Reflection : My school experiences in relation to learning computation.

Hello and good day mate! How are you today? I wishing you all the best and may God bless us all. Okay, for this week entry I would talk about my school experiences in relation to learning computation.


As far as I can remember, I never had encounter any experiences in relation to learning computation during my school visits, either back at Malaysia or in here. Therefore, I will try my best to remember and relocate my memories during my previous education in primary school. First and foremost, there is lack of learning computation back in my old school as my Mathematics teacher does not give more emphasize regarding this concept. The learning is focusing on the traditional ways which is by using " 'borrow-and-pay-back method' or formal vertical algorithm"(Bobis, Mulligan & Lowrie 2008, 14). Since this method has being introduced at the early stage in Mathematics, I find that it is easy to solve any Mathematical problems especially in addition, subtraction, multiplication and division. However, there is disadvantage in applying the method towards children's thinking and mental development. As the result, they would have difficulties to do the mental computation by themselves. That what I has experience during my Mathematics class in this semester.


After attending the workshop, I realise there is a room of improvement that can be done back in Malaysia. There are heaps of methods and strategies that teacher can choose to promote and develop children's mental computation. One of my favourites is by using the hundred chart ( 99 chart). This chart is interesting and fun to play with. Furthermore, children are  able to 'see' the process of adding and subtracting by moving the indicator; for example, button, on the chart. Besides, I find that it is easy to be used!

Hundred chart

99 chart.

In conclusion, hundred chart is the best ways to introduce and teach the concept of mental computation to children. This method helps them to be familiar with the teaching and ideas of computation.


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Mental computation strategies

What is mental computation? Mclntosh, (2005, p.5) describes computation as "an addition, subtraction, multiplication or division leading to an exact answer, or the process of achieving this". Therefore, mental computation is " a calculation performed entirely in the head, with only the answer being written" (Mclntosh 2005, 5).

Hundred chart
Bobis, Mulligan & Lowrie (2008) explain that hundred chart is a well-known representation of numbers 1-100 (or 0-99) that has a multitude of uses for developing counting, patterning, base ten, addition and subtraction, and multiplication and division fact knowledge. The use of partitioning and sequencing ('split and jump') methods can be assisted through the complementary use of the hundreds chart.

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

Addition & Subtraction

One way to teach addition and subtraction concepts to children is by using the Tens frame. Tens frame will help children to understand the concept of addition and subtraction easily as they can see how the action of  'adding' and 'take away' is being done.

Tens frame

Here is an example on how to teach addition with Tens frame.

8 + 5 = ?

8 + 5 = 13

Click here for online activity for Tens frame. Butterfly Ten Frame

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Early multiplication and division

There are two aspect in multiplication. 

An efficient way of adding sets of equal numbers of objects

(a) 3 sets of 2, or 3 twos

(b) Sets of 2 put out 3 times

Magnification, often associated with enlargement or scale.

(a) 3 times as many as 2 ( 3 times 2)

(b) A set of 2 trebled   

(Biggs & Sutton 1983, p.52)

Division is the reverse operation of multiplication
There are two aspects in division. The two aspects are sharing and subtraction.


"In sharing, a collection of objects (or a quantity) is divided into a given number of equal sets (or parts): objects in as et are then counted. The subtraction aspect is sometimes called the grouping or measuring aspect" (Biggs & Sutton 1983, p. 62).


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Early addition/subtraction

According to Biggs and Sutton (1983, p. 35) addition is "the putting together of two or more sets of objects (or numbers) and finding the total." 
Meanwhile, subtraction is the reverse operation of addition which is taking away a number of amount from one number. 


In addition, the process can be shown by using MAB (Mutli-base Arithmetic Blocks) or match sticks. By using this material, children able to see the process of 'putting together of two or more sets of objects' (Biggs& Sutton 1983, p. 35).

The sum of these blocks is 10 + 10 + 3

Teacher can ask the children to count and tell the amount of the blocks. The same method can be applied in subtraction by 'taking away' some of the amount of the blocks.

There are also other ways for teacher to teach subtraction in class. 

Take Away 
Rose had 8 cupcakes and gave 3 to her friend Maria. How many does each child have?


Comparison
10 children wanted to play on the playground at recess and 5 wanted to stay inside. How many more wanted to play to play on the playground?


Completion 
Henry had 5 books and he picked up some more from a rack. Now he has 7. how many did he pick up?


