Modeling Real Life Situations in Teaching Mathematics - Earthquakes and Logarithms-

1. Modeling Real Life Situations in Teaching Mathematics-Earthquakes and Logarithms- -- NatalijaBudinski Primary and grammar school ”Petro Kuzmjak” RuskiKrstur Serbia nbudinski@yahoo.com Teaching Mathematics and Statistics in Sciences: Modeling and Computer-aided Approach Novi Sad May 2011

2. This presentation proposes modeling based learning as a tool for learning and teaching mathematics. • An example of modeling a real world problem related to logarithims is described

3. In this presentation we introduce modeling process to students in a belief that it could contribute toward a better understanding of learning and teaching mathematics. • We place mathematics in real context and focus on why mathematics exists in the first place.

4. Modeling in The Teaching Process • Studying a mathematical model of a real-world situation can provide students with insights that are hidden during a nonmathematical study of the same situation. • 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 nextFigure), 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.

6. “What are the objectives of modeling?” Goals of modeling are • prediction • design • testing of possibilities in order to make a decision • development of a deeper understanding of a phenomenon • adequately portray realistic phenomenon

7. The real situation • youtube.YouTube - TSUNAMI IN JAPAN 2011 MARCH 11 WHIRLPOOL CAUSED BY TSUNAMI RARE VIEW EVER_3.flv

8. Live coverage from BBC News • 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) north-east of Tokyo. • A state of emergency has been declared at a nuclear power plant, where pressure has exceeded normal levels.

9. 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 system failed. • Taken from: www.bbc.co.uk/news/world-asia-pacific-12709598

10. What is a tsunami? • 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 earth-quakes. • Tsunami is a Japanese word for “harbor wave.” • The mathematics of logarithmic scales helps us understand how earthquakes are measured.

11. 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 earthquakes. • The Richter scale is an example of an “exponential scale,” or a “logarithmic scale”.

12. The real problem No 1 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?

13. Mathematical model • 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 be 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 ''standard earthquake'‘ (whose amplitude is 1 micron =10-4 cm).

14. Mathematical solution • Let I1 represents the intensity of The Indian Ocean earthquake and I2representsthe intensity of The Great East Japan earthquake. • We are looking for the ratio of the intensities:

15. Solution of the real problem • The Indian Ocean earthquake was two times as intense as The Great East Japan earthquake

16. Model accepted or refused • At this stage, the strengths and weaknesses of the model should be discussed. That involves reflecting upon the mathematics that has been used. • Students should verify the initial conditions • Students should be encourage to use their access to computer facilities.

17. The 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 several benefits. • 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 features. • Once a mathematical model exists, the technical skills of traditional school mathematics come out.

18. This 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 traditional teaching

19. References Mathematical Modeling: Teaching the Open-ended Application of Mathematics, Joshua Paul Abrams, www.meaningfulmath.org Geogebra in mathematics teacher education: the case of quadratic relations, Lingguo Bu and ErhanSelcukHaciomeroglu, MSOR Connections Vol 10 No 1. February 2010 – April 2010 Boaler, J., Mathematical Modelling and New Theories of Learning (2001), Teaching Mathematics and its Applications, Vol. 20, Issue 3,p. 121-128. Doerr, H., English, L., A modelling perspective on students’ mathematical reasoning about data, (2003) Journal for Research in Mathematics Education, 34(2), 110-136 Galbraith, P., Stillman, G., Brown, J., Edwards, I., Facilitating middle secondary modelling competencies. (2007), In C. Haines, P. Galbraith, W. Blum, S. Khan (Eds.), Mathematical modelling (ICTMA12): Edu., eng. economics, Chichester, UK: Horwood, 130-140.

20. Henn, H.-W., Kaiser, G., Mathematical Modeling in school-Examples and Eperiences, (2005), In Mathematikunterricht in spannungsfeld von Evolution und Evaluation, Fesband fur Werner Blum, Hildesheim Franzbecker, 99-108 p. Hohenwarter, M., Hohenwarter, J., Kreis, Y., Lavicza Zs., Teaching and calculus with free dynamic software Geogebra, (2008), 11th International Congress on Mathematical Education, Mexico. Kaiser, G., Schwarz, B. Mathematical modelling as bridge between school and university, (2006), ZDM, 38 (2), p. 196-208. Lamon, S. J., Parker, W. A., Houston, S. K. (Eds.), Mathematical modelling: A way of life, Chichester, (2003), UK: Horwood Mason, J., Modellingmodelling: Where is the centre of gravity of-for-when teaching modelling? (2001), In J.Matos, W. Blum, K. Houston, S. Carreira (Eds.), Modelling and mathematics education, Chichester, UK: Horwood. Stillman, G., Brown, J., Challenges in formulating an extended modelling task at Year 9, (2007), In H. Reeves, K. Milton, & T. Spencer (Eds.), Proc. 21. Conf. Austr. Assoc. Math. Teachers. Adelaide: AAMT . Stillman, G., Galbraith, P., Towards constructing a measure of the complexity of applications tasks. (2003), S.J. Lamon, W. A. Parker, & S. K. Houston (Eds.), Mathematical modelling: A way of life (pp. 317-327). Chichester, UK: Horwood.