Pengetahuan Awal Siswa Sebagai Modal Pengenalan Konsep Aljabar

Setiap siswa mempunyai pengetahuan awal yang dapat digunakan sebagai modal dalam belajar aljabar. Namun disisi lain, tantangannya adalah bagaimana memberikan pemahaman yang cukup sehingga siswa mampu menghubungkan pengetahuan awal yang mereka punya dengan sebuah persamaan di dalam aljabar yang menggunakan dua variabel. Hal ini tergantung pada kreativitas guru, bagaimana seorang guru dapat memodifikasi dan menyusun instruksi-instruksi yang dapat menghubungkan pengetahuan awal siswa dengan konsep aljabar.

Kebanyakan buku  memulai pengenalan aljabar langsung dengan simbol. Padahal, pengenalan aljabar dapat dilakukan dengan memanfaatkan pengalaman yang pernah dialami siswa. Sebagai salah satu contohnya siswa dapat diberi pertanyaan: Jika ada dua angka, jumlah kedua angka 35 dan selisih keduanya 13. Berapakah kedua angka tersebut? Sebagai seorang guru, kita dapat dengan mudah mengenali bahwa persoalan mengenai mysteri number tersebut merupakan permodelan dari dua persamaan dan dua variabel.

x + y = 35           dan            x - y = 13

Namun sesuai dengan pengetahuan awal yang dimilki siswa, ia akan mencoba menyelesaikan persoalan persamaan linear ini dengan pendekatan non symbolik, seperti menebak dua angka yang memenuhi persyaratan di atas. 

Bilangan pertama	20	21	22	23	24	25
Bilangan kedua	15	14	13	12	11	10
Jumlah	35	35	35	35	35	35
Selisih	5	7	9	11	13	15

Namun banyaknya pasangan bilangan yang berjumlah 35 yang ditemukan siswa, hanya akan ada satu pasangan bilangan yang berjumlah 35 dan mempunyai selisih 13.

Proses pembelajaran ini di dalam kelas dapat dilakukan dengan diskusi berpasangan. Masing-masing diberi permasalahan, kemudian dibentuk grup secara berpasangan agar masing-masing dari mereka dapat bertukar pikiran tentang bagaimana menyelesaikan permasalahan tersebut. Kemudian perwakilan masing-masing kelompok maju ke depan kelas untuk menyampaikan hasil diskusi berpasangan, sedangkan siswa lainnya memberikan tanggapan. 

Source: Students today come to fi rst-year algebra with considerable prior experience and a wide range of skills. Teachers need to modify their instructional strategies accordingly. (Kasi C. Allen)

MATHEMATICS INNOVATIVE LEARNING BY ETHNOMATHEMATICS

By

 Venti Indiani

11313244010

Ethnomathematic consists of two words. They are ethnic and mathematics. Ethnic means culture. So it can be said that ethnomathematics is the study of the relationship between mathematics and culture. From the meaning of the word ethnomathematics may be can not represent the education, but we have to know that ethnomathematics developt by educators, not only scientist in pure mathematics.  The history of Mathematics grow in society civilization. There is a society, there is a civilization. It means that both of them can not be apart.

            In education also can not be apart from science, then the question is, is mathematics science? Well according the Emanuel Khan’s theory, that can be called science if contains shyntetic and apriori. Shyntetic usually linked to experience, then apriori linked to the logic. Based on that, mathematics education include on science because mathematics education containt shyntetic and apriori. While in pure mathematics only containt apriori. Pure mathematics just concern in consistency of thruth.

            That is proved that mathematics is a science, then how about ethnomathematics? Science or not? Let see. Ethnomathematics are closely related to experience, where experience are represent apriori. Then where is the synthetic part of ethnomathematics? For learn ethnomathematics, of course we need logic (shyntetic). So that we can called ethnomathematics as a science.

Ethnomathematics is something innovative. It means that ethnomathematics teach us how to learn mathematics in innovative way, where mathematics linked to ethnic or culture around. So what we teach to the children more constextual. Unfortunately, in Indonesia the teacher still become curriculum oriented. Teacher seem like bounded by curriculum. They just teach the student to chase a perfect mark in national examination.

 Ethnomathematics provides various source education, various learning activity, and various experience context. Actually, ethnomathematics is on children world. Because we will learn concrete mathematics by ethnomathematics. Then concrete is very closely to children. That is why ethnomathematics teach us how to apply student centered learning. Student centered learning is an approach to education focusing on the needs of the students, rather than those of others involved in the educational process, such as teachers and administrators. This approach has many implications for the design of the curriculum, course content and interactivity of courses. Student-centred learning is focused on each student's needs, abilities, interests, and learning styles, placing the teacher as a facilitator of learning.

To support innovative learning or student-centred learning, so what can the teacher do? The position of teacher are as the participant, executive, and facilitator. Participants means that teacher participate in learning process. Excecutive means that teacher with students do the learning process. And facilitator means that teachers have to facilitate what the students need. Teacher must know what students need to develop the capability or potency of the students. In innovative learning teacher should not only as the excecutive, but also as the developer of curriculum. 

