Reflection on Session 4

Tonight's lesson started with a Mind Reading Game with digits 1 to 9.  When we told Dr Yeap the first number (out of 2 numbers) we had in mind, he was able to tell us the final difference!  How freaky it is that somebody can read your mind!  Everything came to light when we compared and made connections among the number patterns.  Dr Yeap's further explanation with the base ten materials made it even clearer for us to see how it worked and why it did not matter what the second number was.  Indeed, every idea has a pictorial and concrete version, and it dawned on me that the CPA Approach by Jerome Bruner is applicable to adults as well.

We do not play with a fraction of a marble

Next, we went on with addition and subtraction.  We learned that quantity comes in 2 forms: continuous and discreet. 

Money and kilogrammes are of continuous quantity and they can be expressed in decimal and fractions.  Items like marbles will be of discreet quantity.  For example, we do not use 1/4 on a marble as we see it as a whole; 1/4 marble is considered a broken marble.

Bascially, there are 3 situations for addition and subtraction:



Change situation

In change situation, there is an initial quantity, a change in quantity, and a final quantity.

Example, Tommy has 37 marbles. He gave Peter 19 marbles.  How many marbles has Tommy left?

Here, we can see a lapse of time, and the unknown is the final quantity.  Take note that the unknown can also be the initial, or the changed quantity, depending on the question.

Part-whole situation

In part-whole situatiion, there are at least 2 parts and the whole.



Example, There are 37 students in a class.  19 students are present.  How many students are absent?



When using manipulatives to teach part-whole situation like the one above, care has to be taken that we do not physically take the manipulatives (which represent part) away from the whole.



Compare situation

In compare situation, there are 2 quantities that are being compared. 

Example, I have $37.  I have $19 more than you.  How much do you have?

Often than not, we teach children that 'more' or 'together' means 'add'.  How wrong! We cannot apply this in the problem above.  This is a bad 'keyword strategy' that can cause misconception!  Math is not about repetition; it is therefore essential that we let children select the operation.  Teachers must give variation after teaching addition and subtraction.  This is important because we want to consciously expose children to variation to the same idea. 

Children learn well when you give them variant idea.

- Zolton Dienes

Following addition and subtraction was time for fraction and some paper folding acitivities.  Hmm... nothing to do with origami, though.
Do you know that words like 'fourth' and 'fifth' are nouns?  When it comes to fraction, we should say, for example, 'two fifth', and not '2 upon 5', or '2 out of 5'.  I'm guilty of saying that to my students.  Well, many of us do that but that is not the correct way.  Children cannot relate when they are asked to add '2 upon 5' to '3 upon 5'.  If we are to prepare children well, we have to consider the language that we use. 

In fraction, being equal does not mean it must be identical.

Consider these:

Do they look identical?

They may look different but yet represent the same amount. 

Now let us look at fractions at 3 levels:

Concrete Level

A portion can be cut out for comparison.

Pictorial Level

These are equivalent fractions. 1/8 and 1/8= 2/8 = 1/4

Abstract Level

We can work out the formula and prove that area A is equal to area B.

And now... division time...

We have learned that there are 3 meaning in addition.  For division, there are 2, namely sharing and grouping meaning.

Grouping - Example, in 12, there are 3 groups of 4 i.e. 12 divided by 3 is 4.

Sharing - Example, when 12 cookies are shared among 4 children, each child will get 3.

                               12 divided by 4 is 3.

During class, we learned to solve this problem:

In 3 fourths, how many fourths are there?

Who would have thought that 3/4 divided by 1/4 can be so easily solved by simply looking at a picuture?

Yes, and the answer is 3!

There was a lot to learn in tonight's lesson but it was so enlightening!  Thank you Dr Yeap, for teaching us simple methods to understand.  They are so much more meaningful than formulas that I can never understand.  :)