YUMMY YUMMY YUMMY =D

COOOOOOKIES!!!!!

OK everyone... just how many cookies do i have?!!? After all the quizzes Dr Yeap put us through... I'd like to try one on you. And knowing all of you, you'll probably figure it out without even blinking...
;)

So, I have a certain number of cookies... which you will figure out once you solve this:

John bought C pencils for $2.00
He sold each one at 10% more of the actual price.
How many pencils had he bought if the profit of sale for each pencil was $0.05?

And THAT my friends are how many cookies i have.

Psst... You got it right? And yes you are right... I have FOUR! And boy were they yummy! :)

(H) Reflection of the course

So we've come to an end of this module.. along the way we reconnected with Pythagoras... got to know Brunner and Dennes... played (while still learning of course!) games, learned tricks, cracked our brains with quizzes and puzzles.. and basically did much more "mathematical" things than I am used to doing even over a year I think! ;) haha..

I started this course dreading the 6 days that i would have to immerse my poor mathematically "un"-inclined brain into all the theories and practices. Completing the module, I can say that... well, it's not like I have developed a sudden love for the subject nor have I become so immersed in it that I would want to be figuring out problems everywhere i went. If given a choice, I think Math would still not be on my list of favourites, or even semi-favourites. Years and years of hatred cannot just be forgotten like that;)

However, I can honestly say, that I do realise now, the importance of the children seeing, feeling, and observing the teacher's love for the subject. Watching the way you spoke about Math, just from the top of your head, Dr Yeap, one can see clearly your love for Math. And even though you might have someone like me in your class, holding the biggest shield i can find against it, your enthusiasm and excitement does rub off on us.

I can also say that i understand now that Math can be fun...there's no denying that. It can be interesting, thought provoking, and carried out in a variety of ways. There are unlimited possibilities and the only thing that could and would stand in one's way would be their own mindset.

Having said this, I am excited to try some of the things i have learnt with my children. Talking about the levels that children pass through, while learning Math, will help me in planning engaging activities for them. The examples from the textbook are also interesting and definitely worth a shot.

What have I learnt from this class? Math can surprise you at times...and when it does, will you be ready, and open to it?!?!

Oh! and not forgetting, the realization that even our preschool children can use calculators to learn Math concepts!

(G) Geometry

Chapter 20 speaks about geometric thinking and geometric concepts. This ties in with the lesson we had dealing with geometry, shapes, and angles. We were asked to find the angles in a pentagon ( a five sided figure) :

Honestly, when I was first faced with the pentagon, and the thought of finding the interior angles, I was stumped.How...?!?! Wait, Why?!?!

What struck me when everyone was sharing their answers and thoughts was how there were many ways in which my classmates choose to find the angles. I was reminded of this when reading Chapter 20. The book states that spatial sense and geometric reasoning is one of the two related frameworks of geometry objectives. Spatial sense is defined as an intuition about shapes and their relationships. This includes the ability to mentally visualize objects and spacial relationships.

This, I realized is what my classmates had done. They had each "turned" the shape around in their mind, and looked for other shapes within the pentagon to help them in finding the sum of the interior angles. Anyone and everyone when consistently provided with shape and spatial relationships over time, can develop spatial sense!

Another thing that has stuck with me all this while about that particular lesson was how children tend to construe a lopsided square as a diamond. I showed the children in my class the same shape and sure enough more than half of them proudly said that it was a diamond. I also realised that the book we used for our Math curriculum did not depict squares as anything other than in the traditional way.

After explaining to them and using concrete materials to show them, i redid the activity with them a week later. This time, however, they all said that it was a square and when asked why they felt this was so, one of my girls replied "of, course it's a square because all the sides are the same still. Teacher Grace, you just put it another way. It is still a square!" Teacher Grace's reaction.....*a great sense of achievement*!! =D

HOW MANY SQUARES DO YOU SEE?

(F) Whole Numbers

Knowing about numbers is far more than just knowing how to count. Time and lots of experiences are needed for children to fully understand number-related concepts.

