20110917 Kuliah 1 - Kuliah 1 - Philosophy of Maths Education

8/3/2019 20110917 Kuliah 1 - Kuliah 1 - Philosophy of Maths Education

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Philosophy and History of Mathematics(Falsafah dan Sejarah Matematik)

TMP 6073

Prof. Madya Dr. Hj. Noor Shah Hj. Saad

Pensyarah Pendidikan Matematik/

Pengarah Pusat Kecemerlangan & Pembangunan Insan, UPSI

[email protected]

Hak Cipta Noor Shah Saad, Hak Cipta Terperlihara
mailto:[email protected]:[email protected]


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Categories of The Knowledge Base

Content knowledge General pedagogical knowledge

Pedagogical contents knowledge (PCK)

Curriculum knowledge

Knowledge of learners and their characteristics

Knowledge of educational context

Knowledge of educational ends, purpose, and value and their

philosophical and historical grounds

Shulman (1986) 7 categories of knowledge


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Content knowledge (Subject matter knowledge)

- Substantive structure:

Knowledge of the major facts, concepts, principles withina field and the relationships among them.

- Syntactic structure:

The nature of enquiry in the field, and how new knowledge is

introduced and accepted in that community, history of theknowledge in the discipline


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Knowledge of Educational Ends, purposes, andvalues, and their philosophical and historicalgrounds.

Phil h Hi f


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Philosophy & History ofMathematics

Falsafah Matematik- Falsafah- Matematik- Falsafah Pendidikan Matematik- Falsafah Pendidikan Kebangsaan

Cabang-cababang Falsafah- Metafizik- Etika- Logik

- Epistemologi

Bidang-bidang falsafah- Logikisme- Intuisisme

- Formalisme

PART I

Phil h & Hi f


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Philosophy & History ofMathematics

Falsafah Matematik

- Falsafah- Matematik- Falsafah Pendidikan Matematik- Falsafah Pendidikan Kebangsaan

Cabang-cababang Falsafah- Metafizik- Etika

- Logik- Epistemologi

Bidang-bidang falsafah- Logikisme- Intuisisme- Formalisme

Sejarah Matematik- Matematik Islam- Matematik Barat- Matematik Cina- Matematik India

Pengajian tentang falsafah tidak lengkap tanpa unsur sejarah yang

bernah mencorak perkembangnya.


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Falsafah

- Berasal daripada sebtuan Latin philosophia bermaksud Cinta kepadakebenaran

- Eropah Barat ilmu fizik (Mathematical Principles of naturalPhilosophy)

- Peradaban Islam falsafah dimaksudkan sebagai ilmu warisanpemikiran Yunani, khususnya Aristotle, Plato dan Neo-Platoisme yangdisaring dalam acuan islam.Ibn Sina, al-Kindi, al-Haytham & al-Farabi ahli falsafah Islam.

- Ilmu yang berkaitan dengan pemikiran yang menghubungkan alamtabii dan alam ketuhanan.

- Zaman moden, pengjian tentang alam tabii disebut sebagaisains tabii iaitu sebagai ilmu fizik. Manakala metafizik adalah ilmuberkaitan dengan ketuhanan.


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Matematik

- Bilakah matematik bermula?Tiada jawapan yang tepat tetapi matematik muncul seawalkemunculan insan di muka bumi.

- Koleksi ilmu yang dibina berdasarkan aksiom, berbentuk kuantitatifatau kualitatif, yang mengkaji hubungan antara kedua-dua aspektersebut yang dibina secara deduksi atau induksi.

- aspek kuantitatif dan kualitatif ini berkembang secara selari di manafaktor pengerak kajian matematik bukan bermula dengan aspek

kuantitatif tetapi bermula dengan falsafah dan aspek kualitatif.

- Matematik adalah ilmu untuk mencari hakikat kebenaran.

- Matematik adalah ilmu perantaraan antara kuantitatif ke aspekkualitatif, mengetahui hakikat diri dan pencipta (Euklid).


