SESSION SIX: 26TH SEPTEMBER 2013, SATURDAY

Today is the last lesson for our module. =)

We had our quiz 2 today. So dead man. I only thought of the answer after I submitted my paper. *faint* Totally stuck at this question for the longest time.

QNS: Write a problem sum for “3 ÷ ⅔ = 4½”

ANS:

I have a 3m long ribbon. How many ⅔m of ribbon can I cut out from the 3m ribbon?

OR

I have 3 bottles of water. How many cups of ⅔ filled of water can I get?

To end off our module, we played an interesting game in group of 3s. We played the game “Salute”.

All you need for this game is just a stack of poker cards. So basically, this is how you play:

1.    Form group of 3. Place the stack of cards in the middle.

2.  Player 1 and 2 will take a card each from the stack of cards.

3.   Player 3 will then say “Salute” and the other 2 players will have to place the cards on their forehead without looking at it.

4.  Player 3 will then multiply the 2 numbers together and player 1 and 2 will have to guess the card that they have,

5.  After being familiarize with the game, we can also modify the game; instead of multiplying the numbers, we can add the numbers together.

So this marks the end of our module on “Elementary Mathematics”. It has been an interesting and fruitful week with Dr. Yeap. I had fun solving the different problems given to us.

The most important thing that I have learnt and can bring back to my classroom is the CPA approach.

CONCRETE à PICTORIAL à ABSTRACT

It is important for us teachers to identify which stage the children are at and provide them with the appropriate guidance so that they will be able to understand the concept taught and do it. 

SESSION FIVE: 27TH SEPTEMBER 2013, FRIDAY

Today is the fifth lesson with Dr. Yeap.

We played with Tangrams today again! Instead of using the tangrams to form rectangles, we formed squares today. So, here are some of the ways that we can form squares with tangrams.

We tried using from 1 piece to all 7 pieces to form the square. However, my group somehow could not figure out how to form with 5 & 6 pieces.

Tangrams are very interesting materials that we can provide for children to explore and play with. I feel that it stretches the children’s thinking to find out the different ways to form a shape or use them to form different figures like this.

Another interesting problem that we were given to think about today is:

Way to prove that the sum of the interior angles of a triangle is 180©:

A brilliant way thought by Rowenna; cut out a random triangle, then cut out all the angles and fix them together. The angles will eventually form a straight line and angles on a straight line sum up to 180©.

That's all for today. 

Tomorrow’s the last lesson~~ 

SESSION FOUR: 26TH SEPTEMBER 2013, THURSDAY

FOURTH LESSON WITH DR. YEAP TODAY~

Today’s agenda: fractions, multiplications and polygons

After doing problem 13 and 14, we discovered that “9” is a magical number!!

Some tricks for doing multiplications of 9…

 

Ever wonder why it only happens to “9”?? Let’s think about it…

PROBLEM OF THE DAY

Problem 17: Making polygons using geo board.

Joining dots on the geo board with straight lines to form different polygons, what are the different polygons that you can make?

We tried making different kinds of polygons with only 1 dot in the middle. There were small polygons and big polygons. Then we compared it to the small square and find out the area of the polygon that we have made.

I had fun trying out different ways to form polygons with 1 dot inside and tried to form the biggest polygon that I can make and it was 12 times of the square. The smallest one that I made was 2 times of the square. BUT one of our classmates managed to create a polygon that was only 1½ times of the square!

QUOTE OF THE DAY…

“Mathematics is an excellent vehicle for the development and improvement of a person’s intellectual competencies.”

That’s all for today’s lesson. 

SESSION THREE: 25TH SEPTEMBER 2013, WEDNESDAY

Third day of Elementary Mathematics with Dr. Yeap, MORE problems and QUIZ!!!

3 THINGS THAT WE LEARN IN MATHEMATICS:

• Conceptual – cardinality
• Procedural – procedures in doing math sums
• Conventional – things that need to be exposed to, for example, rote counting

PROBLEM OF THE DAY:

Problem 9: Addition of 2 digits numbers to form 2 digits number answer.

We created our digit cards from 0 to 9. We have to use the number cards that we have to form addition sums. It was fun and required much thinking. After manipulating with our digit cards, here are some observations that we have found:

The digit “0” can only be used in the sum.

The digit “9” can only be used in the ones place.

The largest number that we can have the answer of is 98.

The smallest number that we can have the answer is 39.

Problem 11: What are the different ways to share a piece of rectangular chocolate equally among 4 persons?

