Common European Numeracy Framework

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One of the most important higher order skills in numeracy


Adults bring already with them everyday knowledge ands skills on virtually every topic. With this knowledge and skills they are able to address and solve certain problems in their own way. If new knowledge and sklills is now imparted without reference to this everyday knowledge, there is a serious chance that the new knowledge and skills will never become effective. In the CENF is implicated we want to build on these previous experiences and lead the learners to a higher level in everyday mathematics. 


  • Which numeracy situations are most common?
  • Which numeracy situations have a huge impact on the dily life of people?
  • What is actually managing a situation as numeracy competence?



You own situation

Ask people to focus on a recent and regular day in their own life. Let them wite down the numeracy decison they made from waking up in the morning to going to bed in the evening.

Let people pair and share the results.

Discuss how many numeracy decisions a citizen takes on average on a daily basis. 

Numeracy all around you

Aks particpants to clear their minds and take in a quick presentation. Show the participants a Powerpoint with 80 numeracy situations at a speed of 2 seconds per sheet (takes slightly over two minutes).

Aks particpants what comes to tehir mind when they see the presenttaion. Ciolect the findings and summarize.

Home, society and work

Ask participants to describe what are typical numeracy sitauations in daily life at home, in societal life, in work related situations.

How distinctive are the situations or do the participants experience a big overlap?








Managing situations as an important part of numeracy competences is used probably for the first time by ALL (Adult Literacy and Lifeskills survey).
ALL focuses on numeracy not as a portfolio of passive skills but as an active pattern of behavior, such as managing situations, solving problems, and responding to quantitative information, which could be said to characterize numerate adults (Gal et al. 1999).

Quantitative Literacy: Why Numeracy Matters for Schools and Colleges
The definition was referred to by Steen and Madison in their influential publication from 2003.

Later the concept found its way in the assesment frameworks for the first and second cycle of PIAAC. 


  • Gal, I., van Groenestijn, M., Manly, M., Schmitt, M. J., & Tout, D. (1999). Numeracy Framework for the International Adult Literacy and Lifeskills Survey (ALL).
  • Madison, B. L., & Steen, L. A. (2003). Quantitative Literacy: Why Numeracy Matters for Schools and Colleges. National Council on Education and the Disciplines.
  • Tout, D., Coben, D., Geiger, V., Ginsburg, L., Hoogland, K., Maguire, T., Thomson, S., & Turner, R. (2017). Review of the PIAAC Numeracy Assessment Framework: Final Report. Australian Council for Educational Research (ACER).
  • Hoogland, K., Diez-Palomar, J., & Maguire, T. (2019). Towards a second cycle of PIAAC. In B. Kelly, D. Kaye, G. Griffiths  Dalby, Diane, & J. Stacey (Eds.), Boundaries and Bridges: Adults learning mathematics in a fractured world. Proceedings of the 25th International Conference of Adults Learning Mathematics: A Research Forum (ALM) (pp. 67–68). UCL Institute of Education.
  • PIAAC Numeracy Expert Group. (2009). PIAAC Numeracy: A Conceptual Framework. In OECD Education Working Papers, No.35 (Issue 35). OECD.
  • OECD. (2021). The Assessment Frameworks for Cycle 2 of the Programme for the International Assessment of Adult Competencies. OECD.
 Further reading
  • 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.
  • Hoogland , K. (2010). 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
  • Kapur, M., & Bielaczyc, K. (2012 ). Designing for Productive Failure. Journal of the Learning Sciences, 21(1), 45-83. doi: 10.1080/10508406.2011.591717
  • Kolb, A. Y., & Kolb, D. A. (2009). The Learning Way: Meta-cognitive Aspects of Experiential Learning. Simulation Gaming, 40, 297-327.
  • 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. (Eds.). Tracking adult literacy and numeracy: Findings from longitudinal research. New York: Routledge, S. 59-81
German literature
  • Kaiser, H. (2009). Bausteine für ein Rahmenkonzept zur Förderung alltagsmathematischer Kompetenz. Zürich: SVEB. Knowledge Types – Integrated Learning Model
  • 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.
  • Gallin, P., & Ruf, U. (1990). Sprache und Mathematik in der Schule. Zürich: Verlag Lehrerinnen und Lehrer Schweiz.