My Reflection

It has been a very interesting module for me. Though Math has never been my favourite subject and in fact I never did well all along. However; I had a change of mind set after sitting through those activities - exploring and thinking through those problems. This module had opened my mind to learn to enjoy Math. One particular activity I enjoyed most was the Dice activity. It was very engaging and stimulating. When I played this game with the kids; they were so amused and fascinated. The game went on for half and hour with great fun and laughter. After going through this course; I know one thing for sure that children learn Math through concrete experiences in a fun and engaging manner. Math need not be dull, boring and solemn. As a teacher; my responsibility is to instill in them a mind of curiosity to find out, to investigate and think of possible solutions as they engage and learn. Through it all; children will also learn to perserve and develop thinking skills.

Cookies: Only 1 (lucky for me since I am not good in Math)

Geometric Thinking

SPATIAL SENSE is a word used to describe about relationship between shapes. It is an ability to see see spatial relationship between shapes and visualize them in our mind and move them around in our mind. This is mind bogging; something which I have been struggling all along. Like the writer says that some of us think we are not born with that spatial sense and he said it was not true. But geometry was my weakest topic in my Math subejct. That was why I struggled during the geometry activity. I could not see the relationship of those shapes neither could I mentally calculate their angles. However, as I read this textbook I begin to eliminate my fear of geometry and understand more about its ideas. According to Van Hiele; there are 5 levels of geometric thoughts; from level 0 to level 4. Interestingly; most of our nursery children begin at level 0 as they learn about shapes such as square, circle, oval and triangle. Children who can explore, touch and feel objects and classify them according to the shapes are at level 1 which is visualisation.
I believe it is important to provide children with lots of opportunities to explore with solid shapes from the basic square, circle, triange, oval then move on to rhombus, hexagon, octagon, so on. Providing them with such concrete experiences with geometric activities help build a foundation of geometric ideas in them.

Here's a catchy song for young children to learn about shapes - 'Shape Song'. Hope you all like it. Enjoy. http://www.youtube.com/watch?v=3pQCfyoLF54&feature=related

Number Sense

I agreed with Howden (1989) who said that "good intuition about numbers and their relationships develops gradually as a result of exploring numbers, visaulizing them in a variety of contexts"). Evidently, children need to explore with concrete materials to discover number relations and patterns and through their explorations; they make connections and build bigger ideas and understanding. The text emphasized that early number sense demand significant attention in Pre-K and K children so as to establish a solid foundation. It also emphasized that counting is the most impotant tool that young children will first develop which eventually will be reduced as children construct new relaltionships in numbers and build new ideas.

Some of the Number sense activities that are being practised in our preschools are introduced in the book, such as:

i)  Numeral writing and recognition - Children are given sand paper number cards to trace to develop sensorial learning as well as number recognition.

They also learn to count objects according to the number to understand its value.

Children also learn to match numbers to number cards; which is a common math activity in Singapore preschools.

To further reinforce their concept on counting; teacher will allow the children to practise by working on worksheets.

ii) Another number sense activity that our preschools practise is mainly  taught in the K2s : build it in parts. In a typical K2 classroom; a teacher would give connecting cubes to teach children number concept such as 2 and 2, 2 and 5, 5 and 3. Children use different colour cubes for each number and connect the cubes together and thereafter count on to find out the total number of cubes. By counting on; children learn that 2 and 2 will make 4 cubes and so on.

Some activities that are not common or practised in Singapore are: The double Maker which uses the calcuator. Another one is: Add a Unit to Your Number. 

Technology

I used to have the understanding that K children should always learn to count with concrete objects only and should not be exposed to the usage of calculators as they may become reliant on them or do not know how to count by themselves at all. However, I was wrong till I read the the passage under the heading of "Benefits of calculator Use". I was rather surprised to learn that research studies have proven that calculators can help K students to improve their "basic skills with paper-pencil task operations and in problem solving" and with "long-term experience using calculators performed better overall than children without such experience on both mental computation and paper and pencil problems. (page 113). And on another passage it says "Research results reveal that students who frequently use calcultors have better attitudes toward the subject of mathematics (Ellington,2003). Which I believe so as children will be intrigued and fascinated with the results and answers that appear on the screen. Certainly, they will want to try out other math questions to find out more answers. By doing so, children will naturally continue to explore on that calculator and thus they also become more confident and develop positive attitude in learning Math.

I enjoyed trying the the "Attribute Blocks"from the website "NLVM" under the section on "Measurement"  This Math activity begins from simple to complex which is suitable for Nursery children to K2. The activity begins from one attribute and gradually increases to 4 attributes. It requires the child to identify the common attribute in the oval shape (shape, size or colour) and then drag and drop the correct attribute/s into the oval shape. It also allows the user to check if the answer is correct or wrong. The class teacher can also do it with the children over a projector screen or each child can do it on their own  at the computer. Through this activity; children can learn to identify colours, shapes and sizes and also enhance their visual discrimination.

Place Value

In my opinion; after using the sticks to teach the children tens and ones and followed by the use of blocks and coins; I will introduce:
i)  The place value chart. Reason being; children at this juncture had already grasped the concept of tens and ones in concrete experience, associating their knowledge to pictorial cards - Place Value Chart will solidify and further enhanced their understanding of tens and ones.

ii)  Next I will introduce to them the tens and ones notation. At this point; children would have understood 34 is 3 tens and 4 ones.

iii) Then with this understanding of 34 is 3 tens and 4 ones; I will introduce the expanded notation of 30 + 4 which is more complex.

iv) Next, I will introduce the numeral 34; as children by now will understand that 30 + 4 means 34.
v) Then the most complex is the number word "thirty-four" which I will introduce at the end.

When my team members and I tried to create different problem sums based on the question on 39 x 4. We were seemingly stuck with only 3 variations. We had been taught from young the fixed methods of doing Math. So naturally; when we did this Math activity in class; our perceptions were rigid and lacked creativity. As I read the chapters on problem solving; I learned this important value - a paradigm shift! 

A teacher needs to have a paradigm shift. That as teachers we need to change our philosophy of how we think how children learn and how best we can help the kids. In the past; we used to learn Math as a subject with no concrete learning nor understood the concepts and neither did we do them tangibly which ended up with so many of us didn't do very well in Math in schools. Now, as preschool teachers we re-learn how to problem solve Math. Interesting indeed! As I look at the same problem 39 x 4 again; I adopt some strategies from the textbook on "Problem Solving Strategies" I tried using models, drawing a picture, using Guess & Check or even made a table or chart - to see the problem from different ways. Such methods I had never used before and I began to see new ideas and not so afraid to try problem solving. One important aspect I have learned in teaching children's problems; is to let the children talk about the problem they are solving. Ask them how they solve the problem? or why do they solve it that way? Why is their solution makes sense? Asking them such questions help them to reflect and rethink. As I think about these strategies; I am reminded once again to look at problem solving with different perspectives- paradigm shift. 

On 2nd September night; we had a fun time trying out some new math concepts with Dr Yeap. I enjoyed doing the Dice game and watching the video on how Dr Yeap taught the Pri 1 by using the dice. Playing this game set my mind thinking and problem solving. As I played the game; I could imagine how it would fascinate a young child's mind. This game makes me want to find out why it total up to 6? 8? 10? or any other number. It encourages me to analyze, question and reason as well. Moreover the dice are very colourful and attractive. Using dice to teach Math to our school kids will definitely stir up their interest to learn.