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Introduction

Hello and Good Day Everybody !
I am a new teacher in the school named Sekolah Menengah Kebangsaan Datuk Bendahara. This school is situated in Jasin, Melaka.
I am accepted to be one of the Guru Sandaran Terlatih (GST) here. There are 10 of us, my batch joined the schools in 27th June 2011.
In this blog, I share with you my experience and great things that are happening to me in the school.
There are also notes and things for good English class usages, so feel free to browse them whenever there are gaps between classes.
My mentor here is Hajjah Zaorah and she has been guiding me to be a better English teacher.
Thank you !
.
In this blog, I have uploaded
Literature lesson plans for form 4 and 5
working papers, reports after programmes, yearly uniform body reports, weekly reports, sponsorship letters, sample of memos and thank you notes, short stories and others.



Happy teaching, teachers !
Here is a good link to English Materials:

http://www.ppdjasin.edu.my/unitakademik/index.php?option=com_content&view=article&id=47&Itemid=54

Pengikutku, Sila jadi pengikut untuk blogs saya !

Wednesday, June 6, 2012

HBMT 3403 TEACHING MATHEMATICS IN FORM TWO (1)




FACULTY OF EDUCATION AND LANGUAGES


HBMT 3403 TEACHING MATHEMATICS IN FORM TWO
oumOCTOBER 2011








LETAKKAN NAMA ANDA DISINI (EEISH COPY JE KEE)








Tutor
MR.
 
 








Introduction
Mathematics is knowledge that come from observation on nature. Mathematics is a logic system that shows the formula, that creates the language of Mathematics such as symbols, rules and operations.
Mathematics is a way of thinking that is used to expand on reasoning and reach to a conclusion from the existence of the universe.Mathematics is also interpreted as an art form, because it contains its language and patterns in an interesting shapes.
A character in Mathematics is Mathematics contains language, symbols and operations. The basic of the language system is the grammar. In the Mahematics language, the grammar consists of rules, theorems and formula that connects the symbols.

According to Piaget, the mathematics language is abstract and only secondary school students can understand it. Students in primary schools cannot understand the mathematics symbols that are abstract without relating it to their concrete experience.  Thus, teaching the Mathematics language must be related to their experience , relate it with teaching aids and concrete items. For example, when we want to teach on Mathematics, we relate to the spupil’s daily experience, for example, I am purchasing three items at the store, at these prices, RM 19.95, RM9.98 and RM 29.97. About how much money am I spending ? The fastest way to solve this problem is to round off and approximate. The first item costs about $20, the second about $40, and the third about $30; therefore, I am spending about $90 on your shopping spree. Rounding is often an excellent heuristic for arriving quickly at approximate answers to mathematical problems.
A problem is a situation that an individual wants to resolve arises but no solution is readily apparent. It is also a situation which the individual is confronted by something he/she does not recognise that he/she cannot apply any model to solve for the unknown. In order to solve the unknown the individual undergoes the problem solving. It is the process by which the unfamiliar situation is resolved.

A problem to an individual may not be a problem to another. For example, determining the number of people in three cars in which each car consists of five people may be a problem to some elementary school learners. They might solve the problem by placing chips in boxes or making a drawing  to represent each car and each person, and then counting to determine the total number of people.

Hayes (1981) described problem as finding an appropriate way to cross gap.”two major parts of problem solving are representing the problem and searching for a means to solve the problem. For example, in solving an algebra word problem, you must translate the problem into an internal representation such as equation, and you must be able to apply the rules of algebra and arithmetic to solve the equation (Mayer, 1983) Mayer focuses on techniques aimed at improving the representing phase of problem solving such as translation training and schema training, and techniques aimed at improving the searching phase of problem solving such as strategy training and algorithm automaticity.

Another strand of thinking that appears to support the ‘conjecture-first’ approach to thinking may be drawn from the words of that classic problem solving text by Polya (1945); ‘How To Solve It’. This booklet is aimed at mathematicians. It provides a suggested methodology to tackle the creative process of solving mathematical and geometric problems. His ‘steps’ are:

“First. You have to understand the problem”

Second. Find the connection between the data and the unknown. You may be obliged to consider auxiliary problems if an immediate connection cannot be found. You should obtain eventually a plan of the solution.

