## Sunday, 27 October 2013

### Numeracy Experience Session 6: FINALE to Elementary Mathematics! (28/09/13)

It's the last day of class! Felt happy because this meant, another module of my Degree programme is coming to an end! An inch closer to Graduation! Hehehe.... On a serious note, I felt good sharing valuable information with all of you and getting to know that others have also benefitted from my learning.

Last night we explored shapes. And yes, when we talk about shapes, we don't only explore the sizes but also, determining the areas. Simple finding of area of the triangle, I can manage. For me to explore areas of peculiar shapes where I need to dismantle the parts to create a rectangle and triangle out of them, can be quite challenging for me. No, it's not Numeracy. It's not the concept. It's just, ME. As if that's not worse enough for me, Dr Yeap actually got all of us to work with our table mates to create a covered box using a rectangular shaped paper. The rule: It does not matter how big or small the box is, but ensure that the box is fully covered with no opening. True enough, my group's covered box turned out to be a paper bag! Arrgghhh!!

Surprise! We had quiz again this morning! Yes, true! This time, we were asked to write word problems related to the topic given. It was quite a breeze and was glad that it was not as mind boggling as per the previous quiz where we had to logically find the letter of our name that stands at the 2013th place. Geez.

Since today was the last session, the activities that we did was quite fun and light-hearted. We attempted Birthday Graphs and a game called "Salute".

SALUTE: A game meant for 3 persons (you can add more players for a more challenged game). One person will say "SALUTE" and when he/she says that, the other two players will hold up one number card each, on their forehead. The one who says "SALUTE!" will multiply the two numbers and say out the total. Players will guess the number on their forehead. - - - trust me, the kids will love it, just like we did!

And yes, it's a wrap! I hope all of you out there have enjoyed my blog entries. It's not an easy feat for me, as this is my first time doing up a blog site. I do hope that my sharing with you has benefitted you as a parent in enhancing your children's grasp and foundation on Numeracy. Math is not easy to all but once you get a hang of it, you'll do just fine.

Keep in touch!

Lots of love,

### Numeracy Experience Session 5: Exploring Shapes (27/09/13)

It's Friday!!! Why am I so excited? It's because....Dr Yeap has given us time to explore the museums and find appropriate art pieces for us to work on for our upcoming group assignment. And....lesson will only begin at 7pm, instead of the usual 6pm. So, my friend and I visited the nearest Singapore Art Museum and let me tell you a secret. *whisper* That was my first time entering a museum to look, view and appreciate the art pieces. Really! Ok shh....don't tell my students in school okay?

Tonight in class we explored with shapes via Tangrams. Dr Yeap gave instructions for us to get 7 pieces of Tangrams (2 large triangles, 1 medium triangle, 2 small triangles, 1 square and 1 parallelogram) from him. With that 7 pieces of Tangrams, we need to identify and explore how many different sized squares can we come up with.

Of course, after attending Elementary Mathematics for the 5th night, we tried to "outsmart" Dr Yeap and created a shape with a square within.

Needless to say, Dr Yeap rejected the idea, as what he was looking for was a whole square and not a square within. So much for trying to outsmart him...Hehe...

Another interesting problem that we explored was with regards to finding the area. The question was: With a rectangle-shaped paper, cut or tear out 2 congruent triangles. Then, with 1 congruent triangle, try to make it back into a rectangle. How do you then find the area of the rectangle? When I was copying this problem onto paper, I was actually quite puzzled with the expectation of this question. The first part about tearing out 2 congruent triangles from a rectangle-shaped paper, that was quite clear. However, it was the second part that was drumming my brain cells until I literally gave up and await for the solution. The solution? Genius.

﻿

What I discovered from Dr Yeap in today’s session:

Shapes are not 3D. Shapes are 2D.

Signing off till another note,

Hi all,

So how have all of you been? I've shared my three-days of Numeracy experiences with you here on my blog. Anyone has actually attempted the problems that I have laid out to you?

Yes? How was it? Easy? Difficult?
No?!  Well, you should. Get a feel of how your children (and me!) encountered them in their Numeracy class in school. Hehe...

