What I Can Reflect about psychological aspect, if the student is comfronted with the following questions
Solve the quadratic equation bellow by equip a quadratic
1.a. x2-2x=24
2.b. x2+8x+10=0
3.c. 3x2-2x-5=0
Generally, we can classify the students into two groups in this situation.
First, students who have never received the lesson materials about the quadratic equation.
if the student is comfronted with the question above, then there are some expressions that will appear are:
1. Confused
Confused is a psychological phenomenon that indicates a person / individual difficulties to solve a problems
Usually, these students have the curiosity, but are only want to know without any effort to solve it. Don’t try find any other references in the form of asking people in a more capable and learn other books.
2. Indifferent
Indifferent is the symptoms of psychological that look a problem as something that is not important to note even to be resolved. These students are basically haven’t the interest to know these new materials.
3. Angered
Angered is the symptoms of psychological indicates that the individual / someone wants to know more about something. The beginning is difficulties, but eventually he was able to solve them. Behind the curious person that there is strong intrinsically motivated. Intrinsic motivation be encouraged to seek solutions from the problems that are faced. Beside that, person needs ekstrinsic motivation such as facilities or support facilities. It can be a lesson books adequate and people who have the ability.
Second, students who have never received the lesson materials about quadratic equation.
If a student is comfronted with the same question like the first students, then there are two possible psychological symptoms of people who appear
1. Students Capable
Capable here means that students have the ability to solve the problem. The ability of students in problem solving is variated . In general, these capabilities can be classified into two categories:
• do with the fast / smoothly
This means that the students complete the questions provided with a smooth or without difficulty. This is influenced by some factors, such as the understanding lesson materials well and training regularly solve problems about quadratic equation.
• do slowly
Mean when solve problem, students find difficulties, although in the finally able to resolve these problems. Students in this, basicly have been able to resolve the problem, but because of a lack of mastery and understanding lesson material and rarely exercise the exams, so that when faced with the problem of these constraints.
2. students not capable
This is the meaning that students can not afford the exams at all, although the materials have been received. Factors that affect:
• forget
materials that have been mastered, but because of a case, the material is missing from the recall.
• Not understand at receive lessons
This is a challenge for us as educators and human potential of educators in general in Indonesia. How to make enjoy the atmosphere of learning in the classroom, so students receive the material properly.
Jumat, 12 Desember 2008
Rabu, 03 Desember 2008
PSYCHOLOGY OF MATHEMATICS EDUCATION
Problem Solving in Mathematics
MULYADI P.MAT R (07301241008)
GOALS
The ultimate goal of any problem-solving program is to improve students' performance at solving problems correctly. The specific goals of problem-solving in Mathematics are to:
1. Improve pupils' willingness to try problems and improve their perseverance when solving problems.
2. Improve pupils' self-concepts with respect to the abilities to solve problems.a
3. Make pupils aware of the problem-solving strategies.
4. Make pupils aware of the value of approaching problems in a systematic manner.
5. Make pupils aware that many problems can be solved in more than one way.
6. Improve pupils' abilities to select appropriate solution strategies.
7. Improve pupils' abilities to implement solution strategies accurately.
8. Improve pupils' abilities to get more correct answers to problems.
MATHEMATICAL PROBLEM DEFINED
A problem is a task for which:
1) The person confronting it wants or needs to find a solution.
2) The person has no readily available procedure for finding the solution.
3) The person must make an attempt to find a solution.
FOUR PHASES IN SOLVING A PROBLEM
In solving any problems, it helps to have a working procedure. You might want to consider this four-step procedure: Understand, Plan, Try It, and Look Back.
Understand -- Before you can solve a problem you must first understand it. Read and re-read the problem carefully to find all the clues and determine what the question is asking you to find.
What is the unknown?
What are the data?
What is the condition?
Plan -- Once you understand the question and the clues, it's time to use your previous experience with similar problems to look for strategies and tools to answer the question.
Do you know a related problem?
Look at the unknown! And try to think of a familiar problem having the same or a similar unknown?
Try It -- After deciding on a plan, you should try it and see what answer you come up with.
Can you see clearly that the step is correct?
But can you also prove that the step is correct?
Look Back -- Once you've tried it and found an answer, go back to the problem and see if you've really answered the question. Sometimes it's easy to overlook something. If you missed something check your plan and try the problem again.
