Delivering Math Concept through an Art Piece

How can one teach Math concept or provide Mathematical experiences through an Art Piece? I learned that it can be challenging but definitely possible.

I went to the Singapore Art Museum today on a mission to find an art piece that I can use to provided mathematical experiences in differentiated learning. There were many pieces that allowed us teachers to choose the right one for the right type of learning. I have listed some examples below: 

#1

Look at this art piece. This is located at the Singapore Art Museum, Learning Gallery 1, titled Singapore Idols Grasscutters by Jing Quek. 

What are some mathematical experiences can you provide to your child through this art piece? 

• Number Bonds up to 10

• Classifying

• Counting

• Multiplication/ Division

• Patterning

#2

This art piece, in a form of stop motion animation, is located at the Singapore Art Museum, Learning Gallery 2, titled Tromarama by Zsa Zsa Zsu. Though it is in a form of music video, you can use screen shots to look at the pieces.

Through this piece, the following mathematical concepts can be provided:

• Sorting
• Patterning
• Comparing
• Measurement

Whoever said Maths is boring has not ventured enough yet!!!

Fun with Angles on Day Five

Let's learn about TRIANGLES...

In a triangle, the three angles always add to 180°:

A + B + C = 180°

One of our problems that we had to solve today was on angles in a triangle. We were all given a piece of paper and was asked to cut it into triangles. Upon cutting, the question that was asked was how do you that all the angles add up to 180°??

There were several ways that were discussed among my group, one of it being Lily Wei's method:

4 + 6  and 1 + 3 is 90 degrees respectively.
1 = 2
2 + 5 + 7 = 360 degrees - ( 1+ 6 + 4 + 3)
Which is 360 degrees minus 2 (90 degrees) = 180 degrees!!

Another method that i thought of was to fold the triangle in the following manner and you will see that it works out to be 180° for each of the four triangles. 

A course mate of mine provided the following method: When you cut away the corners and place the cut pieces in a straight line, it forms half a circle. As a full circle is 360°, half a circle will be 180°.

Are you able to find more ways? Share it with me if you find one :)

Patterns: Day Four

Observe this series of number: 

1, 4, 9, 16, 25, 36, 49

Do you see a pattern or a sequence? If you don't, it's okay. And this is what I learnt today. It takes time  and practice for my eye to catch the patterns. I have to look at it carefully and think, what is it that makes the numbers get bigger. Once you get the pattern, you will find yourself extending the pattern or looking for other different patterns to work with. 

The number nine is  interesting to work with in terms of  patterns. 

Let's take a look at some patterns...

Pattern #1

21 - 12 = 9   (9 x 1)

31 - 13 = 18  (9 x 2) The number 2 came about by subtracting 1 from 3

41- 14 = 27   (9 x 3)  Following  pattern, number 3 came about by subtracting 1 from 4

Therefore 91-19 = (9 x 8) = 72

Pattern #2

A website which explores more on the patterns with number nine: http://www.blackdouglas.com.au/taskcentre/lansdel1.htm

After analyzing patterns involving the number nine, naturally i wanted to look for other kinds of patterns using other digits. Below attached is a video that i found online involving the number 6 and 4, using  5 point star method.

More Challenging Problems @ Day Three

First problem which had my attention...

We were to use the digits 0 to 9 to form sums that gave us two digit answers by having two digits adding to another two digits, without using any digit twice. Below were some of the sums that i did. It might look plain and boring here but i was given mini digit cards so i concrete materials to produce the sums.

Then we were challenged to think deeper. 

What is the largest two digit answer possible?

Answer: 98 (Many possible ways such as 57+41 , 61+37...)

What is the smallest two digit possible? 

Answer: 39 (Only one way, which is 25 + 14)

I thought that this would be an interesting problem for the early primary to work with as it allows them to explore number bonds.   

The other problem which had me interested at the second impression was Fractions!!!

Sharing 3/4 of a cake between two people - How much cake does one person get?

