## Thursday, 1 September 2011

### Reflection on Session 6

This was the last lecture we had for this module. I once again had an enriching lesson which I enjoyed. Two main activities that were of my interest:
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 MRT Station
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﻿1. We had to go down to the MRT station to count the height of the staircase from the top to the bottom!!
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This was how I actually calculated..  I counted that there were four flights of stairs and the first flight had 16 steps. So naturally I thought all the 4 flights had 16 steps each. But I realized I was wrong when I walked down all the way to the bottom. I realized that there were 16, 16, 16, 14 (steps accordingly to the flights). Then I paused again and thought that I should not be counting the in betweens of the flights of steps. Finally I was not convinced and I walked all the way up, counting each step.

Lastly, I counted a total of 62 steps. Each step was approximately 14cm.
Answer: 62 steps multiply by 14cm = 868cm.

 Kidney Beans Activity
2. Another activity that probably shocked me was the activity where we had to make a box to fit 15 kidney beans! That was when I had to apply the knowledge and understanding of volume and capacity. However, after looking at the job done by my group, I think I need to better understand and estimate the capacity or volume of something! The box we build could actually fit 45 kidney beans! How embarrassing!!

On the whole, this has really been an enriching module and I have learnt more than I thought I would have.

Thank you Dr Yeap!

### Reflection on Session 5

 Fractions
Session 5 was an enriching lecture that I experienced in class. There were a few things that I learnt which were not new to me but somehow when Dr Yeap explained it to the class, I saw new understandings to it. An example is: How many 1/2s are there are in 3/4? In the past, as a student, I would use the common Math solution and solve the question. However, now I am able to see a new light in these kind of questions and I am able to better understand the concept of these kind of questions. Previously, I saw these kind of questions as a typical Math question to solve but now its about first understanding the question, seeing a model pattern in it, and then finding the answer.

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 Join The Dots
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Another interesting activity that I enjoyed was the 'Join The Dots'. I thought that was something good to do when we need to get our heads cracking. It was amazing to know that the squares could be drawn in so many ways! From that one activity, I must say that I started to believe that anything is possible in Math and I must learn how to look at different ways of solution to the final answer.

One thing that refreshed my memory after secondary school days is:

5 tansformation of shapes..

1. Reflect
2. Rotate
3. Translate
4. Stretch
5. Shear
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## Thursday, 25 August 2011

### Reflection on Session 4

Lecture on 25 August was a bit more special for me because Dr Yeap went through the group and final assignments! I was happy because I've been waiting to get started on the final assignment so that I can get over and done with it! So.. finally I can get cracking on it!

Dr Yeap started the class very interestingly with a "mysterious" game. Initially I was really shocked that he could find the difference of the two numbers. Then I realize that this must be one of his "trick" game that involves a pattern. From this lesson, I learnt that it is really important to find a pattern so that we are able to analyze "what comes next". I really enjoyed the lesson. Another lesson involved us to fold papers of different shapes into 4 equal parts. It was nice when the whole class shared their views on why they think the 4 parts are equal and how they proved so. The different working methods from some of my classmates proved successful and I was pleased with myself to have contributed  one idea as well. I guess I was happy because that earned me a PEG! This lesson was simple yet enriching because it has given me new ideas as to how I can tackle such questions for the children in my class.

 Different methods to prove that all 4 sides are equal
Towards the end, Dr Yeap went through with us something that I have probably never thought existed in word problems. I knew that different word problems are structured in different ways but I never knew that these structures have a name!! The different structures I learnt about are:

1. Join Problem

2. Seperate Problem

3. Part - Part Whole Problem

4. Compare Problem

And lastly.. of course once again.. THE QUIZ was interesting! Looking forward to the next session and of course THE QUIZ!! :)

*Actually.. the quiz is quite a good idea. When I am able to solve the problem and get the answers, I feel like I am so smart! Hahaha! At least I am able to relive some of my childhood days!! (Really just like a child!!)

### Reflection on Session 3

Session 3 was done by Peggy Foo and she covered two case study of Lesson Study. Initially, I was wondering what lesson study was all about when she asked us for our views. Then I gathered that it could probably be something like a lesson observation that we have during our field practicum. She showed us a video of a teacher conducting her lesson in class and there were observers doing a lesson study on that. Everyone in my class shared their views on both the negative and positive things that we could gather from her lesson conducted. It was interesting to know what the rest of my classmates had to share about their thoughts. I learnt a few things that it a good reminder for me when conducting a lesson in my own class..

 Cubes Fixing
Some thoughts:

1. Seating arrangement

2. Classroom management

3. Flow/ Sequence

4. Manipulatives/ Use of materials

5. Participation/ Engagement/ Involvement

With these same points in mind, we also shared our views with Peggy Foo on the lesson she had conducted with some K1 students. She was really generous to have shared the video on the lesson she had conducted!

Towards the end of class, we were engaged in a fun activity where we had to fix cubes. We worked as a group to share ideas on how to fix as many structures as we can with 5 cubes in each structure.It was real great fun!

