developing the attitude and creativity in...
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DEVELOPING THE ATTITUDE AND CREATIVITY IN MATHEMATICS
EDUCATION
Paper to be Presented at The International and The Fourth National Conference on Mathematics Education 21-22
July 2011, FMIPA UNY
By
MarsigitYogyakarta State University
Indonesia
7/20/2011M
arsigit, Indonesia
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HERMENEUTICS OF LEARNING MATH
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7/20/2011M
arsigit, Indonesia
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7/20/2011M
arsigit, IndonesiaHERMENEUTICS OF LEARNING MATH
Theories
Practical/ImplementWill
Attitude T. Math
Math Concept
Math Skill
Math Exper
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7/20/2011M
arsigit, Indonesia
ICEBERG VOLCANOWest Indonesia
ATTITUDE TOWARD …..MATHEMATICS
ATTITUDE OF….MATHEMATICS(MATHEMATICAL THINKING)
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T S U N A M I’S ATTITUDE
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VULCANO’S ATTITUDE
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arsigit, Indonesia
Pheno-menon
Curiosity/Ammusing
Disaster
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arsigit, Indonesia
MATHEMATICAL PHENOMENA
Disaster…for Students
Curiosity/Ammusing…for Students
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arsigit, Indonesia
Mathematics is student’s thinking, and therefore…..
MATHEMATICS is…..The Student himself
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Idst Trnr
Tech Prgm
Old Hum
PrgrsEduc
Pub. Educ
Poli-tics
Radical right
Conservative
Conservative/liberal
Liberal Demo-cratic
NturMath
Body of Knowledge
Science of truth
Structu-re of truth
Process ofThinking
Social Activi-ties
Mral Val.
Good vsBad
Pragmatism
HierarkhiesPaternalistics
Humani-ty
Justice, Free-dom
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Idust Train
Tech Pragm
Old Hum.
Progres Educ.
Public Educat
Theory Sciety
Hierarchy,Market Orientati-on
Hierarchy Hierarchy Well-fare Need a reform
Nature Stdent
Empty Vessel
Empty Vessel
Character Building
Student Orient.
Psych.Develop
Theory Stdnts’Ability
Talent and Effort
Talent Talent Develop-ment
StudentNeeds
Culture,Relative
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Idstrl Train
Techn Pragm
Old Hum
ProgrsEduc
Public Educ
Aim MathEduc
Back to Basic (Arithme-tics)
Certifica-tion
Transfer of knowledge
Crea-tivity
Math.Cons-truct
Th.Learning
Work Hard,Exercises,Drill,Memorize
ThinkingAnd practice
Understanding and Applica-tion
Explo-ration
Auto-nom,Inter-action
Th. Teaching
Transfer of knowldge (transmi-tion)
External Motivation
Expository Const,Develp
Discus,Investigation
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Idstrl Train
TechPragm
Old Hum
ProgreEduc
Public Educ
Resources
White Board, Chalk,Anti Calcula-tor
Teaching Aid
Visual Teaching Aid for motiva-tion
Various resources/environment
SocialEnvirontment
Evaluation
External Test
ExternalTest
ExternalTest
PFolio,Assessment
PFolio,Social Context
Diversity
Monoculture
Desentrali-zation
Competent Based Curricu-lum
Multiple Solution,Local Culture
Heterogonomous
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7/20/2011M
arsigit, Indonesia
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7/20/2011M
arsigit, Indonesia
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EMERGING MATHEMATICAL ATTITUDE AND CREATIVITY
7/20/2011M
arsigit, Indonesia
Traditional Innovative
Teacher
Students Constructive Teaching
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7/20/2011M
arsigit, Indonesia
FORMALMATH
SCHOOLMATH
Teacher
Students Constructive Learning
EMERGING MATHEMATICAL ATTITUDE AND CREATIVITY
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PHENOMENOLOGY OFMATHEMATICAL ATTITUDE
(HUSSERL) 7/20/2011M
arsigit, Indonesia
Idealized
Abstracted
MathPhenomenaEpoche
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The Component of Math Attd.7/20/2011
Marsigit, Indonesia
Inside your MIND(Superserve)
Outside your MIND(Subserve)
3
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The Component of Math Attd.7/20/2011
Marsigit, Indonesia
Inside Your MIND(Unique)
Outside your MIND(Plural)
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The Component of Math Attd.7/20/2011
Marsigit, Indonesia
Inside your MIND(analytic/coherence)
Outside your MIND(synthetic/
Correspondence)
3+2=53 book + 2 book = 5 book
3 pencil + 2 pencil = 5 pencil
3 book + 2 pencil = 5 ?
