My Experience in Learning Mathematics
Mathematics indirectly is the knowledge that has been studied by many people since they born. For example is to know the normality of the baby, the doctor will account the amount of the baby’s part body such as the complete of 10 fingers. And up to know, many people use mathematics to help them solving their daily life problems.
Many people have their own experiences in learning mathematics. I as the student also have my own experience. Sometimes I find some difficulties in learning mathematics. It may caused by some factors. Here there are my experiences in learning mathematics. :

1. Understand the concept.
To solve mathematics problems, it is important to know the concept of mathematics. However the form of the mathematics problem, if we understand the concept, we can solve it well.

2. Draw the picture that reflects the condition of the geometry question.
For example if we want to find the distance of a point in edge of a cube to the diagonal space, it will easier to draw it first. This way will help us to get the true condition and find the true answer.

3. Remember and apply the formula to solve the mathematics question.
Not to think instantly, but there are some mathematics problems that can be solved by some formulas. Such as to find the distance of two points P (3,1)
and Q (0,1). We don’t need to draw it in the Cartesian coordinate because we have simple formula of distance of two points then we get PQ = 3.

4. Account the calculation correctively.
It needs a patient when we try to find the true value of some calculation. Because based on my experience (and most of students), to account some difficult calculation of mathematics problem quickly but incorrectively may cause the wrong result. Perhaps, we can also be helped by calculator or mathematics program in computer.

5. Imagine mathematics question as the real problem on the daily life.
It will help us to make a solution of the question. For example, for the elementary students, it will easier to study linear equation system not on the variable in x and y, but make a simple sample like a book or a pencil. This way hopefully will give a good representation in understanding the concept and the using of mathematics.

6. Learning mathematics on group.
Learning mathematics individually sometimes become ineffectively when we cannot find the true solution or cannot understand the problems. So learning mathematics on group becomes a good answer because it will make a good teamwork to solve the problem. Member of group that has more ability on learning mathematics can help the others. Group also has big influences in growthing the motivation.

7. Have a hard motivation in learning mathematics.
Hard motivation will strengthen the efforts to learn mathematics, although we must face many difficulties.

Quantitative Method for Uncovering & Processing Data related with Psychology of Learning Mathematics at School

Psychology (from Greek), consist of two word psyche & logos. Psyche means soul and logos means science. So psychology is the science dealing with the mind and with mental and emotional processes includes human and animal behavior that can only be identified by the phsycologic symptoms. The symptoms are: cognition, affection, conation, psychomotor.

Learning is a behavioral changing process as the result of interaction among persons and their environment in order to fulfill their needs. Reber (1988) gives 2 definitions that is

• Learning as the process of gaining information & experience.
• Learning is the changing of reaction ability permanently as the result of exercise reinforcement.

Mathematics is the study of numbers, shapes and space using reason and usually a special system of symbols and rules for organizing them (Cambridge Advanced Learner's Dictionary)

Mathematics (noun) is

1. the group of sciences (including arithmetic, geometry, algebra, calculus, etc.) dealing with quantities, magnitudes, and forms, and their relationships, attributes, etc., by the use of numbers and symbols
2. the act or process of using any of these sciences; computation (YourdDictionary.com)

From those definitions, we can conclude that psychology of learning mathematics is the science studies about the situation, behavior, emotion and symptoms of students that happen in the process of gaining information and experience about mathematics.

In the frame of psychology of learning mathematics, we can use quantitative methods to uncover & processing the data.

Quantitative methods are research techniques that are used to gather quantitative data - information dealing with numbers and anything that is measurable. Statistics, tables and graphs, are often used to present the results of these methods.

Inferential statistics as one kind of quantitative method is statistics used to reach a decision. With inferential statistics, we are trying to reach conclusions that extend beyond the immediate data alone. For instance, we use inferential statistics to try to infer from the sample data what the population might think. Or, we use inferential statistics to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study. Thus, we use inferential statistics to make inferences from our data to more general conditions; we use descriptive statistics simply to describe what's going on in our data.

Quantitative method has strict procedures to decide the research variables. It is expressed by its four basic assumptions i.e. ontology (basic reality of social symptoms), epistemology (basic reality of science), basic truth of human, and axiology (the aim of research). By the strictness, quantitative methods will give the objective assessment in order to gain the true decision.