Third. Carry out your plan

Fourth. Examine the solution obtained” [1945, p. xvi]
Polya then provides further elaboration of what he meant under the second step in terms of needing to seek analogous problems that have been solved. He suggests using existing solutions to old problems. This is further understood by his elaboration of the third step which he states as testing to see if the old analogous solution or at least similar concepts work for the new problem. Polya, who is a well respected author on problem solving, is therefore not suggesting that solutions come after reasoning about alternatives. Rather, he suggests that you search for a conjecture solution (from an analogous problem) and then think about its usefulness for the current problem. This again seems very much like Dewey’s advice and the advice of argumentative inquiry: conjecture something that might work, and then think about the feasibility of this solution carefully.

HEURISTICS FOR PROBLEM SOLVING
This is a set of heuristics that has been proven to be successful with students and teachers at all levels of instructions

Read the problem

  1. Note key words
  2. Describe the problem
  3. Visualise the action
  4. Restate the problem in your own words
  5. What is being asked for ?
  6. What information is given ?

Explore

  1. Organise the information
  2. Is there enough information ?
  3. Is there too much information ?
  4. Draw a diagram or construct a model
  5. Make a chart or table

Select a strategy

  1. Pattern recognition
  2. Working backwards
  3. Guess and test
  4. Simulation or experimentation
  5. Simplify the problem
  6. Organised listing or make a table
  7. Logical deduction
  8. Using formula

Solve

  1. Carry out the strategy
  2. Use computational skill
  3. Use geometric skills
  4. Use algebraic skills
  5. Use elementary logic

Look back

  1. Check your answer
  2. Find another way
  3. What if... ?
  4. Extend
  5. Generalize

Another strand of thinking that appears to support the ‘conjecture-first’ approach to thinking may be drawn from the words of that classic problem solving text by Polya, 1945)  ‘How To Solve It’. This booklet is aimed at mathematicians. It provides a suggested methodology to tackle the creative process of solving mathematical and geometric problems.

His ‘steps’ are:
“First. You have to understand the problem”

Second. Find the connection between the data and the unknown.

Third. Carry out your plan

Fourth. Examine the solution obtained” [1945, p. xvi]

Polya then provides further elaboration of what he meant under the second step in terms of needing to seek analogous problems that have been solved. He suggests using existing solutions to old problems. This is further understood by his elaboration of the third step which he states as testing to see if the old analogous solution or at least similar concepts work for the new problem. Polya, who is a well respected author on problem solving, is therefore not suggesting that solutions come after reasoning about alternatives. Rather, he suggests that you search for a conjecture solution (from an analogous problem) and then think about its usefulness for the current problem. This again seems very much like Dewey’s advice and the advice of argumentative inquiry: conjecture something that might work, and then think about the feasibility of this solution carefully.



In the past, ratio and proportions were used in architecture, paintings and sculptures. Today, we use them in many daily situations, they are used not only in preparing chemicals, but also in shopping and cooking.

For this task, I have taken Chapter 5, ratio, Rates and Proportions The Concept of ratio of Two Quantities (page 86), the Concept of Proportion to solve Problems (page 9). The textbook that I am using is Mathematics Textbook Form 2 Volume 1 2003, Arus Intelek Sdn Bhd. Cheang Chooi Yoong, Khau Phoay Eng, Yong Kien Cheng ISBN 983-150-241-8.


Ratio
For the first question, I have decided to use the strategy of simulation, that is, I use pictures to show the syrups and the water used.For the second question , I use the Maths formula.


Pak Salleh has 10 cups of syrup and he can make 40 cups of drinks. Unfortunately, he spilled 6 ½ cups of the syrup. How many cups of drinks can he prepare with the balance ?

1)     Understand the problem
10 cups of syrup= 40 cups of drinks
 How much can we make with 6 1/2 of syrup ?


2) Decide on the plan
I use simulation and I draw the syrup and water.

3)     Carry out the plan


1 cup of syrup                                       =                 4 cups of drinks








 




½ cup of syrup                  =                                         4/2













 



½ cup of syrup makes 2 cups of drinks.








 












3 cups of syrup                  X 4





=12 cups of drinks





6 ½                                                     = 12 cups + 2 cups

































 







So, 6 ½ of syrup makes 14 cups of drinks


Ratio of syrup to water
=1           :                 4


 



Solve this: how much is ratio of ½ syrup ? 


 



So, the formula is 4/2=2








 


Therefore, ½ syrup is 2 to water


 



= ½: 2
The amount of syrup is proportional to the amount of water.

