Group Work - measuring the steps

My group answer:

Each step is 15cm.

There are 64 steps altogether.

Therefore the total height is:

64 x 15 = 960cm.

At the end of this learning journey...

What we learn with pleasure we never forget.

Alfred Mercier

Although it was just a 24hr course, this whole experience brought me a better understanding in what is math all about, how should it be taught (by understanding how children learn, good practices and the guiding principles - e.g. CPA approach) , the different ways of assessment and the correct terms to use in math.

It made me reflect the way we should carry out our math lesson. We should constantly get children to reason, connect ideas and think logically. Other than planning lessons, we should also take advantage of learning opportunities that happen naturally and turn them into teachable moments. Using these meaningful moments will bring a powerful impact on their learning. To add on, we should also ask open-ended questions to encourage children to think and allow children to explore different ways in solving problems.

We have to always keep in mind that it is the process that matter and we have to let children learn through their own mistake by letting them correcting it themselves.

Providing formulas or steps-to-follow will never do any good to children. They will be 'trained' to 'follow' closely and if they forget the formulas or steps, THAT IS THE END.

"If we do not have struggles and challenges in our work, we will never grow strong and capable. If life has no difficulties, we will become weak and helpless."

Lim Siong Guan, Head, civil service

Well,everything ends. But I will continue to seek for new knowledge in teaching math!

Thank you (Dr Yeap) for being such an inspiration; You brought me to look at Math from a new perspective! :) Math is never dull again!

Day 6

Day 6 - 31st August 2011

Assessment

Assessment is to aid the teacher in identifying the areas that the child needs to improve on and most importantly, use it to help the child improve!

There are many different form of assessment and they can be formal or informal. On top of that, assessment can also be in variation. Instead of getting children to work out the word problem, teachers can get children to come up with word problem. Assessment can also be a form of oral test or interview. I totally agree that teachers have to identify and be clear of what they are going to assess so that they can choose the right instrument.

"An instrument that does not measure what it supposed to measure is an invalid assessment."

Dr Yeap Ban Har

An invalid example that was shared in the class would be:

[Drawing of hr/min hand to tell time]

When we want to assess whether the child is able to tell time, simply just ask the child to tell it verbally / read the clock!! Why bother to ask them to draw the clock and the hr/ min hand. Children who are able to tell the time might not be able to draw the face of a clock. Thus, it is an invalid assessment.

SO TRUE!!!

Next, I totally agree with the point - when we are teaching time, get children to relate it to everyday event! I had experienced this before with my class of K2 and they soon began to develop the habit of looking at the clock before lesson, after lesson, tea break etc. Incidental learning is the most beautiful form of learning :)

Lastly,

Never under estimate the capacity of a small container.

(PS: This activity can be another form of assessment!)

Day 5

Day 5 - 26th August 2011

Division in fraction

1. Grouping meaning (e.g. in 12, how many groups of 4 are there?)
2. Sharing meaning (e.g. 12 is equally shared among 3)

The condition for division in fraction is, the unit must be the same with that grouping.

e.g.

...Fractions seems to be easier after this lesson... :D

George Pick's Theorem

First, we were asked to draw as many different sizes square on the dots diagram. I was only able to come up with 6 different squares. When our classmate shared their no. 7 square, I began to see from another perspective!

After which, we had to calculate the area of those squares. It is interesting that we can find out the answers by dividing the square up, moving and joining them back so we can see a unit easily.

Following, we had to come up with a shape (any kind) that uses only 4 dots. The class came up with many different ones (polygon); some were big, some were small. We proceeded to calculate the area of those polygons - which is not easy at all!

... and...someone save the day!!

*Thumps up* to my classmate who figure out the formula!

Area = (p + i) -3

Writing it out allowed me to see the pattern clearly :) The formula makes calculating of those polygons so much easier :D

Day 4

Day 4 - 25th August 2011

Expose variation in word problems

3 situations in an addition/ subtraction problem:

1. Change problems (unknown can be the final, change or initial)
2. Part-part whole problems (e.g. there are 37 students in a class. 19 students are present. how many students are absent?)
3. Comparison problems (comparing at least 2 quantities. e.g. i have $37, you have $2 more. how much do you have?)

Children do not learn well through repetition. Exposing children to a variation of word problems encourage children to use the same concepts to work with different problems. This will help teachers to find out how well the children understand.

Fractions

The condition for naming is to first form equal parts.

The idea of 1 fourth:

We were all given a piece of square paper to fold it into four equal parts.

It was clearly demonstrated to us that no matter how we fold the square paper, as long as we get four equal parts, we can name it!

However, being equal does mean it have to be identical! - idea of variation.

And lastly, from this activity we experienced the process of CPA!

Day 3

Day 3 - 24th August 2011

Lesson study

Case study 1 /2:

K2 lesson on more than, less than.

What I learn :

1. When we are comparing, use identical items.

(So that children will focus on comparing more/less and not the properties of the items.)