Then the necessary part of innovative learning is about the teaching method. There are some methods, for example explaining, demonstrating, collaborating, and teaching by learning. Explaining is the process of teaching by giving spoken explanations of the subject that is to be learned. Lecturing is often accompanied by visual aids to help students visualize an object or problem. Demonstrating is the process of teaching through examples or experiments. For example, a science teacher may teach an idea by performing an experiment for students. A demonstration may be used to prove a fact through a combination of visual evidence and associated reasoning. Demonstrations help to raise student interest and reinforce memory retention because they provide connections between facts and real-world applications of those facts. Then, collaboration allows students to actively participate in the learning process by talking with each other and listening to other points of view. Collaboration establishes a personal connection between students and the topic of study and it helps students think in a less personally biased way. Group projects and discussions are examples of this teaching method. Teachers may employ collaboration to assess student's abilities to work as a team, leadership skills, or presentation abilities. And the last is learning by teaching. In this teaching method, students assume the role of teacher and teach their peers. Students who teach others as a group or as individuals must study and understand a topic well enough to teach it to their peers. By having students participate in the teaching process, they gain self-confidence and strengthen their speaking and communication skills. As the innovative teacher we should compile all the methods so that the learning process will be better.

MATHEMATICS INNOVATIVE LEARNING BY ETHNOMATHEMATICS

By

 Venti Indiani

11313244010

Ethnomathematic consists of two words. They are ethnic and mathematics. Ethnic means culture. So it can be said that ethnomathematics is the study of the relationship between mathematics and culture. From the meaning of the word ethnomathematics may be can not represent the education, but we have to know that ethnomathematics developt by educators, not only scientist in pure mathematics.  The history of Mathematics grow in society civilization. There is a society, there is a civilization. It means that both of them can not be apart.

            In education also can not be apart from science, then the question is, is mathematics science? Well according the Emanuel Khan’s theory, that can be called science if contains shyntetic and apriori. Shyntetic usually linked to experience, then apriori linked to the logic. Based on that, mathematics education include on science because mathematics education containt shyntetic and apriori. While in pure mathematics only containt apriori. Pure mathematics just concern in consistency of thruth.

            That is proved that mathematics is a science, then how about ethnomathematics? Science or not? Let see. Ethnomathematics are closely related to experience, where experience are represent apriori. Then where is the synthetic part of ethnomathematics? For learn ethnomathematics, of course we need logic (shyntetic). So that we can called ethnomathematics as a science.

Ethnomathematics is something innovative. It means that ethnomathematics teach us how to learn mathematics in innovative way, where mathematics linked to ethnic or culture around. So what we teach to the children more constextual. Unfortunately, in Indonesia the teacher still become curriculum oriented. Teacher seem like bounded by curriculum. They just teach the student to chase a perfect mark in national examination.

 Ethnomathematics provides various source education, various learning activity, and various experience context. Actually, ethnomathematics is on children world. Because we will learn concrete mathematics by ethnomathematics. Then concrete is very closely to children. That is why ethnomathematics teach us how to apply student centered learning. Student centered learning is an approach to education focusing on the needs of the students, rather than those of others involved in the educational process, such as teachers and administrators. This approach has many implications for the design of the curriculum, course content and interactivity of courses. Student-centred learning is focused on each student's needs, abilities, interests, and learning styles, placing the teacher as a facilitator of learning.

To support innovative learning or student-centred learning, so what can the teacher do? The position of teacher are as the participant, executive, and facilitator. Participants means that teacher participate in learning process. Excecutive means that teacher with students do the learning process. And facilitator means that teachers have to facilitate what the students need. Teacher must know what students need to develop the capability or potency of the students. In innovative learning teacher should not only as the excecutive, but also as the developer of curriculum. 

Then the necessary part of innovative learning is about the teaching method. There are some methods, for example explaining, demonstrating, collaborating, and teaching by learning. Explaining is the process of teaching by giving spoken explanations of the subject that is to be learned. Lecturing is often accompanied by visual aids to help students visualize an object or problem. Demonstrating is the process of teaching through examples or experiments. For example, a science teacher may teach an idea by performing an experiment for students. A demonstration may be used to prove a fact through a combination of visual evidence and associated reasoning. Demonstrations help to raise student interest and reinforce memory retention because they provide connections between facts and real-world applications of those facts. Then, collaboration allows students to actively participate in the learning process by talking with each other and listening to other points of view. Collaboration establishes a personal connection between students and the topic of study and it helps students think in a less personally biased way. Group projects and discussions are examples of this teaching method. Teachers may employ collaboration to assess student's abilities to work as a team, leadership skills, or presentation abilities. And the last is learning by teaching. In this teaching method, students assume the role of teacher and teach their peers. Students who teach others as a group or as individuals must study and understand a topic well enough to teach it to their peers. By having students participate in the teaching process, they gain self-confidence and strengthen their speaking and communication skills. As the innovative teacher we should compile all the methods so that the learning process will be better.