3 book + 2 pencil = 5 ?
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The Component of Math Attd.7/20/2011
Marsigit, Indonesia
Inside your MIND(abstract)
Outside your MIND(concret)
X=30
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The Component of Math Attd.7/20/2011
Marsigit, Indonesia
Inside your MIND(Realistic Math: Vertical)
Outside your MIND(Realistic
Math:Horizontal)
1½¼
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THE APPROACH TOMATHEMATICAL ATTDITUDE
(EBBUT AND STRAKER, 1995)
1. Mathematics is a search for PATTERN and RELATIONSHIP
2. Mathematics is PROBLEM SOLVING activity
3. Mathematics is a mean of INVESTIGATION
4. Mathematics is a mean of COMMUNICATION
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arsigit, Indonesia
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1. Attempting to grasp one’s own problems or objectives or substance clearly, by oneself•Attempting to have questions•Attempting to maintain a problem consciousness
•Attempting to discover mathematical problems in phenomena
Mathematical Attitude(Katagiri, 2007)
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2. Attempting to take logical actions•Attempting to take actions that match the objectives
•Attempting to establish a perspective•Attempting to think based on the data that can be used, previously learned items, andassumptions
Mathematical Attitude(Katagiri, 2007)
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3. Attempting to express matters clearly and succinctly•Attempting to record and communicate problems and results clearly and succinctly
•Attempting to sort and organize objects when expressing them
Mathematical Attitude(Katagiri, 2007)
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4. Attempting to seek better things•Attempting to raise thinking from the concrete level to the abstract level
•Attempting to evaluate thinking both objectively and subjectively, and to refine thinking
•Attempting to economize thought and effort
Mathematical Attitude(Katagiri, 2007)
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Public Criticism andReformulation
Objective Knowledge of Mathematics(Math Attitude)
Subjective KnowledgeOf Mathematics
(Math Attitude)
Personal Reformulation(Math Attitude & Creativity
SOCIAL NEGOTIATIONPROCESSES
(Attitude Toward Math, Math Attitude,
Creativity)
Adapted from P. Ernest (1991)
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Public Criticism andReformulation
Objective Knowledge of Mathematics(Math Attitude)
Subjective KnowledgeOf Mathematics
(Math Attitude)
Personal Reformulation(Math Attitude & Creativity
SOCIAL NEGOTIATIONPROCESSES
(Attitude Toward Math, Math Attitude,
Creativity)
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7/20/2011M
arsigit, Indonesia
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EVIDENCESINDICATE:
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THE STUDENTS ARE TO DEVELOPMATHEMATICAL ATTITUDE AND CREATIVITY
THROUGH SOME FOLLOWING ACTIVITIES:
1.Identifying or describing the specific mathematics :a. in the routine activities b. in the non-routine activities
2. Schematizing, formulating and visualizing a problem in different ways
3. Discovering relations among mathematical concepts
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arsigit, Indonesia
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7/20/2011M
arsigit, Indonesia
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THE STUDENTS ARE TO DEVELOPMATHEMATICAL ATTITUDE AND CREATIVITY
THROUGH SOME FOLLOWING ACTIVITIES:
4. Discovering regularity arousing from the concepts of “routine activities”
5. Recognizing isomorphic aspect in different problems
6. Transferring a real world problem to a mathematical problem
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arsigit, Indonesia
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7/20/2011M
arsigit, Indonesia
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THE STUDENTS ARE TO DEVELOPMATHEMATICAL ATTITUDE AND CREATIVITY
THROUGH SOME FOLLOWING ACTIVITIES:
7. Striving to represent daily problems in a related mathematical formula
8. Strived to prove regularities of consisting concepts
9. Refined and adjusting mathematical models
10. Performing vertical mathematization by employing different models
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ICEBERG APPROACH TO MATH ATTD.
