Many international studies accentuate that the use of technology encourages
a student-centered and autonomous work in class.
The technologies offer the opportunity that students work independently
on computers, explore mathematical objects and relations and solve different
problems autonomously. This will succeed, if every student has his/her own
access to a computer. Then the learners can work alone, in pairs and also
in the plenary. When the social set in class fits very well, you will reach
the best results to activate the learners and spend much more effectively
study time than in the traditional teacher-centered classroom interaction.
While solving the task all students are required to work actively. Each
student has the opportunity to pursue his/her own ideas, to try it out and
then to share it in class.
Furthermore, working alone and in pairs take away the fear of being exposed
in class. In addition to that, the students work autonomously and they can
take time as much as they need to understand the given task. An exchange
of ideas is taking place. "I did it this way and how did you do it?" Such
a student interaction, where learners discuss in a lively way, provides
a networked knowledge, which is more flexible and sustainable.
Some references:
- Heid, M. Kathleen; Blume, Glendon W. (2008c). Technology and the Teaching and Learning
of Mathematics. In: M. Kathleen Heid und Glendon W. Blume (Hg.): Research on Technology
and the Teaching and Learning of Mathematics: Syntheses, Cases, and Perspectives. Re67
search Syntheses. 2 Bände. Charlotte, North Carolina: National Council of Teachers of
Mathematics (NCTM) (1), S. 419-431.
- Barzel, Bärbel (2007): "New technology? New ways of teaching - No time left for that!". In:
International Journal for Technology in Mathematics Education 14 (2), S. 77-86.
- Neill, Alex (2009): Key Findings From the CAS Pilot Programme. In: The New Zealand Mathematics
Magazine 46 (1), S. 14-27.
The TI-Nspire™ and the program GeoGebra present so-called multi-representational
systems, because they incorporate spreadsheets, geometry software, plotting
graphs and partly also computer algebra.
The interaction between the different forms of representation is very profitable.
The learners can discover connections between the different representations
and learn in a networked way and get different perspectives on the same
problem.
As a result, various approaches are supported, so one student may choose
a more algebraic way (by using the CAS- tool) and the other student a more
constructive way or a third a numerical way. The different types of learners
in a class can be addressed by using their individual approaches. The changing
between the different types of mathematical representations is considered
to be essential for the development of mathematical concepts.
Please consider the aspect about Multiple Representations in Module 5.
Some references:
- Kaput, J. (1992).Technology and mathematics education.In D. Grouws (ed.),
Handbook of research on mathematics teaching und learning (pp. 515-556).NewYork: Macmillan.
- Zbiek, R.; Heid, K.; Blume, G.; Dick, Th. (2007): Research on Technology in Mathematics Education - A Perspective of Constructs.
In F. Lester (ed.), Second handbook of research on mathematics teaching and learning (pp. 1169-1207). Charlotte, NC: Information Age.
- Duval, R. (2006).A cognitive analysis of problems of comprehension in a learning of mathematics.
Educational Studies in Mathematics, 61, 103-131.) .
- Ainsworth, S. E. Bibby, P.A., Wood, D. J. (1998). Analyzing the costs and benefits of multi-representational learning environment.
In: M. W. van Someren, P. Reimann, H.P.a. Boshuizen& T. de Jog (Eds.),. Learning with Multiple Representations, 120-134
In this example you can see
how with the help of technology we can provide rich instructions
to students. On the left side there is a screencast with precise instructions and on the right
side, there is an applet where students work [they follow the left side instructions].
The majority of resources provided in Module 1 can be used in such way.
As we need as much screen width as possible, the link above opens in a
new window.