Page 146 - Učilnica za življenje

Darjo Felda, Mara Cotič and Daniel Doz

Emphasizing Real Situations
For developing mathematical literacy, it is necessary to emphasize real situa-
tions rather than problems that have already been ‘stripped of unnecessary
situational elements.’ Such problems are, in a sense, already mathematized.
Their solving can be represented by a model like the one developed by Pollak
(1979).
According to this model, there is no phase between the real situation and
the mathematical model. The problem is actually ready for mathematical
processing, so the mathematical solution of the problem is simultaneously
a solution that fits the real situation.
Problems from everyday life usually require thorough consideration; rele-
vant data must be extracted, and the right solving strategy that leads to the
mathematization of the problem must be found. The mathematical solution
then needs to be verified, as it does not necessarily align with the everyday
life situation. Blum and Leiss (2007) illustrated the process of solving such a
problem with a cycle model According to this model, the solver of a realis-
tic problem first constructs a model of the situation. This model reflects the
understanding of the real situation, indicating how the solver actually sees
or experiences the real situation described in the problem. The model of the
situation depends on the individual, their personal understanding of the real
situation, and their experiences with similar real situations. It is not necessar-
ily true that the model corresponds to the situation since it often happens
that especially students at the beginning of schooling do not pay enough
attention to all the circumstances indicated by the given realistic problem.
Usually, the real situation is complex, and the model is already a somewhat
simplified version where the solver omits some information and focuses on
those that are essential for solving the given realistic problem. The transition
from the real situation to the model is not systematic-it is merely a kind of
subjective experiential view of the situation, showing the individual’s ten-
dency to approach similar situations in a particular way.
The model of the situation forms the basis for creating a realistic model.
The solver consciously idealizes and simplifies the model of the situation,
which for them is actually the real situation or that part of the real situation
they perceive as crucial for solving the given realistic problem. Knowledge
and insights, not necessarily mathematical or not solely mathematical, lead
the individual to a realistic model.
A realistic model can be presented with an appropriate picture or descrip-
tively,relyingmoreorlessonthemodelofthesituation.Inthephaseofmath-

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