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Mathematical Literacy, Mathematical Modeling, and Realistic Mathematics Problems

tal mathematization is a kind of schematization of the situation, allowing the
introduction of mathematical tools. The activity that follows, related to math-
ematical processes or algorithms, solving the problem, generalizing the situ-
ation, and further formalization, is vertical mathematization. It is not always
easyto determinewherehorizontalmathematization transitionsinto vertical
mathematization (Treffers, 1987).
For successful learning of mathematics, both horizontal and vertical math-
ematization are necessary, as this enables the active participation of each
individual in acquiring knowledge. Students need enough time to bridge
the gap between their informal knowledge and formal mathematical knowl-
edge. Thisisnot alinear but acyclical process –studentsshouldacquire the
strategyofcyclicallytransitioningbetween horizontalandverticalmathema-
tization to refine their understanding of mathematics.

Recommendations
Based on the findings of the research of Felda (2011) and Cotič and Felda
(2011), policymakers and educators should thoroughly change the way math-
ematics is taught and learned, where so-called factual knowledge holds a
central place, and even problem-solving is subordinated to the learning of
procedures.
The National curriculum emphasizes the importance of problem-solving
skills (Ministrstvo za šolstvo in sport in Zavod Republike Slovenije za šolstvo,
2011) and there have been increasing efforts for so-called subject integra-
tion, where mathematics is often meant to be ‘connected’ with other sub-
jects (Krek et al., 2008), ultimately with the sustainability goals set by the
United Nations. It seems that everyone remains confined to their ‘field,’ and
any potential integration classes are treated merely as a necessary evil im-
posed ‘from above.’ Even primary school teachers, who impart knowledge
from various ‘fields,’ do not recall any other during a specific ‘field’ lesson.
In this way, students learn to ‘compartmentalize’ mathematical knowledge,
whatever it may be, into a precisely defined slot that must be opened when
mathematics is on the schedule.
In today’s world, where we aim to convey much more than just routine
knowledgetostudents,thedesireanddemandforteachingproblem-solving
skills in mathematics are even more prevalent. From the perspective of math-
ematics didactics, we can identify fundamental elements of problem-solving
skills (metacognition, communication, heuristics, attitudes and prejudices,
expertise, etc.), but it is not possible to definitively define how to teach these
skills effectively (Cotič & Felda, 2011).
Based on research (Felda, 2011; Cotič & Felda, 2011), it is evident that stu-
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