1 cup of syrup                                       =                 4 cups of drinks


 



½ cup of syrup   =     4/2













 



½ cup of syrup makes 2 cups of drinks.


3 cups of syrup                  X 4 water




=12 cups of drinks




So, 6 ½ of syrup makes                               = 12 cups + 2 cups

































 










So, 6 ½ of syrup makes 14 cups of drinks

The ratio of syrup to water
=1:4


 



Solve this ratio: ½ : ?


 



4/2=2








 


Therefore, ½ :2


 


The amount of syrup is proportional to the amount of water.




1)     Check the answer.
½ cup of syrup equals to 2 cups of drinks, so
6 ½ cups of syrup means
½ X 6 ½   =
                 = 14 cups of drinks







Maths formula


Pak Salleh has 10 cups of syrup and he can make 40 cups of drinks. Unfortunately, he spilled 6 ½ cups of the syrup. How many cups of drinks can he prepare with the balance ?

1)     Understand the problem
10 cups of syrup= 40 cups of drinks
 How much can we make with 61/2 of syrup ?

2) Decide on the plan
I use Maths formula

3)Carry out the plan
10 cups of syrup=40 cups of drinks
40/10=4

So, 1 cup of syrup makes 4 cups of drinks
How much can ½ cup of syrup makes drinks ?
So, 4 / 2=2
It means ½ cup of syrup makes 2 cups of drinks.
3 cups of syrup X 4 =12 cups of drinks.
6 1/2 cups of syrup makes 14 cups of drinks.

The ratio of syrup to water is 1so, what is the ratio of water if syrup is ½ ?
4/2=2
Therefore the ratio of syrup ½ to water is 2= ½ :2

The amount of syurp is proportion to the amount of water.

4)Check the answer

1 cup of syrup makes 4 cups of drinks
and ½ cup of syrup makes 2 cups of drinks.
6 ½  cups of syrup makes 14 cups of drinks

Second question

The ratio of cows to bulls in Pak Salleh’s farm in Ayer Pa’abas, Melaka is 5:7. There are 48 more bulls than cows. After one year, 3 bulls are transferred to Pak Samad’s farm, and Pak Salleh buys 5 new cows. Find the ratio of cows to bulls in Pak Salleh’s farm.

1)     Understand the problem

The ratio of cows to bulls is 5:7
Cows is x and bulls is y.
Cows =48 is more than bulls

2)     Decide on the plan
We use the formula method.
We find X first and we use linear equation.

3)     Carry out the plan

x= cows
y=bulls

x:y=5:7
x/y =5/7


This is the first equation

y=48+x

     x
______= 5
48+x       7


7x + 240 + 5x
7x-5x=240
2x=240
x=240/2
x=120
Put the new x value into the first equation

y=148+x
y=148+120
y= 168

After a year,
Bulls: 168-3=165
Cows:120+5=125
New ratio=125:165
25:33

4)     Check the answer
Find the ratio of cows to bulls in Pak Salleh’s farm.
Bulls: 168-3=165
Cows:120+5=125
New ratio=125:165
25:33

The second method
The ratio of cows to bulls in Pak Salleh’s farm in Ayer Pa’abas, Melaka is 5:7. There are 48 more bulls than cows. After one year, 3 bulls are transferred to Pak Samad’s farm, and Pak Salleh buys 5 new cows. Find the ratio of cows to bulls in Pak Salleh’s farm

1)     Understand the problem


Cows:bulls=5:7
The difference between cows and bulls =48
3 bulls are transferred and 5 new cows are added.
 Find the new ratio of cows:bulls


4)     Decide on the plan
I use simulation and experimentation method.

5)     Carry out the plan

2 parts represent 48 animals.
1 part represent 48/2=24 animals
5 parts represent 5 X 24=120 cows
7 parts represent 7 X 24=168 bulls
\
After a year,
Bulls=168-3
=165
Cows=120=5
=125
New ratio=125;165 (divide both by 5)
=25:33

5)     Check the answer
25:33=125:165
125-5=120 cows, 165+3=168 bulls
Female:male=120:168 (divide both by 24)
=5:7