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Iceberg Approach in Realistics Mathematics (Moerlands, 2004 in Sutarto, 2008)
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7/20/2011M
arsigit, Indonesia
![Page 46: DEVELOPING THE ATTITUDE AND CREATIVITY IN …staffnew.uny.ac.id/upload/131268114/penelitian/DEVELOPING+THE+… · PFolio, Assess ment. PFolio, Social Context. Diver sity. Monocult](https://reader034.vdocuments.mx/reader034/viewer/2022050215/5f60c44b23ab9443f4274f3e/html5/thumbnails/46.jpg)
7/20/2011M
arsigit, Indonesia
![Page 47: DEVELOPING THE ATTITUDE AND CREATIVITY IN …staffnew.uny.ac.id/upload/131268114/penelitian/DEVELOPING+THE+… · PFolio, Assess ment. PFolio, Social Context. Diver sity. Monocult](https://reader034.vdocuments.mx/reader034/viewer/2022050215/5f60c44b23ab9443f4274f3e/html5/thumbnails/47.jpg)
7/20/2011M
arsigit, Indonesia
![Page 48: DEVELOPING THE ATTITUDE AND CREATIVITY IN …staffnew.uny.ac.id/upload/131268114/penelitian/DEVELOPING+THE+… · PFolio, Assess ment. PFolio, Social Context. Diver sity. Monocult](https://reader034.vdocuments.mx/reader034/viewer/2022050215/5f60c44b23ab9443f4274f3e/html5/thumbnails/48.jpg)
7/20/2011M
arsigit, Indonesia
![Page 49: DEVELOPING THE ATTITUDE AND CREATIVITY IN …staffnew.uny.ac.id/upload/131268114/penelitian/DEVELOPING+THE+… · PFolio, Assess ment. PFolio, Social Context. Diver sity. Monocult](https://reader034.vdocuments.mx/reader034/viewer/2022050215/5f60c44b23ab9443f4274f3e/html5/thumbnails/49.jpg)
7/20/2011M
arsigit, Indonesia
![Page 50: DEVELOPING THE ATTITUDE AND CREATIVITY IN …staffnew.uny.ac.id/upload/131268114/penelitian/DEVELOPING+THE+… · PFolio, Assess ment. PFolio, Social Context. Diver sity. Monocult](https://reader034.vdocuments.mx/reader034/viewer/2022050215/5f60c44b23ab9443f4274f3e/html5/thumbnails/50.jpg)
7/20/2011M
arsigit, Indonesia
![Page 51: DEVELOPING THE ATTITUDE AND CREATIVITY IN …staffnew.uny.ac.id/upload/131268114/penelitian/DEVELOPING+THE+… · PFolio, Assess ment. PFolio, Social Context. Diver sity. Monocult](https://reader034.vdocuments.mx/reader034/viewer/2022050215/5f60c44b23ab9443f4274f3e/html5/thumbnails/51.jpg)
EVIDENCESINDICATE:
7/20/2011M
arsigit, Indonesia
![Page 52: DEVELOPING THE ATTITUDE AND CREATIVITY IN …staffnew.uny.ac.id/upload/131268114/penelitian/DEVELOPING+THE+… · PFolio, Assess ment. PFolio, Social Context. Diver sity. Monocult](https://reader034.vdocuments.mx/reader034/viewer/2022050215/5f60c44b23ab9443f4274f3e/html5/thumbnails/52.jpg)
IN ORDER TOPROMOTE MATHEMATICAL ATTITUDE
AND CREATIVITY:
The teachers need to have clear picture of the NATURE OF SCHOOL MATHEMATICS, REALISTICS MATHEMATICS, and CONSTRUCTIVE TEACHING
7/20/2011M
arsigit, Indonesia
