By Naafi Awwalunita
Introduction
Mathematics has special characteristic among almost all of the subjects. It is not an easy job yet it is not difficult one to teach mathematics. Mathematics is the root of all science, the main logic that plays an important part to human’s thinking, the oldest science which evolve the world, and indeed the most neutral subjects ever because you can use mathematics everywhere and it is already there since the very first time God create the universe.
Mathematics teaching also has their own way as if it is a trip which has a lot of directions that lead you to one place. Every teachers/parents/anyone could have their ways to teach mathematics. It is goes as well as each country does. Each country has its own history, history left them culture, culture is growing and slowly evolving due to the globalization. So does mathematics, it has history behind and now it is developed by various scientist due to the globalization.
What is mathematics teaching across multicultural context actually? In this paper, I would explain some of the mathematics teaching on each country based on their culture. There will be different difficulties and its way to solve the difficulties. Those information are available on http://apec-lessonstudy.kku.ac.th/ By knowing mathematics teaching across multicultural context, we can actually learn and share experience or we could adapt it in our country instead, if in fact some of other country had succeeded with certain method. A. Indonesia
The teachers delivered unstructured indications of the constraints for developing textbook for Vocational Senior High School mathematics. The most difficulties they feel to face if they should develop textbook for junior mathematics is about their lack of skill and knowledge of writing mathematical textbook. The others big problems are the difficulties in managing and allocating the time. They indicated others constraints as: it needs a budget; it is not easy to determine the theme of the book; it is not easy to collect supporting data; it is difficult to develop interesting and good illustration textbook; it is difficult to dig up the idea or concepts of textbook and its paradigm; it is not easy how to develop curriculum-based textbook; it is difficult to develop comprehensive textbook; and, it is not easy how to use simple, communicative and standardized language. Small of them indicated that they still have difficulties in developing thematic textbook; difficulties in developing textbook as students’ guide to learn; difficulties in developing problem solving activities; difficulties in promoting students as active learner; as well as, it is not easy how to adapt psychological aspect of students learning mathematics e.g. students’ motivation.
The efforts of developing textbook for Vocational Senior High School mathematics should always put the concern of the criteria of good textbook. Specifically, for the needs to develop textbook for junior mathematics we need to have a clear picture on how to plan and implement activities in the classroom the following: problem solving activities, reasoning and proof, mathematical communication, mathematical connections, mathematical representation, the role of technology, content arrangement and skills development, content appropriate and relevant, wide range of student interests and abilities, and materials easy to follow and understand. In the case of developing the layout or design of textbook we may consider the following: the objectives given for each section; exercises and activities relevant to learning objectives; developing the relevant and useful graph, tables, charts, visuals; cross -curricular learning exhibited; clearly and appropriately defined some key term; and reading level and language use appropriate to students. The problem solving based mathematics textbook in the Vocational Senior High School can be developed based on the criteria outlined by Polya and Pasmep that are: (1) Trial and Error, (2) Making diagram, (3) Trying the simple problem, (4) Making Table, (5) Finding the pattern, (6) Breaking down the goal, (7) Considering the possibilities, (8) Thinking Logically , (9) Reversing the Order, and (10) Identifying the impossibility.
B. Vietnam
In Vietnam, the use of dynamic external representations in communicating, learning and teaching mathematics has increased dramatically. Learners must be able to interpret and use external representations for their own reasoning, investigating, and for communicating mathematics with others. Since 2006, we have designed dynamic models for teaching and learning middle and high school mathematics with the Geometer’s Sketchpad (Tran Vui et al., 2007, 2009), the teachers and students have used these models in exploring school mathematics.
The use of dynamic external representations promotes students’ understanding of school mathematical concepts. Research indicates that positive gains in understanding of mathematical topics appear in cases when multiple modes of dynamic mathematical external representations are used effectively (Lieven V. et al., 2010). Multiple modes of representation improve transitions from concrete manipulation to abstract thinking, and provide a foundation for continued learning. This study investigates the effectiveness of dynamic external representations in helping students reason and investigate school.
Vietnamese mathematics teachers believe that classroom activities are of outmost importance for students learning mathematics. In particular, the use of dynamic external representations encourage students to incorporate many different types of representations into their sense-making, the students will become more capable of solving mathematical problems and understanding underlying concepts. The dynamic external representations really help students practice flexible reasoning and investigate mathematics with relevant curriculum. The processes of solving mathematical problems such as trial and error, conjectures, refutations and generalizations were elements that characterized students’ work with these representations. Flexible thinking and problem solving require external representations with an adequate structure and procedures.
C. Japan
Since lesson study was introduced in the U.S. in the late 1990s, numerous schools and teachers have used lesson study as a major part of their professional development. Although many U.S. lesson studies follow the process as described by researchers, the process is not always as effective as it could be. The power of lesson study comes from a close analysis, during the post-lesson discussion, of the impact of the research lesson on students (Lewis, et al., 2006). Such analysis depends in turn on high quality data collected during the lesson. But, most teachers have had few opportunities to practice collecting data during a lesson, and so the data collected during lessons is typically not very rich or detailed. This limits the depth and richness of the post-lesson discussion and, therefore, the entire lesson study process.
