One
of the things that concerns educators when teaching in the classroom is how to embed math
concepts to students so that students can understand
the lesson. So the students are not just enter
a formula to resolve the problem but the student
can use his understanding as logic to solve
a problem. So
that, educators need to conduct research on
the management of class actions is good. From
this post can be seen that students can understand mathematics concepts through
their own discoveries,
through sharing with
friends so they can understand math concepts.
This study brings an inspiration for me
to be able to do something that can make the learning better.
LESSON STUDY ON MATHEMATICAL THINKING: Developing Mathematical Methods in Learning the Total Area of a Right Circular Cylinder and Sphere as well as the Volume of a Right Circular Cone of the Indonesian 8th Grade Students Marsigit, Mathilda Susanti, Elly Arliani Yogyakarta State University, Indonesia
Posted on
20.36
- by Siti Nuruniyah
Dalam studi ini, para peneliti berusaha untuk mengungkap aspek upaya siswa dalam mengembangkan metode matematika dalam mempelajari total luas sebuah silinder lingkaran tegak dan bola serta volume kerucut lingkaran tegak dari siswa kelas 8 SMP.
Krygowska (1980) dalam Bonomo MFC menunjukkan bahwa matematika harus diterapkan pada situasi alami, dalam setiap masalah nyata yang muncul, dan untuk menyelesaikannya, perlu menggunakan metode matematika. Pengetahuan, keterampilan, dan metode matematika merupakan dasar untuk mencapai pemahaman tentang ilmu pengetahuan, informasi, dan bidang pelajaran lain di mana konsep-konsep matematika adalah pusat. Studi ini menemukan bahwa guru memiliki peran penting untuk mendorong siswa mereka untuk mengembangkan metode matematika.
Dalam Lesson Study, para peneliti berusaha untuk mengungkap gambaran di mana guru diupayakan untuk mempromosikan metode matematika dalam mempelajari total luas sebuah silinder lingkaran tegak dan bola serta volume kerucut lingkaran tegak. Hasil penelitian yang amat terlihat dapat dinyatakan bahwa metode matematika siswa dapat ditelusuri melalui skema kegiatan belajar mengajar sebagai berikut:
1. Masalah Pembentukan dan Pemahaman itu muncul ketika para siswa:
a. Mengamati model tertentu dari silinder lingkaran tegak, mengamati model tertentu dari bola, dan mengamatii model tertentu kerucut lingkaran tegak
b. mengidentifikasi komponen-komponen dari silinder lingkaran tegak, bola, dan kerucut lingkaran tegak
c. mendefinisikan konsep silinder lingkaran tegak, bola, dan kerucut lingkaran tegak,
d. mendapat pertanyaan dan pemberitahuan dari guru untuk mencari konsep-konsep
d. mendapat pertanyaan dan pemberitahuan dari guru untuk mencari konsep-konsep
2. Membangun Perspektif ketika para siswa:
a. menggunakan model yang konkret untuk mencari luas total silinder lingkaran tegak, area bola dan volume kerucut lingkaran tegak
b. belajar bahwa tinggi silinder yang tepat adalah sama dengan lebar persegi panjang tersebut; dan keliling lingkaran adalah sama dengan panjang persegi panjang
c. panduan belajar guru untuk memahami prosedur bagaimana untuk mencari volume kerucut lingkaran tegak
c. panduan belajar guru untuk memahami prosedur bagaimana untuk mencari volume kerucut lingkaran tegak
d. pisah-pisahkan model silinder lingkaran tegak menjadi komponen-komponennya
3. Solusi muncul ketika para siswa:
a. mencoba untuk mencari tahu luas permukaan silinder lingkaran tegak
b. mencoba untuk mengetahui total luas silinder lingkaran tegak
c. mencoba untuk mengetahui luas bola
d. mengumpulkan data dari pengukuran volume kerucut dibandingkan dengan volume silinder
A. Introduction
Giving understand to the students is not easy. Need a various methods in the learning so the students can understand the mathematics easily. But in fact, the students still feel different to understanding the mathematics while the teachers have changed their teaching style. Mathematics become an abstract lesson and unknown for their daily life. So need an innovation in the learning of mathematics so the mathematics become near with the daily life.
