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 14th SEFI MWG seminar joint with IMA (eds. B. Alpers et al.), Loughborough 2008, available as download: here

(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 14th 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 14th SEFI MWG seminar joint with IMA (eds. B. Alpers et al.), Loughborough 2008, available as download: here

(accessed 10 March 2010)

 

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

(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: London, pp. 34-48.

 

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, Boston, MA.

Available as download: here

(accessed 10 March 2010)