Today's lesson was very engaging. We learnt a card trick from Ms Foo and I want to try this out not only with my students but my family as well. I need to go prepare the number flash cards as soon as possible. Once again it helped that my mind was fresh and I had a friend to work with. While she was trying to solve the problem and murmuring to herself I managed to take down notes so we wouldn't forget how we derived at the solution.

Another interesting activity we had was paper cutting.

Paper cutting is something I've liked to do when I was younger. I liked folding the origami papers and cutting them to create patterns. After beginning my working life I stopped. It was definitely nice to experience one of my favourite hobbies again. I also realized that I had been creating patterns without realizing it. This has made me realize not to take any knowledge for granted. If I had understood the patterns I had made younger, maybe I would have known the solution to this problem earlier.

I also learnt about differentiated learning. Different levels in learning for the students. Differentiations can be in the content, the process or the product. by differentiation in content, children could be engaged in different concepts. E.g. number bonds or counting. Differentiation in process could be done by engaging in different learning centre activities and differentiation by product could result in different answers from the children. Differentiation is something that I'm quite familiar with but it now helps to know the different ways of differentiating.

## Sunday, 18 August 2013

### Reflection 5

The lesson began with some activities shown from http://gregtangmath.com/. I tried these activities and found myself glued to the laptop for a while as I tried the interesting activities. I enjoyed the math stories especially "the grapes of math." The sums were not as simple as they seemed when I first tried them. I realized I was too impatient as I did not read the text first. When I realized they actually contained some hints, I used these hints to help me solve the problems. This is one website I would definitely like to try with my students. it was interactive as well as attractive with so much of colours. Definitely a place I would like to go to again and again.

Tonight's problem on angles was a tough one. I had almost forgotten all the math rules for angles and here I had to refresh them again to solve the problem.

Well after much analyzing, discussion, questions and arguments, we finally managed to solve the problem. Looks like have to go back to my secondary math textbook to solve a primary 6 math question because I don't remember learning in primary school. Is it really necessary for children to be learning angles at this stage? What's the purpose behind it?

Tonight's problem on angles was a tough one. I had almost forgotten all the math rules for angles and here I had to refresh them again to solve the problem.

Well after much analyzing, discussion, questions and arguments, we finally managed to solve the problem. Looks like have to go back to my secondary math textbook to solve a primary 6 math question because I don't remember learning in primary school. Is it really necessary for children to be learning angles at this stage? What's the purpose behind it?

### Reflection 4

We started by doing some problem solving on fractions. Through this activity we came to understand Richard Skemp's theory on instrumental understanding, relational understanding and conventional understanding.

I enjoy doing anything requires me to do hands on. So lesson 13 and 14 had my uttermost attention because they were hands on. After revising fractions, we had a chance to work on pentominoes. We were asked to create different shapes with a given certain number of tiles. I enjoyed working with my partner to create the different shapes. I guess it helps to have a partner who works together with you and motivates you along the way as compared to working alone.

Could try letting children work in groups. This may enhance their negotiation and social skills.

Lesson 14 was on Georg Pick's theorem.

This activity was easy once we knew the solution to solve it. To count the number of dots and divide it by 2. But when seeing Pick's formula A=I + b/2 - 1,

I was wondering if the 1 signified the dot that we leave inside the diagram?

I enjoy doing anything requires me to do hands on. So lesson 13 and 14 had my uttermost attention because they were hands on. After revising fractions, we had a chance to work on pentominoes. We were asked to create different shapes with a given certain number of tiles. I enjoyed working with my partner to create the different shapes. I guess it helps to have a partner who works together with you and motivates you along the way as compared to working alone.

Could try letting children work in groups. This may enhance their negotiation and social skills.

Lesson 14 was on Georg Pick's theorem.

This activity was easy once we knew the solution to solve it. To count the number of dots and divide it by 2. But when seeing Pick's formula A=I + b/2 - 1,

I was wondering if the 1 signified the dot that we leave inside the diagram?

## Saturday, 17 August 2013

### Reflection 3

Today I learnt about subitizing through the dice problem. Subitizing is "instantly seeing how many." And to learn to subitize children need a lot of exposure and scaffolding. They need to be given a lot of opportunities and variations. Guessing the number of fruits in the bag without counting seems like an interesting idea.

For the dice problem, after looking at all sides of one of the die, I was able to visualize the missing number. I did the same with the other die and was able to derive the answer to the problem. My partner who knew that the opposite sides of the die add up to 7 had her own method of coming up with the answer. My classmates shared another method which I felt was a bit long winded. To individually subtract the numbers seen from 21 as all sides of the die add up to that number.

And to solve problems like these children need to have number sense, be able to recognize patterns and generalize and use their metacognition.

I thought this would be an interesting way of subitizing for children. With the dots arranged in this way, would it be easier for the children to subitize?

For the dice problem, after looking at all sides of one of the die, I was able to visualize the missing number. I did the same with the other die and was able to derive the answer to the problem. My partner who knew that the opposite sides of the die add up to 7 had her own method of coming up with the answer. My classmates shared another method which I felt was a bit long winded. To individually subtract the numbers seen from 21 as all sides of the die add up to that number.