Reflection

I have shown these examples to two classes, that is 2A and 2F. These two methods have been shown to them and i have explained it differentlly for both classes. The first class, ihave explained in detail, and the second class, I explain the basics only, I don’t want them to get confused which method to use.
These two classes have different capabilities from each other. 2A can understand the two methods, whereas 2F needs more explanations from the teacher. It looked 2F needed a double period for linear equation topic, and I wish to include this into their end year final examination, and I want both classes to be able to answer the linear equation problems and get A One for Maths
The students are encouraged to apply both methods so they can tell which method is better in a given problem.Usually they like to use the guess and test method because the method is simpler and not confusing. If we compare with the formula or drawing a table method, there are many students who are confused. Perhaps the low achievers will use the guessing method, but they will not get full marks if they write it in the exam paper.So, the teacher will have to stress to them, to use the formula or table method to get full marks. They will get full marks if the method written and the answer are both correct.
\
Suggestions

The ability to solve problem is important for a pupils to master. It relates to our daily lives. This ability must be stressed to them. My suggestions are the problems given must be in the form of a story that relates to the pupil’s lives. Expose students to a few strategies such as Drawing,Find the pattern, Building a table, Try and error and Building word bank. The usage of a certain strategy must be suitable with the problem, and it is easier for the students to solve the problem. The students must know the maths language in problem solving. There are many pupils face problems in solving word problems. This is because they must read the problem, understand it and think what method to be used. So, the sentences that are used must be suitable with the pupil’s understanding. The pupils must be competent in translating the maths problem, from Maths language to their mother tongue and the other way around. Generally, students who are weak in maths make less practice compared to pupils who makes more exercises. Therefore, daily practises, with schedule is required as additional homework, to help them in mastering problem solving. Next, solve problem according to problem solving process.It is important for teachers to give their pupils good questions. In good questions, the facts that are given are presented in the pupils daily lives. The pupils understand that all Maths lessons learnt in classrooms can be applied in their 24/7 lives. They can be used in all aspects of life, whether it relates to Maths or not. The process to solve the problem must follow Polya’s problem solving method that is Understand the problem, Planning a device, Make the plan and Check.


Conclusion

By using the Dewey and Polya’s method, it simplifies the student’s work in finding the answer. The students are taught to organise the information in a manner that makes them undrerstand the information that is given, turn in into mathematical language, decide and carry out the plan. Lastly, they check the answers, look whether it tallies with the question’s requirements. By using simulation and formula, they are able to find the answers, assisted by the textbook. The questions cover the student’s daily experience, where they are taught to apply the heuristics approach to tackle their daily tasks.



References


  1. Bahagian Pendidikan Guru (1998), Pengajaran Pembelajaran Matematik : Pecahan 
    1. Untuk Sekolah Rendah, Dewan Bahasa dan Pustaka, Kuala Lumpur.

  1. Dr. Mahmood Othman (2010), Teaching Mathematics in Year Four, OUM, Kuala
    1. Lumpur.

  1. Frank J. Sweet & Liew Su Tim ( 1987), Pengajaran Matematik KBSR, Penerbit Fajar
    1. Bakti Sdn. Bhd. Petaling Jaya.

  1. Linda Lim, S.F Liew & Ros Dhania, Success Mathematics UPSR, Oxford Fajar,
    1. Selangor

  1. Ling Choi Hong & Aw lai Sin (2010), Penilaian Topik BEST Mayhematics KBSM
    1. Year 1, PEP Publications Sdn. Bhd. Petaling Jaya, Selangor.

  1. Maktab Perguruan Persekutuan Pulau Pinang ( Julai 1995), Penyelesaian Masalah
    1. Dalam Matematik, Bahagian Pendidikan Guru, Kuala Lumpur.

  1. Mohd Nasir Mahmud (2010), HBMT3403: Teaching Mathematics in Form Two,
    1. OUM, Kuala Lumpur.

  1. Mok Soon Sang (2000), Pengajian Matemtik Untuk Diploma Perguruan, Kumpulan
    1. Budiman Sdn Bhd, Selangor.

  1. Zarina Law bt Abdullah & Abdul Latih bin Ahmad (2007), HBMT 1103 Introduction
    1. to Mathematics Education, OUM, Kuala Lumpur
  2. Polya G., 1945, How To Solve It, Princeton University Press, New Jersey.

  1. Krulik, S.Redneck,JA (1989) “Problem Solving A Handbook for Senior high School Teacher”.

  1. (J. R. Anderson, 1990; J. E. Davidson & Sternberg, 1998, 2003; H. C. Ellis & Hunt, 1983; Halpern, 1997a)

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