**Use of Technology**

Advances in information and communication technologies have created many new
possibilities in teaching. Computer visualisations and modelling, computational
capacity of available computer algebra systems and rapidly expanding applications
of mathematical models in many different areas, technical sciences in particular
have consequently influenced mathematical education and have led to a new specific
character of teaching mathematics. Accumulation of the necessary mathematical
knowledge of an engineer has to be performed consistently and in various ways,
by using computers from the very first year of the engineering study. However,
using computers for solving non-elementary mathematical tasks, a deep mathematical
understanding is required.

How to settle the proper proportion balancing the usage of traditional methods
and ICT remains as an everlasting topic for discussions.

There exist many ways how ICT can be utilised in maths education:

• Direct methods - usage in educational process and assessments

• CAS as powerful demonstration tool for lecturer

• CAS for exploring and calculations during maths lessons

• Pocket / graphing calculators

• CAS utilised by students in solving mathematical problems and projects

• E-learning solutions for maths courses

• Computer based assessment

• Indirect methods – additional study resources for self-study and evaluation

• On-line maths courses

• On-line maths databases with electronic resources

• Mathematics support centres

• Usage of web-based materials

• Tutorials by e-mails

• Maths chats on Internet

Adapting the maths educational process
to new ICT environment one must be aware of the risk that this computer-based
learning environment may cause an unexpected
transmission of the bases of “traditional mathematical culture”.
This is not just an efficient mathematical practise supported by currently
available computational tools, but rather a stable amount of core mathematical
knowledge
and ideas, having a strong impact on the overall reasoning, that was always
considered by engineers as natural.

References in the following list comprise some examples of CAS usage in teaching
particular mathematical topics:

• Ideas on how to teach basic concepts of linear algebra to secondary students
using graphing calculator are presented in Verweij (2004).

• The special facilities provided by the computers need new approaches
in teaching mathematical subjects. In some topics computer animation can
greatly increase
the effectiveness of the teaching process. This is especially true in the
theory of differential equations. A short survey on a method applied in the
training of engineers in this field can be seen in Kocsis (2008), where animation
is
used to visualise the dependence of the differential equation solution function
on
settled parameters.

• Teaching and learning Calculus I in a computer algebra supported system
is discussed
in Kovacheva (2008).

•
Notes on how to teach multivariable calculus with understanding and demonstrations
using CASs as visualisation tools see in Velichová (2008).

Computers nowadays play an important role not only as a calculation engine and visualization tool, but also as a communication media and virtual environment. Usage of ICT, e-learning instructional resources and Internet as communication tool in teaching and learning mathematics has been the main topic of several SEFI MWG seminars and has been discussed in many contributions. The latest development shows increasing demand on complex solutions, while in addition to the traditional university study programme schemes with settled contact hours, an additional mathematical support is provided to students via Centres of Mathematics, accessible both virtually and in present form.

Some ideas and solutions are given in the following list of relevant references and links for further study:

•
Creation of mathematical support centre and comments on provided suport to students
and its effectiveness is described in Lawson, D. at all (2006)). See also Symonds
at all (2008) and Ní Fhloinn (2008).

• On exploiting new communication technologies and media in mathematical
support
see Goodband (2008), Rodriguez, de la Villa (2008).

•
Usage of computer exercises as an effective solution in Polcerová (2006).

• General strategies for ICT environment in teaching and learning mathematics
can
be found in Lampret (2004), Sikk (2004), Alpers (2006) and Heinrich
(2006).

Integrating technology into mathematical education of engineers was also
a topic for discussion groups at the MWG seminar in 2006 for
which there is a special
report.

Using computers for assessment still remains a rather questionable
and risky idea:

• A proposal for a combination of an open source learning platform together
with
an open source computer algebra system for generation of custom-made
exercises by CAS-script assessing the answers is given in Risse (2008).

• Analysis of the usage of interactive online mathematics testing and teaching
system for the first year students can be found in Lehtonen (2008).

Some investigations have also been carried on in connection to the students´ approach, reactions and their attitude to the utilisation of new technologies. There is strong evidence that students enjoy well designed web-based learning resources, anyhow ill-considered computer aided teaching and assessment may produce frustration and anxiety. Role of teacher as seems to be evident:

•
Feedback from students and their opinion to the on-line Pilot course in Differential
and Integral Calculus is analysed in Velichová et al.
(2004).

•
Evaluation of students´ reaction to the project on utilising graphing
calculators in teaching linear algebra at secondary schools can
be found in Verweij (2004).

