Reflection

Day 1: 22/08/2011

It was the first day of class and I went to class with much anticipation, even though I felt a little fatigued after a busy day at work.

After a few minutes when I had arrived at class, the class had started and I was greeted with my first math problem to solve:

How do we know which letter is the 99th letter in Dr. Yeap's name and in each of our name?

It was really a brain teaser for me and it has been a long time since I had to solve such a problem.

I realize that after going through much discussions with my friends and racking my brain for an answer, what Dr. Yeap had done was to get us to use our problem solving and reasoning skills to good use.

We had a fun time solving various mathematical problems in class such as we arranged the polka cards in a way that we can get the respective number card after spelling out the name of the number and putting the card back in the deck simultaneously.

I also learnt that there are different uses of numbers such as ordinal numbers, cardinal numbers and nominal numbers and we had to be aware of how we phrase our questions when ask children mathematical questions.

Day 2: 23/08/2011

On the second day of class, we begin the class by playing pick-up sticks. We had a choice to pick up either one or two sticks from the pile, and the last person to pick up the stick or sticks from the pile, is the winner. I felt that the game was really interesting as it got me thinking, what are the 'bad numbers' of sticks that we would not want to be left with, if I would to win the game.

During the lesson, what really left an impression upon me was when Dr. Yeap mentioned that we should not be confused between teaching children and teaching mathematics. It really got me to become more reflective as we teach children to not just have the conventional understanding of mathematical concepts but also the rationale and conceptual understanding of mathematical concept as well.

And, it is alright to let children make mistake and correct themselves so that they will learn to reason, think and reflect on their problem solving strategies.

The lesson was concluded with the broad goals of problem solving and thinking skills and they are:

1) Generalization

2) Communication

3) Visualization

4) Meta-cognition

5) Number sense

Day 3: 24/08/2011

During the third day of class, we examined two cases of lesson studies where we observed how teachers teach in class in the kindergarten setting.

After making my observations of teachers in the videos, I realized how important it is to always reflect and evaluate upon our teaching strategies and practices. And, we can use lesson study to do research and improve our classroom and teaching strategies.

Factors to consider for teaching and classroom strategies:

1) Sitting arrangement

2) Level of engagement/involvement

3) Use of materials/manipulative

4) Flow/Sequence if lesson

5) Classroom management

6) Communication

7) Questioning techniques

8) Attitudes/Disposition

9) Differentiation (according to ability levels)

Day 4: 25/08/2011

It was the fourth day of class and what I had learnt throughout the modules so far was that doing mathematics is about looking at patterns and how to use the patterns to help us to do problem solving.

The first activity of the day really helped me to see patterns when we are doing problem solving - we had to think of two digits, put the numbers to together  and subtract it from the addition of the two digits - the activity is an amazing example to help us to see the connections between the numbers and its pattern.

In this lesson, we also discussed about learning the algorithm of subtraction and how we represent our mathematical workings; in addition, we learnt that quantities can be continuous or discrete and the concept of part-part-whole as a fractional quantity.

I also least that we have to be aware of the language structure that we use to give instructions to children. We should say " 2 fifths" instead of "2 upon 5".

Day 5: 26/08/2011

On the fifth day of class, we learnt how to do division of fractions and using models to represent that concept. I thought that it was really a meaningful way to start the class by thinking about how we are going to use models to explain division of fraction to children.

The question "3/4 ÷ 1/2 = ____" triggered me to think of how to represent it in model form. At first, I misunderstood it and I got 6/8 as my answer. However, after much discussion in class, I had got the correct answer which is 1 & 1/2!!

I also learnt that in division/grouping, the units are the SAME; while in sharing, the units are NOT the same.

Another math concept that I had learnt was shapes and the different transformation: rotation, translation, shear, and reflection.

We also learnt about area and the correct way of saying units², is "square units".

Tessellation was also a fun activity where we had to find out the areas of the different shapes we had created using the tessellation sheet without using actual measurement.

I felt that it was short but fruitful week of learning mathematics in this module. And, I am looking forward to final class for the module on Wednesday!