There are some steps on making research by quantitative methods:

1. Identify the problems. Problems are the differences or gap between the reality and something hoped.

2. Develop the models. Model is a representation of a real world. There are some kinds of models such as physics, logic, and mathematics models. To develop the models, we use some variables that its mark will give the effect of decision taken.

3. Collect the data. we should take an enough sample that can representative the condition real population.
   
4. Make a solution.
5. Examine the solution.
6. Analyze results.
7. Implement the results.

Quantitative method related with measurement of some variables. In psychology, we know about psychometrics. Psychometrics is the field of study concerned with the theory and technique of educational and psychological measurement, which includes the measurement of knowledge, abilities, attitudes, and personality traits. The field is primarily concerned with the study of measurement instruments such as questionnaires and tests.

The first psychometric instruments were designed to measure the concept of intelligence. American Psychological Association in 1995 gives the definition of intelligence as:

Individuals differ from one another in their ability to understand complex ideas, to adapt effectively to the environment, to learn from experience, to engage in various forms of reasoning, to overcome obstacles by taking thought. Although these individual differences can be substantial, they are never entirely consistent: a given person’s intellectual performance will vary on different occasions, in different domains, as judged by different criteria. Concepts of "intelligence" are attempts to clarify and organize this complex set of phenomena. Although considerable clarity has been achieved in some areas, no such conceptualization has yet answered all the important questions and none commands universal assent. Indeed, when two dozen prominent theorists were recently asked to define intelligence, they gave two dozen somewhat different definitions.

Shortly, Intelligence is a property of the mind that encompasses many related abilities, such as the capacities to reason, to plan, to solve problems, to think abstractly, to comprehend ideas, to use language, and to learn.

The instrument to measure intelligence known as IQ test that firstly had been developed by Alfred Binet and followed up by Wechsler and other psychologist. We won’t discuss the contradiction about the use of test IQ. We only make it as an example of measurement on psychology.

Correlation between The Setting Time of Mathematics Learning Period and The Students Learning Mathematics Achievement.

Background

Every students want to reach success on their study, includes mathematics. Their success can be expressed by their achievement in learning mathematics. Achievement is effected by some factors such as motivation, emotion, situation and effort of the students.

School also play role on making the result of mathematics learning process. Here, I want to try to observe about the correlation between the setting time of mathematics learning period and the students learning mathematics achievement. It means that setting time of mathematics learning period such as on the afternoon or after the sport lesson will give an effect to the student prestige.

Theory

Maslow's hierarchy of needs is often depicted as a pyramid consisting of five levels:

1. Physiological Needs

2. Safety Needs

3. Love and Belonging Needs

4. Esteem needs

5. Self actualization

The first lower level is being associated with Physiological needs, while the top levels are termed growth needs associated with psychological needs. Deficiency needs must be met first. Once these are met, seeking to satisfy growth needs drives personal growth. The higher needs in this hierarchy only come into focus when the lower needs in the pyramid are met.

Based on the Maslow’s Theory, student as a human also have some hierarchy needs. The basic / first needs are Physiological needs such as eat, drink, sleep, or break and many others. When they learn mathematics, they won’t be enjoying if their physiological needs aren’t fulfilled yet. The setting time of learning mathematics period incorrectly will give bad effect to the student’s motivation. For instance, if the mathematics period is set after the sport lesson. It will cause the mathematics learning process become ineffectively because the students still exhausted or maybe feel hungry after doing sport activity.

Edward Lee Thorndike (behaviorist psychologist) also gives “the law of readiness”. It is concerned with the student’s arousal. Student who ready to learn mathematics will have full spirit & hard motivation to follow the learning process. It can be looked when the school set the time of learning mathematics on the morning or at the first period schedule. Students will study enthusiastically because they still feel fresh and get ready.

Experiment

To know the implication of the setting time of learning mathematics to the student’s achievement, we can make a simple experiment. Choose three different first class of junior high school as the samples. Then apply to each class the different setting time of learning mathematics such as mathematics period on 07.00 a.m. for class 1A, mathematics period after sport lesson for class 1B, and mathematics period on the last period of time for class 1C. By doing this, teacher can see the different attitude reaction of the student during the mathematics lesson. Teacher also may make a mathematics test to the three classes, and its assessment & marks will show variation among the students based on their arousal to face the test.

Questioner

Beside experiment method, teacher has another way to know the correlation between the setting time of learning mathematics and the student’s learning mathematics achievement. The questions could be:

1. What time do you want to learn mathematics at school?

2. What do you feel if you learning mathematics after sport lesson or at the last period of schedule?

3. Do you think that the bad setting time of learning mathematics period influences your result test ?

etc...