And of course, the class had to end with THE quiz! It was a great attempt once again! Looking forward to the next session and quiz yet again!! :)

## Tuesday, 23 August 2011

### Reflection on Session 2

﻿﻿﻿﻿﻿﻿﻿﻿ Session 2 started with a quiz that went really well for me! I was surprised that I could come up with two solutions out of four during the quiz. This was a good start for the class and also a motivation for the rest of the sessions for the module. Dr Yeap went through a few different lessons with us and I really enjoyed some of them very much. The lesson on the dice was one fun "trick" that I will definitely want to use with the children in my class. It is something really new that I have learnt from Dr Yeap. The take away sticks lesson is also another lesson I can share with my students. Teaching them to recognize good numbers and bad numbers during a game (which we played in class) will be interesting for them as well! In this lesson, I learnt something very simple yet deep from Dr Yeap.. "We are teaching children, we are not teaching Mathematics." This sentence is a good reminder for all teachers! The lesson was also wrapped up with..

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 Take Away Sticks ﻿
﻿﻿5 things that we teach in a Mathematics programme:

1. Generalization
2. Communication
3. Visualization
4. Metacognition
5. Number Sense

Looking forward to the next quiz and session!
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### Reflection on Session 1

﻿﻿﻿﻿
 Lesson 3
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The first lesson in class was really interesting for me not only because it was fun but also because I was surprised at how our lecturer, Dr Yeap, was able to make us think ALL the time!! I really thought my brains were going to burst!! But I must admit that it was real good fun and most importantly I learnt so many new things that I probably would not have thought I could learn. The different lessons that Dr Yeap went through with us: Name problem, Sound of Numbers, Ten Frames, Arrange the Cards, Number Tiles Puzzles. These lessons included little tricks which surprised me! The lesson that amazed me the most was "Arrange the Cards" simply because through that lesson , I was motivated to use my brains more effectively. I was not able to realize what the trick was when Dr Yeap allowed us to try the game on our own. When he was going through the procedure with the whole class, that was when I told myself that it was such a simple thing to solve yey I was not able to do it!! I was really feeling awkward because I felt that it was quite embarrassing!! I decided to use my brains more effectively for the second lesson.. :)

## Thursday, 18 August 2011

### Reading Reflections on Chapter 1 & 2 : Teaching Mathematics in the Era of the NCTM Standards, Exploring What It Means to Know and Do Mathematics

Mathematics to me as a young child was a subject that I studied for and practiced doing problem sums because I was told to do so. I was told by my parents that it is a subject that I must concentrate on because it is important for me to do well in it. As time passed and I grew, I really did not like the subject very much mainly because I found it difficult, tricky and the most boring part of it was that there was always only one right answer to a question! That was how, I drifted away from liking Mathematics.

Of course, when I became a pre school teacher, I realized how fun and interesting Mathematics could be! After reading through Chapter 1 and digesting the National Council of Teachers of Mathematics (NCTM)'s Principles and Standard for School Mathematics, I feel so relieved. The six principles sums up a high quality mathematics education that is so promising. One particular quote from the NCTM that I totally support is:

"Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well". (NCTM, 2000, p.16)

I totally support this because I believe that every child has a different learning phase and technique and therefore, the teacher should be able to understand that before challenging them further. I do not believe that any child is not capable of doing Mathematics, it is just how a teacher changes the situaton for the child to learn. Teaching Mathematics in this era would involve learning through concepts and tapping on their capabilities and that is how the children are able to learn. Becoming a good mathematics teacher would also mean that one has to have a positive attitude, have persistence and she must be ready for changes. I believe that with a positive attitude, a teacher can bring her students to new heights of learning. Teachers should also be ready for changes as it makes the subject more "relaxed" and not too "structured". As there can only be one answer to a question in Mathematics, I do not believe that there can only be one method to go about solving it. When children are open to solutions to an answer, they are willing to try. If they are told to be rigid, they may withdraw.

Therefore I believe that loving Mathematics is not only about following the curriculum and teaching standards, it is also about the teacher and if she wants to make a change in her classroom.

How is Mathematics best learnt?
In Chapter 2, it is stated that there can be a setting for doing Mathematics. I believe that a productive classroom can benefit the children very well. As stated in the classic book Making Sense (Hiebert et al.,1997), the author described four features of a productive classroom from where children can learn from one another:

1. Ideas are the currency of classroom

2. Students have autonomy with respect to the methods used to solve problems

3. The classroom culture exhibits an appreciation for mistakes as an opportunity to learn

4. The authority for reasonability and correctness lies in the logic and structure of the subject, rather than in the social status of the participants.

These four features best describes my feelings towards a good classroom environment for Mathematics to take place.

What Does It Mean to Learn Mathematics?

Fig 2.8 on pg 20 shows a model that best describes how does one learn Mathematics. I totally agree that by using ideas that we already have to construct new ideas, we are acutually developing a connection between the ideas. The more we do so, the better we are understanding. This should be understood ny all teachers so that there is a common understanding ground that we are all standing on.

Conclusion of my understanding

Mathematics is a subject full of ideas and concepts. What we teachers can do is to ensure that we adopt some startegies that best fits into our classroom and implement it. We should ensure that all children learn something out of Mathematics and have a love for this subject because it is indeed a beautiful subject. I really hope to learn and share more in class.