PDM – Analysing situations


In order to present life-world-related requirements in everyday mathematics, it makes sense to first form and visualize a model. Students move in several worlds in everyday mathematical situations. The CENF model expresses this fact very well. Only arithmetic leads to learning difficulties.

Modeling is a teaching method that helps learners to analyse an everyday situation and make their own assumptions visible, communicable and correctable. Based on this, mathematical concepts and computational techniques are to become more comprehensible. The method is generally applicable to tasks at all levels. Beginners (X1, X2) should benefit the most.

Relation to Common European Numeracy Framework

Key issues

The point is that the teachers:

  • recognize that learners are moving in multiple worlds at the same time during mathematical tasks. Each of these three worlds should master them sufficiently (problem solving, mathematizing, arithmetic). The three worlds they coordinate as part of a problem-solving.
  • understand that “just computing” causes learning problems
  • construct everyday situations in a model way using an example to experience for yourself and get to know the idea behind them
  • experience a playful approach (little text) to mathematics
  • reflect on the experiences gained and combine it with the theory taught
  • make the teaching method usable in courses with adults

Suggestions for PDM meetings

///Editor comment: you see three ways to refer to an underlying pdf: text link, direct link, embedded

PD – Activity 1                       How warm does the water has to be? (See ppt)

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

PD – Activity 2                       …….

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

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.

Reflexion                                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


///Editor comment: there are two ways to refer to a video: direct link, embedded

Relevant videos

Dual coding theory

Modeling numeracy lessions

Bar Modelling


Dual coding theory Teachers role



Mieke van Groenestijn & Lena Lindenskov, eds ( 2007 ): Mathematics in Action Commonalities across Differencesa Handbook for Teachers in Adult Education; Chapter 4 – examples and conclusions

L. Hefendehl-Hebeker, T. Leuders & H.-G. Weigand (19009, Eds.), Mathemagische Momente, Berlin: Cornelsen. Kaiser (2009). Modelle bauen und begreifen. Mehr als blindes Rechnen bei angewandten Aufgaben. (pp. 74-85).

Roth, W.-M. (1994). Thinking with hands, eyes, and signs: multimodal science talk in a grade 6/7 unit on simple machines. Interactive Learning Environments 4(2): 170-18