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Falsafah Pendidikan Matematik(The Philosophy of Mathematics Education)

- Isu tentang what is the nature of mathematics-most perfect of all science (Lakatos, 1986)-queen of all science (McGinnis, Randy, Shama, McDuffie, Huntley, King &

Watanabe, 1996)-a science in its own right (Mura, 1995)

The way we learn and teach mathematics within the classroom and theschool environment (Southweel, 1999)

Platonistjust entity out there waiting to be discovered

Then it will be enough for schools to present the curriculum instruction as amere collection of facts, definitions and algorithms.

Teaching mathematics would be like just transmitting an immutable body ofknowledge that students have to accept as a perennial facts without anyreasoning.


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Polya (1986), mathematics is both demonstration and creation.

Demonstration is achieved by proofs while creation consists ofplausible reasoning that includes guessing

Mathematical methods are not perfect and cannot claim absolutetruth. Mathematics truth is not absolute but relative because in facttruth is time dependent (Grabiner, 1986) and space dependent(Wilder, 1986).

Mathematical methods are also space dependent because differentpeople cultures have different ways of doing and validating theirmathematical knowledge (Ascher, 1991).

Schwabs (1961) issues related to mathematics curriculum

Subject (mathematics) The learner of mathematics The mathematics teacher The milieu of teaching (relationship of mathematics teaching and learning)

its aims Society in general


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Stephen Brown (1995) philosophy of mathemaatics ofeducation focus on:

Philosophy applied to or of mathematics education?

Philosophy of mathematics applied to mathematicseducation or to education in general?

Philosophy of education applied to mathematicseducation?


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1. Philosophy Overall

2. Philosophy of Mathematics

3. Philosophy of Education

MATHEMATICSEDUCATION

Application

Different applications of Philosophy to MathematicsEducation


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Issues of the philosophy of mathematics education

1. What is mathematics?

How can its unique characteristics be accommodated in aphilosophy?

What philosophy of mathematics have been developed? What is their impacts on teaching and learning of mathematics?

What is the rationale for picking out certain elements ofmathematics for schooling? How can mathematics be conceptualized and transformed for

education purpose? What values and goal are involved? How do mathematicians work and create new mathematical

knowledge? How does history of mathematics relate to the philosophy of

mathematics? Is mathematics changing as new methods and information and

communication technologies emerge?


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2. How does mathematics relate to society?

How does mathematics education relate to society?

What are the aims of mathematics education? (ex: the aims of

mathematics teaching?)

Are these aims valid?

Whose aims are they? For Whom?

Based on which values?

The aims of teaching, and learning of mathematics?

How does mathematics contribute to the overall goals of society and education?

What is the role of the teaching and learning of mathematics in promoting orhindering social justice conceived in terms of gender, race, class, ability and critical

citizenship? How is mathematics viewed and perceived in society?

What impact does this have on education?

What is the relationship between mathematics and society?

To whom is mathematics accountable?


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3. What is learning (mathematics)?

What assumptions, possibly implicit, underpin views oflearning mathematics?

Are these assumptions valid? Which epistemologies and learning theories are assumed? What are constructivist, and other theories of learning

mathematics? Do they have any impact on classroom practice? What elements of learning mathematics are valuable? How can they be and should they be assessed? What is the role of the learner?

How important are affective dimensions including attitudes,beliefs and values in learning mathematics? What is mathematical ability and how can it be fostered?


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4. What is teaching (mathematics)?

What theories and epistemologies underlie the teaching of mathematics? What assumptions, possibly implicit, do mathematics teaching approaches rest

on? Are these assumptions valid? What means are adopted to achieve the aims of mathematics education? Are the ends and means consistent? What methods, resources and techniques are, have been, and might be, used

in the teaching of mathematics? What theories underpin the use of different information and communication

technologies in teaching mathematics? What is it to know mathematics in satisfaction of the aims of teaching

mathematics? How can teaching and learning of mathematics be evaluated and assessed? What is the role of the teacher? What mathematical knowledge does the teacher need? What impact do the teachers beliefs, attitudes and personal philosophies of

mathematics have on practice? How should mathematics teachers be educated? What is the difference between educating, training and developing

mathematics? What is the role of research in mathematics teaching and the education of

mathematics teachers?


