Learning Of Mathematics
Oleh : alkusaeri
Background
Study of mathematics is one of subject given in the school, starts from primary school until upper comprehensive school, of course, expected in process of the study can reach optimal result, that mathematics which is introductory science in everyday life can be application by each and everyone who is studying it.
Till now in the study, mostly we have not known is that mathematics actually, so that often finds difficulty in learning, given the mathematics essence is expected by the teachers can plan good study, because in its the study must cover, how the student can think mathematics and expansion of position through mathematics study.
Related to that, along with development of epoch hence innovation always is done, to process study to become more maximumly and reachs purpose of expected. If it is seen from the study style in the existing in reality, there is two teacher style in teaching namely conventional teaching style and inovatif teaching style. Following will be explained some things related to mathematics study.
1. Tendencial Logic
What laid open by Kant about source of knowledge has truth which relative, depended from the aspect of each approach, however, from the aspect of different approach source of knowledge that is reality and ability thinks.
Reality as source of knowledge because of without there are clearly will which be comprehended not possible is the knowledge will emerge. Because the science haves the character of objective, as laid open by ( Af. Chalmers, 1983:1). Scientific knowledge is knowledge that is believable, because she has been proved its the truth objectively. This opinion gets support from filosof empiricism stream, what tells that knowledge of the man do not be got through rational common sense which abstraction but through via concrete experience. ( Jujun, 2003:51). According to our understanding how the importance of condition of reality developed as source of knowledge that is clear and as according to condition of epoch, because reality would sticking with condition of the.
Temporary, ability thinks very important of the role in developing reality as perceivable knowledge by public at that moment. Because without there are ability thinks, hence man will not possibly can observe real condition clearly, as opinion, sight the inductivism naïf, that science starting from observation ( Af. Chalmers, 1983:2) and do that shall have organs indera which healthy and is normal, related to condition observed, it is of course we must do it with a mind without there are even little prejudice., this opinion also with reference to rationalism stream opinion, which mendasrkan understanding to x'self and ratio.
Both above understandings even so impressed interferes in, however is each other supports in menumakan a knowledge, because each stream has limitation, the rasionalis will pious of difficulty in replying an its the problems if its way of thinking still doubting and questioned, and burden of proof with facts having the character of konkrit, whereas the emprism would not would possibly holds views it, because the reality it is possible that haves the character of not consisten, so that its the truth is also still be questioned, causing need to be proved with arguments that is is supporting its(the truth.
Above description that is source of knowledge based on by ability to think and observes man, besides there is another source of knowlodge,is apocalipse, where apocalipse is knowledge submitted by the infinite through the courier, and its truth cannot be questioned again.
Related to mathematics science, both source of knowledge above joined to to become one, because itself mathematics kalupun Till now has not there are circular agreement to define is that mathematics, do not mean mathematics cannot be recognized. Like has have been phrased by Soedjadi ( 1985:5) as knowledge of mathematics has some characteristics, that is that mathematics object is not konkrit but abstraction. Given the observation object of mathematics, we can know mathematics essence that is at the same time knowable also way of berfikir mathematics by ET. Ruseffendi ( 1980:148) lays open: The mathematics arisings from man minds is relating to idea, process and common sense. Mathematics consisted of four wide knowledges that is: Aritmatika, Aljabar, Geometry and Analisa. Besides mathematics be the queen science, its intention that the mathematics not depend on other study area.
From the explanation, perceivable that ability thinks thing having the character of very important abstraction of the existence, however shall be supported with symbol-simbol which is clear, as supporting facilities for concept concrete which still having the character of abstraction
2. Reflection Teacher’s Style of Mathematics Teaching by Identifying Their Utterances
Business for increases quality of education in Indonesia of course remain to is executed, and in socializing, that all side involving in it involves is active in the business, however various constraints resulting the business doesn't run at ease accross the board, the business covers, curriculum repair, improvement of teacher professionalism, levying of supporting facilities for infrastructure, and not aside from gives understanding about various study models to teacher through seminars, training, work shop, etc. With a purpose to applicable in the school is each and realized it study process which inovatif.
Identification of Style teachs mathematics teacher told by Student Teacher of In-service Training of Certification Program of Secondary, very stand-out of difference of style teachs between teachers which still teaching with traditional style and style teachs teacher which inovatif, however both the styles is each happened influenced by some factor. At school which has owned facility and supporting facilities for other supporter would very enables develops various study models the each class, however problem education in Indonesia is complectly so that not all schools can apply study model maximaly.
