Introduction
The
level of competency among standard four students are different from each other.
This assignment aims to expose to the latest techniques that has been proven in
schools. These techniques are entertaining and educational, in other words they
are edutaining. The first activity tackles the problem the students are
careless when they subtract. Students must be able to identify the words and
phrases that are used in the question and determine what algorithm is needed. solve
4 major problems in solving division task. In division, the students use the
times-table and subtraction method. It also tests students on the skills of
recognising small and big numbers.
Students
are introduced to the concept of subtraction using the formula. They are shown
on how to solve the dividing number on the white board. They are given a
problem, and they have numbers from 1 to 9 printed on cards, and they arrange
the numbers according to the correct method. They use the buttons to represent
zero. The exercises are shown, and they In this assignment, the aim is to
expose to the latest techniques that has been proven in schools. These
techniques are entertaining and educational. The errors are visible at question
sample no 1, 2 and 3.
First error: The
students are careless when subtracting between 2 numbers.
They
comprehend the questions and they arrange the numbers in a normal way, but the
error happens when they did not subtract correctly, they become careless. This
makes them to make an error. They arranged the numbers according to the
standard method, but they subtract upwards. This error happens when they have
done an error when they multiply the number. When they cannot find the correct
way, they do not make correction, instead they carry on subtracting. For example,
1526 / 20= They still do this 15-20=5. The standard method is to subtract 152
to 140, which is the nearest and a lower value than 150(152-140=12).
The
pupils understand the concept of division, they divide the numbers according to
the normal way, it is just that they are do not subtract correctly, such as
23-3= 19, 15-3=9 and 18-4=8. It makes the error and then the error will affect
the method .It happened when the pupils is careless because they want to finish
up answering quickly. A simple subtraction such as 26-3 will be answered as 24.
The problem with dividing is it will involve only subtraction and
multiplication, and there is no addition, but if the student makes an error in
the process of dividing, then it will not get the correct answer. This is perhaps
they are hasty in doing the work, or they subtract mentally but they are unable
to complete the task.
Second error: Students
do not understand the concept.
Students
come to school with varied language experience. While some students utilize Standard
English, others may use a local dialect or speak a different language at home.
There will be some children who speak very little even though they may talk a
lot at home. One of the errands of teachers is to extend their use of language.
Speech not only facilitates the child’s successful manipulation of objects but
also control the child’s own behaviour. In this case, misunderstanding will
happen, and the students are not able to grasp a question’s requirements. Students
have a low competency level and they do not understand the concept of the
question.
The question requires the students to answer by division, but the
students answer by addition and subtracting. Students also do not understand
what the question means, although the question is in Bahasa Malaysia and
English, they are in both languages. They also do not understand the technical
terms, when it is presented as a case study, and that makes them not to be able
to understand it. They are able to solve the problems when they are presented
in numbers only.
When
they read a case, such as Mr Salleh divides his RM 5 for all of his 5 sons. How
much will one son gets? Instead of dividing the amount RM using the normal way, they multiply RM 5 with
5= RM 25. The second sample is Ali has 235 stamps and he gives them equally to
his three siblings. How many does one has? In this case the student just use
the concept of subtraction, that is 235-3= 232, so he thinks each siblings get
232 stamps which is illogical. The second error is they do not understand the
meaning of the technical terms, for example, they understand the meaning of the
words, they can read either in Bahasa or English or both, but they do not get
what the question wants. This situation makes them not be able to fulfil the
questions’ requirements. They must divide between 2 numbers, but they happened
to add together, subtract from one another and multiply between the two numbers
Third error: The
students did not write zero number at the end of the answer.
Zero
is one of the most important concept in maths. Zero is used as a place holder:
For example in number 400 ,the zero after 4 tells students that the "tens'
column is empty and the zero on the right tells that unit' column is also empty.
The only column with any value is the hunderds column. Students would have
written 400 as only 4 , which is not the number they meant,if there would not
be anything to indicate that two right-hand columns were empty. Students would
not be able to distinguish 19081 from 1981 if zero is there.
The students think the zero number do not have
a value, valueless, such as when zero stands on its own. They think zero put at
the end of a number, such as 300 carry similar value when they are put in front
of a number, like 003. The first error
is visible in the first question, where the zero number is not written. The
solution is there is a game of dividing, where the answers need to be arranged.