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5. What is the status of mathematics education as knowledgefield?

What is the basis of mathematics education as a field of knowledge? Is mathematics educations a discipline, a field of enquiry, an interdisciplinary

area, a domain of extra-disciplinary applications, or what? What is its relationship with other disciplines such as a philosophy, sociology,

psychology, linguistics, etc.? How do we come to know in mathematics education?

What is the basis for knowledge claims in research in mathematics education? What research methods and methodologies are employed and what is their

philosophical basis and status? How does the mathematics educations research community jugde knowledge

claims? What standards are applied? What is the role and function of the researcher in mathematics education?

What is the status of theories in mathematics educations? What is the impacts of research in mathematics education on other

disciplines? Can the philosophy of mathematics education have any impact on teaching

and learning mathematics, on research in mathematics education, or oonother disciplines?


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Falsafah Pendidikan Kebangsaan

Pendidikan di Malaysia adalah suatu usaha yangberterusan ke arah lebih memperkembangkan potensiindividu secara menyeluruh dan bersepadu untukmelahirkan insan yang seimbang dan harmonis dari segi

intelek, rohani, emosi danjasmani berdasarkankepercayaan dan kepatuhan kepada Tuhan. Usaha iniadalah bertujuan untuk melahirkan warganegaraMalaysia yang berilmu pengetahuan, berketerampilan,berakhlak mulia, bertanggungjawab dan berkeupayaanmencapai kesejahteraan diri serta memberi sumbangan

terhadap keharmonian dan kemakmuran keluarga,masyarakat dan negara

(PPK, KPM, 2003)


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Falsafah Pendidikan Kebangsaan

Pendidikan di Malaysia adalah suatu usaha yangberterusan ke arah lebih memperkembangkan potensiindividu secara menyeluruh dan bersepadu untukmelahirkan insan yang seimbang dan harmonis dari segi

intelek, rohani, emosi danjasmani berdasarkankepercayaan dan kepatuhan kepada Tuhan. Usaha iniadalah bertujuan untuk melahirkan warganegaraMalaysia yang berilmu pengetahuan,berfikir secara kritisdan kreatif, berketerampilan, berakhlak mulia,bertanggungjawab dan berkeupayaan mencapai

kesejahteraan diri serta memberi sumbangan terhadapkeharmonian dan kemakmuran keluarga, masyarakatdan negara

(PPK, KPM, 2003)


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Matlamat

Kurikulum Matematik Sekolah Menengah bertujuan untuk membentukindividu yang berpermikiran matematik dan berketerampilanmengalikasikan pengetahuan matematik dengan berkesan danbertanggungjawab dalam menyelesaikan masalah dan membuatkeputusan, supaya berupaya menangani cabaran dalam kehidupanharian bersesuaian dengan perkembangan sains dan teknologi (PPK,KPM 2003


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Aims of Mathematics Education

The aims of mathematics education can be a hotly contested area, especially

when new curricula are being developed or disseminated through a national orregional education system.

Ernest (1991): Identified 5 different groups

Industrial Trainer aimsback-to-basics: numeracy and social training in

obedience (authoritarian)

Technological Pragmatist aimsuseful mathematics to the appropriate level and

knowledge and skill certification (industry-centred)

Old Humanist aimstransmission of the body of mathematical knowledge

(mathematics-centred)

Progressive Educator aims

Creativity, self-realisation through mathematics(child-centred)

Public Educator aimscritical awareness and democratic citizenship via mathematics

(social justice centred)

20110917 Kuliah 1 - Kuliah 1 - Philosophy of Maths Education

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