Irfan Rusmar Presentation About Modelling and Application in Mathematics Education

8/7/2019 Irfan Rusmar Presentation About Modelling and Application in Mathematics Education

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The Role of MathematicalModelling by Using Real WorldMathematics in Lower

Secondary School(Opportunities and Problems)

ByIrfan Rusmar


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Modelling Cycle in Mathematics

Extra-mathematical

worldMathematics

(Cited in Galbraith et al)


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The Process of MathematicalModelling

Specify the real

problem

Formulate a

mathematical model

Solve the

mathematical

problem

Interpret the solutionCompare with realityCommunicate theresult


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Definition of Modelling inMathematics

Mathematical modeling is a process of

structuring the extra-mathematical(from the real world) to decide suitablemathematics content, to working

mathematically within mathematics.


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Modelling in Lower SecondarySchool

Most primary and lower secondarystudents are difficult to motivate:

Mathematical Concepts Methods

Techniques

Terminology Results


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Modelling in Lower SecondarySchool

Unless:

Clear references to the use ofmathematics

Relevance of mathematics to extra-

mathematical context and situation(Real World Mathematics)

(Galbraith, n.d)


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Real World Mathematics

According to Blum (1993),

Realistic Mathematics means that theproblem situations should beexperientially real for student, from out

side of mathematics.


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Why Real World?

basically in the use of mathematics youhave to formulate problems fromoutside of maths as well as solving themafter you succeeded in formulatingthem (Pollak, n.d: 111)

realistic teaching is an appropriate

method for quantitative literacytraining (Steen, 1998,2001; Alsina, n.d).


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Everything that has to do with

Nature

Society

Culture


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Including:

Everyday life as well as school anduniversity subjects or

Scientific and Scholarly disciplinesdifferent from mathematics.

(discussion document of ICMI Study;Alsina, n.d)


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All of these because:

Students will appreciate their creativityor discover their limitations.


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Mathematical Modelling - The Real

World Approach

Contribute giving more meaning to the

teaching and learning mathematics.

Helps learners to understand the lesson.

Helps learners to understand how models in

mathematics are invented.

(Turmudi, et al, n.d)


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We as a teacher should know:

Why we teach the lessons Do we believe what we have said? Are the results practical, and are the answers

reasonable? Encourage students to be able to construct theirown ideaDont say: What is the solution for this problem? or Prove

itHowever Here is the situation, can you figure out what is

going on?


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How to teach the students inrealistic math modelling?

According to Griffin (2011), there are four methodsof teaching real world mathematical modelling:

Suggest several examples of how mathematics skillscan be used in the real world. (For instance, countingmoney and calculating bank account)

Use daily materials and objects to prove equations

and formulas. (For instance, devise a lesson ofgeometry to find the formula of the volume of a cube,by giving them real object of a cube and placesomething inside)


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How to teach the students inrealistic math modelling?

Take the class outdoors to illustrate conceptsin their books. (For instance, bring our studentsoutside the classroom to measure the height ofa tree by using its shadow)

Start and end the lesson by reviewing the basicterms of the lesson and relating it to the

equations and concepts with the activity.Read more: How to Teach Students About Math in the Real World |eHow.com http://www.ehow.com/how_7771004_teach-students-math-real-world.html#ixzz1CMyiSOB9
http://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.html


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Issues of Real WorldMathematical Modelling in

Indonesian Context

Lack of using real world materials Students are not interested in constructing

their own ideas

Lack of evaluation of research (designresearch) for realistic mathematics


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Suggestion

According to Mousoulides (n.d), in attempt toprovide a coherent framework formathematical modelling at school level isorganized into three strands:

Situates a mathematical modelling as a problemsolving activity

Discusses modelling activities, by presentingthe principles for designing and implementingmodelling activities in classroom

Contextual nature and assessment ofmathematical modelling.


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Opportunities in Modelling

Lead to the development of students'application-oriented learning

Help students to understand and tocope with the real world

Provide rich opportunities for studentsto develop their ideas

Help teachers to develop anunderstanding of students thinking.


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Problems in Modelling

Instruction and assessment (required alot of time)

Students Point of View (math lessonsand examinations more demanding)

Teachers Point of View (Teaching moredemanding)

(Blum, 1993)


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References Alsina, C.(2007). Less chalk, Less words, Less symbols, More objects, More Context, More

actions. Cited in Modelling and Applications in Mathematics Education: The 14th ICMI Study.

Springer. New York.

Kaiser, G. Maab, K.(2007). Modelling in Lower Mathematics Classroom-Problems and

Opportunities. Cited in Modelling and Applications in Mathematics Education: The 14th ICMI

Study. Springer. New York.

Galbraith, P. et al.(2007). Introduction. Cited in Modelling and Applications in Mathematics

Education: The 14th ICMI Study. Springer. New York.

Pollak, H. (2007). Mathematical Modelling- A Conversation with Henry Pollak. Cited in

Modelling and Applications in Mathematics Education: The 14th ICMI Study. Springer. New

York.