Can you check the result?
Can you check the argument?
Can you derive the result differently?
Can you see it at a glance?
PROBLEM-SOLVING STRATEGIES
1. Make a table
2. Make an organised list
3. Look for a pattern
4. Guess and check
5. Draw a picture or graph
6. Work backwards
7. Solve a simpler problem
The list of problem-solving strategies above is by no means exhaustive. You may like to read up on some other strategies such as
(i) Reading and restating problem.
(ii) Brainstorming
(iii) Looking in another way
(iv) Making a model
(v) Identifying cases
Note: Different strategies can be used to solve the same problem.
PROBLEM EXTENSION
Goals for Extension
1) Lead pupils to generalisation
2) Introduce or integrate other branches of mathematics
3) Provide opportunities for divergent thinking and making value judgements
Principles for Extending a Set of Problems
At a party I attended recently, I noticed that every person shook hands with each other person exactly one time. There were 12 people at the party. How many handshakes were there?
Principle for Problem Variation New Problem
A. Change the problem context/ setting (e.g., party to a Ping-Pong tournament). A. Twelve students in Ms.Palmer's fifth-grade class decided to have a Ping-Pong tournament. They decided that each students would play one game against each other students. How many games were played?
B. Change the numbers (e.g., 12 becomes 20 or n). B. At a party I attended recently, I noticed that every,person shook hands with each other person exactly one time. There were 20 people at the party. How many handshakes were there? That if there were n people at the party?
C. Change the number of conditions(e.g., instead of the single condition that "every person shook hands with each other person exactly one time," we add the condition "Tim shook hands with everyone twice." C. At a party I attended recently I noticed that every person but the host,Tim, shook hands with each other person exactly one time. Tim shook hands with everyone twice (once when they arrived, once when they left). There were 12 people at the party. How many handshakes were there?
D. Reverse given and wanted information (e.g., in the basic problem you are given the number of people at the party and you want to find how many handshakes there are; the reverse is true in the new problem). D. At a party I attended recently I noticed that every person shook hands with each other person exactly one time. If I told you there were 66 handshakes, could you tell me how many people were at the party?
E. Change some combination of E. context, numbers' conditions, and given/wanted information (e.g., in problem E both the context and the numbers have been changed). Note: There are 11 combinations possible! E. All 20 students in Ms. Palmer's fifth-grade class decided to have a Ping-Pong tournament. They decided that each student would play one game against each other student. How many games were played?
REFERENCES
1. CHARLES, R. I. AND MASON, R. P. AND NOFSINGER, J. M.AND WHITE, C. A.
Problem-Solving Experiences In Mathematics. Addison-Wesley Publishing Company; 1985.
2. DOLAN, D. T. AND WILLIAMSON, J.
Teaching Problem-Solving Strategies. Addison-Wesley Publishing Company; 1983.
3.MEYER, CAROL AND SALLEE, TOM.
Make It Simpler. Addison Wesley Publishing Company; 1983.
4. POLYA G.
How To Solve It. Princeton University Press; 1973.5.
CAROLE GREENES, JOHN GREGORY AND DALE SEYMOUR.
Successful problem Solving Techniques. Creative Publications, Inc.
MULYADI P.MAT R (07301241008)
GOALS
The ultimate goal of any problem-solving program is to improve students' performance at solving problems correctly. The specific goals of problem-solving in Mathematics are to:
1. Improve pupils' willingness to try problems and improve their perseverance when solving problems.
2. Improve pupils' self-concepts with respect to the abilities to solve problems.a
3. Make pupils aware of the problem-solving strategies.
4. Make pupils aware of the value of approaching problems in a systematic manner.
5. Make pupils aware that many problems can be solved in more than one way.
6. Improve pupils' abilities to select appropriate solution strategies.
7. Improve pupils' abilities to implement solution strategies accurately.
8. Improve pupils' abilities to get more correct answers to problems.
MATHEMATICAL PROBLEM DEFINED
A problem is a task for which:
1) The person confronting it wants or needs to find a solution.
2) The person has no readily available procedure for finding the solution.
3) The person must make an attempt to find a solution.
FOUR PHASES IN SOLVING A PROBLEM
In solving any problems, it helps to have a working procedure. You might want to consider this four-step procedure: Understand, Plan, Try It, and Look Back.
