__Modelling competencies and their
teaching__

*certain kind of mathematical challenge* of
a given situation” (see also Niss 2003). Correspondingly,
they define mathematical modelling competency as “someone’s insightful readiness
to carry through all parts of a mathematical modelling process”.

In order to elaborate the term further by identifying
sub-competencies, one must therefore look at the parts of a modelling process.
It seems to be agreed in the community of researchers on teaching mathematical
modelling (cf. Maaß 2006, Kaiser 2007) that the modelling process can be
split up into the following steps:

- One
starts with a real world problem which might be clearly formulated or might
first need further clarification
- Then
one sets up a real model by identifying the objects that are of interest
and their relationships (simplification)
- This
has to be translated to a mathematical model (mathematization)
- Within
the mathematical model a solution of the translated problem must be found
- This
solution is to be interpreted in real world terms
- The
solution and the overall process is validated in the real world (e.g. by
comparison with real data obtained by observation or trials).

Having competence to carry out the modelling process
can now be split up into having the sub-competencies for each part of the
process.

- “meta-cognitive
modelling competencies”, i.e. being aware of the overall process and the
position and meaning of the sub-processes when doing modelling
- Structuring
real world problems and working goal-directed
- Argumentation
and documentation competencies
- Knowledge
of the potential of mathematical modelling for problem solution and positive
attitude towards using this potential.

- “degree of coverage”: which sub-competencies are covered?
- “radius of action”: in which contexts and situation
can the competency be activated?
- “technical level”: how advanced are the entities and
tools used?

**Literature and Links**

*Contributions
at SEFI MWG Seminars:*

^{th} SEFI Maths Working Group Seminar in Vienna,
Prague: Vydavatelstvi CVUT, 77-85.

(available as download:here,
accessed 10 March 2010)

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

*Further Literature:*

*For the Learning
of Mathematics* 20, 3-11.

*Teaching Mathematics and its Applications* 22(3), 123-139.

^{th} ICMI
Study,

*Mathematical Thinking and
Learning* 8: 3-36.

*Zentralblatt
für Didaktik der Mathematik (ZDM)* 38(2), 113-142.

^{rd} Mediterranean Conference on Mathematical Education,

*General books
on mathematical modelling and modelling courses:*

^{nd} Edition, Houndmills/Basingstoke: Palgrave.

^{rd} Edition,