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Mathematical Literacy, Mathematical Modeling, and Realistic Mathematics Problems

fore students should be appropriately guided and directed when they first
encounter them in the early stages of their education. To avoid exerting too
much influence on their problem-solving process, which they should de-
velop as independently as possible, we should offer students less complex
problems from which they can more easily extract the necessary information
and data to create an effective and sufficiently simple model of the situation.
However, we must not prevent students from solving realistic problems on
the grounds that their knowledge is not yet effective enough, as they need to
continually develop and enhance appropriate strategies for solving realistic
problems, incorporating their knowledge and skills.

Mathematical Modelling and Mathematical Literacy
Mathematical modelling is important because it helps in recognizing math-
ematical models in our everyday environment, thus (Blum & Borromeo Ferri,
2009):

– It helps children and adolescents understand the world;
– It supports learning mathematics in terms of motivation, concept for-
mation, and understanding;
– It aids in developing various mathematical competencies and associ-
ated skills;
– It helps in understanding mathematics as a discipline.

Using modelling makes mathematics more meaningful to students be-
cause typical word problems are often just an artificial ‘real-life’ disguise for
mathematical problems that present no challenge to the student – engaging
with these tasks is extremely boring math-for-math-sake.
Mathematical modelling is also challenging for teachers, as it requires not
only mathematical knowledge but also knowledge and experience gained
from everyday life. Many teachers fear that students will not acquire the
knowledgeorachievetheappropriatelearningobjectives.Accordingto their
belief, only with ‘traditional’ teaching methods can they determine if the
learning goal has been achieved. Modelling seems to them ‘scattered’ and
time-consuming, beyond their control.
As mentioned earlier, students have difficulties with modelling, as it re-
quires complex cognitive processes. The very first step, when it is necessary
to create a model of the situation, is a real challenge for students. If the real-
istic problem is presented as a word problem, they need to immerse them-
selves in the appropriate problem situation and apply knowledge and ex-

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