## Monday, October 14, 2013

### The math journey never ends!

Absent from class due to School Sports Day Event.

I would like to thank Dr Yeap for sharing with us all the fun and interesting, and most importantly effective methods of making math fun for us, and for our children that we teach. Math is never boring, and never complicated. We have to be open to many other ways to see it all work out, and it is never about just finding the answer, but always about the process.

A video on how to make math fun for preschoolers!

### A Trip to the Museum (Group) and Fun with Tangrams

Trip to SAM (Singapore Art Museum)

Parts of the museum were under renovation but we enjoyed out visit there appreciating and discussing what each art piece meant. Some were profound with cartoon characters and depictions and symbols such as people wearing masks etc. Michelle and I were struck by a piece which showed two men wearing masks, and holding symbols, in an attempted handshake. It really shows how distrust and backstabbing can take effect on two people, who may seem pleasant on the outside. We saw a few pieces that showed unity and the Singapore spirit amongst different groups, and got down to choosing our art piece for our assignment.

Back to class and this!

Making Squares using Tangrams:

How many pieces are you able to fit into a square?

A little video to show you how...

And fun with more shapes....

### Session 4: Fractions and Geo boards

I discovered two videos and this one shows an interesting way of adding fractions! Multiplying them is easy, but adding them is a whole other story. This video is worth a watch!

Add them all up and what do you get?

This other video also shows the usage of Geo boards which we did in class with Dr Yeap to form polygons etc. Pull and twist those rubberbands and what do you get?

### Session 3: Of Knowledge and Division

Quiz Day!

Feeling the nervousness once again, and having unpleasant memories of math tests. But...wait...

Dr Yeap explaining the process and meaning of the problems to us, e.g. where we went wrong etc while trying to solve the problems was really helpful to us!

Procedural knowledge VS Conceptual Knowledge

Procedural knowledge - knowing what to do
Conceptual knowledge - understand why you are doing what you do

Enrichment VS Acceleration

Generally, Singapore does everything in acceleration. Even though it is known as "enrichment". Sound familiar? Teaching lessons ahead of time and children knowing more and more formulas but not fully understanding them = acceleration!

Enrichment is all about building up from what the child knows. For e.g., from concrete to pictorial(cubes to drawing), exploring possibilities(adding a new shape or colour) and looking for repetitive patterns in the environment (floor tiles, wall patterns etc.)

Qn: Why don't they ever do that for major exams?
I think that would really help you improve if you know where you went wrong, and help you to be confident in understanding the process to solve the problem! Especially a math one!

A video on simple dividing...

And another on dividing a rectangle in threes...

Time to solve a problem!
Qn: How can you divide a piece of chocolate equally among 4 persons?

Some possible methods:

Sharing of ideas...

Ready for some yummy chocolate? :)

### Session 2: Teaching of whole numbers

Dr Yeap introduced us to the usage of ten frames today. I thought, how apt!, as my K2s are currently learning all about tens and ones, moving to numbers greater than 20, and this is a great tool to help them!
They will learn to solve addition and subtraction problems, and learn number relationships.

Our fun times with ten frames using beans that Dr Yeap gave us during class to count and explore:

Ways to make 18..

Game with a partner... how many moves till I win? Remove two or three beans first?

Here's a video on the usage of ten frames:

The very next day, I let my children make ten frames of their own and they succesfully formed numbers within ten after a few fun rounds of getting used to using the ten frames.

This picture shows one of my students and his way of forming the number 5, with one red bean on the yellow paper, and four red beans on the other. They were sharing that number bonds have similar methods with ten frames as the question is asked: "___ and ____ make ?" I'm really glad that they understood the concept and enjoyed exploring with the beans and ten frames.

Indeed, as children learn to count, first starting from 1 to 10, then to 20, then to 30, 40, 50 and leading to 100, it can get confusing with so many numbers. Do they really understand the relationships between these numbers, especially when it comes to the tens?

Dr Yeap explained to us that some children cannot:
-rote count
-classify or sort
-do one to one correspondence
-understanding of cardinal numbers

And we teachers get frustrated and wonder which part do they need help in....

How then do we help these children?
Give them concrete materials to explore and play with :)

Cubes, beans, shapes etc. Let's have fun!

Also, how do we help children understand the terms of cardinal, ordinal and nominal numbers? Dr Yeap gave us some helpful insights in the explanation of what each term means as we teachers often get confused with the meanings.

This video also explains the terms:

An insightful session indeed!

### Session 1: Creating a mathematical climate in the classroom

Welcome to a new module, fellow classmates!

Reflecting back, I was a bit apprehensive at first when I knew it was going to be a math module as I was never good at math in primary and secondary school. My math journey spiraled downwards when application of complex formulas didn't make sense to me after Primary Four and I rarely had Math teachers who had the time to explain and be patient with me. Most just hurried me along to find the answer and got impatient. Scoldings were common, sad to say. Tuition didn't help and math was a ever growing nightmare. I was relieved that after Sec 4, I didn't have to sit for another math paper again though failing it at O levels caused a big ? for future studies. So the problem didn't end there.

Then when I became an early childhood educator, I knew I had to face my fears or my students would be just like me and it would plague them throughout their academic years. Attitude changed, time to solve the problems! Head on, let's go!