Similar shapes:

Rectangles

Triangles

Different shapes

I was really amazed that there are actually so many ways that we can share a rectangular chocolate among 4 persons.

That’s all for today~~ 

SESSION TWO: 24TH SEPTEMBER 2013, TUESDAY

Second session with Dr. Yeap, what did we learn and solve today?

I’ve learnt new words today…

ü Subitize: able to perceive a number of items without counting.

ü How manyness: the quality or state of being many.

INTERSTING PROBLEMS OF THE DAY…

Problem 6: Beans! Take a random number of beans and count down by 1 or 2. The person to count to 0 is the winner.

This activity really requires us to think carefully and strategize when the number of beans got fewer. And after playing for a few times, we realized that we can actually predict who is the winner when there is left with 5 beans.

We also identified some “bad” numbers; which means when it’s our turn and the numbers of beans left are 3, 6 and 9; there is a high possibility that we are going to lose.

Problem 7: Ten Frames! Find out the different methods that we can solve “5 + 7 + 6” using ten frames.

As a class, we found many different ways. The most straight forward method; counting on; counting in fives, counting in sixes, counting in tens and many other.

I personally feel that this is a good learning approach to teach children addition and counting in tens. I would like to incorporate ten frames into my lesson plan and hopefully, it would benefit them and help them in their learning.

Dr. Yeap also shared with us on for people who are unable to do rational counting, there are 4 contributing factors:

1. Classify: unable to group the same items together.

2. Rote counting: unable to rote count in order.

3. One-to-one correspondence

4. Do not have the conceptual understanding of cardinal number (do not know how to appreciate that the last number uttered represents the size of the object.

*interesting fact

In the Jewish culture, the children in schools like to ask a lot of questions as their parents would ask them how many questions did they asked in school.

And lastly to end off with this video that Dr. Yeap shared with us. Very catchy and nice song to tell us about “Jack and the beanstalk” story. 

SESSION ONE: 23RD SEPTEMBER 2013, MONDAY

First thought that I have when I saw the module title; YAY!! Mathematics, my favourite subject. BUT!! When I saw the textbook that was given and started reading, that’s where all the problems come!! I don’t really quite understand the text and there are so many words!!

    

BUT… after the first lesson with Dr. Yeap:

ü I HAD FUN!!

ü And… MANY brain cells killed when solving the different problems.

The activity that I enjoyed most is the tangram. Though it is nerve-wracking to figure out how to place the different pieces to form a rectangle, but I felt a sense of accomplishment when my group managed to form a rectangle with all the 7 pieces.

Then we tried out using only 3 pieces to make a rectangle. Who knows that we can actually use different pieces to form rectangles of the same size??!!

*IMPORTANT POINTS THAT I HAVE LEARNT:

ü Mathematics is NEVER about memorizing. SERIOUSLY!!

ü There can never be only 1 way to solve a problem.

ü Discussing with others help us to reflect on our own methods and compare.

LOOKING FORWARD TO SOLVING MORE PROBLEMS IN CLASS TODAY~~ J

Note to parents

Ever faced problems when teaching your child math? Ever experienced explaining the problem over and over, yet they still don’t understand? Don’t worry! Here are some tips to help you…

For one to be an effective teacher in teaching mathematics, he or she needs to have knowledge of mathematics and understanding of the way your child learns mathematics.

The ways of teaching mathematics have been changing over the decades to provide the best education for the children. Teachers now seldom use the approach of memorizing, drilling and copying as these do not prepare children for the real act of doing mathematics. On the other hand, teachers have to think and use different medium and techniques to teach children mathematics. For instance, relating the problems to their daily lives or allowing them to have concrete materials to work with or real life experiences.

In order to allow children to develop mathematical understanding, it is important to create an environment that offers children opportunities to learn. For instance, allow them to explore the sums first rather than to tell them the answers straight and allow them to ask questions instead of asking them to just listen. We could also use technologies that they are familiar with like computers and smart phones to enhance their understanding. For example, showing them a video on the computer that teaches fractions or having educational games on phones that they can play with and learn at the same time.

There is a common core standard that guides teachers on what to teach for mathematics for different age group. The concepts that children learn get more complex as they grow older and it is important for children to have a good foundation before proceeding to more complex stuff. Therefore, we as teachers and parents cannot expect the children to know how to solve the complex sums without them learning the basics. 

Reference 
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2014). Elementary and middle school mathematics: Teaching developmentally (8th ed.). USA: Pearson Education Limited.