The zero is represented with buttons, instead of writing the zero number on
manila cards.
Fourth error: They
divide a small number with a bigger number.
The
students divide the first number’s value with the dividend that involved two
digits. They cannot understand that a one digit number cannot be done in such a
way. When they get a question, such as
1526/20, they divide the first two digits of 1526, that is 15 with 20 and they
arrive at the solution, 15 can be subtracted with 20, and they subtract
upwards. They receive the first equation to be 5. When they proceed, they
subtract 52 with 40, which is the nearest multiplication number to 20, that is
20 X 2= 40.
Improvement:
Improvements for First
error: The students are careless when subtracting between 2 numbers.
Stress
to the pupils to multiply the correct way, on how to get the nearest value for
a number, for example, 5 multiply by what number will get 12, or the nearest and
has a lower value from it. arrange the
bigger number must be on top of the smaller number. Ask them to count correctly
and if possible, use realias such as marbles, straw or sempoa. When it involves
a subtraction between 2 digit number, they will find they have to regroup
during the subtraction process. In this part, teacher shows the way to
subtract, such as 24-16= ?
Improvements for Second
error: Students do not understand the concept.
The way to effectively translating and solving word problems is to
read the problem fully. Tell students do not start trying to solve anything
when they only read half a sentence. They have to get a feel for the whole
problem; try first to see what information it has. The students must coin out
the phrases that indicate that an operation is required.
The students are given the keywords, teacher stresses on the key
words such as difference, balance and remainder, plus and addition, equal
sharing, grouping involving dividing and altogether. They are exposed to examples
of case studies related to the usage of the keywords. They are also given more
exercises to solve the problems, to familiarize the students with problem
solving. The students highlight the keywords in the question so they can see
clearly the question’s needs.
There
are special names for each number in a division: dividend ÷ divisor = quotient.
Let us look at the example, 12 is the dividend, 3 is the divisor and 4 is the
quotient.
Remind
the students about key words such as remainder, difference, sharing, plus and
altogether. Vary and add more problem solving so the pupils will become
familiar. The students must read the questions carefully, underline the key
words in the question.
Improvements for third error:
The students did not write zero number at the end of the answer.
Remind
the students that a zero has value , and it is essential to put the zero when
it is required. A zero before a number has zero value, but a zero after a
number has value. Ask every students to
solve problems on the board.
Improvements for fourth
error: They divide a small number with a bigger number.
While
teaching, stress to the students that a one digit number cannot be divided for
a 2 digit number. Teacher gives simple questions that involves dividing a one
digit number, then dividing a two digit number. Teacher makes group work and
peer teaching so the students understand.
Activity for First
error: The students are careless when subtracting between 2 numbers
Students
are gathered into groups of four. They are given cards containing numbers, each
card has a number written on it. They are given 9 situational cases and 1
direct question. They have to arrange the numbers so it represents the question
using the number cards.
They
solve the problem in groups. When it’s discussion time, every group will show the numbers they have
arranged on their desk.
For example:
Salleh has 45 books and
he gives 14 books away to his friend. How many books does Salleh has now ?
Arrange the number
cards so they represent the standard method of subtraction :
|
4
|
5
|
|
-
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4
|
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4
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1
|
They are given case
studies and they arrange the numbers in the correct order as above.
The Case Studies:
1. Karim has 18
pencils. He gives 11 pencils out as birthday gifts. How many pencils does Mr. Karim
have left?
2. Our teacher, Mrs.
Wistrom has 23 cookies. She gives 16 cookies to Mrs. Zarling, the school nurse.
How many cookies does Mrs. Wistrom have left?
3. Jalil has 62
marbles. He gives 22 marbles to Dan. How many marbles does Jalil have left?
4. There were 51 fish
swimming by the pier. 28 fish swam away. How many fish were left swimming by
the pier?
5.Salleh had 100
goldfish. She gave 30 goldfish to her friend, Mary. How many goldfish does
Colleen have left?
Activities
- The students are put into groups of four.
- They are given the number cards and they are given straightforward questions
- They are asked to arrange the numbers so it forms the steps to subtract. They subtract the numbers.
- Teacher checks their work and corrects mistakes.
Activity for Second
error: Students do not understand the concept.
