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Mathematical Literacy, Mathematical Modeling, and Realistic Mathematics Problems

ematization, thought processes shift from the realistic model to mathemati-
cal content. Appropriate pictures or descriptions take on mathematical sym-
bolism or language, resulting in a mathematical model of the real situation-
a mathematical problem. By using a suitable problem-solving strategy and
chosen mathematical procedures, the solver arrives at a mathematical solu-
tion or result.
By interpreting the mathematical result, which arises from the mathemat-
ical solution of the mathematized realistic model, we return to the realistic
model, which has meanwhile transformed into a realistic solution. The inter-
pretation processinvolvesestablishingconnectionsbetween themathemat-
ical solution and the model of the real situation’s solution.
The solver of a realistic problem thus faces the important task of verify-
ing and confirming the consistency of the realistic solution with the model
of the situation, which actually represents their understanding of the given
real problem situation. Many children often exhibit intuitive verification of
consistency when they cannot explain why they have adopted or rejected
a particular solution. They rely on their feelings or experiences. Of course,
students must be encouraged to verify the realistic solution and confirm de-
cisions based on an appropriate explanation for the development of mathe-
matical literacy.
Justification, which is based on the model of the situation as created by the
problem solver, is also important for the exchange of opinions with other
solvers who have created different models of the situation. The exchange
of opinions means presenting the solution to the initial problem situation
by multiple solvers, who thus either confirm the identity or similarity of the
solution or point out certain discrepancies that require further appropriate
handling of the problem situation.
There is often a slightly different depiction of solving a realistic problem, in
which it is particularly emphasized that the preparation of the real model and
the mathematization also involves the use of non-mathematical knowledge
(Borromeo Ferri, 2006) if the given task requires it.
In thismodel,thefirst phaseinvolvesconstructingamentalrepresentation
of the situation while understanding the given task. The problem-solving
process concludes with verifying the realistic result and confirming its con-
sistency with the mental representation of the situation, which reflects how
the solver understood and envisioned the real situation. In our opinion, the
connections between the mental representation of the situation and the ac-
tual real situation should also be addressed at the end. Several solvers en-
counter potential deviations due to different ‘views’ of the real situation or

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