Page 148 - Učilnica za življenje

Darjo Felda, Mara Cotič and Daniel Doz

varying understandings of the task associated with the realistic problem. In-
dividual solvers will identify potential missteps in certain phases or proce-
dures of solving the realistic problem and focus on making appropriate cor-
rections.
In our view, the depiction of solving a realistic problem is inadequate from
the perspective of utilizing non-mathematical knowledge. It is true that, in
addition to mathematical knowledge, other knowledge is required when
transitioning from the mental representation of the situation to the realistic
model and from the latter to the mathematical model. It is particularly im-
portant to emphasize the experiences and problem-solving strategies that
the solver has already developed. Non-mathematical knowledge is also nec-
essary and crucial when transitioning from the mathematical result to the re-
alistic result and from the realistic result to the mental representation of the
situation. When interpreting the mathematical result and verifying whether
the realistic result aligns with the data and information from the mental rep-
resentation, to complete the ‘phase cycle,’ we are no longer in the ‘mathe-
matical field’ – we must rely on non-mathematical knowledge or everyday
life insights.
It isalso important to focuson thefirst phaseof problem-solving.Themen-
tal representation cannot be merely a reflection or a mental image of the real
situation. Before the solver moves towards creating a realistic model, they
develop a mental representation that generally is not identical to the real sit-
uation. In the representation, those elements of the real situation that the
solver believes are not crucial for solving the given realistic problem ‘fade,’
while those that will be included in the subsequent phases of the problem-
solving process are ‘strengthened.’
Thus, already in the first phase, the solver intervenes in the process and
modifies the objective reality of the real situation. Here, their experiences,
if they have encountered a similar situation before, or their beliefs are cru-
cial. It is necessary to add a final phase, which is the connection between the
mental representation of the situation or the model of the situation, as it was
named in the previous depiction, and the real situation. The solution to the
realistic problem, which the solver has accepted and incorporated into the
mental representation, must be situated in the real situation and checked for
consistency with all elements of that situation. The solver receives confirma-
tion that they have developed an appropriate mental representation, which
they can recall and suitably adjust for new parameters of a similar realistic
problem in the future.
It is necessary to recognize that realistic problems are complex, and there-

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