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CAYEN Final Report 

Alternate Title





University Of Education of Freiburg 


Matthias Zeller, Bärbel Barzel, Paul Drijvers 




University of Education 


Institute for Mathematics  


Freiburg, Germany 


Results on Learning of Algebra from the CAYEN project
1. In lessons using the black-box-approach (in which the equation is unknown), CAS pupils who were taught with an emphasis on math principles mastered new challenges in algebra well and were able to work independently. 
2. Use of CAS makes it possible to get an overview of a topic at the beginning, simply by trying out new commands. Thus, with CAS it is easily possible to learn many aspects of a mathematical topic in parallel.
3. In our analysis of pupils’ written comparisons of graphic, numeric and symbolic representations, in the CAS-group we noticed many positive comments about advantages of algebra. An effect was that they were more motivated to use algebra and inserted it more often in open tasks.
4. CAS pupils master the transition from arithmetic to algebra more easily.
CAS students accept the output of the calculator as a common means of expression and realize the relevance of algebra. Furthermore, early in the curriculum they perceive the versatility of algebraic work in contrast to arithmetic approaches. By using CAS the pupils learned many commands and algebraic transformations; it did not matter that they could not do them all in a technology-free way. By contrast, GC-pupils sometimes had difficulties in accepting that the same underlying rules are valid in algebra and arithmetic. They argued that their calculators should be able to handle expressions with variables, if the same rules would be valid.
5. CAS-pupils’ argumentation concerning algebra included more mathematical arguments and was more objective than the argumentation of the GC-pupils.
6. We observed that the thoughts of pupils using CAS were on a high algebraic level and included reference to many concepts.




TI-Nspire, CAS, Germany, Algebra 

Document Content

General claims
These are general claims about benefits of CAS, drawn from the project literature review.  The CAYEN study provides some kinds of confirming evidence for many of them.
1 CAS supports the development of conceptual knowledge.
2 Technology-independent math competencies may still be acquired when using CAS.
3. The use of mathematical language is activated by use of CAS
4. Technical skills (of using CAS) complement mathematical competencies meaningfully in the sense of instrumental knowledge.
5. CAS supports a unified and principle-based treatment of mathematical topics (as opposed to the common tendency to teach math topics in a highly fragmented way).
6. CAS supports the integration of open-ended tasks and the use of multiple individual ways of solving them.
7. Use of CAS can help teachers to use more student-centered methods. The lessons can be more flexible, allowing students to be more self-directed.  This frees the teacher to give more attention to individual students.  However, at the beginning, these new lesson types require more preparation effort.
Created at 4/5/2012 9:38 AM  by SP017\rfoshay 
Last modified at 4/5/2012 9:38 AM  by SP017\rfoshay