Plenary lecture
Interactive web-based resources and a new perspective on algebra and geometry.
Jean Flower, University of Brighton
This paper will reflect upon the use of DaC (dynamic geometry and computer
algebra software) in two contexts - two undergraduate Linear Algebra courses
taught at different UK universities. The main questions of this strand will
be considered in the light of this experience.
It is hard to compare the two linear algebra modules and claim that one was
"more successful" than the other. One covered more pure algebra topics,
whereas the other included more applications of Linear Algebra. Both used
DaC. One used Maple and JavaSketchpad, and the other used TI92's algebra
and Sketchpad on the PC. The students on one module were mainly training to
become teachers, whereas the students on the other were studying for a mix
of maths degrees, heading for business.
Is it necessary to achieve widespread use of DaC throughout a course for
best benefits? The students who had a wider exposure to Sketchpad in a
range of modules over many semesters made better use of the Linear Algebra
images than the students who were unfamiliar with DGS. How do the costs
(time as well and money) of introducing DaC in a single module compare with
the benefits?
Is it necessary to integrate DaC into assessment at the same time as its
introduction to the teaching? The students whose assessment included a
Maple test learned to use Maple mainly for the purposes of completing the
test, whereas the students with TI92s used them more widely to shortcut rote
algebra. Use of the handheld technology was not required for successful
completion of the course, but the TI92s were used more widely.
How can we tie in a DaC approach to a subject whose key texts take a more
traditional approach? There is a mismatch between the students' experience
of Linear Algebra in the classroom (and in the website) and the students'
experience of Linear Algebra from books. Does this contribute to confusion?
Can we make use of this contrast to deepen understanding of the different
facets of a subject?
The use of DaC allows for revitalisation of some "tough" topics which were
getting taught later on in a degree. Tasks which required intensive
numerical calculation can now be completed quickly, allowing more space for
understanding the results of the calculation. The use of technology itself
can provide relevant applications for study (eg. computer graphics).
Different approaches to proof and argument contrasts axiomatics (a
traditional way in to Linear Algebra) with investigation (assisted by DaC).
What is the relationship between working on the computer and working with
paper and pencil? This question is critical when introducing DaC into
courses which maintain traditional assessment strategies like exams, where
students may not have access to DaC.
Looking at the changing nature of algebra and geometry is like trying to
gaze into a crystal ball. But we can have some fun looking there.
Back to strand 5
| 
The Fifth International
Conference on Technology
in Mathematics Teaching