The book suggests that the teaching of number sense be carried out through high quality learning activities. Children's natural interests in mathematics should be enhanced and used to make sense of their physical world. At the same time, their maths curriculum should be based on knowledge of children's linguistic, cognitive, physical, and social and emotional development. Math activities should be integrated with other activities and vice versa.

I believe that teachers in preschools do take into account children's development and natural interests. However I do question how much of this knowledge is incorporated into the lessons that they plan for the children in their classrooms. In many classrooms, and to a few teachers and parents, math is always about counting, adding, and subtracting. They do not take into account children's natural interests and as a result, math is not used to its fullest potential to help children make sense of their physical world.

However, Math curriculums in many centres do try to integrate math activities with other activities. The math curriculum used in my centre centers around songs, stories, poems, physical activities, and hands-on activities. These activities are more prominent in the curriculum for the younger aged children. While there are still many hands-on activities and a wide variety of materials used in the curriculum for the older children, the songs and music&movement aspect of it is kept to a minimum. I do wonder why this is so.

Some of the activities in the book are being practised in preschool centres here are :

• The relationships of More, Less, and Same.
• Counting On and Counting Back

Activities that I believe are not being practised in preschool centres here are:

• The use of calculators for numeral recognition
  (I personally liked this idea...and as usual think...why haven't we thought of it before?!)
• Anchoring Numbers to 5 and 10
  

Dear Dr Yeap,

My blogs are not completed yet. Please please please do not assess them until the end of the month. OK? :) Thank you!

The-now-addicted-to-cube soduku,
Grace;)

(E) Using Technology to Teach Mathematics

In this day and age, almost every child is exposed to technology in one form or another. The children are skilled at using these technologies and one cannot deny that it is growing to be part of their daily lives. It is no wonder then that technologies play an important role in children's education as well.

Chapter 7 impressed upon me how essential technologies are both for learning and teaching. Rather than it being a once-a-week, touch-and-go lesson, technology can be used to enhance students' opportunities to learn math.

One of the technologies mentioned in the book was the use of calculator. I have never thought of using a calculator to help children learn concepts such as problem solving and counting on. However, after reading about it, i couldn't help but think how obvious it was and wonder why we never thought of it. A calculator!! for teaching MATH!! Now, who would have thought of that! ;)


I used a calculator in school, but only when I was in Secondary school. Back then it was used to key in random numbers from our worksheets, maybe a cosine or two and tadah! I'd arrive at some answer which I did not know for sure was the correct answer. When we got bored of all of that we used the calculator to find ways to key in numbers to make "words or sentences" like "1 177155 4" which translated to I MISS U.

Reading Chapter 7 also made me realise that electronic manipulatives have advantages over the physical models. One of which is unlimited materials with easy clean up. Students can begin a new problem easily with just a click of the mouse.

I enjoyed using the Shape Tool on the Illuminations website. The shapes could be cut, expanded, and rotated among other things to make new shapes and patterns. It was so interesting to see all the various activities and tools that parents and teachers can use to help children learn various math concepts. The activities were fun and definately brought the idea "unlimited materials with easy clean up" to play.

(D) Sequencing of the five tasks

We were asked to sequence the five learning tasks mentioned below for place value (34). This is the sequence that I would use with my students after they have been introduced to 3 tens and 4 ones using the bundles of sticks :

• Place Value Chart
  Since the children have been introduced to 3 tens and 4 ones through the use of concrete materials (the bundles of sticks), I feel that the next step would be to use the place value chart. This will help children to understand the place value of the 3 tens and 4 ones they have seen and learnt about earlier.
  
• Numbers in Tens and Ones
  Introducing numbers in tens and ones next will help the children expand on what they have learnt from the concrete representation of 3 tens and 4 ones.
  
• Expanded Notation
  The next step would be to introduce children to the expanded notation of 34. This shows children the symbolic representation of 3 tens and 4 ones individually.
  
• Numbers in Numerals
  Numbers in Numerals should be introduced to children before numbers in words. After showing children how 34 is represented in expanded notation, teachers should explain and introduce children to this same number written in numerals so that children can see how 3 tens and 4 ones can be represented in numerals.
  
• Numbers in Words
  In my opinion, numbers in words should be introduced to children as the last task.