INDEPTH THINKING ABOUT MATHEMATICS EDUCATION

We know that a lot of people assumed mathematics is difficult.Where as the assumption is false.They not know that mathematics is interesting,dynamic and flexible. This is considered normally because each people have assumption which different.

Look at  that What is the  different younger people and older people in learn mathematics?It is different.Younger people,they are pattern of thinking is concrete material, so it requires an example of the object being studied environment.In other that object things is fact.And their capability to problem solve very different than older people.While older people, they have a more abstract ideas so as to recognize objects real or abstrak.Because method of thingking them is higher ability and their understanding of a problem is more thorough and detailed.
           We know that mathematics is object thinking. Object thinking is mathematics has value.Mathematics is to abstract.To abstract is take character only certain.To idealize is mathematic have basis principle.

In addition there different between mathematics school and mathematics university. To find out we will learn about school mathematics that have been put forward by Ebbutt and Straker (1995:10-63) in the Ministry of Education (2003) defines school mathematics as follows:

1.    Mathematics as search activity patterns and relationships.

The implication of this view of learning are: provide students the opportunity to conduct discovery and investigation patterns for determine relationships, providing opportunities for students to experiment with different ways, encourage students to discover the sequence, difference, comparison, grouping, etc. encourage students to draw a general conclusion, helping students understand and find a relationship between understanding one another.

2.    Mathematics as problem solving activities

The implication of this view of learning are: provide an environment that stimulates learning math math problems, help students solve math problems using his own way, helping students find the information needed to solve math problems, encourage students to think logically consistent, systematic and develop documentation systems records, develop kompetnsi and skills to solve problems, helping students know how and when to use various visual aids / media math education such as: term, calculators and so on.

3.    Investigation activity

Mathematics is an activity to seek and investigate the truth of a theorem that is, before it used.In this theorem will show that The implications of this to learning are: to encourage initiative and provide an opportunity to think differently, encourage curiosity, the desire to ask, competence and support about competence, appreciate the unexpected discovery as it function than consider it a mistake, encourage students to discover the structure and design of mathematics, encouraging students to appreciate the discovery of other students, encourage students to think reflexive, and does not recommend using only one method alone.

4.    Mathematics as a means of communicating

The implication of this view of learning is: to encourage students to recognize the nature of mathematics, encouraging students to make an example the nature of mathematics, encouraging students to explain the nature of mathematics, encouraging students to justify the need for math activities, encouraging students to discuss math problems, encouraging students to read and manulis mathematics, appreciate language mother of students in discussing mathematics.

In addition there we know that characteristics student in learn mathematics, where the character is as follows:

·      Student have  good motivation and appersaption.

This indicates that the student is really like to mathematics making it easier for him in learning and understanding mathematics.

·      Individual students

Individual students who tend difficult to be approached but would be more comfortable when they do it themselves, so the teacher's role here is only to monitor if he has trouble.

·      Incolaboration with other

Students are like that is indicates that the student like cooperation with his friend, he usually active in the learning activities.

·      Mathematics in contextual

Studying mathematics is a contextual meaning to see where the position of mathematics and showed mathematics is real and interest for example, in daily activity we often see people pay things with money.So we need creat learning methematics contextual in show problem.In learning mathematic contextual will be student development capabilty in analysis and understanding problem which showed.

  

Mathematical Learning

Research in mathematics education has been no less productive, but implementation of that research often leads to difficult questions such as “how much technology is appropriate,” and “in which situations is a given teaching method most effective.”  In response, this paper combines personal observations and education research into a model of mathematical learning.  The result is in the spirit of the models mentioned above, in that it can be used to guide the development of curricular and instructional reform. 

Before presenting this model, however, let me offer this qualifier.  Good teaching begins with a genuine concern for students and an enthusiasm for the subject.  Any benefits derived from this model are in addition to that concern and enthusiasm, for I believe that nothing can ever or should ever replace the invaluable and mutually beneficial teacher-student relationship.

This section briefly reviews the research results in mathematics education and applied psychology that most apply to this paper.  This is far from exhaustive and no effort is made to justify the conclusions in this section.  Interested readers are referred to the references for more information.

Decades of research in education suggest that students utilize individual learning styles (Felder, 1996).   Instruction should therefore be multifaceted to accommodate the variety of learning styles.  The literature in support of this assertion is vast and includes textbooks, learning style inventories, and resources for classroom implementation (e.g., Dunn and Dunn, 1993).  

Moreover, decades of research in applied psychology suggest that problem solving is best accomplished with a strategy-building approach.  Indeed, studies of individual differences in skill acquisition that suggest that the fastest learners are those who develop strategies for concept formation (Eyring, Johnson, and Francis, 1993).  Thus, any model of mathematical learning must include strategy building as a learning style.

           This results in 4 types of learners:

·        Concrete, reflective:  Those who build on previous experience.

·        Concrete, active: Those who learn by trial and error. 

·        Abstract, reflective:  Those who learn from detailed explanations. 

·        Abstract, active: Those who learn by developing individual strategies

Although other models also apply to mathematics, there is evidence that differentiating into learning styles may be more important than the individual style descriptions themselves (Felder, 1996).

Finally, let us label and describe the undesirable “memorize and regurgitate” method of learning.  Heuristic reasoning is a thought process in which a set of patterns and their associated actions are memorized, so that when a new concept is introduced, the closest pattern determines the action taken (Pearl, 1984).  Unfortunately, the criteria used to determine closeness are often inappropriate and frequently lead to incorrect results. 

            As a result, there must be an intermediary—i.e., a teacher—who develops allegories for the students, who determines how much allegorization, integration, and analysis should be used in presenting a concept, and who insures that students learn to think critically about each concept.  And once students can think critically, the teacher will need to synthesize for many of the students by presenting problem-solving strategies and creating new allegories.

            To be more specific, this model suggests the following roles for the teacher in each of the 4 stages of concept acquisition:  

• Allegorization: Teacher is a storyteller.
• Integration:  Teacher is a guide
• Analysis:  Teacher is an expert
• Synthesis: Teacher is a coach.

Space does not permit me to elaborate on each role, but let me point out one that I feel should not be neglected.  Students who have talent are too often bored or even stifled in our educational system.  If we accept that a coach is someone who applies discipline and structure to creativity, then clearly these are students who need to be coached.  In particular, teachers need to insure that synthesizers realize that there is creativity in mathematics, and they need to show that such creativity is both enjoyable and rewarding. 

Sumber: Jeff Knisley,Department of Mathematics,East Tennessee StateUniversity