2. Placing items in a line/ cluster?

(placing items in a line is at an easier level compare to placing items in a cluster.)

3. Use different representation (such as graph chart) to show more / less.

Besides, I also learn that we have to take note of :

-The seating arrangement during activities

-Giving quality instructions

-Asking questions to stimulate thinking

-The design of task to provide differentiated instructions to cater to different needs

-Use of manipulative/ materials

-Sequence of lesson

Case study 3:

Ms Peggy's lesson

Three things i would take away from her lesson:

1. The way to ask questions to stimulate children's thinking.

2. To take note of the different ability of the children and come up with differentiated instructions (using the same activity) to engage all the children.

3. Using of open ended materials.

I love the way Ms Peggy asked questions and using all opportunities as "teachable moment". In addition, I can see that the children were really engaged and learning math through a fun way. I will definitely take note of all these good practices! :)

Fun with 5 unifix cubes - Learning the idea of conservation of number.

This is a great hands-on activity to get children to be creativity and at the same time learn the idea of conservation of number!

Day 2

Day 2 - 23rd August 2011

Take 1 or 2

This activity focuses mainly on counting (1,2). To cater to children with the higher ability, using the same activity, we can challenge them by finding the bad number.

From this, i learnt that activities should always have different levels to challenge children's thinking. It is important as teachers to be able to observe the children in the class and give differentiated instructions to cater to different needs.

Magic Dice

Another 'magical' activity which integrates addition, finding patterns and communicating math ideas!

How Children learn Math

Children learn through the CPA approach (Jerome Bruner)

1. Concrete Experiences

2. Pictorial

3. Abstract

Children will not learn anything by memorizing.

"Using memory to learn is using the HUMAN WEAKNESS to learn."

(That's why we invented paper to jot things down!)

-Dr Yeap Ban Har

Day 1

Day 1 - 22nd August 2011

Which letter is the 99th letter? (BAN HAR)

(I was amazed by the way you integrate math into your self-introduction.)

The first thing that came to my mind was, "oh no! We will have to count all the way to 99!" As i started counting and writing down with my partner, we realized that numbers ending with 9 always end up at letter N. We continue counting to be sure of our prediction. And true enough :) , number 99 ends at letter N! However, this does not seems to work on all words (number of letters make the pattern different.)

It was interesting that the class came up with different methods to solve this problem. Coming up with different solutions really encourages us to think and make connection to the problem. What I learnt from this activity was, for every problem there will be different solutions to it. It doesn't matter which way you do it as long as you can justify it!

Ten Frames

Great way for children to do counting as it provide children with concrete experience and visualization!

For a simple question like: 5+7 = ___

We can use a ten frame to introduce different methods in solving, such as counting all (adding) or counting on (with the knowledge of commutative property of addition).

And in order to do meaningful counting, children first need to learn classification, rote-counting, one-to-one correspondence, and using number(s) to represent the quantity.

Ordinal number - Tells position with respect to space and time.

"Who is third in the race?" - using a picture.

A common error. We can't answer this question because the race is not finished!

This is so true and I didn't really realized until today!!

Magic Poker Cards - Spelling card trick!

Activity like this really motivates me in finding the reason behind it! :)) It makes me reflect upon the way math should be taught. Remembering how learning math can be so much fun would definitely make a change in the way I should start teaching math.

lastly, I believe children will love Math when they begin to see the real 'magic' within!

Reflection: Chapter 1 and 2

Math is a subject i love to hate!

But...

After reading the two chapters, I realize why I hated Math so much - I had never make any connection to what I had learn. I learn by rote, forcing my little brain to remember all the formulas and keep practicing (10 years series) and hope that similar questions will appear during exams.

Chapter 1 has given me a perception on how we as educators should teach math. The 6 principles gave me a clear understanding on what kind of support and environment we should provide for children to enhance learning. Next, the 5 process standards demonstrate the process which children should acquire and apply their mathematical knowledge. It is important that these 5 processes are integrated during learning and teaching so that children can develop mathematical ideas, justify their ideas through logical thinking , connecting and expressing mathematical ideas. I came to realize this is a more meaningful way in learning math as these processes add to a deeper understanding.

Chapter 2 gave me a clear understanding that learning math is not only about drilling. It is about building on from prior knowledge, rich interaction, opportunities for reflective thought, encouraging children to build connections on what they know to what they are learning-multiple approaches, making mistakes, reflect and clear the misconception, scaffolding and acknowledging that every child is unique. To develop a better understanding, educators can use multiple representations (such as manipulatives and models) to support them. It is kind of sad that I don't grow up learning math that way. Realizing the benefits of relational understanding motivates me to seek for more strategies that I can implement to enhance children learning.

Lastly,I hope that more educators will come to understand that learning math is not about drilling, so that children will learn in a meaningful way, acquire the concepts and apply what they learn in real world situations.