Division, How To Teach??

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 Post subject: Division, How To Teach??
PostPosted: Thu Oct 22, 2009 12:21 am 
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KiasuGrandMaster
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Hi ,

Does anyone have any idea how to teach division? Do not have any division table in the bookshop yeah!


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 Post subject: How to Teach Division
PostPosted: Fri Oct 23, 2009 11:35 am 
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OrangeBelt
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//Editor's note: Topic selected for Portal publication.

In primary school, children are extensively taught how to divide in the abstract form while for us adult, we would simply reach for the calculator and "walah" you have the answer. I pity the children.

Well, to teach division, I would take a 3 step approach. In fact, in any teaching of mathematics, these 3 approaches should be taken systematically. This is called the CPA approach (ask any educator and they should know about this approach for primary math).

Step 1: Concrete

I would start simple. Give the child 4 marbles and 2 cups. Tell the child that he is supposed to SHARE the marbles between the 2 cups. Ask him to place the marbles into each cup one at a time in alternates.

After this has been done, ask the child to tell you how many marbles are there in each cup. The answer would be 2 in each cup.

Tell the child what they have done. The concept of SHARING is actually DIVISION.

One point to highlight to the child would be that after SHARING/DIVIDING, the resultant or answer would be smaller than the number you start with.

Let the child experience a few rounds of this hands-on or concrete activity until they get used to it.

** Extension - In this step you could give the child 5 marbles and ask him to SHARE them with 2 cups. What is left would be the REMAINDER. Explain the concept of remainder.

Step 2 : Pictorial

For this step, the aim is to transfer the hands-on division onto paper. You can start by drawing 4 boxes and thell the child that they need to color these boxes. They need to share/divide the boxes into 2 colors.

Give them 2 different color pencils and asked them to color one box at a time with one color.

Ask them, how many boxes were in one color. The resultant and answer would give the pictorial representation of the answer.

This step can be extended in may ways. It is up to your creativity. I am using boxes as it is similar to the over-used model approached. You can also used lines, circles, cartoon characters and what not in order to keep the interest of the child.

Again, keep repeating this step until they are comfortable with it. Remember to introduce the concept of remainder.

Step 3 : Abstract

This is the final step. At this stage, the concept of division should have set in in terms of cognitive understanding from the Concrete and Pictorial activities.

In this step, we make use of numbers like in a proper question. The child can make use of the PICTORIAL experience and understanding as their working - which again brings us back to model approach.

The goal in this step would be to create the number bond awareness from their multiplication concept.

These steps are good for beginners as you work with single digit numbers or ones value. As the child progresses further, you may start to introduce tens value and hundreds value.

Always remember, take small steps but consistent and systematic. In the long run, it will pay off.

Regards,
NIEtrainedTEACHER


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PostPosted: Sat Oct 24, 2009 8:49 am 
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KiasuGrandMaster
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Thank you! I will keep that in mind when my DD reaches this stage. :)


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 Post subject: Re: How to Teach Division
PostPosted: Fri Oct 30, 2009 7:16 pm 
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YellowBelt
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Joined: Wed Oct 28, 2009 7:26 pm
Posts: 18
NIEtrainedTEACHER wrote:
//Editor's note: Topic selected for Portal publication.

In primary school, children are extensively taught how to divide in the abstract form while for us adult, we would simply reach for the calculator and "walah" you have the answer. I pity the children.

Well, to teach division, I would take a 3 step approach. In fact, in any teaching of mathematics, these 3 approaches should be taken systematically. This is called the CPA approach (ask any educator and they should know about this approach for primary math).

Step 1: Concrete

I would start simple. Give the child 4 marbles and 2 cups. Tell the child that he is supposed to SHARE the marbles between the 2 cups. Ask him to place the marbles into each cup one at a time in alternates.

After this has been done, ask the child to tell you how many marbles are there in each cup. The answer would be 2 in each cup.

Tell the child what they have done. The concept of SHARING is actually DIVISION.

One point to highlight to the child would be that after SHARING/DIVIDING, the resultant or answer would be smaller than the number you start with.

Let the child experience a few rounds of this hands-on or concrete activity until they get used to it.

** Extension - In this step you could give the child 5 marbles and ask him to SHARE them with 2 cups. What is left would be the REMAINDER. Explain the concept of remainder.

Step 2 : Pictorial

For this step, the aim is to transfer the hands-on division onto paper. You can start by drawing 4 boxes and thell the child that they need to color these boxes. They need to share/divide the boxes into 2 colors.

Give them 2 different color pencils and asked them to color one box at a time with one color.

Ask them, how many boxes were in one color. The resultant and answer would give the pictorial representation of the answer.