Ok, on a serious note, I am here yet again to share with you of another night of my mind boggling module. Tonight's module was indeed heavy. Seriously, super heavy. Why? It's because Dr Yeap covered topics on 'Fractions Subtraction', 'Multiplication' and 'Polygon Measurement'. I've always had this 'thing' and negative impression towards fractions since primary school. Now that I have to go through it, the feeling is just 'blearrgh'!

My most favourite activity for the night was actually the Mind Reading game. The instruction was: Think of 2 digits (0 to 9; it can be the same digit or two different digits). Put the two digits together. Then, add the two digits together. Finally subtract the smaller digit from the bigger digit. Discover.
Look at the three images below. What do think is the similarity between the three?

Do you notice that when you subtract the smaller digit from the bigger digit, the answer is actually a multiple of 9? Yes! I didn't notice it until I kept on doing for 3-4 rounds. Wow...Mathematics is magic! Hahaha...

Last but not least, come and join me explore polygon via Tangram. Interesting activity for the whole family to challenge one another. No rubber bands at home? No Geoboards? Who cares? I'm sure most of you out there have a smart phone. Download the Apps from the AppStore and you're good to go!

What I discovered from Dr Yeap in today’s session:
You can teach a child anything but it needs to be enactive. Not all children can accomplish a task, as it will require metacognition.

### Numeracy Experience Session 3: Exploring Numbers: Concepts and Sense (25/09/13)

Arrrgghhh! Quiz Day! I was so nervous about the quiz before I even stepped into the class. It’s been quite some time since I attempted a quiz or test, and of course today was not a day that I was looking forward to. However, when I saw Dr Yeap’s written schedule on the board, I was quite relieved when I saw the quiz was slotted just before break time. Okay, at least it’ll give me time to gain composure and relieve the butterflies in my stomach for now.

I’ve always enjoyed manipulating with numbers, especially the first problem for today: "With numbers from 0-9, use any 2-digit number and add with another 2-digit number, to still get a 2-digit number". As I was doing this activity, I explored with many digits to ensure that they are not only, not repeated, but also to ensure that the outcome is still a 2-digit number. Some of the combination of digits that I attempted was …
42                    43                   28
+36                 +25                 +65
78                    68                   93

What makes it interesting as I explored the combinations, I discovered 9 ways (there could be more) of combining digits and eventually resulted into an outcome of 98. Amazing, right?!
When Dr Yeap shared his other findings on how to solve the above problem, he pointed out something interesting which I have never took note of until tonight. He said, “When teaching Mathematics, do not leave out the nouns. For example, when teaching 25 + 12, instead of saying ‘what is 5+2 and 2+1’ to the children, teacher should say ‘what are 5 ones and 2 ones; what are 2 tens and 1 ten?”.

I thought what he said made sense to me. This will be one way to get out children to be familiarized with the terms ‘ones’ and ‘tens’ even if they are not doing on that topic. In fact, it will help the children to quickly think of the outcome instead of having to do the traditional method of the ‘carry 1’ over to the tens when the number of ones is more than 10.

ALMOST BREAK TIME! Of course, it also meant that it’s quiz time! Trust me, I was so nervous while waiting for the paper to reach me. However, the moment I turned the paper over, I saw a familiar question: a repeat of what I went through in Session 1 i.e. the letter that falls in the 99th position. This time round, it’s changed to ‘the letter that falls in the 2013th position’. Challenging but of course, there’s surely a smarter way of doing it. How did I do it? Do I need to explain? Why not you try it out and see the outcome?

Quiz over and I thought the nerve-wrecking emotion ended there. My, I was wrong! Dr Yeap actually gave us another problem for us to solve and boy, we spent almost one hour and a half thinking and deriving different ways of splitting a rectangle shape (which we literally assumed for it to be a chocolate) equally amongst 4 persons. Here were some ways that I managed to come up with:

What I discovered from Dr Yeap in today’s session:

Enrichment is not about practice. It is about challenging the child further. It is also not about doing the activity/lesson at another time but it’s about adding the challenge within the same activity/lesson.

Sounds tricky to you? Digest it. I did.

Signing off till another note,

### Numeracy Experience Session 2: Holistically Whole Numbers (24/09/13)

Second day of class and excitement level is pumping every second in my footsteps towards the classroom. When I saw the schedule that Dr Yeap has written on the flipchart, I was like, "Oh wow! Another 4 more Mathematical problems for us to indulge in for the night." All the best, Deejah! Hehehe....

