The Positive Aspects of Modeling Process in Teaching Mathematics
The Positive Aspects of Modeling Process in Teaching Mathematics
Primary and grammar school ”Petro Kuzmjak”
Teaching Mathematics and Statistics in Sciences: Modeling and
modeling based learning as a tool
An example of modeling a real
logarithims is described
this presentation we introduce
modeling process to students in a
belief that it could contribute toward a
better understanding of learning and
place mathematics in real context
and focus on why mathematics exists
in the first place.
a mathematical model of a real-world
situation can provide students with insights that are
hidden during a nonmathematical study of the same
The modeling process in mathematical education
tends to follow the didactical cycle of activities and
reach a desirable level of accomplishments of
students’ activities and competencies.
We use a diagrammatic representation (see next
Figure), which encompasses both the task
orientation, and the need to capture what is going on
in the minds of individuals as they work
collaboratively on modelling problems.
Goals of modeling are
testing of possibilities in order to
make a decision
development of a deeper
understanding of a phenomenon
adequately portray realistic
youtube.YouTube - TSUNAMI IN JAPAN 2011
MARCH 11 WHIRLPOOL CAUSED BY
TSUNAMI RARE VIEW EVER_3.flv
Japan's most powerful earthquake since
records began has struck the north-east coast,
triggering a massive tsunami.
Cars, ships and buildings were swept away by
a wall of water after the 8.9-magnitude tremor,
which struck about 400km (250 miles) northeast of Tokyo.
A state of emergency has been declared at a
nuclear power plant, where pressure has
exceeded normal levels.
Thousands of people living near the
Fukushima nuclear power plant have been
ordered to evacuate.
Japanese nuclear officials said pressure inside a
boiling water reactor at the plant was running
much higher than normal after the cooling
A tsunami is an ocean wave that is generated
by a sudden displacement of the sea floor. This
displacement can occur as a result of earthquakes.
Tsunami is a Japanese word for “harbor wave.”
The mathematics of logarithmic scales helps
us understand how earthquakes are measured.
An earthquake is the sudden release of energy in
the form of vibrations caused by rock suddenly
moving along fault lines.
This energy is extremely large and we repesent it
on a scale based on exponents
The idea to use a logarithmic earthquake
magnitude scale was first developed by Charles
Richter in the 1930s.
This scale is used to measure the magnitude of
The Richter scale is an example of an “exponential
scale,” or a “logarithmic scale”.
How many times more
intense was The Indian
Ocean earthquake (2004)
with a Richter magnitude
of 9.3 than The Great East
Japan earthquake (2011)
with magnitude 9.0?
An increase of 1 unit on the Richter scale roughly corresponds to a
multiplication of the energy released by a factor of 10.
In 1935 Charles Richter defined the magnitude of an earthquake to
where I is the intensity of the earthquake (measured by the amplitude of a seismograph
reading taken 100 km from the epicenter of the earthquake) and S is the intensity of a
(whose amplitude is 1 micron =10-4 cm).
Let I1 represents the intensity
earthquake and I2 represents
the intensity of The Great
East Japan earthquake.
We are looking for the ratio
of the intensities:
Using the rules of logarithms we
isolate this ratio:
9.3 9.0 log log
Indian Ocean earthquake
was two times as intense as
The Great East Japan
this stage, the strengths and
weaknesses of the model should be
discussed. That involves reflecting
upon the mathematics that has been
Students should verify the initial
Students should be encourage to use
their access to computer facilities.
act of creating a model forces students to think
deeply about the problem. Translating an imprecise,
complex, multivariate real-world situation into a simpler,
more clearly defined mathematical structure such as a
function or a system of rules for a simulation, yields
For the first step in this process, students identify a list of
variables. As they do so, they discover what they really
know about their problem and what information they
need to determine.
Students must think about the connections between and
among variables, decide which relationships and
structures are the most important to capture
mathematically, and pick the mathematical realm that
offers the best possibilities for expressing all these
Once a mathematical model exists, the technical skills of
traditional school mathematics come out.
teaching method tolerate different kinds of
activities such as research every day situation,
using computers and organizing the learning
process close fitting to contemporary students
and their field of interests
It can be said that modeling based learning is out
of the box, but that is its great advantage over the
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