PDM – Reasoning


Adults already bring with them everyday knowledge on virtually every topic, with which they are able to address and solve certain questions in their own way. If new knowledge is now imparted without reference to this everyday knowledge, there is a danger that the new knowledge will never become effective.

CENF wants to build on these previous experiences and lead the learners to a higher level in everyday mathematics. The aim is to increase the self-confidence of the learners.

This module shows a model of concrete competence based on experience and presents the instruction methods (directly/indirectly).

In order to achieve learning success, it is important to take up the everyday knowledge of the learners and to make it possible for the learners to experience how the new knowledge develops their previous knowledge. The idea of Realistic Mathematics is an instructional method that is ideally suited to achieving learning success.

Teachers reflect on the suitability of these concepts for their teaching and consider examples that they can use. They also keep an eye on the different levels of performance of the learners.

Relation to Common European Numeracy Framework

Key issues

It’s about:

  • to provide a model of effective knowledge and situational competence of adults
  • Represent different learning objectives of adults and derive appropriate teaching methods from them
  • Introduce the instruction methods direct instruction
  • Get to know the approach of Realistic Mathemtics

Suggestions for PDM meetings

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PD – Activity 1                       Reflection, discussion: “Which task is easier?”

                                                To open the subjective perspective of the teachers (prior knowledge, prior beliefs, prior experiences on the theme)

PD – Activity 2                       Mr. Miller has a job interview

To study and discuss two or more examples of how this can be addressed in a Adult Numeracy activity.Mr. Müller has a Job interview       

PD  – Activity 3                       Find your own examples and describe learning paths

                                                To design by/with teachers of one or more Adult Numeracy Activities for his/her own teaching situation, exchange results between the teachers. Discuss.Suggestions

Reflection                                Challenges for teaching?

                                                To reflect on the levels addressed in this mini-module.


Knowledge Theory

Productive Failure

Needs of learning adults

Realistic Mathematics

Self study


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de Abreu, G., Bishop, A. J. & Pompeu, G. (1997). What Children and Teachers Count as Mathematics. In: Nunes, T. & P., B.: Learning and Teaching Mathematics: An

International Perspective. Hove, Psychology Press: 233-263.

Gallin, P., & Ruf, U. (1990). Sprache und Mathematik in der Schule. Zürich: Verlag Lehrerinnen und Lehrer Schweiz.

Kees Hoogland: Realistic Numeracy problems: in Maths At Work – Mathematics in a Changing World; Proceedings of the 17th International Conference of Adults Learning Mathematics (ALM); Oslo, 28th – 30th June 2010, p 58

Kaiser, H. (2009). Bausteine für ein Rahmenkonzept zur Förderung alltagsmathematischer Kompetenz. Zürich: SVEB.

Knowledge Types – Integrated Learning Model http://www.hrkll.ch/typo/fileadmin/Texte/ILM/arten_des_wissens.pdf

Kapur, M., & Bielaczyc, K. (2012 ). Designing for Productive Failure. Journal of the Learning Sciences, 21(1), 45-83. doi: 10.1080/10508406.2011.591717

Thomas Kim, Saul Axelrod: „Direct instruction: An educators’ guide and a plea for action“. In: The Behavior Analyst Today. Band 6, Nr. 2, 2005, ISSN 1539-4352, S. 111–120.

Kolb, A. Y., & Kolb, D. A. (2009). The Learning Way: Meta-cognitive Aspects of Experiential Learning. Simulation Gaming, 40, 297-327.

Lütje-Klose, B. (2003). Didaktische Überlegungen für

Schülerinnen und Schüler mit Lernbeeinträchtigungen aus systemisch-konstruktivistischer Sicht. In: Balgo, R. & Werning, R.: Lernen und Lernprobleme im systemischen Diskurs. Dortmund, verlag modernes lernen, Borgmann: 173-204.

McCloskey, M. (1983). Intutive physics. Scientific American 248(4): 114-122.

Vergnaud, G. (1990). Epistemology and Psychology of Mathematics Education. In: Nesher, P. & Kilpatrick, J.: Mathematics and Cognition. A Research Synthesis by the

International Group for the Psychology of Mathematics Education. Cambridge MA., Cambridge University Press: 14-80.  

Reder, Stephen (2009). The Development of Literacy and Numeracy in Adult Life. In: Reder, Stephen und Bynner, J. M. (Hg.). Tracking adult literacy and numeracy:

Findings from longitudinal research. New York: Routledge, S. 59-81