Education in Indonesia untill now still there is a real far difference between each school, particularly between marginal schools with school residing in beyond the city and has a real near by information access in the effort improvement of quality of education. And if it is observed more residing in education institutes boundary with around town is added again with existence of madrasah that is education institute which below wings of The Ministry of Religious affairs that is in general resides in rural.
However, if us speaking about study, which according ( Elaine, 2008:18) mentions two study definitions, inter alia : “( 1) A relatively permanent change indium response potentiality which occur ace a result of reinforced practice, and, ( 2) A change indium hhuman disposition or capability, which can is retained, and which is is note simply ascribable to the process og growth”. From two this perceivable definitions there are three principles in study that need to be paid attention, firstly, learning yields change of my prila am protege which relative permanent, the role of education perpetrator, specially teacher is as change perpetrator.
Second, protege has potency and ability which is seed basic for involding without desisting, its the meaning, education properly sprinkles this basic ability seed so thrives and changes. Learning process teachs like that, be optimalisation of self potency so that is reached ideal quality.
Third, change or pencapain ideal quality of that barrens of experiencing linear in parallel life process. Mean, learning process teachs of course is part of life x'self, but s(he is design peculiarly, and intention for the shake of reaching of condition or ideal quality like called as to be above. From third explains the, however condition of place of taking place learning process to teach, style teachs teacher is not must like style teachs teacher having the character of traditional, with patch up supporting facilities and condition of area of the is teacher shall remain to be able to point process learning is orienting at condition of student, mean, ability and reasoning of student made as base to develop and increases quality of learning to teach.
So do in study of mathematics peculiarly, Mathematics as science introduction, especially in everyday life, in process of the study, shall follow the condition is environmental around, because his would be useful quicker felt by student which in the end will race its enthusiasm is to be more impetous again in learning.
Teacher as fasilitator in study, shall plan study process of matching with requirement of student and condition of the environmental, and gives opportunity larger ones to student to develop their self
3. The Role of Lesson Study to Improve Teaching Learning of Mathematics
Remembers mathematics to have object having the character of abstraction, however having to still be studied, hence the study must be adapted for ability of educative participant, as laid open by Doman ( 1985), express that if mathematics facts given to children balita as according to its(the ability, they will be able to find x'self the orders in it. Likely, mathematics is not Iesson which is difficult if it is submitted with correct planning.
Planning of study program is expected able to reach purpose of desired, of course rather difficult planning, however, after there are statement that is clear about purpose of desired, hence the problem becomes far of lenih easy. In compiling Lesson Study beforehand is done inspection, that is, my prila beginning and my prila between which must be mastered by student, hereinafter, in planning study, must load, inter alia, purpose of mathematics study, mathematics study matter, source study, strategi study, and assesment. ( Aisyah, 2007: 8-12).
The above mentioned components is each other related systematically in study plan. So in compiling study plan of mathematics shall cover principle, that is scientific, relevant, systematic, consistency, adequate, actual, kontekstual, and flexible. ( Aisyah, 2007:8-5). Because study plan of mathematics is operational activity designed by teacher in it contains phase scenario for the shake of phase about activity of mathematics that is later must be done teacher in class, for the purpose, study plan better be compiled by the teacher because she which will apply it.
4. Do we know what is Mathematical Method?
Katagiri, S.S. ( 2004) indicates that question must is created so that problem solving process elicits mathematical thinking and method. What depicted by Katagiri in thinking acurate mathematics if related to mathematics having the character of abstraction which will be made an understanding which konkrit, more for child of SD which the phase idea still at phase konkrit, of what depicted has covered how the step idea of mathematics starts from abstraction, depicts, analogy, presfective, solution and basis logical mind.
The step sequence would more facilitatingly for student to comprehend mathematics it is of course the process also must pay attention to level of student ability, because difference would level of understanding of schoolchild Dasar with higher level school. Thinks mathematical of very important itself to comprehend matter metematika in intact, which if we see this present condition, most student comprehends mathematics just for need of test only, so they will find difficulties in the application of mathematics if it is given on to different condition.
