All structures that
exist mathematically also exist physically.
Tegmarks Max (en.wikipedia.org)
I would like to relate
the statement above in the explanation and description of Realistic Mathematics
Education. Realistic comes from the word real, of which according to the
Dictionary.com “is based on what is real or practical”. Thus, in my opinion,
Realistic Mathematics Education is realistically mathematizing daily problems
for solutions solely for the benefit of each individual’s daily lives. After
numerous readings and internet search, RME originated from the Netherlands by Hans
Freudenthal a Dutch mathematician, who proposed that since students’ cannot be
viewed as passive receivers of ready-made mathematics, mathematics education
should then be directed to the use of a variety of situations and opportunities
to enable students to reinvent mathematics (Hadi, 2002). In this he infers that
Mathematics should be a human activity (Hadi, 2002). Specifically, the maths problem begins with a daily real world issue, which is then deduced, structured
and simplified into a real model incorporating concepts, relations, conditions
and assumptions for the final formal mathematical model.
Realistic Mathematics
Education Model.
I would like to use
various models to specifically explain and describe Realistic Mathematical
Education.
According to the
diagram above taken from powermathematics.blogspot.com there are 4 levels in
the process of RME which is similar to Blum & Niss (1989), 4 steps of
applied problem solving.
1. Mathematical world
orientation or a real problem situation.
2. Model material or a
real model of the original situation
3. Building stones,
number relations or mathematising
4. Formal mathematics
or a mathematical model.
The first step mathematical
world orientation or a real world problem situation refers to daily lives
problems, for instance, in my case, how can I travel to Fiji, using the
shortest and cheapest flight route? That is an illustration of a real world
problem, that individual mostly travellers are faced with often. The second step
is to create a real model of the
situation from cognition unto paper through simplification, structuralism and
deductivism. In this example, I will then have to identify the various flight
routes to Fiji, their costs and the duration of each flight.There are quite a
number flights from Yorgyakarta to Fiji, for the sake of this short paper, I
will use two, which is flying from Bali (Denpasar) or from Jakarta. If I have
to depart from Bali, then I can transit through Sydney, Melbourne or Brisbane.
However, these 3 transit cities have different costs as well as duration of
flight. But, if I have to depart from Jakarta, then I will have to transit
through Hong Kong. The third step, which corresponds with Building Stones,
number relations or mathematizing is the tagging of prices (numbers) on each of
the routes in relation to their flight duration. Then, the computation of the ready made
mathematical model for evaluation, in solving the problem of the shortest and
cheapest flight route to Fiji which depicts the final step of the process of
RME.
Returning to the sentence, given above, RME as a
thought can be a bridge from the abstract world to the formal world of mathematics.
Eventually,
the models give the students access to more formal mathematical knowledge. In
order to fulfil the bridging function between the informal and the formal
level, models have to shift from a model of to
a model for (Streefland, 1985). Apparently the shift
from the model of the real world to a model for mathematics, has often been a challenge to most student’s
likewise to mathematics educators. However, according to the Contemporary
school of thought of Mathematics Realism such Platonism, Empiricism and
Mathematical monism, have provided various thoughts that can be encouraging and
stimulating into actually, devising ways of contributing into the
simplification of Realistic Mathematics Education. Significantly, as stated by
Tegmarks, “all structures that exist mathematically also exist
physically”. That is, in the sense that "in those [worlds] complex enough
to contain self-aware substructures [they] will subjectively perceive themselves
as existing in a physically 'real' world". In which in relation to
Realistic Mathematics Education, modifying the former to become “all structures
that exist physical, also exist mathematically” this corresponds to his
mathematics universe hypothesis (MUH) which is: Our External Physical Reality
is a Mathematical Structure. Thus, in my opinion, realistically, real life
problems already do exist mathematically, in which, there exist a solution which
needs to be discovered by Man.
Reference
En.Wikipedia.org
powermathematics.blogspot.com