Missing Addend 
Sara made 12 cookies. 7 were chocolate, the rest were yellow. How many were yellow?


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

Forward number sequence.
The process of having a sequence of number in correct order. Example: 1,2,3,4,5,etc...

Teacher can use number cards and ask the children to line up according to their number. This will strengthen their understanding of which number should come first.

Backward number sequence.

Similar with forward number word sequence, the number is in desire order; descending to ascending.

Example: 10,9,8,7,6 etc...

Online game based on forward and bacward number: Count forward backward up to 10

Number word after/before.
The quality to recognize the number order that goes before and after given number.
Before after between up to 10

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Counting

There are 5 main counting principles that children have to understand the concept of counting.

One-to-one principle
"This involves the assigning of one, and only one, distinct counting word to each of the items to be counted. To follow this principle, a child has to be able to partition and repartition the collection of objects to be counted into two categories: those that have been allocated a number name and those that have not. If an item is not assigned a number name or is assigned more than one number name, the resulting count will be incorrect" (Thompson  2010, p.1).

Stable order principle
Comprehension of the correct order of the numerical. Example: after 5 comes 6 then 7 and 8 etc...


Here is an example of online activity that children can participate for further understanding of stable order principle.
Counting



Cardinal principle
'Knowing the last listed number is in fact the number of object present' (Thompson, 2010).



Abstraction principle
"This states that the preceding principles can be applied to any collection of objects, whether tangible or not. Obviously, for young children learning to count it is easier if the objects are tangible and, where possible, moveable, in order to help them to distinguish the 'already counted' from the 'yet to be counted' group. To understand this principle, children need to appreciate that they can count non-physical things such as sounds, imaginary objects or even the counting words - as is the case when 'counting on'" (Thompson 2010, p. 2).



The order-irrelevance principle

This principle refers to "the knowledge that the order in which items are counted is irrelevant" (Thompson 2010, p. 2). It does not matter if the children  is carried out the counting from right to left or vice versa, the item that has being counted will remain in the same amount.

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Subitising

'Subitising is the instant recognition of numericy in a group' (Clements, 1999). By subitising, children are able to recognize the numbers without even counting.


There are two different recognize forms:


Perceptual subitising.
"Recognizing a number without using other mathematical processes" (Clements 1999,p. 401).
For example: Children might "see 5" without using any learned mathematical knowledge.


Conceptual subitising.
"Recognizing the number pattern a s a composite of parts and as a whole, for example: an eight-dot domino" (Clements, 1999,p.401)

Snap card game.

This game is good to enhance students' subitizing skills. The numbers are represented in dot form so children must recognise the number. When the same number appears twice, they can 'snap' the card with their fly swatter or hand.

Teddy bear race home.

This is another games that can be played to teach subitising concept. The child must pick a number for their little toy character. Then they must roll the dice and if their number appears on the dice they get to move their toy one space. This is a perfect example of subitizing as to recognise their allocated number when it appears on the dice they must use this technique.


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Workshop 2

Hello to all my lovely readers. How are you today? I hope that all of you are in the pink of health. For this entry, I'm going to introduce to you a new topic that I learn with Dr Ann Heirdsfield.  
In this workshop, I learnt about number and operation and mental computation. I find this time, the lesson was  interesting, fantastic and challenging at the same time.The highlight of that day will be the activities, where I played 'snap' game with my friends. We make a lot of noises as we have a great time snapping on the cards.


There are several new concepts in Mathematics that I learn in this workshop. Click on each of the links for further information.

                                       Subitising 
                   Counting      

   Forward number backward number sequence

        Early addition and subtraction

           Early multiplication and division

      Number facts strategies

Mental computation strategies

Reflection

Reflection: How do I view Mathematics.

Hello and good day mate! How are you today? I hope you are  having a wonderful and fantastic day. For my first reflection, I will share with you guys on how do I view Mathematics before and after taking the EAB 023 class.

When I was in primary school, Mathematics was my least favourite subjects. This is because I always feel bored when learning Mathematics. There are less interesting activities that can be done during in class which affecting my enthusiasms in learning. Everyday, the lesson is focusing on counting and solving problematical questions. As the result, I was under pressure and stress in answering the questions.


However, my perspective towards Mathematics has change after taking EAB023 class this semester. During in the class, I play a lot of activities and games that related with Mathematics. These activities really help me to enjoy myself while learning at the same time. It was so fun, I did realize that the class was already done for that day.


