Page 150 - Učilnica za življenje

Darjo Felda, Mara Cotič and Daniel Doz

perience from everyday life. Particularly, students at the beginning of their
education prefer to look for numerical data and use a randomly chosen op-
eration, even if the resulting outcome makes no sense. This flawed pattern
of solving word problems is common even among older students; successful
solving of mathematical problems in a ‘real-life’ guise becomes dependent
only on luck in choosing the right operation or procedure and handling the
data correctly.
Realistic mathematics education focuses on guiding the student to ‘invent’
mathematics through mathematization, considering the student’s informal
strategies for solving realistic problems and their interpretations of the solu-
tion or the path to solving it. A realistic problem is not necessarily from ev-
eryday life but from a situation that is not new to the student and that they
have experienced. This means it can also be a ‘pure’ mathematical problem –
a problem from the abstract world of mathematics. Students capable of ab-
straction can expand and deepen their mathematical knowledge by facing
suitable abstract mathematical problems, while others can deepen and ex-
pand it only with sufficiently tangible models or problems from the concrete
world.
An important phase in realistic mathematics education is the so-called
horizontal mathematization, where the student uses their informal knowl-
edge to describe the situation and explain the solution to the problem. When
informal strategies lead the student to solve the problem using mathemati-
cal language or an appropriate algorithm, it is vertical mathematization.
Mathematics teaching in our schools is too focused only on vertical math-
ematization. The teacher usually presents a certain mathematical content
and some examples of applying the new knowledge, followed by exercises
and homework. These exercises or tasks are intended more or less for the
mechanical repetition of the procedure presented by the teacher. The learn-
ing process in such teaching lacks horizontal mathematization; students ex-
perience only formal vertical mathematization. This means that students do
not use their knowledge and do not build a bridge between their already ac-
quired knowledge and new knowledge; instead, they place the ‘novelty’ in
their memory as just another piece of information. If they do not later recall
this information from memory or recall it in connection with a problem that
does not fit, they do not solve the new problem they are faced with.
We must recognize that mathematization is an activity through which ac-
quired knowledge and skills are used to discover new rules, connections, and
structures. With mathematization, we acquire new knowledge and concepts,
refine language, and acquire and practice skills for successfully solving prob-
lems that can be set in a mathematical context or not. In particular, horizon-
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