We sourced for solutions to the problem of "A man and his seven wives...", "Counting down by 1 or 2 until zero, with the use of kidney beans", "Using a 10-frame to count the number of beans Jack has", and "Sharing of 51 eggs amongst 3 persons". This is where we attempted the concept of conventions in finding out different ways of exploring ‘10’ when counting.

In fact, before Dr Yeap got us to solve the second Mathematical problem for the night (counting down with kidney beans), he shared a video in line with possible themes related to the topic i.e. Jack and the Beanstalk. If I was a child, I would enjoy the video as the music was catchy and the lyrics were quite repeated base on the storyline. After watching the video, I was raring with excitement to do the Kidney Beans activity with my partners at our table. It was easier for me to relate, as I felt as if I was Jack, literally counting down the kidney beans. Hahahaha.....I'm sure the children in class would enjoy their Numeracy activities more if teachers make the efforts to embed the element of fun in not only learning, but teaching too!

Oh yes! I was extremely fascinated looking at how Dr Yeap showed us an alternative way to solve calculation, besides the norm of using a calculator or manual working on paper.

This was a new finding for me, as I have never broke a number down into something that’s possibly divisible by the mentioned digit. This method looks logical to me and it’s worth my future attempts when working with big numbers via mental calculations. Forget calculators! Hehehe…

What I discovered from Dr Yeap in today’s session:

There are two different models that teachers can adopt and refer to guide learners:

1.      Acceleration Model – teacher will just teach the students and moving ahead without delving deeper into the topic or concept

2.      Enrichment Model – teacher stays on a particular topic and dwell on it; students will explore more on this area where teacher will work on enriching the topic or concept taught to the child in more than just one session

In a childcare setting, we would love to adopt the Enrichment Model when embarking on Numeracy concepts. However, many a time we will just attempt it via the Acceleration Model, as long as the topics or syllabus are covered based on the planned curriculum. It’s time for us to really look into the time-tabling and dedicate ample time for us to enforce a more solid foundation when it comes to Numeracy.

And I think today my brilliance in Numeracy thinking increased about 15% after attempting the problems laid out by Dr Yeap and gaining new information about the two different models of teaching Numeracy. Not a bad acquisition for a 4 hour learning and re-learning of Numeracy skills. Don't you think so?

Signing off till another note,

## Friday, 18 October 2013

### Numeracy Experience Session 1: Count Your Tricks or Treats (23/09/13)

Blog Entry 2 – review for session 1 on 23/09/13 (Monday)

My, oh my! It has been almost a month since my last entry! I am very sure all of you have been waiting anxiously for my reviews and updates, right? Well, let me first of all apologize to all of you for the late posts due to my tight commitments at work. I am sure my dear parents are aware that I am the Advisor for the Kindergarten Twos’ Year-End Ceremony & Concert event scheduled on 3 November 2013. It is indeed a challenge for me to balance off my school and work expectations. Anyway, this quote that I came across fit me well enough in the situation I am in: "Patience and perseverance have a magical effect before which difficulties disappear and obstacles vanish" (John Quincy Adams). So now I need to inject more substance of patience and perseverance in order for me to have the energy to share with you about the knowledge that I have gained in my Elementary Mathematics module. :)

Even though it has been three weeks since my session with Dr Yeap, the experiences that I want to share with all of you, remain fresh in my mind! Really! On my 1st day of class on 23rd September 2013, the session was a breeze. Content was kept light and entertaining with the activities that Dr Yeap has provided for us to explore. We were kept occupied with solving Mathematical related activities and two of my favourites for the night were:-
Activity 1        : What’s the letter in the 99th position of your name
How to play  : Write down your name on a piece of paper (space them out if you want). Find out what letter would it be at the 99th counting position (do not count the same letter that you last stopped).
Example         :

Learning point:
• This activity was a tedious yet interesting one. It was amazing to note and discover several possible methods while I was doing the above activity in class. The first one was of course the most obvious, which was to count manually till 99 (no, of course I didn’t do that! I was too impatient to even consider this method…hehehe).
• The second method was the one that I attempted to shortcut the process, which was the placement of numbers and digits with a ‘1’ in them such as 1, 11, 21, 31, etc. These are all in the same column in their respective rows. Hence, when I reached 91, it was easy for me to move on to 99 and voila! I discovered the second letter ‘e’ from the left of my name as the letter in the 99th counting position.
• There were two other methods that my classmates figured out such as all numbers with digit 9 in the ones place are all in the same column (9, 19, 29, 39, etc), as well as numbers that are multiples of 10 are all under the first letter ‘e’ of my name. Amazing, right??