Understand -- Before you can solve a problem you must first understand it. Read and re-read the problem carefully to find all the clues and determine what the question is asking you to find.
What is the unknown?
What are the data?
What is the condition?
Plan -- Once you understand the question and the clues, it's time to use your previous experience with similar problems to look for strategies and tools to answer the question.
Do you know a related problem?
Look at the unknown! And try to think of a familiar problem having the same or a similar unknown?
Try It -- After deciding on a plan, you should try it and see what answer you come up with.
Can you see clearly that the step is correct?
But can you also prove that the step is correct?
Look Back -- Once you've tried it and found an answer, go back to the problem and see if you've really answered the question. Sometimes it's easy to overlook something. If you missed something check your plan and try the problem again.
Can you check the result?
Can you check the argument?
Can you derive the result differently?
Can you see it at a glance?
PROBLEM-SOLVING STRATEGIES
1. Make a table
2. Make an organised list
3. Look for a pattern
4. Guess and check
5. Draw a picture or graph
6. Work backwards
7. Solve a simpler problem
The list of problem-solving strategies above is by no means exhaustive. You may like to read up on some other strategies such as
(i) Reading and restating problem.
(ii) Brainstorming
(iii) Looking in another way
(iv) Making a model
(v) Identifying cases
Note: Different strategies can be used to solve the same problem.
PROBLEM EXTENSION
Goals for Extension
1) Lead pupils to generalisation
2) Introduce or integrate other branches of mathematics
3) Provide opportunities for divergent thinking and making value judgements
Principles for Extending a Set of Problems
At a party I attended recently, I noticed that every person shook hands with each other person exactly one time. There were 12 people at the party. How many handshakes were there?
Principle for Problem Variation New Problem
A. Change the problem context/ setting (e.g., party to a Ping-Pong tournament). A. Twelve students in Ms.Palmer's fifth-grade class decided to have a Ping-Pong tournament. They decided that each students would play one game against each other students. How many games were played?
B. Change the numbers (e.g., 12 becomes 20 or n). B. At a party I attended recently, I noticed that every,person shook hands with each other person exactly one time. There were 20 people at the party. How many handshakes were there? That if there were n people at the party?
C. Change the number of conditions(e.g., instead of the single condition that "every person shook hands with each other person exactly one time," we add the condition "Tim shook hands with everyone twice." C. At a party I attended recently I noticed that every person but the host,Tim, shook hands with each other person exactly one time. Tim shook hands with everyone twice (once when they arrived, once when they left). There were 12 people at the party. How many handshakes were there?
D. Reverse given and wanted information (e.g., in the basic problem you are given the number of people at the party and you want to find how many handshakes there are; the reverse is true in the new problem). D. At a party I attended recently I noticed that every person shook hands with each other person exactly one time. If I told you there were 66 handshakes, could you tell me how many people were at the party?
E. Change some combination of E. context, numbers' conditions, and given/wanted information (e.g., in problem E both the context and the numbers have been changed). Note: There are 11 combinations possible! E. All 20 students in Ms. Palmer's fifth-grade class decided to have a Ping-Pong tournament. They decided that each student would play one game against each other student. How many games were played?
REFERENCES
1. CHARLES, R. I. AND MASON, R. P. AND NOFSINGER, J. M.AND WHITE, C. A.
Problem-Solving Experiences In Mathematics. Addison-Wesley Publishing Company; 1985.
2. DOLAN, D. T. AND WILLIAMSON, J.
Teaching Problem-Solving Strategies. Addison-Wesley Publishing Company; 1983.
3.MEYER, CAROL AND SALLEE, TOM.
Make It Simpler. Addison Wesley Publishing Company; 1983.
4. POLYA G.
How To Solve It. Princeton University Press; 1973.5.
CAROLE GREENES, JOHN GREGORY AND DALE SEYMOUR.
Successful problem Solving Techniques. Creative Publications, Inc.
Senin, 01 Desember 2008
presentasi
matematika adalah pelajaran yang menyenangkan , tapi sebagian kecil saja siswa yang tertarik untuk mendalaminya. kenyataan di lapangan ( sekolah2) memang seperti itu. sebagai calon pengajar saya ingin mengetahui pendekatan seperti apa yang harus dilakukan agar siswa termotivasi belajar matematika?
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