workshop 2: lets grow up a bit more~

1·         For the second workshop, I have broaden a little bit my "mathematical horizon" as I explored on subitising, counting, number sequences, addition/subtraction, multiplication, number facts strategies and mental computation. So, I would explain on some of the strategies that adults particularly teachers can practice in order to support the development of these skills which are important for students in order to move to the next stage in growing up with math.
   
      1. Subitising

Children acquire sight recognition of a quantity in subtising where they can automatically know the numbers of objects when they see them (Clements, 1999). Children may develop this ability through mathematical knowledge such as the domino pattern or without them (Clements, 1999). In classroom, teachers can use subitising flash cards (picture below)to teach this skill where numbers are represented via the dots on the cards.

Besides, the koala race game is also suitable to teach children subitising where they can play in groups. Each student will have 1 koala as a counter, then, they will take turn in throwing the dice and the counter can move forward if their chosen number appears on the dice. The winner is the first person who reaches the final.

The fly swatter game is also challenging and enjoyable where it is also played in groups. One person will place the cards and the others will have a fly swatter each person. They have to snap numbered cards that appear twice. Thus, children’s automaticity in subitising can be enhanced through this activity.

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       2. Counting

There are many ways to teach children how to count. Teachers or parent can use story books which are interested for the children. In illustration,  My big book: Winnie the Pooh is suitable for children to learn counting through shared reading whereby the characters introduce the numbers in a sequence and there are also colourful pictures which appeal to them. Teachers can ask guiding questions such as:

• what number do you think come after number 2?
• can you count how many bags of carrot rabbit has in this story? 

These questions will be able to support students to count in meaningful context.

Additionally, technology is also a great choice in teaching children counting skills since they love using technology in learning. For example, in babyfirsttv.com, there are many fascinating videos for children in supporting their learning including counting. The picture beside is on counting one until five where there are 5 chicks and children can follow the video in counting the chicks. Children can also play games which are available in this website.

3. Forward number word sequence/number word after/backward number word sequence/number word before

For these skills, teachers can give children big numbered cards and ask them to arrange them on a cloth line using cloth pegs. For example, for number word sequence, they would arrange from 1,2,3,4,5,6 and etc. They can also comprehend the ideas of number word after, before and backward as they move the cards according to teachers instructions and questions such as: 

• where do you think number 5 should be?, beside which number?
• what is the number before number 11?
• lets read aloud the numbers backward starting from number 12 

This activity is also appeal for children as it involve active participation and movement in classroom. Teachers can also ask children to hold the cards and arrange themselves in order to enhance these skills.

·        4. Early addition/subtraction

Children can practice these skills using concrete objects before they can do addition and subtraction abstractly in their mind (Smith, 2009). Teachers can use many concrete objects which are usually used for counting such as sticks, pebbles or beads. For instance, tens frames can be used to teach addition and subtraction as children can build a clear picture in their mind for computation before they can move on to mental computation. 

addition

Eg: 3 + 2=

Children can use different coloured counters in order to understand the addition. So, 2 greens plus 3 purples equal to 5. The answer is 5

subtraction

Eg: 5 - 2 =

1.

There are 5 koalas on the coach, 3 reds and 2 greens.

2.

Take away 2 green koalas

3.

  So, there are 3 red koalas left on the coach now.

It is easier for children if teachers associate colours in teaching addition and subtraction since they can easily see the idea of 'adding to' or 'take away'.

·         5. Early multiplication/division
       multiplication- teachers can show the multiplication table for children to show that multiplication is by adding sets of equal numbers;for example the table below which explains that 2 multiply by 2  is 2 smiles + 2 smiles.so, the answer is 4. Besides, by using pictures to explain multiplications, children would understand the concept better.

      division- teachers can use the idea of sorting; for example, 6 ÷ 2=, teachers can explain using the stars in picture below that 6 stars divided equally in 2 based on their colours would produce  3 groups of stars. The different colours can help children in comprehending that the stars has been divided equally according to their colours.

     Teachers can also let children play this fun leap froggy division game as they become better in division. The game can be played in groups where each person would take turn in throwing two dices. For instance, the number on the dices are 4 and 6, so, the person can choose the number 46 or 64. Then this number need to be divided by 6 which the full number of a dice. For example, he/she chose 46, so, 46 ÷ 6 = 7 and the balance is 4. Then he/she can move the counter to number 4.  The winner is the first person who reaches the final.This game is very exciting and can improve children division skill.

      6. Number facts strategies for either addition and subtraction or multiplication and division

addition

6 + 9 = ?


6 red dots and 9 black dots.

one of the red dots will fill in the tens frame and the answer is 15. 

children could clearly see this process as the card is folded under to show the changes of red dot.

multiplication

This card can show to children that 10 × 4 is the same with 4 × 10 which equal to 40.

Then, the card can be folded upward to hide the 10th row and show that 9 × 4 is the same with 4 × 9 . The answer is 36.


















7. Mental computation strategies

Teachers can teach mental computation by using hundreds chart especially when solving bigger numbers. There are two types of hundreds chart which are zero hundreds chart and one hundreds chart. Children can use one counter to practice this skill; for example:


using one hundreds chart, 57 + 24  =


1. Firstly, put the counter on number 57



























2. Then, move two row downward which also means add 20



























3.Finally, move 4 box forward to number 81 which means add another 4. So, the answer is 81

Reflection

When I was in in primary school, I  first learnt computation by using fingers and then using pebbles as counters. In learning addition and subtraction, my teacher used language such as add, minus or take away in order to understand the concepts. Then, I moved to using computation using numeral numbers; in illustration, to solve 3 + 2, we would have the standard pattern of,

       3

+    2

----------

      5

------------

This pattern would be used in learning addition, subtraction as well as multiplication. For division, I usually use 

The most interesting things is that I have just realise that there are many other ways in solving mathematical problems for children, after the second workshop. In my opinion, I was drilled to use these solutions during my primary school that I did not explore on other ways in solving addition, subtraction and etc. Besides, these are the standard answers required when answering exam questions in Malaysia as we need to show the computation for exam. I think teachers should let children to explore various ways in learning computation so that their mind would not be rigid to one way in computing numbers. Thus, in future, I would let my students to have their own creative thinking in solving mathematics in order for them to have a better comprehension on mathematical concepts. it is also due to the fact that mathematic is a 'maze' and I should let them use different path in order to get to their destination.


References:

Clements, D. H. (1999). Subitising: what is it? why teach it? Teaching children mathematics ,   5 (7), 400 - 405. Retrieved from Queensland University of Technology Course Materials.

Milne, A. A., & Shepard, E. H. (2010). My big book: winnie the pooh. Bath: Disney Enterprises Inc.

Smith, S. S. (2009). Early childhood mathematics. Boston: Pearson.

Division [ Image]. Retrieved August 29, 2011, from                                                        coolmath4kids.com