ENGLISH FOR MATHEMATICS EDUCATION

Now, everything is oriented in global, we can take one example, Mathematics Education. For make education in Indonesia can be equivalent  with global education,we need English to communicate with other country ( as we know that English is the International Language ).Through English, we will get information from other countries. So, our education will be improved. And also we can upgrade our students capability. So they can compete in global.
When we are talking about education  for Mathematics Education, we must know what capability that we need. The purpose of English for Mathematics Education is to communicate the knowledge, it is mean that people must understand with what we say. Because of it, we must have capability like:

*  Speaking
Without speak we can not communicate with another people. Although we can use a sign, it can not maximum. Sometimes they will difficult to understand about what we mean.

*  Reading
We need reference to make our conception wider. And hope it can increase our opinion. If we can not read, it will be a big trouble. As we know that majority of reference is a text, so we must read or we get nothing. If we did not have reading capability we can be stupid people, because we can not understand the text.

*  Writing
Beside speaking and reading, also we must have capability to write down about what will we say, what our opinion, etc.

*  Expressing
When we communicate with someone we will face a lot of condition. Like happy and sad. For that  condition we must show our sympathy with expression. If we false, everything will be a trouble. So we need that capability too.

*  Listening
In a communication, beside speak we also have time to listen. Listening our friends story or opinion. If we didn’t have capability to listen,  it will make misunderstanding.

*  Translating
If we false translate what another people say, it will make a misscomunication. Then our conversation will be disturb. So we also need that capability.

 * Presenting
One of the important aspect that needed to communicate is to present a idea, opinion, or information. If we didn’t have capability to present that, we never can say what idea in our mind to another people.

There are a lot of capability that we need to be perfect when communicate in English. Beside capability to communicate with English ( speaking, reading, writing, expressing, listening, translating and presenting ) we also need to expert, such as : grammar, tenses, word, sentence, adject, adverb, vocabulary for make sure our capable in good communication. With all of that we can know all words that we use and also understand the sentences.  Hope we can be better  in communicate. But to expert all of that it’s not easy. We need:

o   Will
In process of study English, did you remember about sentences  “where there is a will there is a way”? Without a will, when there is a problem, we will surrender. Because of that, will as important need  for study English. It depend on someway such as: motivation, positive thinking, high spirit, and happiness.

o   Attitude
With all of what we have been studied, our attitude should be reflected of it. It’s can be extended by behaviour, attitude and action.

o   Knowledge
Knowledge absolutely as principle of what we say. Without it we will be confused. It’s contains understanding, concept, definition, etc. With that we can improved our capability.

o   Skill
Skill needed to expert English. Skill can be improved by try, communicate, engage, collaborate, do, arrange, etc. It’s important  but we mustn’t have skill when we want to studied English. Although we didn’t have skill we can increased it. If we have skill but we didn’t use it, it’s became useless.

o   Experience
“Experience is a good teacher”. Everything  that we got from our experience will unforgettable. Because we have been trough it by ourself.

          Now, we knew what  we need to communicate with English,then we need to explain what Mathematics is. When people heard about the word “Mathematics” they will give many opinion, like Mathematics is difficult subject, make confuse, sucks, and just smart people who love it. But between you who like Mathematics will say that all of them are wrong opinion. Actually, Mathematics is the study of patterns. We may have a given problem to solve, but if it is an example of a set of problems that can be solved ( a pattern ) then we can solve it. Mathematics can be studied as an abstraction , that is with out from reference to the real world . However, Mathematics also underpins the very real human advances in science and technology. Mathematics is one of science knowledge that we need in our life. It’s usefull to help our activities like when we shopping, in bank, when build a house, etc.  It have been taught since we as a children. Since we speak, our Mom will teach us abou Mathematics. She taught us to know about number. Not stop until that, when we are in school, it’s a necessary subject. Even, it’s one of a subject that tested in final examination in Elementary School, Junior High School, and Senior High School. In University, we will discuss about : formal math, axiomatic, and deductive mathematics. It’s contains algebra, calculus, geometry etc. Although some of that have been given in school, in University it’s discuss deeper and wider. Another of that, Mathematics also discuss about applied Mathematics. The applied Mathematics containing of function Mathematics in another knowledge.

Mathematics has been studied for thousands of years. Much of our understanding in Mathematics comes from ancient times. Because of its profound importance, Mathematics is a topic studied from early or pre-school ages right through school. It can be studied at as a degree at university and also forms part of engineering and computer science and general science curricula at university. Mathematics is also a widespread subject of research. Mathematics as the King of other subjects,like Physics, Biology, Chemistry, Geography, Economy, etc.

Now, let’s talk about Mathematics Education. In contemporary education, Mathematics education is the practice of teaching and learning Mathematics, along with the associated scholarly research. However Mathematics Education research, has developed into a large field of study, with its concepts, theories, methods, national and international organizations, conferences, and literatures.

At different times and different cultures and country, Mathematics Education has attempted to achieve a variety of different objectives. These objectives have included, the teaching of :

1)   Basic numeracy skills to all pupils

2) Practical mathematics ( arithmetic, elementary algebra, plane and solid geometry, trigonometry ) to most pupils, to equip them to follow a trade or craft

3)   Abstract mathematical concepts ( such as set and function ) at an early age

4) Selected areas of mathematics ( such as Euclidean geometry ) as an example of an axiomatic system and a model of deductive reasoning

5) Selected areas of mathematics ( such as calculus ) as an example of the intellectual achievements of the modern world

6) Advanced mathematics to those pupils who wish to follow a career in Science, Technology, Engineering, and Mathematics fields

7)   Heuristics and other problem-solving strategies to solve non-routine problems

An increasing amount of research has been done in the area of mathematics education in the last few decades. Here are a few if the major results :

1)    Formative assessment 

Is the best and cheapest way to increase student achievement because its contain of  student engagement and teacher professional satisfaction. Effective assessment is based on clarifying what students should know, creating appropriate activities to obtain the evidence needed, giving good feedback, encouraging students to take control of their learning and letting students be resources for one another.