Dr Yeap's introduction and explanations throughout the night created a better understanding of why we can see math differently instead of being afraid of it. Perspectives can change, and methods should be taught differently to enable everyone to understand math and have the confidence to solve the math problem. It takes a light to brighten that dark room. In this case, mine! Thanks Dr Yeap!

My groupmates and I started off by tackling a math problem with our own names.

PROBLEM 1

How would I reach 99 when I write my own name out? Hence starting with 1,2,3,4 counting from right to left...

J A N E
1 2 3 4

METHOD 1: Count all the way to 99 (tedious..)
METHOD 2: Count in 10s each time you see 10s in the "A" column
METHOD 3: Count all the numbers with the digit 9 in the ones place
METHOD 4: Count in multiples of 10

What we also discovered: "A" column can be counted in multiples of 6 which ends up with 96 at the end, and adding a 3, you'll get 99 in the "N" column which is the answer.

Then we figured out that 99 appears to be common in the 3rd letters of names with 6,5,9,7 and 4 letters. Wow! Level up...

PROBLEM 2

We did the card trick, with some poker cards, and here's how we solved it:

Drawing out number words for each number (one, two, three... and so on) and drawing boxes to help with the counting...

O N E, T W O, T H R E E

which led us to the answer after some time of counting:

4,9,10,1,3,6,8,2,5,7

We then double confirmed this by trying out the cards. SUCCESS!

PROBLEM 4

We had fun trying out the different shapes of the tangram to form rectangles...

First with four shapes...

Then with five...

Then with 7!

First night ended with renewed confidence to tackle more math problems. I am starting to see the puzzles fit together :)

## Sunday, September 22, 2013

### Hello Parents!

Hi Parents!

Thank you for dropping by and feel free to check in on fun and creative ways to teach your child math, as well as personal thoughts and sharings by me :)

I have recently been reading perspectives on teaching Math from Elementary and Middle School Mathematics: Teaching Developmentally" by John A. Van de Walle, Karen S. Karp and Jennifer M. Bay-Williams, a textbook from my math module for my course of study. I hope my sharings from the text will be helpful to you as you and your child embark on this learning journey of discovering new ways to learn Math!

Teaching Mathematics in the 21st Century

Mathematical competence opens doors to productive futures - NCTM (2000, p.50)

Indeed, math is needed as we pursue future goals and dreams. It is seen everywhere in our environment. Symmetry in buildings, calculations made when purchase of things are made, and even in the measurements of making delicious cupcakes. Math is used everywhere :)

Children should therefore be encouraged to explore and seek out math solutions in every day problems. They will see that:
• Learning to communicate in math fosters interaction and exploration of ideas,
• It is also important to see how mathematical concepts build on one another in a network of connected ideas.
• Math plays a significant role in art, science, language arts and social studies.
They can then:
• Make sense of problems and persevere
• Reason abstractly and quantitatively
• Model and understand Mathematics
We as teachers strive to help our students appreciate and understand math concepts by:

• Creating an environment that offers all students an equal opportunity to learn
• Ensuring Students' engagement in problem solving, reasoning, communication etc.
• Using technology to enhance understanding, which is useful in today's day and age.
A great learning posture is definitely encouraged for all teachers who are teaching Math. We need to persist and have a positive attitude and be ready for change, as Math is ever changing! And at the end of the day, we need to be reflective and evaluate how well the students have understood our teaching and whether they are familiar with the processes and are able to apply them.

Exploring What It Means To Know And Do Mathematics

Children will come to know that math is all about pattern and order. Different numbers add up to the same total number. In reading story sums, children learn the language of maths using words such as: explain, compare, describe, predict, explore, formulate.

In experiencing discovery using math tools such as cubes, counters, measuring rods, spinners, children have fun with math building and taking away bite size concepts of how more or less works, or a quarter of a fraction is covered, and even measuring cubes to build the Great wall of China!

A personal sharing on projects with my K2s

Mount Fuji with blocks

Great wall of China (Mini version)

During block play: a massive castle structure built by my boys.

My 6 year olds embarked on building famous landmarks a few weeks ago. They were learning about how famous landmarks around the world are built according to equal numbers of bricks, and created their own Great Walls, much to my delight. I was so proud of them at how they calculated equal number of cubes on each side would make their structure sturdy and not fall over. They incorporated colours too, to mark certain portions of their Great Walls. All these encouraged thinking and planning, and they put their problem solving skills to good use when buildings did not stand firm and fall over. I see these skills in their block play as well, and it goes back to building good foundations of equal cubes/blocks on each side, which is Math!

Self discovery is definitely a great platform for children to learn, and with the teachers' guidance in learning how to use the math tools given, the children will be engaged in meaningful activity. Other examples include: two coloured beans help children to learn about number bonds, which build onto addition and subtraction, and shading of coins help children recognise how money looks like, before moving on to discuss the value of money to carry out exchanges in buying things.

We encourage children in their pursuit of learning and they will then be able to recall and retain what they have learnt, which is so important! They develop reasoning skills, improved attitudes and beliefs, and an effective learning of new concepts, with a productive disposition.

More to come soon! May your math journey with your child be a wonderful world of discovery and fun!

Cheers,
Ms Jane