Many kinds of methods have applied in the process of learning mathematics. The teachers have changed their teaching style too. From the traditional method to modern method. Before it, the teacher just explain the material and then giving the task as the assessment. But in know, the teachers have changed. They try to make the students more active, suppose through the small group discussion activity, reflection activity, and make their conclusion which it formulated by the students selves.
Mathematics that very abstract for the students, make the students very difficult to understand and feel the mathematics is not related with the daily life also not meaning for them. The next result, the students difficult to give the meaning of mathematics in the daily life and different to make the mathematics as the part of their life. So that need the learning of mathematics that would approach the mathematics in the srudent’s life that is through give the problem in the mathematics that have related with the students daily life. In the progress country, the learning of mathematical contextual become a solution to give knowledge about mathematics. So the students feel that mathematics become a part of their daily life, near with their life and they feel that mathematics don’t become abstract for them but it’s real and there is in their life also benefit for their life.
Contextual mathematics in many countries may be different. Because the mathematics develop based on the social context and culture from each country. But in nature it is same that is make the mathematics become near with the students life and more real for them.
B. Mathematics Teaching Across Multicultural Context
Different country sure different culture and social context. It is make context mathematics in each country are different. It is to make the students in each country can understand the mathematics more real and near with their daily life. Many researchers have researched about the contextual mathematics in their county. They find that mathematics would easy to understand by the students if the problem in the mathematics as the problem in their daily life. So the students can construct their cognitive skill by their selves. In follow would explain about the mathematics context in several countries.
a. Indonesian context
In Indonesia, mathematics more emphasize on the problem solving activities. The learning not the teacher centered but the students centered, so the students should active. The students are given the problem in their daily life, then by the discussing in their groups they try to construct their cognitive ability. They try to make the solve about their problem. While the teachers try to develop the teaching method that based on their daily life. Especially, the teachers make lesson plan, activity plan, also develop the teaching content. To solve the mathematics problem, the students should can understand the problem, identify the problem, collect the information, and then make the solution plan. When the students make the solution plan, the teacher can evaluate the solution steps by identify their difficulties.
The problem in the problem solving based learning is the teachers difficult to develop the teaching contents. They difficult to make the problem to solve by the students. So need the text book that can lead the students to uncover their knowledge and can help the teachers to teach the material. The text book also can motivated the students, can lead the students to make the solving plan, can facilitated the students in learn, and develop the cognitive scheme.
b. Japanese context
In Japanese context, mathematics as problem solving is learning by the students. The students try to solve the problem by make the pole and illustrated it. From this illustrate they can identify the problem and collect the information to construct the solution. By discuss the problem with another student, they obtain the solution then they share with their friends. Japanese teachers often note that, the real lesson begins after students have finished solving the problem. Students build an understanding of the new mathematical concept as they examine and compare solution methods.
To plan a good problem solving lesson, teachers must anticipate the student solution approaches that will emerge, and plan which approaches to discuss with the whole class. The students need to obtain the motivation. The teacher should give the motivation to the students. There are several ways to motivate the students. First, motivation can be built by seeing one’s students show unusually high interest and effort during mathematics lesson and want to repeat this experience for students. A second way that motivation often develop from experiencing the power of problem solving as an adult learner, and want to recreate this experience for students.
c. Thailand context
The final goal of the mathematics learning is to prepare the students in order Mathematical modeling could be defined as translating encountered problems into mathematical forms by seeing mathematics as a tool for solving problems. can confidently in real world. Mathematical modeling is a form of real world problem solving. The problem solving model is focuses on the developing the mathematical skill to finding the solution and help the students to apply in their life. The problem in mathematics can solve by the modeling. The problem can be translate into mathematical models in order to find the solution.
The mathematical modeling consists of four main stage, that is:
1. Observing the phenomena, skets the problem situation that coheren with the phenomena and then identify the important factors that affect the problem.
