Mathematics is me.

Mathematics values trough problem solving

We are in real life. We need to adapt with many problems in our life. So, what should we do to make easier to solve our problems? One of the way that can we do is ‘study mathematics’. And the question is ‘what is the reason why mathematics can help me when we get a problem?’

Actually, mathematics help us to know about how to read a map to find directions, how to understand weather reports, how to understand economic indicators, how to understand loan repayments, and also how to calculate whether the cheapest item is the best buy. They are examples of the problems that we usually see in our real life.

They are three types of the problem. First, is preparing us for the challenges of life. Mathematics teaches us to solve our problems (in mathematics) with the rule and applying the formula to get the solutions. And if we often think about the complex things we can get the solutions easier than other people who never learn mathematics. Second, is encouraging the development of general knowledge and common sense. So, not all of our knowledge can be applied to get the solutions, and mathematics helps us to choose which one the knowledge that can be applied in our problems. Mathematics gives us ‘non-routine’ problems which require a higher degree of interpretation and organization of the given information rather than just the application of the rule. The last, is engaging us in service to society. We live in social community, so we have to adapt with our society too. Mathematics gives us the ‘real’ problems which is concerned and can be investigated by mathematics rule as the tools to find the solutions.

Now, we talk more about the three types of the problems.

1.      The problems that can be solved by the direct use the rule of mathematics

Let me give examples of the problem that can be solved by direct use the rule of mathematics.

1.      How much money does your father spent for a day?

2.      How much money do you get for buying a toy car?

3.      How many friends do you have in your elementary school?

All of the questions maybe have the different answer depend on each person. And we called it as the Fermi problems. Fermi problem is the problem that has not enough information to be solved. Fermi problems encourage us to think more and more. And we know that there are many flexible problems and also many ways to find the solutions depend on the way of looking at the problems.

2.      Non-routine problems

Non-routine problems are the problems that can be solved not only by using knowledge but by using logical thinking too. For example, what is my lucky number? If I divided it by 7 my lucky number has no reminder. If I divided it by 6 the reminder is 1. If I divided it by 5 the reminder is 2. If I divided it by 4 the reminder is 3.

3.      Real problems

Real problems are the problems that we usually see in our real life. Sometimes we get the problems from our self. And we have to investigate them by our self. The investigational problem more interest to be solved because it happens in my life.

Actually, mathematics is me. Because mathematics always there in my life. Mathematics also help us to solve our problems. Help us to think more and more and if we often think about that, we can choose the way easier to find the solutions of our problems. Everybody uses mathematics whether they realize it or not. Agriculturists determine the proper amounts of fertilizer, water to produce the food. Geologists use mathematics to help them when they want to find oil and study earthquakes. Architects have to know how to calculate loads for finding acceptable materials in design when they want to make design buildings.

Mathematics develops our logical thinking, encourage flexibility and ability to respond unpredictable situations, encourage our curiosity, and make our brains to think faster than before when we want to choose one way to find the solutions.

Source :

http://www.mathgoodies.com/articles/teaching_values.html

The New Paradigm of Teaching-Learning Process of Mathematics, School Mathematics, and Students Learn Mathematics

Mathematics is practice. It comes from human thinking, it is proven and finally mathematics is held become one system. There are two system of mathematics, pure mathematics and school mathematics.

The formal system is called pure mathematics. It is according to the definitions, axiom, and can build many new theorems/axiomatic. Pure mathematics is for older people and they like to think about something new in Mathematics. Long time ago, there was one statement that mathematics is for mathematics. People who could not solve Mathematics problem, were not their business.

The second system, is called school mathematics. School mathematics is needed when we look at the school- one of the place that many students learn mathematics. The teachers have to adapt the condition of their students. So, they will not be exclusive.

School Mathematics. Ebbutt, S. and Straker, A. (1995) said that Mathematics is a search for patterns and relationship, Mathematics is a creative activity, involving imagination, intuition and discovery, Mathematics is a way of solving problems, and Mathematics is a means of communicating information or ideas.

