**Activation of learners**

Activation of learners includes all teaching and learning arrangements
that support the active involvement of learners in the mathematical learning
process. It intends to achieve a sustained development of mathematical
qualifications. In contrast, “non-active” learners display a behaviour which is
more or less restricted to copying presented chunks of knowledge and rote
memorization of definitions and procedures which are forgotten very quickly.

Forms of active involvement include:

- active
listening and processing, asking questions
- relating new
information to existing knowledge
- using all
senses when processing information
- applying
mathematical concepts and techniques in exercises
- experimenting
with (or exploring) mathematical concepts using technology
- applying
knowledge to situations and in projects, acquiring information, setting up
or using mathematical models, interpreting mathematical results and
judging on applicability
- discussing
mathematical issues with other students
- writing reports
with mathematical content

Activation then means to arrange learning in a way that motivates and
requires students to perform such activities and supports them in the process
of doing so by giving guidance and feedback.

Several measures for activation have been proposed. The following list
comprises some examples and gives references to relevant MWG seminar
contributions and other literature and links for further study:

- So-called
concept tests (for short: concepTests) can be included in ordinary
lectures (see Loman&Robinson 2004). These are conceptual multiple
choice questions on which the audience of a lecture can vote. The voting
is taken as a starting point for initiating further discussion. There are
different forms of voting (e.g. with personal identification or
anonymously) and also the technical support varies (from simple cards to
electronic voting systems, see King et al. (2008)).
- Creation of
motivation by demonstrating the relevance for future studies or
professional life and supporting the active information processing by
relating new information to already known concepts (Gavalcova 2008). See
also the SONG approach by Challis&Gretton (2008) on supporting
sustained knowledge by using several senses using different
representations of mathematical concepts and procedures which also include
bodily enactment.
- On the usage
of games in mathematics lectures see Rossiter (2008).
- For
references on experimenting with mathematics using technology see the page
on technology on this web site.
- For
references on using mathematical application projects to activate students
see the page on projects on this web site. Projects but also smaller
activities often include the usage of models and modelling techniques. For
this topic, there is also a dedicated page on this web site.
- Further
strategies for active engagement of students are discussed in Afzal et al.
(2002).

Active learning was also a topic for discussion groups at the MWG
seminar in 2008 for which there is a special
report.

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**Links and literature**

*Contributions to SEFI MWG seminars:*

Booth, S. (2004) Learning and Teaching for Understanding Mathematics, Proc. of the 12th SEFI MWG seminar (eds. M. Demlova, D. Lawson), Vienna 2004, pp. 12-25, available as download here (accessed 2 February 2009)

Gavalcova, T. (2008) On Strategies contributing to active learning,
Proc. of the 14^{th} SEFI MWG seminar joint with IMA (eds. B. Alpers
et al.), Loughborough 2008, available as download:

(accessed 10 March 2010)

King, S.O., Davis, L., Robinson, C.L., Ward, J.P. (2008) Use of Voting
Systems in Lectures at Loughborough University – A Review of Staff Experiences,
Proc. of the 14^{th} SEFI MWG seminar joint with IMA (eds. B. Alpers
et
al.), Loughborough 2008, available as download: here

(accessed 10 March 2010)

Challis, N. & Gretton, H. (2008) Using the SONG approach to teaching
mathematics, Proc. of the 14^{th} SEFI MWG seminar joint with IMA (eds.
B. Alpers et al.), Loughborough 2008, available as download:

(accessed 10 March 2010)

Rossiter, A. (2008) Using games in mathematics teaching, Proc. of the 14^{th} SEFI MWG seminar
joint with IMA (eds. B. Alpers et al.), Loughborough 2008, available as
download:

(accessed 10 March 2010)

*Other relevant contributions:*

Lomen, D. & Robinson, M (2004) Using ConcepTests in Single and Multivariable
Calculus, "Proceedings of the 16th Annual International Conference on
Technology in Collegiate Mathematics." Addison Wesley, available
as download:

http://math.arizona.edu/~lomen/Using%20ConcepTests%20in%20Single%20andMultivariable%20Calculus.pdf

(accessed 8 September 2008)

Ahmed, A., Holton, D., Honor, W. (2002) Developing active learners, in:
“Effective learning & teaching in Mathematics & its applications” (Eds.
Kahn, P. & Kyle, J.), Kogan Page:

Hall, S.R., Waitz, I., Brodeur, D.R., Soderholm, D.H. & Nasr, R.
(2002) Adoption of active learning in a lecture-based engineering class, Paper
presented at the ASEE/IEEE Frontiers in Education Conference,

Available as download:

(accessed
10 March 2010)