Page 142 - Učilnica za življenje

Darjo Felda, Mara Cotič and Daniel Doz

To make learning mathematics creative, students need to be involved in
the practical solving of a realistic problem or another mathematical prob-
lem that has multiple solution paths (Schoenfeld & Sloane, 2016). Occasion-
ally, students need to be challenged with so-called problem investigations
that have multiple solutions and several possible strategies for solving them
(Manfreda Kolar & Hodnik, 2021). Creative exploration and problem-solving
is an excellent way to develop mathematical concepts and is often a use-
ful tool for consolidating procedures. Through exploration and problem-
solving, strategies are primarily honed, often referred to as thinking skills or
logical reasoning in a mathematical context. Within this framework, students
(Advisory Committee on Mathematics Education, 2008):

– Pose questions and hypothesize possible conclusions;
– Choose strategies and representations;
– Use their thinking skills;
– Prove or disprove claims;
– Critically review, check, and evaluate their work;
– Develop patience and persistence to reach a solution.

At the beginning of schooling, realistic problems that students solve must
be very simple. Many studies have pointed out the difficulties students face
when solving realistic problems (cf. Pratiwi et al., 2020). These difficulties are
often in understanding the problem text and finding the appropriate math-
ematical content, as students operate quite randomly with the given data
without considering their connection to the realistic context. Mistakes in
solving are not due to a lack of experience, as it turns out that even the suc-
cess of solving ‘traditional’ problems does not significantly improve, even if
such problems are repeatedly solved (Renkl & Stern, 1994).
Realistic problems are most often solved by mathematizing a non-mathe-
matical situation, which involves (Cotič & Felda, 2011) (Figure 1):

– Constructing a mathematical model based on the appropriate realistic
situation or everyday life situation;
– Solving the constructed mathematical problem;
– Translatingthesolutionofthemathematicalproblem,thatcorresponds
to the mathematical model, back into the realistic environment.
Thebiggestobstacleinsolvingrealisticproblemsisconstructingthemath-
ematical model, as it requires knowledge of the context of the realistic prob-
lem situation and a certain degree of creativity (Winter, 1994).

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