Aug 24, 2009

Epistemology of Mathematics

By Marsigit

Mathematics 1 is about the structure of immediate experience and the potentially infinite progression of sequences of such experiences; it involves the creation of truth which has an objective meaning in which its statements that cannot be interpreted as questions about events all of which will occur in a potentially infinite deterministic universe are neither true nor false in any absolute sense.

They may be useful properties 2 that are either true or false relative to a particular formal system.

Hempel C.G. (2001) thought that the truths of mathematics, in contradistinction to the hypotheses of empirical science, require neither factual evidence nor any other justification because they are self-evident.

However, the existence of mathematical conjectures 3 shows that not all mathematical truths can be self-evident and even if self-evidence were attributed only to the basic postulates of mathematics.

Hempel C.G. claims that mathematical judgments as to what may be considered as self-evident are subjective that is they may vary from person to person and certainly cannot constitute an adequate basis for decisions as to the objective validity of mathematical propositions.

While Shapiro 4 perceives that we learn perceptually that individual objects and systems of objects display a variety of patterns and we need to know more about the epistemology of the crucial step from the perspective of places-as-offices, which has no abstract commitments, to that of places-as-objects, which is thus committed.

He views that mathematical objects can be introduced by abstraction on an equivalence relation over some prior class of entities.

Shapiro 5 invokes an epistemological counterpart that, by laying down an implicit definition and convincing ourselves of its coherence, we successfully refer to the structure it defines.

References:
1 --------, 2004, “A philosophy of mathematical truth”, Mountain Math Software, Retrieved 2004
2 Ibid.
3 Hempel, C.G., 2001, “On the Nature of Mathematical Truth”, Retrieved 2004
4 Shapiro in Linnebo, Ø., 2003, “Review of Stewart Shapiro, Philosophy of Mathematics: Structure and Ontology”, Retrieved 2004 < http://www.oystein.linnebo@filosofi.uio.no>
5 In Linnebo, Ø., 2003, “Review of Stewart Shapiro, Philosophy of Mathematics: Structure and Ontology”, Retrieved 2004 < http://www.oystein.linnebo@filosofi.uio.no>

Aug 19, 2009

Improving Creativities and Understanding of Mathematical Concept for Junior High School Students Grade 2

Examination of Student Final Task
Name of Student: Heri Prasetyo
Departmen: Mathematics Education, Faculty of Mathematics and Science, Yogyakarta State Yogyakarta
Address: Pagotan, Arjosari, Pacitan, East Jawa
Identity : 04301244051, HP: 081911551439
Supervisor: Edy Prajitno, MPd, Endang L,MS
Examiner : Dr Marsigit MA
Day/date: Wednesday, 19th August 2009
Time: 11.00

Chapter I

Title:
Improving Creativity and Understanding of Mathematical Concept through Contextual Approach for Junior High School Students Grade 2, SMP N I Arjosari Pacitan

Backgroud:
Results from observation :
The students were still passive in teaching learning process of mathematics; the level of students curiousity is still low; the students did not brave to deliver the questions; the students were still afraid and not confident to express their ideas; the motivation to solve problems using alternative method were still low; the students only copy the teacher's method.
When the teachers order the students to solve the problems, the students confused how to solve them; the students tended to wait teacher's initiative.
Students' perception:
Most of the students felt to have difficulties to understand mathematical concepts e.g. the students could not solve the problems after getting explanation from the teacher; the students felt to easily forgot mathematics concepts.
Teacher's perception:
The students had their difficulties in learning mathematics; there were the problems how to prepare the students to get high achievements in the national final examination (leaving examination).

Identification of the research's problems:
1. Students' passiveness in learning mathematics
2. Low motivation of students in learning mathematics
3. There are difficulties how to solve problems using various methods
4. Students lack of confident in delivering the question
5. Students curiosity were still low
6. Contextual approach is perceive as one alternative to improve students' creativity and understanding of mathematical concepts.

Limitation of problems:
Research was limited at teaching learning the Cube and Cuboid at the 2 grade of Junior High School.
The aspect of creativity covers (William in Munandar, 1992, p 88): thinking smoothly, thinking flexible, thinking originality, thinking specifically, taking the risk, challenging, curiosity, and respecting.
The aspect of understanding (Sri Wardani, 2006 p 8): representing the concepts, classifying the object in term of their characteristics, determining the examples as well as non-examples, employing and selecting certain procedure, applying the concepts to solving the problems.