Blum, W. (1993). Mathematical modelling in mathematics education and instruction. Cited in

Teaching and learning mathematics in context, edited by Breiteig (etc.), 1993, Ellis Horwood

Limited Chichester. S. 3-14. Retrieved on 29th January 2011 in http://oai.bibliothek.uni-kassel.de/bitstream/urn:nbn:de:hebis:34-2009051227366/1/BlumModelling1993.pdf
http://oai.bibliothek.uni-kassel.de/bitstream/urn:nbn:de:hebis:34-2009051227366/1/BlumModelling1993.pdfhttp://oai.bibliothek.uni-kassel.de/bitstream/urn:nbn:de:hebis:34-2009051227366/1/BlumModelling1993.pdfhttp://oai.bibliothek.uni-kassel.de/bitstream/urn:nbn:de:hebis:34-2009051227366/1/BlumModelling1993.pdfhttp://oai.bibliothek.uni-kassel.de/bitstream/urn:nbn:de:hebis:34-2009051227366/1/BlumModelling1993.pdfhttp://oai.bibliothek.uni-kassel.de/bitstream/urn:nbn:de:hebis:34-2009051227366/1/BlumModelling1993.pdfhttp://oai.bibliothek.uni-kassel.de/bitstream/urn:nbn:de:hebis:34-2009051227366/1/BlumModelling1993.pdfhttp://oai.bibliothek.uni-kassel.de/bitstream/urn:nbn:de:hebis:34-2009051227366/1/BlumModelling1993.pdf


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Mousoulides, N.G. (n.d). Mathematical Modelling for Elementary and Secondary school

Teachers. [Online]. Retrieved on 4th February 2011 in

http://ucy.academia.edu/NicholasMousoulides/Papers/368696/Mathematical_Modeling_for

_Elementary_and_Secondary_School_Teachers

Griffin .(2011). Ehow.com. How to Teach Students About Math in the Real World |eHow.com . [Online}. Retrieved on 29th January 2011 in

http://www.ehow.com/how_7771004_teach-students-math-real-world.html#ixzz1CMyiSOB9

Turmudi, (n.d). Mengurangi Rasa Cemas Belajar Matematika Dengan MenampilkanMatematika Eksploratif Untuk Merangsang Siswa Belajar. Retrieved on 29th January 2011 in

http://file.upi.edu/Direktori/D%20-

%20FPMIPA/JUR.%20PEND.%20MATEMATIKA/196101121987031%20-%20TURMUDI/F10-

Unisba.pdf
http://ucy.academia.edu/NicholasMousoulides/Papers/368696/Mathematical_Modeling_for_Elementary_and_Secondary_School_Teachershttp://ucy.academia.edu/NicholasMousoulides/Papers/368696/Mathematical_Modeling_for_Elementary_and_Secondary_School_Teachershttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://file.upi.edu/Direktori/D%20-%20FPMIPA/JUR.%20PEND.%20MATEMATIKA/196101121987031%20-%20TURMUDI/F10-Unisba.pdfhttp://file.upi.edu/Direktori/D%20-%20FPMIPA/JUR.%20PEND.%20MATEMATIKA/196101121987031%20-%20TURMUDI/F10-Unisba.pdfhttp://file.upi.edu/Direktori/D%20-%20FPMIPA/JUR.%20PEND.%20MATEMATIKA/196101121987031%20-%20TURMUDI/F10-Unisba.pdfhttp://file.upi.edu/Direktori/D%20-%20FPMIPA/JUR.%20PEND.%20MATEMATIKA/196101121987031%20-%20TURMUDI/F10-Unisba.pdfhttp://file.upi.edu/Direktori/D%20-%20FPMIPA/JUR.%20PEND.%20MATEMATIKA/196101121987031%20-%20TURMUDI/F10-Unisba.pdfhttp://file.upi.edu/Direktori/D%20-%20FPMIPA/JUR.%20PEND.%20MATEMATIKA/196101121987031%20-%20TURMUDI/F10-Unisba.pdfhttp://file.upi.edu/Direktori/D%20-%20FPMIPA/JUR.%20PEND.%20MATEMATIKA/196101121987031%20-%20TURMUDI/F10-Unisba.pdfhttp://file.upi.edu/Direktori/D%20-%20FPMIPA/JUR.%20PEND.%20MATEMATIKA/196101121987031%20-%20TURMUDI/F10-Unisba.pdfhttp://file.upi.edu/Direktori/D%20-%20FPMIPA/JUR.%20PEND.%20MATEMATIKA/196101121987031%20-%20TURMUDI/F10-Unisba.pdfhttp://file.upi.edu/Direktori/D%20-%20FPMIPA/JUR.%20PEND.%20MATEMATIKA/196101121987031%20-%20TURMUDI/F10-Unisba.pdfhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://www.ehow.com/how_7771004_teach-students-math-real-world.htmlhttp://ucy.academia.edu/NicholasMousoulides/Papers/368696/Mathematical_Modeling_for_Elementary_and_Secondary_School_Teachershttp://ucy.academia.edu/NicholasMousoulides/Papers/368696/Mathematical_Modeling_for_Elementary_and_Secondary_School_Teachers

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Irfan Rusmar Presentation About Modelling and Application in Mathematics Education