Really, we should very glad to be in mathematics education. It is a lot of lesson here and we have to more experience. As a aspirant teacher, we must indeep thinking about mathematics education.
The differences between mathematics between young and older people are physically was different. Younger people, they concrete material of mathematics from daily life. And adult people, they can thinking abstract.
In formal (for adult people), mathematical objects such objects thought. Thought objects obtained from a concrete object with doing "abstraction" and "idealization". Abstraction is an activity in which only take the properties only certain thing to think about or studied. Idealization is to assume perfect activity existing properties.
For example, there were two numbers, 1 and 3. Suppose 1 was written bigger than 3 in size. As adult people, we can conclude that 3 is greater than 1. Because the value of 3 is greater then the value of 1. But, younger people will think 1 is greather than 3 because they just thinking in something real.
Material of mathematics in school and university is different. Mathematics in school have concrete material of mathematics from daily life. And mathematics in university, the material being complicated and abstract, consist of definitions, theorems, axioms,etc.
· From Mr. Marsigit's paper we know that Ebbutt Straker (1995: 10-63) defines school mathematics, as follows:
1. Mathematics as search activity patterns and relationships
The implication of this view of learning are: gives students the opportunity to conduct discovery and investigation patterns to determine the relationship, provide an opportunity for students to perform trial premises in various ways, encourage students to discover the sequence, difference, comparison, grouping, etc , encourage students to draw general conclusions, help students understand and find relationships between understanding one another.
2. Mathematics as a creativity that requires imagination, intuition and invention
The implication of this view of learning are: encourage initiative and provide an opportunity to think differently, encourage curiosity, desire to ask, the ability to refute and the ability estimates, appreciate the unexpected discovery as beneficial rather than consider it a mistake, encourage students to discover the structure and design mathematics, encourage students to appreciate the discovery of another student, encourage students to think reflexive, and does not recommend using only one method alone.
3. Mathematics as problem solving activities (problem solving)
The implication of this view of learning are: provides mathematics learning environment that stimulates the emergence of mathematical problems, help students solve math problems using his own way, help students find the information needed to solve problems mathematics, encourage students to think logically, consistent, systematic and develop a system of documentation / records, develop the capability and skills to solve problems, help students learn how and when to use various visual aids / media such as mathematics education: term, calculators, etc.
4. Mathematics as a means of communicating
The implication of this view of learning are: encourage students know the nature of mathematics, encourage students to make an example the nature of mathematics, encourage students to explain the nature of mathematics, encourage students to give reason the need for math activities, encourage students to discuss issues mathematics, encourage students to read and write mathematics, respect students' mother tongue in talking about mathematics.
· Characteristics of Student Learn Mathematics
From Mr. Marsigit's paper we also know that Ebbutt and Straker (1995: 60-75), gave his view that the potential for students can be developed optimally, assumptions about the characteristics of learners and subject implications for learning mathematics are given as follows:
1. Pupils will learn math if they have motivation
The implications of this view for the business teachers are: provide activities that fun, attention to the desire of students, build understanding through what i known by students, creating a classroom atmosphere that supports the activities learning, provide activities that match learning objectives, provide a challenging activity, provide activities that give expectations of success, respect for each student achievement.
2. Pupils learn mathematics in its own way
The implications of this view are: students learn in different ways and with different speeds, each student who requires special experience connect with his experiences in the past, each student has a background socio-economic back cultures. Therefore teachers need: know the strengths and weaknesses of their students, planning activities according to the level of student ability, build knowledge and skills he obtained a good student at school and at home, using the record student progress (assessment).
3. Pupils learn math either independently or through collaboration with his friend
The implications of this view for the business teachers are: provide an opportunity learning in a group to train co-operation, provide learning opportunities the classical to provide opportunity to exchange ideas, gives opportunity for students to conduct their activities independently, involves students in decision-making on activities to be done, and teaches how to learn mathematics.
4. Pupils need a context and in different situations in learning mathematics
The implications of this view for the business teachers are: provide and using various props, provide opportunities to learn mathematics in various places and circumstances, provide an opportunity to use mathematics for various purposes, develop an attitude of using mathematics as tools to solve problems at school and at home, appreciate contribution to the tradition, culture and art in the development of mathematics, and help students assess their own mathematical activity.