Now, we want to get more detail about four statement in above.

a. Mathematics is a search for patterns and relationship

As a search for pattern and relationship, mathematics can be perceived as a network of interrelated ideas. Mathematics activities help the students to form the connections in this network. It implies that the teacher can help students learn mathematics by giving them opportunities to discover and investigate patterns, and to describe and record the relationships they find; encouraging exploration and experiment by trying things out in as many different ways as possible; urging the students to look for consistencies or inconsistencies, similarities or differences, for ways of ordering or arranging, for ways of combining or separating; helping the students to generalize from their discoveries; and helping them to understand and see connections between mathematics ideas. (ibid, p.8)

b. Mathematics is a creative activity, involving imagination, intuition and discovery

Creativity in mathematics lies in producing a geometric design, in making up computer programs, in pursuing investigations, in considering infinity, and in many other activities. The variety and individuality of children mathematical activity needs to be catered for in the classroom. The teacher may help the students by fostering initiative, originality and divergent thinking; stimulating curiosity, encouraging questions, conjecture and predictions; valuing and allowing time for trial-andadjustment approaches; viewing unexpected results as a source for further inquiry; rather than as mistakes; encouraging the students to create mathematical structure and designs; and helping children to examine others’ results (ibid. p. 8-9)

c. Mathematics is a way of solving problems

Mathematics can provide an important set of tools for problems- in the main, on paper and in real situations. Students of all ages can develop the skills and processes of problem solving and can initiate their own mathematical problems. Hence, the teacher may help the students learn mathematics by: providing an interesting and stimulating environment in which mathematical problems are likely to occur; suggesting problems themselves and helping students discover and invent their own; helping students to identify what information they need to solve a problem and how to obtain it; encouraging the students to reason logically, to be consistent, to works systematically and to develop recording system; making sure that the students develop and can use mathematical skills and knowledge necessary for solving problems; helping them to know how and when to use different mathematical tools (ibid. p.9)

d. Mathematics is a means of communicating information or ideas

Language and graphical communication are important aspects of mathematics learning. By talking, recording, and drawing graphs and diagrams, children can come to see that mathematics can be used to communicate ideas and information and can gain confidence in using it in this way. Hence, the teacher may help the students learn mathematics by: creating opportunities for describing properties; making time for both informal conversation and more formal discussion about mathematical ideas; encouraging students to read and write about mathematics; and valuing and supporting the diverse cultural and linguistic backgrounds of all students (ibid. p.10)

(marsigitmateri-workshop-qitepphilosophymatheduclesson-study-teamfinal.pdf)

Now, we are going to talk about learning mathematics. There are many factors to indicate when the learning mathematics process are effective, such as :

a.       Students have motivation,

b.      Studens have collaboration with other in learning mathematics,

c.       Students can learn mathematics individually,

d.      Students can learn mathematics contextually.

To make the students have four aspects in above, the teachers have to change the paradigm of teaching-learning process.

An old paradigm, the teachers have function to transfer the knowledge to the students. The teachers give and direct the students. So, there is no chance for the students to develop their logical thinking. The teachers have mission to deliver instructions.

The students like a seed that can grow up and produce a fruit by their self. So, the students must be given many times to develop their own mind. The teachers in here are not to transfer the knowledge but to be a facilitator for the students to facilitate when they learn mathematics. The new paradigm is called constructivism.

There are many things that can be done by the students because in the new paradigm, the students have a chance to speak up their ideas, share with their friends and also try to explain their ideas in public. The teachers give times to share their experiences, so the students try to imagine, think creatively, and build their models and theorems when they try to expose their ideas. And finally, they can identify and evaluate about their mistakes and how to make better than before.

The nature of constructivism is interaction among the students and the teachers to get mathematics objectively. Maybe, they will pass the process like try to publish something that we have learned, justify by the teachers and they will get a new knowledge about mathematics.