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 (Chung Wei, Darling-Hammond, & Adamson, 2010; Guskey & Sparks, 2002; National Research Council, 2003; Supovitz & Turner, 2000; Wiliam, 2006). Lesson study is a supporting structure that enables teachers to make fundamental changes in their practice, by developing their skills to design, observe and reflect on lessons through collaboration (Lewis, Perry, Hurd, & O'Connell, 2006; Marble, 2007; J. Stigler & Hiebert, 1999; Akihiko Takahashi & Yohida, 2004; Yoshida, 1999).
D. Singapore
Lesson Study has become increasingly popular in Singapore schools as it provides opportunities for teachers to enhance their professional knowledge through collaborative efforts in designing a lesson plan, observing a real lesson and discussing observations of student learning. Such a collaborative learning platform allows teachers to identify critical factors or stimulus such as the choice of tasks, use of variations, use of manipulatives and use of effective questions to promote mathematical thinking for different ability learners. Such findings can be made more explicit in teacher training to help teachers plan and design their lessons (with a focus on mathematical thinking) more effectively.
They are also useful in refining Mathematics textbooks since there is evidence that the four factors have already appeared in the Singapore’s Primary Mathematics textbooks but perhaps more can be done to improve the quantity and quality of open-ended tasks and good questions in textbooks for different levels (including preschool and secondary levels). This professional knowledge gained by teachers through lesson lessons is arguably more real, explicit and ‘accessible’ as it is backed up by actual observations of student learning in the real classroom settings. This calls for further research on the effectiveness of Lesson Study as an alternative form of professional development for teachers versus traditional workshops in training settings
E. Russia
In 2003 Russian Science and Education Ministry had accepted the decision to include the probability theory and statistics into the regular school course of mathematics. By this moment elements of probability theory and statistics were already presented in main school textbooks more than ten years.
The accepted document provides gradual, stage-by-stage inclusion of these sections, giving the chance to pedagogical community to get ready for new subject.
In 2004-2008 many textbooks come out – new special books [2, 3, 4, 11] as well as the supplementary chapters for regular textbooks [6, 8, 9, 10, 12, 13, 17].
For a number of years the textbooks were passing test in schools. Some manuals have been offered for the Russian schools. When a transition period was over, the statistics and probability theory have taken their place in curricula for 7-9 grades. Now we need the analysis and judgment of the first results.
Let's notice that the probability textbooks and courses have been created when we had no teaching traditions in these sections of mathematics. Such position provoked authors on comparison with available universities textbooks which are usually written as manuals in application areas. Therefore universities textbooks often use the various terms for the same concept, various notations for the main objects and formulas.
There are many other difficulties Russian have stumble over. That is why some authors groups decided to join their efforts and develop methodological ideas and positions about unification the main concepts for junior school stochastic course. It is very important as well as creating the unified notation and terminological base
Scattering charts is absolutely new for Russian school. When working with them it is the convenient case to talk about variety of relations in the world around us. Moreover, scattering chart may be successfully tied with affine function that is studied mainly in 7 and 8 grades.
On April 3 seven-graders of Moscow school 1000 have shown the lesson pursuing some specific goal. Russian are not striving to demonstrate skills of the teacher or new teaching technologies and wonders. What Russian tried to do is to show how to work with new and unaccustomed things in math course.
F. Brunei
Teachers in Brunei Darussalam generally use recommended textbooks or books supplied by the Ministry of Education in order to teach their students. Some of the the teachers only rely on those books while there are some who would look at other books or surf the internet in order to get ideas on how to teach a mathematics topic effectively. Lessons are changed or adapted accordingly to suit the different levels of pupils in the classrooms. This paper would examine the design of a lesson in the topic of “comparing fractions” at year 4 level. The research lesson was designed according to the recommendations from the recommended text- book with changes to make the lesson more interesting.
In order to create something interesting and fun as the lesson starter, the teacher plays the musical chair game with the pupils. The purpose of the introduction is to define the word ‘compare’ and ‘size’. Before the game started, pupils were asked to guess who will win the game and why. Some say the bigger girl will win because she is stronger and could push away the small girl and other say the smaller girl will win because being small, she is quicker.
After the game was played and the bigger girl won, the teacher then connected the words bigger and smaller, stronger and weaker, quicker and slower to the word ‘compare’ and bigger and smaller or shorter and taller to ‘size’. She then proceeded clarify that in comparing fractions, the size of the fraction is important. She also asked the students why we need to compare fraction in real-life.
The pupils were excited with the game, however were not very responsive to the questions. I am quite sure that it is the language issue and the meanings were lost in the excitement of the game. Although the class enjoyed the introduction, most of the observers thought the definition could be done in a simpler way. The lesson can be considered a success if we consider pupils’ participation in class. The children were active, participative and looked interested in the lesson. However, they still need to improve in terms of communication, reasoning or mathematical thinking.