Problems Formulation:
How to conduct teaching learning of mathematics through contextual approach which can improve students' creativity and understanding of mathematics of Grade 2 Students of Junior High School.

The Aim of the Research:
To improve students' creativity and understanding of mathematics through contextual approach which can improve students' creativity and understanding of mathematics of Grade 2 Students of Junior High School.

The Benefit of the Research:
1. To empower the teacher in teaching learning mathematics through contextual approach.
2. To empower the students' competencies in improving their creativities and understanding the concepts of mathematics.
3. To improve students' achievement in mathematics
4. To empower the school in innovating mathematics teaching learning process.

Chapter II: Theoretical Review
Definition of mathematics; Learning concept; Teaching learning concept
Creativity; Understanding the concept of mathematics, Contextual Approach

Chapter III: Method of Research
Type of research: Collaborative Class Room Action Reearch
Setting: Venue: SMPN I Arjosari, Pacitan; Time: March-April 2009
Subyect: 36 students of Grade 2 SMPN I Arjosari; 17 male students and 19 female students
Design of the research: Kemmis and Taggart model of CAR: Planning, Action, Observation, reflection
Instruments: Researcher, Questionnaire for students' creativities, Observation Sheet, Interview Guide, Field Note, and Test
Data collection: Observation, Interview, Docummentation,Questionnaire, Test
Analyses Data: Data Reduction, Table of Data, Triangulation of Data, Conclusion.
Indicators: Improvement the average of the percentage of aspects of students' creativity from Cyclus; Improvement the average of the percentage of students' understanding of mathematics from cyclus one to others.

Chapter V: Conclusion
1. Constructing the mathematical concepts: teaching learning process was started by contextual problems and employing concrets materials.
2. Finding out the mathematical concepts: through students works sheets which were developed based on contextual problems. These students works sheets were completed by cube and cuboid models.
3. Questioning the mathematical concepts: the students delivered the questions to their mates or teacher. The teacher should actively initiated to stimulate students' mathematical thinking.
4. Learning society: the optimum number of students in the group to actively discuss is 4 students.
5. Modeling of mathematical concepts: the models could come from the students when they present their answer in front of the class. Modeling could also come from the teacher.
6. Reflecting the results of learning: teacher conducted dialog with the students about the results of learning. The teacher could also give the students problems.
7. Authentic assessment: the teacher assess the students activity, their discussions, their presentations, and the results of students works sheets.

Aug 18, 2009

Syllabus for Philosophy of Mathematics Education

Yogyakarta State University
Faculty of Mathematics and Science
Academic Year 2009/2010
By Dr Marsigit MA


Philosophy of Mathematics Education
Syllabus


Subject Lesson : Philosophy of Mathematics Education
Study Program : Mathematics Education
Lecturer : Dr. Marsigit, M.A.
Code : MMP 211
Credit Semester : 2 (Semester 6)

Standard Competency :
To have experiences in synthesizing the ontological, epistemological, and axiological aspects of mathematics and mathematics education.

Description :
The lesson of Philosophy of Mathematics Education has 2 credit semester. The aim of the lesson is to facilitate the students of mathematics education to have experiences to learn and synthesize the theses and its anti-theses of the ontological, epistemological, and axiological aspects of mathematics and mathematics education. The lesson covers the in-depth study of the nature, the method and the value of mathematics and mathematics education. The material objects the philosophy of mathematics consist of the history of mathematics, the foundation of mathematics, the concept of mathematics, the object of mathematics, the method of mathematics, the development of mathematics, the hierarchy of mathematics and the value of mathematics. The material objects of the philosophy of mathematics education consists of the ideology and the foundation of mathematics education as well as the nature, the method and the value of education, curriculum, educator, learner, aim of teaching, method of teaching, teaching facilities, teaching assessment. Teaching learning activities of this lesson consists of the expositions by the lecture, classroom question and answer, sharing ideas, experiences, students’ assignments, students’ presentation, scientific papers, and browsing as well as developing internet website. The competences of the students cover their motivations, their attitudes, their knowledge, their skills and their experiences. These competencies are identified, assessed, and measured through their teaching learning activities, their assignments, their participations, the mid semester test, the final test and portfolios.

Aug 17, 2009

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