## Friday, 11 November 2011

### gREEN aPPLES

The apples are arranged in alternating rows of 5 and 4 accordingly. Thus, two end of the tray display 5 apples in the row and the other two ends have 4. To arrive at this arrangement there must be 4 rows of 5 apples and 3 rows of 4 apples alternating.

4 X 5 + 3 X 4
= 20 + 12
= 32

To explain this to K2 children, I will use patterning. Instruction will be:
There are some apples in a tray. The apples are arranged rows of 5 and 4 apples such that two opposite ends have 5 apples and the other two opposite ends have 4 apples. Using cubes show the arrangement. Count the total number of apples on the tray.

# Session 6 31 August 2011

The story How Big is a Foot is a stimulating story to set the reader wonder. I have encountered this kind of problems in my class when using non-standard measurements. Students come up with differing answers. Using the term ‘about’ is good way of relating the measurement. The use of language plays a key role in Maths.
Going down to the MRT station was eventful. All that I had was a small ruler. The amount of interaction at the station was equivalent to the interaction children get into when engaged with activities.

A new finding ‘The ruler’s marking does not start at zero, there are gaps without any marking at the two ends.’  Ha ha then how are we going to measure? We used the corner of the step to measure to get the height of each step.

There were four flights of steps. After counting one flight my group decided to multiply it by four, but decided to make sure and went to count the flights individually. The last flight of steps had only 14 steps, while the other three had 16 steps. Oh oh! Luckily I went down to count the steps with Denise or would have made a mistake here.
So my calculations will be as follows:
3 flights of 16 steps
1 flight of 14 steps
The height between each step is about 14.5cm

(3 X 16) + (1 X 14) X 14.5cm
= 48 + 14 X 14.5
= 62 X 14.5cm
= 899cm
The height is about 899cm.

The discussion on volume and capacity enlightens the difference between them. Volume is the space occupied and capacity is the space available in a container. Similarly, teaching the concept of time to children was another discussion, which was very related to preschoolers. It is very essential for children to comprehend that sixty minutes make an hour. Children are able to tell time by the hour and by using the multiples of 5. The comprehension of hour is always a missing info.

The caterpillar story is an eye-opener. I may also be guilty of killing the butterfly because sometimes helping comes in naturally. So the development gets hindered. Well, now that I am aware, it is time to be thoughtful of the way I react, interact and render help to my students. Hopefully, I don’t kill any more butterflies.

# Session 5 26 August 2011

Drawing different types of squares was easy. However, finding the area of each was interesting. Some squares needed to be cut and pasted to form a whole or half of the square to find the area. Or it is the half of something that needs to be joined to see the whole. Lastly, when working with polygons, a bigger shape was needed to cover the irregular polygon. Taking away unwanted area revealed the area of the polygon. There is no one-way to work it out. As long as I can make sense of the shape and work out to find area it can be correct, I think. Knowing the area of a square and using it to work out the area of a polygon is very engaging. Very keen eyes and relating the shape is important to get the shapes and it's area.

Pick’s theorem is not so clear to me. I need more time to work on it to further understand the way it works.

# Session 4 – 25 August 2011

We are very used to getting approval for any little thing we do. Therefore as teachers we have trained our students to get approval from us. Now, the hit of today’s lesson for me is not to display any form of body language when students do some mistakes or achieve a correct answer. How to stop that???
I always felt that something is not finalised when Dr Yeap does not give any answers to the activities that we were engaged in during class. I was wondering why and I got my answer now. He is role modelling leaving the students to come up with their own decisions.  I feel that it could be sometimes difficult to leave kids without any form of approval. Alternatively, prompting students with questions and suggestions would make them think and reason out. Direct approval or disapproval could be avoided. I will have to try this out with my class before agreeing with this approach.

