**Monday 22 August 2011**

This evening we were reintroduced to how numbers are used in different ways.

1. Cardinal numbers

2. Ordinal numbers

3. Nominal numbers

4. Numbers used in measurement

5. Numbers used in proportion

I feel that the ten frame is a good tool to help very young children visualize amounts and numbers.

I realize that it is very important for teachers to help their students visualize and see patterns in order to help them understand concepts and do mathematics better.

Pre-requisites to counting- Children must be able to:

1. Classify

2. Rote count

3. Understand one-to-one correspondence

**Tuesday 23 August 2011**

**Games, games and more games.**If only my Math lessons were just like today’s lesson, I would probably have done much better!

Patterns are everywhere! The ability to look for and see patterns is an important skill every child should acquire. All patterns have rules and terms that are either repeating or growing.

According to MOE’s website, mathematics should be a vehicle for children to develop logical thinking; to become independent learners and to be able to correct one’s own mistakes and make appropriate decisions. This is similar to Jerome Bruner’s theory on Constructivism. Bruner's theory emphasizes the significance of categorization in learning. "To perceive is to categorize, to conceptualize is to categorize, to learn is to form categories, to make decisions is to categorize." Interpreting information and experiences by similarities and differences is a key concept. I am so happy that MOE has adopted the CPA approach to teach young students tackle math.

**Mathematics is:**

- Generalization

- Communicating ideas

- Visualization

- Dealing with information

- Developing number sense

**Wednesday 24 August 2011**

Lesson Study- How important is it in Professional Development?

This evening, we were asked to observe two case studies and were tasked to identify factors of good math teaching and learning. I learned that it is important to give opportunities for differentiated learning so that the advanced learners are challenged and will not get bored; on the other hand, the average of slower learners work at their pace of understanding.

We, as a group concluded that a good lesson comprises of these aspects:

1. Physical infrastructure- how the children were seated.

2. Children’s involvement

3. Teacher’s ability to ask appropriate open-ended questions

4. Classroom management

5. Use of manipulatives and charts so as to scaffold slower learners.

**Mathematical investigations**should be divergent in nature. It should allow for exploration and experiment and it should also communicate the process and result.

**Thursday 25 August 2011**

I didn’t think that I would enjoy doing fraction problems. However, by using concrete experiences and pictorial cues (folding and cutting paper), I managed to solve them! And not by the methods taught to me when I was in school eons ago!

This evening, Dr Yeap again emphasized how important experiences are to young children when doing Mathematics. It is a must for them to look at the concrete before abstract application. Teachers of mathematics should engage young children in thought-processes, so as to understand the sums and justify the rationale behind a solution they have found. The correct answer is not always important but whether the child is able to communicate his ideas or method.

**Friday 26 August 2011**

I am guilty of giving children “artificial stimulus”, which is a signal to tell children of my approval or disapproval to their answers. Instead, I should be d be eliciting answers from the children by asking them questions to prod them to think logically through a problem and get them to communicate their solutions.

# This evening, I had a lot of fun solving the “dot- puzzles”!

# Pick's Theorem

George Pick’s simple geometry theorem allows us to find the area of any polygon that is embedded on a lattice or grid. It is especially useful for concave polygons, for which the usual textbook area formulas do not work.

Pick's Theorem works wonderfully on a geoboard, where students can design wild polygons with rubber bands stretched over the nailheads.

Pick's Theorem simply has us count up the number of points on the boundary of the polygon (where the rubber band touches a nailhead) and divide this number in half. Then add the number of points in the interior of the polygon (inside and not touching the rubber band) and subtract 1. We can write the formula like this: Area = B/2 + I - 1. For the polygon to the left, there are 16 boundary points and one interior point, so the area is 8/2 + 1 - 1 = 8 square units.

**Wednesday 31 August 2011**

The book “How Big is a Foot” by Rolf Myller was a refreshing way to start a Math lesson. At the school where I work, we have been using stories to promote the connection between mathematics and children’s literature. All children love listening to stories and what better way to bring across a concept to them!

The highlight of tonight’s lesson was going down to the MRT station to solve yet another fun Math problem. Taking the classroom outside breaks the monotony of the lesson and showed us that “Math Is Everywhere!” Here is my solution:

There were a total of 62 steps.

Each step is about 14.8 cm in height.

62 X 14.8cm Answer = 917.6 cm

I must admit that I have enjoyed this module thoroughly and am certainly looking at Mathematics through New Eyes!