2) Effective instruction

For helping students gain conceptual understanding are making connections and intentionally struggling with important ideas. Research in the 70s and 80s concluded that skill efficiency is best attained by rapid pacing, direct traditional teaching and and a smooth transition from teacher modeling to error-free practice. More recent research shows that students who learn skills in conceptually oriented instruction are better able to adapt their skills to new situations.

3)  Students with difficulties

Students with genuine difficulties (unrelated to motivation or past instruction) struggle with basic facts, answer impulsively, struggle with mental representations, have poor number sense and have poor short-term memory. Techniques that have been found productive for helping such students include peer-assisted learning, explicit teaching with visual aids, instruction informed by formative assessment and encouraging students to think aloud.

4) Homework

Homework which leads students to practice past lessons or prepare future lessons are more effective than those going over today's lesson. Assignments should be a mix of easy and hard problems and ideally based on the student's learning style. Students must receive feedback. Students with learning disabilities or low motivation may profit from rewards. Shorter homework is better than long homework, and group homework is sometimes effective, though these findings depend on grade level. Homework helps simple skills, but not broader measures of achievement.

5) Bilingualism

Most bilingual adults switch languages when calculating. Such code-switching has no impact on math ability and should not be discouraged.

6)  Learning statistics

When studying staticstis, children need time to explore, study and share reasoning about centers, shape, spread and variability. The ability to calculate averages does not mean students understand the concept of averages, which students conceptualize in a variety of ways—from a simplistic "typical value" to a deeper idea of "representative value." Learning when to use mean, median, and mode is difficult.

7)  Algebraic reasoning

It is important for elementary school children to spend a long time learning to express algebraic properties without symbols before learning algebraic notation. When learning symbols, many students believe letters always represent unknowns and struggle with the concept of variable. They prefer arithmetic reasoning to algebraic equations for solving word problems. It takes time to move from arithmetic to algebraic generalizations to describe patterns. Students often have trouble with the minus sign and understand the equal sign to mean "the answer is...."

     

What can we learn from research? Instead of just looking at whether a particular program works, we must also look at why and under what conditions it works. Teachers can adapt tasks used in studies for their own classrooms. Individual studies are often inconclusive, so it is important to look at a consensus of many studies to draw conclusions. Theory can put practice in a new perspective. For example, research shows that when students invent their own algorithms first, and then learn the standard algorithm, they understand better and make fewer errors. Such findings can have an impact on classroom practice.

The method or methods used in any particular context are largely determined by the objectives that the relevant educational system is trying to achieve. Methods of teaching mathematics include the following:

• Conventional approach - the gradual and systematic guiding through the hierarchy of mathematical notions, ideas and techniques. Starts with arithmetic and is followed by Euclidean geometry and elementary algebra  taught concurrently. Requires the instructor to be well informed about elementary mathematics, since didactic and curriculum decisions are often dictated by the logic of the subject rather than pedagogical considerations. Other methods emerge by emphasizing some aspects of this approach.
• Classical education - the teaching of mathematics within the quadrivium, part of the classical education curriculum of the Middle Ages , which was typically based on  Euclid's Elements taught as a paradigm of deductive reasoning.
• Rote Learning - the teaching of mathematical results, definitions and concepts by repetition and memorisation typically without meaning or supported by mathematical reasoning. A derisory term is drill and kill. In traditional education, rote learning is used to teach multiplication tables, definitions, formulas, and other aspects of mathematics.
• Exercises - the reinforcement of mathematical skills by completing large numbers of exercises of a similar type, such as adding vulgar fractions or solving quadratic equations.
• Problem Solving - the cultivation of mathematical ingenuity, creativity and heuristic thinking by setting students open-ended, unusual, and sometimes unsolved problems. The problems can range from simple word problems to problems from International  mathematics competitions such as the International  mathematics olympiad. Problem solving is used as a means to build new mathematical knowledge, typically by building on students' prior understandings.
• New Math- a method of teaching mathematics which focuses on abstract concepts such as set theory , functions and bases other than ten. Adopted in the US as a response to the challenge of early Soviet technical superiority in space, it began to be challenged in the late 1960s. One of the most influential critiques of the New Math was  Morris Kline's 1973 book Why Johnny Can't Add. The New Math method was the topic of one of Tom Lehrer's most popular parody songs, with his introductory remarks to the song: "...in the new approach, as you know, the important thing is to understand what you're doing, rather than to get the right answer."
• Historical method - teaching the development of mathematics within an historical, social and cultural context. Provides more human interest than the conventional approach.
• Standards-based Mathematics- a vision for pre-college mathematics education in the US and Canada , focused on deepening student understanding of mathematical ideas and procedures, and formalized by the National Council of Teachers of Mathematics which created the Principles and Standards for School Mathematics.

So, when we talk about English for Mathematic Education, we talk about the combination between three components that explained before. English for Mathematics Education is how English communicate the Mathematics material in teaching and learning process.

Sources :

http://en.wikipedia.org/wiki/Mathematics_education

http://englishformathematiceducation.blogspot.com/

http://www.mathematics.me.uk/