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**Links and literature**

*Contributions to SEFI MWG seminars:*

Kleiza, V., Purvinis, O. (2004) Teaching of Mathematics and Mathematical Modelling Using Computer Applications, Proc. of the 12th SEFI MWG seminar (eds. M. Demlova, D. Lawson), Vienna 2004, pp. 77-85, available as download here (accessed 7 February 2009)

Lampret, V. (2004) Understanding of Mathematics is Prerequisite for Efficient Use of Computers, Proc. of the 12th SEFI MWG seminar (eds. M. Demlova, D. Lawson), Vienna 2004, pp. 86-94, available as download here (accessed 7 February 2009)

Norstein, A., Velichová, D., de la Villa, A. (2004) Maths on the Web: Do Students Prefer Computers and E-learning or Do They Stick to Their Teachers?, Proc. of the 12th SEFI MWG seminar (eds. M. Demlova, D. Lawson), Vienna 2004, pp. 118-126, available as download here (accessed 7 February 2009)

Sikk, J. (2004) Calculus for Engineers: A Conceptual Modelling Paradigm, Proc. of the 12th SEFI MWG seminar (eds. M. Demlova, D. Lawson), Vienna 2004, pp. 141-147, available as download here (accessed 7 February 2009)

Verweij, A. (2004) The Graphing Calculator and Linear Algebra, Proc. of the 12th SEFI MWG seminar (eds. M. Demlova, D. Lawson), Vienna 2004, pp. 148-154, available as download here (accessed 7 February 2009)

Alpers, B. (2006) The Mathematical Expertise of Mechanical Engineers, Proc. of the 13th SEFI MWG seminar (eds. M. Demlova, D. Lawson), Kongsberg 2006, pp. 148-154, available as download here (accessed 7 February 2009)

Heinrich, E. (2006) A New and Easy Access to Computer Algebra, Proc. of the 13th SEFI MWG seminar (eds. M. Demlova, D. Lawson), Kongsberg 2006, pp. 18-19, available as download here (accessed 7 February 2009)

Lawson, D. et al. (2006) Developments in Mathematics Support in the United Kingdom, Proc. of the 13th SEFI MWG seminar (eds. M. Demlova, D. Lawson), Kongsberg 2006, pp. 20-28, available as download here (accessed 7 February 2009)

Polcerová, M. (2006) Computer Exercises in Teaching Mathematics, Proc. of the 13th SEFI MWG seminar (eds. M. Demlova, D. Lawson), Kongsberg 2006, pp. 38-41, available as download here (accessed 7 February 2009)

Alpers, B. (2006) Discussion on Integrating Technology into the Mathematical Education of Engineers, Proc. of the 13th SEFI MWG seminar (eds. M. Demlova, D. Lawson), Kongsberg 2006, pp. 65-67, available as download here (accessed 7 February 2009)

Goodband, J. at all (2008) Exploiting new technologies in mathematics support, Proc. of the 14th SEFI MWG seminar (eds. M. Demlova, D. Lawson), Loughborough 2008, pp. 65-67, available as download (accessed 7 February 2009)

Kocsis, I. (2008) Using a computer-animated graphical approach to teaching differential equations, Proc. of the 14th SEFI MWG seminar (eds. M. Demlova, D. Lawson), Loughborough 2008, available as download (accessed 7 February 2009)

Kovacheva, T. (2008) Computer Algebra System Supported Environment for Teaching and Learning Calculus I, Proc. of the 14th SEFI MWG seminar (eds. M. Demlova, D. Lawson), Loughborough 2008, available as download (accessed 7 February 2009)

Lehtonen, K. (2008) Testing and Teaching Mathematics with Interactive Online Technology, Proc. of the 14th SEFI MWG seminar (eds. M. Demlova, D. Lawson), Loughborough 2008, available as download (accessed 7 February 2009)

Ní Fhloinn, E. (2008) Supporting Engineering Students within a Maths Learning Centre Environment, Proc. of the 14th SEFI MWG seminar (eds. M. Demlova, D. Lawson), Loughborough 2008, available as download (accessed 7 February 2009)

Risse, T. (2008) A Poor Mans TA – Testing and Assessing Mathematical Skills by CAS-Scripts, Proc. of the 14th SEFI MWG seminar (eds. M. Demlova, D. Lawson), Loughborough 2008, available as download (accessed 7 February 2009)

Rodriguez, G., de la Villa, A. (2008) E-materials, E and B learning: a practical approach, Proc. of the 14th SEFI MWG seminar (eds. M. Demlova, D. Lawson), Loughborough 2008, available as download (accessed 7 February 2009)

Symonds, R., Lawson, D., Robinson, C. (2008) Promoting Student Engagement with Mathematics Support, Proc. of the 14th SEFI MWG seminar (eds. M. Demlova, D. Lawson), Loughborough 2008, available as download (accessed 7 February 2009)

Velichová, D. (2008) Multivariable Calculus with Understanding and How to Assess It, Proc. of the 14th SEFI MWG seminar (eds. M. Demlova, D. Lawson), Loughborough 2008, available as download (accessed 7 February 2009)

*Other relevant contributions:*

Sárvári, C. (2003) Network Based Maths Teaching Using CAS, In ZDM – The nternational Journal on Mathematics Education available from Springer-Verlag, available as download (accessed 10 March 2010) http://subs.emis.de/journals/ZDM/zdm032a5.pdf

Yorke, P. Mathematics teaching with
Computer Algebra, Spreadsheets and Graphing Calculators, available as download
(accessed10 March 2010)

http://www.mcs.surrey.ac.uk/Personal/R.Knott/compAlgGraphCalc.html