They
are told a simple formula, everything that is the same item can only be added
together or subtracted from., and everything that are now coming from the same
category can only be multiplied or divided. Explanations are given as a case
study:
Mr Salleh divides his
RM 5 for all of his 5 sons. How much will one son gets?
RM 5 is money
5 sons is people.
Both of them are coming
from a different category, which is money and people, so the formula that we
have learnt just now is, everything that is the same item can only be added
together or subtracted from., and everything that are now coming from the same
category can only be multiplied or divided. So, the numbers cannot be added
together or subtracted from, they can only be divided. This method makes the
students to come up with the formula RM 5/5= RM 1.
The second sample:
Ali has 235 stamps and he gives them equally
to his three siblings. How many does one has?
235 is the number of
the stamps and 3 refers to the amount of siblings that are humans, so they
cannot be added like this: 235+3=? or 3 subtracted from 235, which will result
like this: 235-3=?. They can be formulated as 235/3= or 235 X 3=.
The question has used
the word ‘gives them ‘ so the operation of division is required.
The terms are presented
on cue cards, and they are extracted from case study questions. For example,
Ali has 235 stamps and
he gives them equally to his three siblings. How many does one has?
The phrase gives them
equally:
|
gives
them equally
|
The students are given 4 cards which contain 4
different symbols, they are symbols for divide, multiply, addition and
subtraction. They show to the class what is the symbols that is meant by the phrase
gives them equally.
Activity for Third
error: The students did not write zero number at the end of the answer.
Students are gathered into groups of four. They are given
cards that have a number for each card. Students will be given 4 division questions.
Starting with the first question,
teacher will tell the groups what specific amount of numbers and
subtraction symbols will be used. All the numbers and symbols that teacher have
told must be arranged into the normal way of division.
They are given a case study.
For example, they are given 2640 / 12. They are given 5
cards containing a zero number each, 5 cards containing the 2 number each, and
three cards, each has 4 number. They are given the subtraction symbol (-) three
cards.
Activity:
- The class is briefed on the importance of doing division using the normal way, that is from top to bottom.
- They are shown on one sample, how to divide a three digit number with a 2 digit number
- Teacher tells of the division game, where they cannot use a pencil or papers to solve the division problem. Instead, they will use cards .They are given a set of divison cards and 5 division questions. Teacher tells the cards that will be used, and they set aside cards that are not used for question number one.
- They solve the first question by arranging the cards and symbols.
- Teacher looks at their activity.
Cut
out the cards
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0
|
0
|
0
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0
|
0
|
|
2
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2
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2
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2
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2
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4
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4
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4
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|
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Division symbols to be
used:
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÷
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÷
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÷
|
Give questions that
require a single or a number of zeros at the end of the answer.
- 4000 ÷4 =
- 2000÷4=
- 100÷4=
- 500÷5=
Ask them to arrange the
numbers according to the normal method.
Activity for fourth
error: They divide a small number with a bigger number.
They
are given all the number cards, but they are given an extra card, which is the ‘ X
’ card. We put the card where a number should not be put. It will avoid the
students from putting any numbers in the empty space. Another method is the
teacher arranges the X card before the student solve the problem. For example:
They cannot understand how a one digit number
can be divided with a two digit. It looks like they try to make the number to
be able to subtract. When they see 230 divided with 25, they will just subtract
23 with 25, (23-25) and they put the balance as 2. This makes all the rest of
the work as wrong. The solution is to determine which
number can be subtracted with another number. They choose a number from
category A to be divided with a number from category b.
Activity:
1) Teacher mentions the importance of subtracting correctly.
2) Draw an arrow to link which number in column A can be divided with
number in column B.
Sample:
A B
5 7
14 16
30 10
14/7= 7
3) They choose a number from category A with category B and write the
question.
Conclusion
It takes quite some time to let
students master the skill of division, as it involves subtraction and at the
same time it requires the students to master the times-table as well.
References
Dr Mahmood Othman.
(2011).HMBT3103 Teaching Mathematics in
Year Four. Kuala Lumpur . Open University Malaysia
Wan Yusof Wan Ngah et
al. (2005). Mathematics Teachers
Guidebook Year 4. Kuala Lumpur. Dewan Bahasa Dan Pustaka
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