Conclusion

After taking some samples, making experiment or questioner, and doing some calculation of statistic data, we can make a conclusion whether the setting time of learning mathematics has positive or negative correlation to the student’s learning mathematics achievement.

What I can reflect about psychological aspect if the student is confronted with the following questions:

Ali has some of pencils and spidols. The amount of Ali’s pencils and spidols are 16. If the prices of all of those things are Rp50.000, 00, so linear equation system that deals with the condition is

x + y = 16 x + y = 16 2x + y = 7 2x + y = 7

A. {ax + by = 50.000 B. {x + y = 50.000 C. {4x + 2y = 10 D. {4x + 2y = 10

The problems of linear equation system in mathematics subject are come up from the matter of daily life. If the student faced by this question, there are some psychological aspect that will be discussed here.

1. Student can imagine this question as the representative of their daily life problem.

Pencils and spidols are the usual things that often uses by students. The amount and the price of those things also can be thought by them. Then, they can make a mathematics sentence by this condition by sampling those things in some variables. Student can name the amount of pencils as “x” and spidols as “y”. And then, the price of pencils called “a” and spidols called “b”. So that suitable answer for the question is A that is,

x + y = 16

A. {ax + by = 50.000

2. The format of the question is Multiple Choices will influence the student’s answers.

Before discuss the effect of multiple choices for the students, let firstly we learn about the meaning of multiple choices.

Multiple choices are a form of assessment in which respondents are asked to select one or more choices from a list. Multiple choice items consist of a stem and a set of options. The stem is the beginning part of the item that presents the item as a problem to be solved, a question asked of the respondent, or an incomplete statement to be completed, as well as any other relevant information. The options are the possible answers that the examinee can choose from, with the correct answer called the key and the incorrect answers called destructors. (Taken from wikipedia)

The question is in form of multiple choice tests where the stem is the information about Ali’s pencils and spidols, the amount and the prices of them. Then the problem should be solved by the students is to make a linear equation system that deals with the condition. While the options are some answers consists of 4 choices that is A,B,C and D. Only one choice gives best answer of the question.

The multiple choice form of the question has some advantages such as

1. Student’s answer can be recalled by the options.
2. In the larger numbers of the students, it will be an effective technique to do assessment of student’s ability. Because it takes less time to correct or evaluate the wrong and the true answers.
3. Multiple choice questions lend the teachers to the development of objective assessment items; however, without teacher training, questions can be subjective in nature. Because this style of test does not require a teacher to interpret answers, students are graded purely on their selections.

Beside the advantages, multiple choice format tests also give bad impact to the student. There are several disadvantages of multiple choice format tests that are:

1. The teacher couldn’t measure the true student’s mathematics ability.

It is because of some students answer the question only by “guessing”. The term "multiple guess" has been used to describe this scenario because the students may attempt to guess rather than determine the correct answer.

2. Students are used to think instantly.

It happens because multiple choices is oriented in the result, not in the mathematical process. Students only think about how to select the best answers that fulfill the question. Sometimes they think backwardly, by substituting the options to the question and then chose the option that fulfills the question correctly.

3. A student who is incapable of answering a particular question can simply select a random answer and still have a chance of receiving a mark for it. So the multiple choice test becomes a fortunate or unfortunate moment.

4. By multiple choices, students can make a gambling by changing the first answer. Changing from "right to wrong" may be more painful and memorable, but is probably a good idea to change an answer after additional reflection indicates that a better choice could be made.

3. Why the linear equation system always uses variable “x” and “y”?

Unconsciously, everything on mathematics always labeled with the symbols “x” and “y”. If it is evaluated from psychology aspect, it will construct public (student) opinion that only symbols “x” and “y” as a label or remark used in mathematics. Why don’t we use other symbols such as p, q, m, n, k, l etc.? Using of other symbol will change the perspective of student in learning mathematics. Even for the students that learn mathematics firstly, it will be more interesting to use symbols such as picture, unique form (in the case of Ali’s problem, it can use picture of pencil and spidols.

finally, I have my own blog

Finally, I have my own blog.
Hope that I can develop my knowledge and share it to another people by this blog.
Bismillahirrohmanirrohim...


semangat!!
semangat!!

chaiyo!!
chaiyo ganbate!!
&keep fight on study ^^