Pays attention to the condition, by Burner in the learning theory arising four teorema/dalil to relate to teaching of each mathematics as “ theorem and theorem”, fourth of theorem is : ( 1) Contruction Theorem; ( 2) Notation Theorem; Contrast and Variation Theorem; and ( 4) conectivity Theorem, fourth of the theorem not for be applied one by one, however combinable as according to characteristic or mathematics topic is being studied and characteristic from learning student.
5. Do we know what is Mathematical Attitude?
From various definition about learning, one of the purpose is realizing man is acting and kind hearted of exaltus ethic, the thing also implicit in purpose of national education, as in arranging in Sisdiknas, 2003. also as that expressed by Gagne, that learning is process enabling man to change tune in permanent, in such a way that the same change will not happened in the situation new. Till now we formulate elementary interest based on taxonomy Bloom with three domains, is : cognitive domain, affective domain, and psikomotor domain.
By Gagne divides result of learning to become five kapability categories as follows; ( 1) information verbal; ( 2) skill intlektual; ( 3) Cognitive strategy; ( 4) Position; and ( 5) skill motorik. Fifth result of this learning also included in result of mathematics learning, related “ Mathematica Attitude” this included in result of learning “ skill intlektual” which including at order forming learning, because in study of order mathematics is formed based on concepts which have been studied, and is statement verbal. So every will finalize permaslahan of mathematics shall follow the order.
Related to forming of position also cendrung response to in stimulus precise on the basis of penilain to the stimulus, response given by someone to one objects might possibly in the form of response which are positive and or negativity response, depends on is the important object or no.
EXPLANATION
Knowledge is a thing which have never released in our life, so that all facts which seems to be becoming source of knowledge for man who developed through ability to think it, from dual of the thing also is found various science types is including mathematics.Mathematics in general terms is knowledge compiled consistently based on deductive logic. Bertrand Russell and Whitehead in the masterpiece trying to proves that mathematics theorems basically is statement of logic.
Aware of important meaning in everyday life, hence mathematics is applied to to become a fundamental subject at education program, so that in process of his(its there is assorted of method in its(the study. In process of his own study shall, teacher must have ability to choose correct method so that mathematics matter can be submitted correctly to student as according to its(the development. Because mathematics which with reference to abstraction ideas given the symbols lapped over hierarchically and its(the common sense is deductive, clearly the mathematics learning is activity of high mental ( Herman, 1988:8).
More detailedly, in study also must be able to develop mathematical patterned thinking and mathematic attitude, because pembelajarn mathematics also leads to cognate ability expansion, afektiv, and psikomotorik. So, that study of mathematics can be felt its(the benefit is directly in everyday life, shall pay attention to condition and student ability, causing study process can run with efektiv and can be comprehended by all students.
Refrence
A.F. Chalmers, 1983. Apa itu yang dinamakan ilmu. Hastamitra. Jakarta
Jujun S. Suriasumantri.2003. Filsafat ilmu (sebuah Pengantar Populer). Pustaka Sinar Harapan. Jakarta
Soedjadi, R. (2000). Kiat Pendidikan Matematika di Indonesia: Konstantasi keadaan masa kini menuju harapan masa depan. Jakarta: Dirjen Dikti
Rusfendi, E.T. (1980). Pengajaran matematika modern untuk orang tua murid guru dan SPG seri kelima. Tarsito.Bandung
Elaine B. Jhonson, Ph.D,. 2008. Contextual Teaching & Learning. Mizan Learning Center (MLC). Bandung
Doman, G. 1985. Ajaklah Balita Anda Belajar Matematika. Yayasan Essentia Medica Yogyakarta.
Nyimas Aisyah. 2007. Pengembangan Pembelajaran Matematika SD. Dirjen Dikti. Jakarta
Shikgeo Katagiri (2004)., Mathematical Thinking and How to Teach It. in Progress report of the APEC project: “Colaborative Studies on Innovations for Teaching and Learning Mathematics in Diferent Cultures (II) – Lesson Study focusing on Mathematical Thinking -”, Tokyo: CRICED, University of Tsukuba. Gagne, Robert. 1983. The Condition Of Learning. Japan: Holt saunders
Bertrand Russell. 1965, On the philosophy of science. The Bebbs-Merril, New York.
Herman Hudojo. 1988. Mengajar Belajar Matematika. Depdikbud Dirjen Dikti. Jakarta
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