So parents and fellow blog readers, which letter in your name stands at the 99th count? Would you be able to discover other possible ways to attain the solution? Do let me know here, okay. :)

Activity 2        : Card trick
How to play  : Get a stack of cards numbered from 1 – 10. Shuffle them in such a way that as you spell out the number words in chronological order, the card that you hold up matches the number word that you have just spelt (o-n-e = 1)
Learning point         : To tell you frankly, as I am uploading this entry onto my blog, I have yet to understand why there is a need for the cards to be shuffled and placed as in the image below, in order to meet the objective of the game.

Positioned from left to right: 7, 5, 2, 8, 6, 3, 1, 10, 9, 4
(7 to be placed at the bottom of the deck, and 4 being the top of the deck of cards)

Mathematically, I can't figure out the reason. However, LOGICALLY I may be able to reason it out. *winks* If we were to look at the arrangement of cards from the right, let us spell 'one'. O-n-e. And the number card positioned after we end the spelling is the number '1'. With that, we can chuck the '1' aside and continue to spell 'two'. T-w-o. And the number card positioned after we end the spelling is the number '2'.
Anyone of you out there game enough to try this out?

What I discovered from Dr Yeap in today’s session:
• There are procedures BUT there are no rote procedures
• 0 to 9 are digits (single); but numbers are all figures and numerals (two digits) such as 43, 76, etc. As teachers, be clear of the terms ‘digits’ and ‘numbers’ when teaching Numeracy to children

Till we meet again in my next blog entry! Very soon, I'm pretty sure! Toodles!

Yours sincerely,

## A Head Start to a Mathematical Journey ...

Dear parents,

I am pleased to share with you of my latest reading on Numeracy, based on the first two chapters of ‘Elementary and Middle School Mathematics: Teaching Developmentally’ (8th ed.) by Van De Walle Karp Bay – Williams.

Everyone is capable of teaching and delivering Mathematics even when the subject is said to be a challenging one.  However, according to the authors, ‘there are two essential components towards becoming an effective teacher of Mathematics and they are our knowledge of Mathematics and how students learn Mathematics’.  No doubt, as teachers (and adults who guide our young children or students) we tend to be rigid with our way of teaching Mathematics with the presence of and reference to structured resources and curriculum.  Giving our young children a head start in Mathematics is equally important as facilitating them with the recommended techniques suited to their level of readiness; simple to complex and concrete to abstract.  We know our children learn best through hands-on experiences and the more they manipulate items with their senses, the more able they will be in attempting problem solving.

There are many different ways of solving Mathematical problems and these are all dependent on the way we ourselves learnt Mathematics in our younger days.  Teachers can play their part in facilitating the children to acquire the skill of Mathematics by crafting from prior knowledge, providing opportunities to talk about the subject, reflective thinking, encouraging multiple approaches and many more.  When it comes to understanding Mathematical concepts and ideas, children can make use of various modes to represent their thinking and demonstrating their capabilities in acquiring it.  These can be in the form of, as mentioned earlier, the use of concrete and hands-on materials such as manipulative, counters, everyday items (like bread tags) and others; ranging to pictorial cards and written symbols.

Children need to be encouraged and facilitated in an open ended channel so that they would be able to source for alternative strategy or solution to crack the Mathematical problems or concepts that they are working on.  They are, after all, constructors of knowledge.

It is no mean feat to get our children to gain proficiency in Mathematics.  With that, I do agree with the authors of this book, “To respond to students’ challenges, uncertainties, and frustrations you may need to unlearn and relearn mathematical concepts, developing comprehensive understanding and substantial representations along the way.”

Signing off till another note,