This step can be extended in may ways. It is up to your creativity. I am using boxes as it is similar to the over-used model approached. You can also used lines, circles, cartoon characters and what not in order to keep the interest of the child.

Again, keep repeating this step until they are comfortable with it. Remember to introduce the concept of remainder.

Step 3 : Abstract

This is the final step. At this stage, the concept of division should have set in in terms of cognitive understanding from the Concrete and Pictorial activities.

In this step, we make use of numbers like in a proper question. The child can make use of the PICTORIAL experience and understanding as their working - which again brings us back to model approach.

The goal in this step would be to create the number bond awareness from their multiplication concept.

These steps are good for beginners as you work with single digit numbers or ones value. As the child progresses further, you may start to introduce tens value and hundreds value.

Always remember, take small steps but consistent and systematic. In the long run, it will pay off.

Regards,
NIEtrainedTEACHER



I agree with NIEtrainedTEACHER - this is Maths101 at NIE... lol.

Just to reiterate, the CPA approach is for learners to experience the learning. Hence, the activity will create the understanding.

Experience teachers, thrives on "teachable moments" to engage pupils in experiential learning as oppose to "route" learning. Don't get me wrong here - there is still a place for "route" learning as a workout for the mind, but ultimately, concepts that is built through experiences will last longer and bring pupils to what education psychologists refer to as, the Zone of Proximal Development (ZDP).

Here is another point to take note of when, or I would say before, you teach division.

Division falls under the four basic operation namely addition, subtraction, multiplication and division.

Now these are "taught" chronologically. Here's a summary of how the four basic operations are related.


1. Addition and Subtraction

Addition is the inverse of subtraction and vice versa. That is the reason why the two operations are taught in tandem with one another, with the ultimate goal of bringing the child's cognitive to the abstract thinking (vid the CPA approach)


2. Addition and Multiplication


Now the teaching of multiplication can proceed by introducing the repeated addition concepts. Concepts of groupings are dealt with here so as to allow easy transition when division is introduce later. Ultimately, the objective here is for pupils to create the awareness about how multiplication is related to addition.


3. Multiplication and Division


Here is where, the relationship between multiplication and division are related as an inverse. You can forget about "division table" and all that stuff. If this concept is not formed, the learner will definitely have difficulty later.


4. Division and Subtraction

As much as I would like to spoon-feed you guys by telling you the relationship between Division and Subtraction, I shall refrain myself... Purely because, I want you "engage" you. So tell me how is Division related to subtraction?... :? That's right. Repeated subtractions. Kudos to you... :celebrate:


Regards,
exTEACHER


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 Post subject:
PostPosted: Sun Nov 01, 2009 11:39 am 
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KiasuGrandMaster
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Hi exTEACHER

I'm pleased to know that my method is just like yours. :D

I'm not a teacher but I think it is logical for kids to know their numbers first then follow the steps that you mentioned.

I post my method on the "How to teach multiplication" topic. Mine not a very detailed explanation like yours.

When I teach, I make do with the things available at home. Like chocolate, cakes, lego (to do bar chart) etc.


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 Post subject:
PostPosted: Fri Nov 13, 2009 10:39 pm 
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YellowBelt
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Joined: Wed Oct 28, 2009 7:26 pm
Posts: 18
EN wrote:
Hi exTEACHER

I'm pleased to know that my method is just like yours. :D

I'm not a teacher but I think it is logical for kids to know their numbers first then follow the steps that you mentioned.

I post my method on the "How to teach multiplication" topic. Mine not a very detailed explanation like yours.

When I teach, I make do with the things available at home. Like chocolate, cakes, lego (to do bar chart) etc.


Hi En,

The Math Primary School Syllabus revolves around what is know as the spiral curriculum.

Meaning the topics taught will be revisited again and again every year. The only difference is that is will escalate to a higher concepts and caters to different Specific Instructional Objectives (SIOs).

You are at the right track if you can relate you teaching to real life examples.

I would also try to cater for different learning styles for my class during lessons. That is the reason why teaching has really come along way since our time where the traditional "chalk-and-talk" methods are less used. Note; less used - not totally left out. :wink:

That's why I sometimes get remarks by my other colleagues,"How I hear alot of laughter, singing and "noise" coming from your class?" lol.

Well this had alot to do with this guy name Gardner and his theory on Multiple Intelligences(MIs). He believes that learners learner from different learning styles. There are about 7 or 9 MIs if I remember correctly. So it may help if you can cater to their strength rather than their weakness.

Just my 2 cents worth, En.

Regards
exTEACHER

oh PS. - Great job on making do with things availbale at home! :celebrate:

PPS. - I have to be more selective at school. For example some parents are quite particular with certain things like food stuff and all that.


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