uni-lj.si/wikiji/GeoGebraWiki).

• Relation between “mathematical answer” and result obtained from computer tool – some practical examples how students internalize the notion of “correct result” when working in different environments with different tools will be given

• Openness of construction process

One of the task for students is also to prepare detailed explanation of approach in solving a certain mathematical problem, we observed several problems students have. Besides the obvious ones like the difficulties in using appropriate mathematical language, there are also “technical” ones in usage of tools.

Lokar-CADGME2014-165_a.pdf
Lokar-CADGME2014-165_b.pdf

An approach to the study of systems of equations with GeoGebra: learning opportunities provided by the integration of CAS view

Fernando Jorge Bifano, Alejandra Almiron, Leonardo José Lupinacci

UNSAM, Argentine Republic

Solve systems of equations in school -at least in Argentina- is usually a task for students is presented in a series of techniques that "allow” find your solution. Generally, these techniques work as an end in themselves. Finally and as a strategy of “verification" tends to give a “new resolution method”: graph.

How to overcome educational obstacles that are generated from a fragmented approach of knowledge? What can make the DGS, in particular the CAS environment? What epistemic and instrumental value (Artigue 2002) acquires the techniques work with software? Redefine work with pencil and paper?

These and other questions will try to provide theoretical elements for didactic reflection on the potential guarding technologies for teaching mathematics. Specifically, this paper attempts to examine a series of dynamic problems (Bifano & Villella, 2012) to study the intersection of manipulating different parts of the same equations and reflections that have emerged from experience working with teachers to solve and analyze such problems.

Search the conditions for a system of equations has solution engage students into an exploration´s work and the establishment of guesses to try and find the answer. The multiple connections that enable the integration of GeoGebra different views (Hohenwarter & Jones, 2007), it contains a teaching which enables other potential opportunities for reflection on the nature of mathematical work.

Moreover, the inclusion of an artifact in class -computer - produced changes in both the types of problems that can be proposed, such as the type of classroom management that this requires (Balacheff, 1997). In this sense, the contributions of Trouche (2004) on the processes of instrumental genesis can guide the discussion about the different instrumental genesis that shaped the class.
Bifano-CADGME2014-129_b.pdf