At first, it seemed like a nightmare to me. I know how to get to the answer but when i saw the fraction that i had to work with, 3/4 divided by 2, I had a mental block!!! (Got me thinking about my secondary school mathematics)

Luckily, I had dearest course mates to the rescue and i enjoyed the process of working out the fraction sum :) The two methods that i did. Same answers but different way of looking at the model...

All About Counting... Day Two

There was so much to learn about counting today. 

Rote Counting
It's about saying numbers in an order, and is mastered before rational counting. E.g. 
1 2 3 4 5 6 ....
3 6 9 12 15 18...

Rational Counting
It's about counting numbers to represent objects (quantities)
E.g. 2 Apples, 5 Bananas





There are some factors which stops children from learning how to count. For example, if a child cannot classify or rote count, he cannot count. If the child does not understand one to one correspondence, or has no conceptual understanding on cardinal number, he cannot count.

The TEN FRAMES tool was introduced today and I think it is an excellent tool for children to learn counting. The attached video shows how Ten Frames can be used to enhance children's learning on counting, number relations and making ten.

In relation to counting, a new word that i learnt today: Subitize

It is the ability to perceive quickly, at a glance, the number of objects in a set without counting. The number can vary from people to people, starting from as little as 5 to as much as 1000. 

Why work in pairs or groups? Day One...

There were four PROBLEMS presented to us today, the first one being "Which letter counted 99".

My way of getting the 99th letter...

When I was working alone, I only saw one method, but when i work with my group mates, more methods were revealed.

My group mate's way of identifying the 99th letter.. counting from 1 to 99. 

And then, when you put the entire class together, more methods came up such as, counting in 10's till you reach 100, and you take one step back to 99th.!!! Talk about the effectiveness of working in an appropriate environment/classroom and peers.

Then came another PROBLEM... The Tangram challenge... Look at the picture on the right.

We had to something along this line, creating rectangles with 5 and 7 shapes. It was difficult, but with peers assistance and ideas, it was made possible.  

Working together with peers in an appropriate environment is important. Teacher's often engage children in pair or group work, and it is not just to enhance a child's social skills, but to deepen his/her level of thinking. As i have seen today, one problem, many methods, many solutions. Getting the answer is not important, but how you get it matters! Exploring, discussion with friends, persistence and looking out for patterns do go hand in hand...

As quoted by Dr.Yeap, "As you share, you will reflect, and that is a formation of knowledge." 

A TEACHER’S POINT OF VIEW - Newsletter for Parents...

You may have gone through school years with a love and hate relationship with mathematics. You would have hated it for all the formula that you had to memorize  or having to decode letters in equations in the name of algebra or for having to deal with a simple case of miscalculation which affected your entire problem sum. But you would have also loved it when you feel that excitement of solving an equation or a problem sum.

Now years later, as a parent of preschoolers, you might be in a loss thinking how your children are going to react towards Math and how you are going to help them  acquire mathematical knowledge. Fear not, as there are guides available that are produced and used by schools and Ministry of Education.

An example: Principles and standards for school mathematics (NCTM, 2000) provides guidance on what is to be taught.

Some of you might be wondering, “I know what my child is learning and now, I wish to be part of his/her learning as well. But I am not a teacher, so HOW CAN I TEACH MY CHILD?”

As stated in the Elementary and Middle School Mathematics, (2013, p. 9), “...Families’ and teachers’ attitudes towards mathematics may do enhance or detract from students’ ability to maths.”

The first step that you have to take is to embrace Mathematics. Destroy the hate in you towards Mathematics and by showing liking towards it, there will be a positive  impact on your child.

The second step that you will take is to understand that in this 21^st century, the answers do not matter as much as the process your child takes in learning maths. They are no longer in a traditional classroom where it is all about textbooks, workbooks, memorizing  drilling or copying. “Do as I do” is ineffective. Engage them in doing mathematics that permits them to: 

When we understand and teach Mathematics according to the constructivism and sociocultural theories, which allows children to use their own knowledge and experience to solve Maths problems, we will be soon phasing out generations that say, “I cannot do Maths! It’s too hard!”