![Page 53: DEVELOPING THE ATTITUDE AND CREATIVITY IN …staffnew.uny.ac.id/upload/131268114/penelitian/DEVELOPING+THE+… · PFolio, Assess ment. PFolio, Social Context. Diver sity. Monocult](https://reader034.vdocuments.mx/reader034/viewer/2022050215/5f60c44b23ab9443f4274f3e/html5/thumbnails/53.jpg)
7/20/2011M
arsigit, Indonesia
![Page 54: DEVELOPING THE ATTITUDE AND CREATIVITY IN …staffnew.uny.ac.id/upload/131268114/penelitian/DEVELOPING+THE+… · PFolio, Assess ment. PFolio, Social Context. Diver sity. Monocult](https://reader034.vdocuments.mx/reader034/viewer/2022050215/5f60c44b23ab9443f4274f3e/html5/thumbnails/54.jpg)
The teachers need to organize presentation, demonstrate and interconnected relationships among the components of mathematical attitude
7/20/2011M
arsigit, Indonesia
IN ORDER TOPROMOTE MATHEMATICAL ATTITUDE
AND CREATIVITY:
![Page 55: DEVELOPING THE ATTITUDE AND CREATIVITY IN …staffnew.uny.ac.id/upload/131268114/penelitian/DEVELOPING+THE+… · PFolio, Assess ment. PFolio, Social Context. Diver sity. Monocult](https://reader034.vdocuments.mx/reader034/viewer/2022050215/5f60c44b23ab9443f4274f3e/html5/thumbnails/55.jpg)
7/20/2011M
arsigit, Indonesia
![Page 56: DEVELOPING THE ATTITUDE AND CREATIVITY IN …staffnew.uny.ac.id/upload/131268114/penelitian/DEVELOPING+THE+… · PFolio, Assess ment. PFolio, Social Context. Diver sity. Monocult](https://reader034.vdocuments.mx/reader034/viewer/2022050215/5f60c44b23ab9443f4274f3e/html5/thumbnails/56.jpg)
The teachers need to promote students’ mathematical attitude and creativity on using concrete materials (i.e., manipulatives) before proceeding to semi-concrete materials (e.g., pictorial representations); and before proceeding to abstract problems (e.g., numerical representation)
7/20/2011M
arsigit, Indonesia
IN ORDER TOPROMOTE MATHEMATICAL ATTITUDE
AND CREATIVITY:
![Page 57: DEVELOPING THE ATTITUDE AND CREATIVITY IN …staffnew.uny.ac.id/upload/131268114/penelitian/DEVELOPING+THE+… · PFolio, Assess ment. PFolio, Social Context. Diver sity. Monocult](https://reader034.vdocuments.mx/reader034/viewer/2022050215/5f60c44b23ab9443f4274f3e/html5/thumbnails/57.jpg)
7/20/2011M
arsigit, Indonesia
![Page 58: DEVELOPING THE ATTITUDE AND CREATIVITY IN …staffnew.uny.ac.id/upload/131268114/penelitian/DEVELOPING+THE+… · PFolio, Assess ment. PFolio, Social Context. Diver sity. Monocult](https://reader034.vdocuments.mx/reader034/viewer/2022050215/5f60c44b23ab9443f4274f3e/html5/thumbnails/58.jpg)
The teachers need to develop methods to uncover the variations of all problem types lead the students to make generalizations (e.g., that all fractions represent parts of a whole)
7/20/2011M
arsigit, Indonesia
IN ORDER TOPROMOTE MATHEMATICAL ATTITUDE
AND CREATIVITY:
![Page 59: DEVELOPING THE ATTITUDE AND CREATIVITY IN …staffnew.uny.ac.id/upload/131268114/penelitian/DEVELOPING+THE+… · PFolio, Assess ment. PFolio, Social Context. Diver sity. Monocult](https://reader034.vdocuments.mx/reader034/viewer/2022050215/5f60c44b23ab9443f4274f3e/html5/thumbnails/59.jpg)