Classifying addition and subtraction into concepts of part – whole, change and comparison covers situations in which these skills are applied. I now have a better view of presenting the story sums to students. When students get to view it in these situations, better understanding takes place for the thinking process to be stimulated.
We explored fractions using materials to divide into equal parts. Fractions are not so difficult as I have always thought. Using concrete materials to see the parts made it very easy. Folding equal parts with a rectangle paper and further dividing it to smaller parts was interesting. Viewing different ways of folding equal parts was an eye-opener, especially four equal triangles in a rectangle.

# Session 3 - 24 August 2011

This session conducted by Ms Peggy Foo is a reinforcement of how a lesson is planned and executed. After which, an evaluation is done to further improve the lesson.
There are two main points that I valued. The first one is regarding evaluating a lesson. Asking for other teachers’ input to further enhance the lesson is constructive. Discussions makes one view what went wrong and right and to make relevant changes to enhance the learning process.
Secondly, to be prepared for differentiation, which can be easily overlooked, thus causing problem with classroom management. Being a little more prepared is always useful.
Making structures with fixed number of unifix cubes was interesting. Working in a group was fun, especially when we two of us made the same structure and had to place them together to know that they are same. Interesting visualization!
Bring back the tangrams was useful. I asked my five year olds to form the shapes and it was interesting to observe kids flipping and turning the pieces and coming up with new shapes. It kept the kids engaged for quite a while. A lot of interaction in the form of thinking was taking place. When I attempted it by myself, there was times when I had to scratch my head. It made me wonder how the kids in my class were able to place back the larger version of the tangram in the form of puzzle(pic. below) quite easily after a few attempts.
It was a day to revisit and reflect on the way I plan lessons for my class. Useful reminders to include more ideas to keep kids thinking.

# Session 2 - 23 August 2011

The video on the dice game brought awareness to how much we know about the materials we use in our daily teachings. I am aware that a normal dice has six sides and numbers or dots of 1 to 6 on each side. This game with the two dice made me learn that the total of the opposite side in a dice is 7. A simple game that can be played with the preschoolers, too.
During my primary school days (1970s), solving long divisions was like a nightmare. I can never get it correct, until I started explaining the steps, or rather memorise the steps. There was no understanding of tens and ones or any other skills. Not until I started teaching my own children did I get the understanding of how it should be done to make a child understand.

Jerome Bruner’s CPA approach well suits with the way children learn. In our childcare children are given concrete materials to explore. Then pictures are used and only when necessary abstract thinking is introduced. Not only for maths but also for any subject matter the CPA approach applies.

I enjoyed playing the sticks game in Lesson 6. Making a bad number brings in a lot of quick calculations to win the game. I played the game a few times with Elsie. We realised that proper calculation leads one to win the game. When children play it repeatedly, they will be able to comprehend the bad number concept. There is addition and subtraction involved in this game.
The five key points on generalization, visualization, communication, number sense and metacognition was experienced through the various activities that we did in class today. Via communication, students display their understanding and teachers assess the learning that has taken place.

## Sunday, 28 August 2011

### Daily Class Reflection

Session 1 22 August 2011
In today's session all activity was interesting. The first activity was solving a problem with names. It was engaging and i was able to see a pattern in it. In doing math, there is always a pattern involved. It is a matter of seeing it. How do I get to see it? I feel that it prerequisites like multiples and counting in groups are necessary for observing patterns and it just does not appear in one look.
I learned that ordinal numbers could be separated as numbers in space and time. Although we introduce this concept to children, there are always little things that get missed out and we end up making mistakes without realising that children are getting confused. The use of language plays a key role in relating concepts to learners regardless of experience.

Most names had the ninety-ninth place on the third letter of their names. I am very sure that in my name it is on the fifth letter, although there was a discussion involved and someone saw it at the third letter.
I was able to solve the problem of the cards and it's spelling using the cards. This was an exciting activity because after working it out, I had to check if I did it correctly. I felt like a child as I spelt out the numbers. A sense of achievement at the end.
I feel that this whole course is going to set me thinking if i have been teaching math to my studeents to make them think to solve problems in various ways rather than to get the correct answer.