And to solve problems like these children need to have number sense, be able to recognize patterns and generalize and use their metacognition.

I thought this would be an interesting way of subitizing for children. With the dots arranged in this way, would it be easier for the children to subitize?

## Wednesday, 14 August 2013

### Reflection 2

Tonight's lesson was all on numbers. Lesson 6 really had me challenged as I tried to figure a two digit number to multiply by a one digit number so I could get an answer. Sounded easy until I realised that I had to create the numbers with only 1 set of number tile.

This was a constraint and it was challenging as I tried to think of multiplication sums that did not required the numbers to be repeated. Managed to come up with a few solutions though. Proud of myself. From a person who hated math to someone who could solve math problems.

The ten frame was also an interesting activity. As a student, it helped me see numbers visually and the questions asked helped to build on my prior knowledge of numbers. For example, counting. I can visualise this as an activity I could conduct with my K1 students to teach them concepts like conservation of numbers and one to one correspondence.

Looking forward to learning more about math..

This was a constraint and it was challenging as I tried to think of multiplication sums that did not required the numbers to be repeated. Managed to come up with a few solutions though. Proud of myself. From a person who hated math to someone who could solve math problems.

The ten frame was also an interesting activity. As a student, it helped me see numbers visually and the questions asked helped to build on my prior knowledge of numbers. For example, counting. I can visualise this as an activity I could conduct with my K1 students to teach them concepts like conservation of numbers and one to one correspondence.

Looking forward to learning more about math..

## Tuesday, 13 August 2013

### Reflection 1

MATH!!! We were enemies since I started school. We could never get along well with each other and he always was ahead of me in exams. I didn't make an effort to be friends with him until today.

And I think I made the right choice as I really enjoyed today's lesson. Could have been the way the lesson was conducted. Through concrete materials and hands on lessons as I'm a kinesthetic learner. There were no explanations required with the tangrams. Just the materials on the table and instructions to create triangles. And there we were my classmates and I trying to figure out the different ways to create rectangles with the given pieces. It didn't matter that we made mistakes along the way. There was a lot of discussion and arguments between us but who cared as "I WAS HAVING FUN WITH MATH!!!"

I learnt about the CPA approach of Jerome Bruner.

And also how children learn math:-

1) through exploration

2) role modelling

3) scaffolding

I must say I truly enjoyed tonight's lesson. Looking forward to more tomorrow. Thanks Dr Yeap!!!

And I think I made the right choice as I really enjoyed today's lesson. Could have been the way the lesson was conducted. Through concrete materials and hands on lessons as I'm a kinesthetic learner. There were no explanations required with the tangrams. Just the materials on the table and instructions to create triangles. And there we were my classmates and I trying to figure out the different ways to create rectangles with the given pieces. It didn't matter that we made mistakes along the way. There was a lot of discussion and arguments between us but who cared as "I WAS HAVING FUN WITH MATH!!!"

I learnt about the CPA approach of Jerome Bruner.

**C**oncrete**P**ictorial**A**bstractAnd also how children learn math:-

1) through exploration

2) role modelling

3) scaffolding

I must say I truly enjoyed tonight's lesson. Looking forward to more tomorrow. Thanks Dr Yeap!!!

## Saturday, 10 August 2013

### Pre Course Reading Chapter 1 & 2

This is how I viewed math. I was one of the 5 of the 4 who believed I can't do math. But reading the text just changed my views and this is how I would like to view math now.

There are six principles fundamental to a quality mathematics
education. They are Equity, Curriculum, Teaching, Learning, Assessment and
Technology.

-Equity
principle is about setting high expectations for all students.

-A curriculum
needs to be coherent and focused on important mathematics.

-The teacher
plays a very important role in bringing enjoyable math experiences into the
classroom. To provide a high quality education, teachers need to understand the
math contents they are teaching, know the learning styles of the individual
students and select meaningful tasks that will enhance learning.

-Learning is
enhanced when students are allowed to evaluate their own ideas as well as their
peers’ ideas. This helps them develop their reasoning and sense making skills.

There are about five process standards
which students need to acquire and use as mathematical knowledge. The five
processes are problem solving, reasoning and proof, communication, connections
and representation.

Also there are 6 major components that are important
to allow students to develop mathematical understanding. These components
include:-

* Creating an
environment that offers all students an equal opportunity to learn

* Focusing on a balance
of conceptual understanding and procedural fluency

* Ensuring active
student engagement in the National Council of Teachers of Mathematics

(NCTM)process

standards (problem solving, reasoning, communication, connections and representation)

(NCTM)process

standards (problem solving, reasoning, communication, connections and representation)

* Using technology to
enhance understanding

* Incorporating
multiple assessments aligned with instructional goals and mathematical

practices

practices

* Helping students
recognize the power of sound reasoning and mathematical integrity

So how do we each math?

o Build new knowledge from prior knowledge

o
Provide opportunities to talk about
math

o
Build opportunities for reflective thought

o
Encourage multiple approaches

o
Engage students in productive
struggle

o
Treat errors as opportunities for
learning

o
Scaffold new content

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