2. Conjecturing the relationships among factors and interpreting them mathematically to obtain a model for the phenomenon
3. Applying appropriate mathematical analysis to the model
4. Obtaining results and reinterpreting them in the context of the phenomenon under study and drawing conclusions
This process can repeated until we obtain the appropriate to make prediction and we have the conclusion that related with the real world. The modelling would help the students to knowledge and through the modelling the students understand about the problem easily.
d. Russian context
In here would explain about contextual mathematics in Russia, that is about the statistic and probability in the elementary school. In university, the students learn about statistic and the probability after they learn about the random value, distribution, varians, etc. But in the elementary school to learn about the probability, we should to teach by intuitive because the students have no understanding about the random variable, the distribution, random value, etc because their cognitive not yet reach it. So, in this context try to learned about probability in elementary school without the probability theory.
To represented the data, the main methods are make the table or make the chart. It will make easier the students to understand the information. In discussing the real statistic data they can illustrate the random changeability in the world. Thus they prepare the visual conceptual foundation for new and important concepts: random experiment and probability of the elementary outcome. The students can see the data formalization and description on lifelike statistics material.
The process of the learning is by devide the students into several groups. Each group is given the different problem. By dicussing in the group, they find the solution. Then the teacher ask their feed back by reflection. The students explain about their problem to another friends.
e. American context
Student learning in mathematics has been a concern in the U.S. for at least 65 years. Effective assessment plays an important role at all stages of teaching mathematics. At the front end, formative assessment data enables the teacher to understand and anticipate individual students’ learning needs. During the lesson, the teacher needs to monitor students’ learning processes in order to adjust the flow and substance of the lesson to maximize students’ learning. And after the lesson, assessment of student learning informs the teacher about the effectiveness on the lesson and enables him or her to reflect on how it might be improved.
Teachers need to be able to design lessons that are tuned to students’ extant knowledge and prior learning experiences. The teacher must also assess students during a lesson in order to adjust the flow of the lesson to meet the each student’s needs. Developing these skills should be at the core of effective teacher professional development. To develop these competencies, lectures and workshops are not enough. Teachers must have a reliable supporting structure with authentic opportunities to design, implement and reflect on lessons through collaboration with other teachers.
To develop these competencies, lectures and workshops are not enough. Teachers must have a reliable supporting structure with authentic opportunities to design, implement and reflect on lessons through collaboration with other teachers. The power of lesson study comes from a close analysis, during the post-lesson discussion, of the impact of the research lesson on students.
C. Conclusion
Mathematics that very abstract for the students, make the students very difficult to understand and feel the mathematics is not related with the daily life also not meaning for them. The learning of mathematics contextually become a solution to give knowledge about mathematics. Contextual mathematics in many countries may be different. Because the mathematics develop based on the social context and culture from each country. But in nature it is same that is make the mathematics become near with the students life and more real for them.
Different country sure different culture and social context. It is make context mathematics in each country are different. Many researchers have researched about the contextual mathematics in their county. They find that mathematics would easy to understand by the students if the problem in the mathematics as the problem in their daily life.
In Indonesia, mathematics more emphasize on the problem solving activities. The learning not the teacher centered but the students centered, so the students should active. To solve the mathematics problem, the students should can understand the problem, identify the problem, collect the information, and then make the solution plan. When the students make the solution plan, the teacher can evaluate the solution steps by identify their difficulties.
In Japanese context, mathematics as problem solving is learning by the students. The students try to solve the problem by make the pole and illustrated it. From this illustrate they can identify the problem and collect the information to construct the solution. To plan a good problem solving lesson, teachers must anticipate the student solution approaches that will emerge, and plan which approaches to discuss with the whole class.
In Thailand context, to make the mathematics more contextual is trouhg the mathematicals modeling. Mathematical modeling is a form of real world problem solving. The problem solving model is focuses on the developing the mathematical skill to finding the solution and help the students to apply in their life. Mathematical modeling could be defined as translating encountered problems into mathematical forms by seeing mathematics as a tool for solving problems.
In Russian context, they try to learned about probability in elementary school without the probability theory. To represented the data, the main methods are make the table or make the chart. It will make easier the students to understand the information. In discussing the real statistic data they can illustrate the random changeability in the world.
In American context, they try to develop the assesment. Effective assessment plays an important role at all stages of teaching mathematics. At the front end, formative assessment data enables the teacher to understand and anticipate individual students’ learning needs. Teachers need to be able to design lessons that are tuned to students’ extant knowledge and prior learning experiences.
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