7/20/2011M
arsigit, Indonesia
![Page 60: DEVELOPING THE ATTITUDE AND CREATIVITY IN …staffnew.uny.ac.id/upload/131268114/penelitian/DEVELOPING+THE+… · PFolio, Assess ment. PFolio, Social Context. Diver sity. Monocult](https://reader034.vdocuments.mx/reader034/viewer/2022050215/5f60c44b23ab9443f4274f3e/html5/thumbnails/60.jpg)
The teacher need to develop various methods of teaching, various learning resources, and various interaction/communication
7/20/2011M
arsigit, Indonesia
IN ORDER TOPROMOTE MATHEMATICAL ATTITUDE
AND CREATIVITY:
![Page 61: DEVELOPING THE ATTITUDE AND CREATIVITY IN …staffnew.uny.ac.id/upload/131268114/penelitian/DEVELOPING+THE+… · PFolio, Assess ment. PFolio, Social Context. Diver sity. Monocult](https://reader034.vdocuments.mx/reader034/viewer/2022050215/5f60c44b23ab9443f4274f3e/html5/thumbnails/61.jpg)
7/20/2011M
arsigit, Indonesia
![Page 62: DEVELOPING THE ATTITUDE AND CREATIVITY IN …staffnew.uny.ac.id/upload/131268114/penelitian/DEVELOPING+THE+… · PFolio, Assess ment. PFolio, Social Context. Diver sity. Monocult](https://reader034.vdocuments.mx/reader034/viewer/2022050215/5f60c44b23ab9443f4274f3e/html5/thumbnails/62.jpg)
The evidences indicated that most teachers still have problems in developing mathematical attitude in the frame of mathematical world orientation to formal form of mathematics.
7/20/2011M
arsigit, IndonesiaIN ORDER TO
PROMOTE MATHEMATICAL ATTITUDEAND CREATIVITY:
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7/20/2011M
arsigit, Indonesia
![Page 64: DEVELOPING THE ATTITUDE AND CREATIVITY IN …staffnew.uny.ac.id/upload/131268114/penelitian/DEVELOPING+THE+… · PFolio, Assess ment. PFolio, Social Context. Diver sity. Monocult](https://reader034.vdocuments.mx/reader034/viewer/2022050215/5f60c44b23ab9443f4274f3e/html5/thumbnails/64.jpg)
Material model of mathematics and searching the relationship help the teacher to develop method to encourage students to develop their mathematical attitude and creativity.
7/20/2011M
arsigit, IndonesiaIN ORDER TO
PROMOTE MATHEMATICAL ATTITUDEAND CREATIVITY:
![Page 65: DEVELOPING THE ATTITUDE AND CREATIVITY IN …staffnew.uny.ac.id/upload/131268114/penelitian/DEVELOPING+THE+… · PFolio, Assess ment. PFolio, Social Context. Diver sity. Monocult](https://reader034.vdocuments.mx/reader034/viewer/2022050215/5f60c44b23ab9443f4274f3e/html5/thumbnails/65.jpg)
7/20/2011M
arsigit, Indonesia
![Page 66: DEVELOPING THE ATTITUDE AND CREATIVITY IN …staffnew.uny.ac.id/upload/131268114/penelitian/DEVELOPING+THE+… · PFolio, Assess ment. PFolio, Social Context. Diver sity. Monocult](https://reader034.vdocuments.mx/reader034/viewer/2022050215/5f60c44b23ab9443f4274f3e/html5/thumbnails/66.jpg)
THANK YOU
7/20/2011M
arsigit, Indonesia