The Method To Solve Multiplying Problem

A. Introduction

Mathematical thinking is the mathematical mode of thought that we use to solve any

problem in our daily life including at schools. It can be defined as applying mathematical techniques, concepts and processes, either explicitly or implicitly, in the solution of problem. It is, according to Katagiri (2006), the most important ability that mathematics courses need to instill because it makes students able to think and make independent judgement. He also said that mathematical thinking allows for an understanding of the necessity of using knowledge and skills as well as learning how to learn by oneself.

Teaching should focus on mathematical thinking. Teachers need to first think of how they can help children appreciate and gain the ability to use mathematical thinking. When children get stuck, rather than helping them directly with useful knowledge and skills, teachers must prepare a way to teach the mathematical thinking required to elicit the knowledge and skill and moreover to teach the attitude that leads to this thinking methods. According to Katagiri (2004), mathematical thinking can be divided into three categories:

§ Mathematical Attitudes

Mathematical attitudes is a very important affective factor in determining students behaviour in mathematical thinking and problem solving because students’ attempts in mathematical thinking depend on how interested they are in problem solving or the lesson.

§ Mathematical Method

Mathematical thinking related to mathematical methods as consisting of inductive thinking, analogical thinking, deductive thinking, integrative thinking, developmental thinking, abstract thinking, thinking that simplifies, thinking that generalizes, thinking that specializes, thinking that symbolizes and thinking expressed with numbers, quantifiers and figures.

§ Mathematical Content

Mathematical thinking related to mathematical content include ideas of sets, units, expressions, operations, algorithms, approximation, fundamental properties and formulas.

B. Observation

In this observation, I ask to one child, he is:

Name : Dipta

Class : 5

School : Elementary School

This is my interview with him:

1. Have your teacher teach you about multiplying system?

Answer: Yes, my teacher was teach me about multiplying.

2. Are you understands?

Answer: Yes, but sometime I can’t do the exercise.

3. What your problem?

Answer: I still difficult to multiply big number.

From this interview I think that Dipta just memories and he don’t understand about the method. But, when I give him a question about multiplying I know that he know the basic method in multiplying. This is the question :

1. Calculate the value of : 12 x 5 = …..

Dipta’s answer is 60

From this problem, he give a right answer. And I ask him, how he solve that problem, he write 12+12+12+12+12=60. It prove that he know about the method, not just memories. But, he difficult to multiply the big number because he should adding much operation.

C. Conclusion

From the observation, researcher can conclude that:

1. The children know about the method of multiplying, because from the interview he explain the right method.

2. The teacher should teach another method. Children have a problem when he must multiply the big number, in this situation the adding method can’t use again.

Reference:

http://pbmmatmarsigit.blogspot.com/2008/12/reflection-on-teaching-of.html

http://www.crme.kku.ac.th/APEC/PDF%202007/Madihah%20Khalid.pdf

The Power of Category and Networking

In Immanuel Kant philosophy, a category is a pure concept of the understanding. The word category comes from the Greek. It’s mean "that which can be said, predicated, or publicly declared and asserted, about something." A category is an attribute, property, quality, or characteristic that can be predicated of a thing. "…I remark concerning the categories…that their logical employment consists in their use as predicates of objects." Kant called them "ontological predicates."

According to Immanuel Kant, "Our ability to judge is equivalent to our ability to think." A judgment is the thought that a thing is known to have a certain quality or attribute. For example, the sentence "The rose is red" is a judgment. Kant created a table of the forms of such judgments as they relate to all objects in general.

• Quantity

o Universal

o Particular

o Singular

• Quality

o Affirmative

o Negative

o Infinite

• Relation

o Categorical

o Hypothetical

o Disjunctive

• Modality

o Problematical

o Assertoric

o Apodictic

This table of judgments was used by Kant as a model for the table of categories. Taken together, these twelve fold tables constitute the formal structure for Kant's architectonic conception of his philosophical system.

• The table of categories

ü Quantity

o Unity

o Plurality

o Totality

ü Quality

o Reality

o Negation

o Limitation

ü Relation

o Inherence and Subsistence (substance and accident)

o Causality and Dependence (cause and effect)

o Community (reciprocity)

There are two elementary principal of category. First is identical, for example: A=A. Second, contradictive principal and the example B is not A. We can see many references in the power of category and networking, in noumena or phenomena. In noumena, there are two criteria category, that is category (categorization) and networking. Where the categorization, we must know the definition, the function, the purpose, and the component of the reference. And in phenomena, there are many step to be a real dream. We must know the category of highlighting ideas in our work, such as: the title, the abstraction, the introduction, the power of category, the power of networking, the relationship, the conclusion, and the reference.

The power of the network can create a bigger, national, global, or local presence than you could create on your own. This categorization has been important to us and helped us develop a much better methodology on how best to utilize our network. Having said that, we also realize that if our never ask, we will never know and we just never know who might know whom, for it is a small world. Network can be divided into three categories or four if we include friends.

There are four predefined relationship categories:

§ Hierarchical: Relationship types that are used to connect objects that have a hierarchical relationship

§ Peer to peer: Relationship types that are used to connect object that have a peer relationship.

§ Support: Relationship types that connect supporting objects to another object (for example, you can connect a News object to a Spreadsheet object).

§ Precedence: Relationship types that connect precedence objects to data resources (for example, you can connect a Precedence object to a File object). Objects that are connected with this category of relationship are displayed in the Information Catalog Center Show Lineage Tree window.

So, with networking we can build good relationship with each other.

Reference :

http://en.wikipedia.org/wiki/Category_(Kant)

TO UNCOVER THE PHENOMENA

The phenomena, we discusses about psychological indication. One of the phenomena is trauma. Trauma caused by an incident without clarification. The effect of trauma is depending on readiness of each individual. Readiness or in psychology called apperception is important factor because it can describe how far effect which hitting someone. More weaken the readiness of someone, ever greater the effect of trauma that happened.

In daily life, common people often think that trauma is a bad thing and it defined in negative meaning. Trauma describes as psychological trouble, like phobia, shock, or in serious condition can make someone become crazy. Nevertheless, in psychology, trauma is not only effect caused by bad thing but also can caused by happily things. One of the examples is surprise, it happen, when someone get something special and never think it before.

Humans must have experienced something every day. Events in can be fun or maybe not fun. But basically any event that we reach will have their own meaning. Extraordinary events that could cause trauma to us. For example I had never experienced a motorcycle accident, after that I afraid wasn’t riding a motorcycle. This is what we call the trauma, but the trauma it should be removed because if we live in the trauma, we feel afraid to try. But after some time we reach the trauma that would be lost, if the injury is not too much pressure on us.

Trauma is the result, and the result is always supposes a cause. Trauma can occur, because caused by one or several factors that accumulate each other. Furthermore, trauma in itself may cause further trauma, and that is, because of the trauma might have been other traumas.