 Apart from that, learning Mathematics can be fun and exciting if teacher knows how to create the conducive environment for children. Teacher should produce and prepare heaps of Mathematics resources in the class so children are able to use them in learning. These resources can even be as simple as a collection of shells or buttons. They might seem be useless, but with these material children are able to use them as learning tool and then construct their own learning. Now, I realize that teaching Mathematics is fascinating and motivating. The key to a successful in conducting of Mathematics class is by integrating fun, enjoyable and meaningful activities with the lesson for the children to learn.

Patterning

Patterning  involves 'identifying the form and order of a given arrangement of objects, describing the arrangement and repeating the arrangement' ( Irons, 1999.).
Children explore pattern on four levels; recognize, describe, extend and create pattern.

           
There are three types of patterning


Repeating patterns
This pattern required children to repeating the sequences such as red,blue,red,blue...

Repeating patterning: Colour and shape.

 Growing patterns
 1,2,3,4,5,6, or 2,4,6,8 or smaller to bigger

Growing patterning.

Click here for more example of growing pattern games.     How Does My Pattern Grow?
Growing patterns





Relationship patterns

It is where two numbers are linked using some sort of functions. This pattern is related with the multiplication operation.

Number of boxes	Number of crayons
1	8
2	16
3	24
4	32

Table

Picture

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Ordering

" Ordering involves arranging objects, pictures, groups or events according to the relations between them based on increasing or decreasing amount of an attribute. It requires three or more objects or pictures to do the ordering" (Irons 1999, 6).

Ordering block according to their height 

In the beginning process of ordering, teacher should start with object that has the same colour. This is to avoid the children from getting confuse.
Once they have familiarised the concept of ordering, teacher can challenge their understanding by asking them to order objects with different attributes such as using different colour of blocks. 









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Comparing

Irons (1999, p. 5) explains that "comparing is based on relations between amounts of an attribute that two objects possess".
The process of comparing uses only two objects, even though more than two objects may be in the group.
Comparing is used in measurement topics of length, mass, capacity, area and time.
Children begin to compare objects by using words. Generally, comparing word consist of 'er' word.

Tall - Taller

Small - Smaller

Big - Bigger 

Long -Longer

There are plenty of interactive games on the internet which will help them to understand the concept of comparing. 

Click here to play the:

 Longer and shorter game.

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Sorting

Biggs and Sutton (1983, p. 16) describe sorting as "looking at a set of objects and deciding how the objects are with similar qualities (or the same) and how they are different."


"At an early stage the ability to discriminate attributes, by sorting, helps children to sort objects into subsets, to match these one-to-one and subsequently to count and calculate. 
At a later stage, this process of selection helps children to select variables (attributes in many different situations, including some in algebra and geometry; for example, an algebraic description of odd numbers, squareness, etc.)" (Biggs & Sutton 1983, 16).

Sorting the objects according to the attribute. 

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Matching

"Matching activities focus on the 'sameness' of attributes. Children select objects or pictures that have to share some common attributes. Children then describe why the objects or pictures match, using language associated with the attribute they have selected" (Irons 1999, 3) .

Matching according the colour and shape of the objects. 

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Identifying and describing attributes

"Attributes are characteristics, features, qualities,properties, traits, particulars or specifications of objects. Common attributes which young children notice are colour, shape, size,sound, taste, texture, type of material and the object's function or use. When children engage in activities that require the use of the senses,
they are exposed to new vocabulary and learn lexis that are relevant for each attribute" (Iron 1999, 3) .

Q : What can you describe about this object?

A: Both of them are cone. One is red and the other is blue.

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Workshop 1

For my first workshop, the learning was focusing on the beginning processes. This topic was interesting and insightful for me.
The beginning processes are vital in learning Mathematics for the young children. These processes serve as a "guide for planning and facilitating learning experiences within early childhood environment " (Iron 1999,27).
There are 6 beginning processes that a child has to master to ensure his/her successful development in Mathematics.

Identifying and describing attributes.

Matching

Sorting

Comparing

Ordering

Patterning

Introduction

According to Kirbes-Zaleta & Bradshaw (2003, p. 379), "young children learn by playing, and they first learn mathematics through exploration that develops naturally from their curiosity and experiences. They count, build, draw, model, and measure the world around them."

Based on the above  statement, this blog is created and introduce the knowledge of  a diversity of Mathematics related games and activities for young children whilst also acquiring appropriate on my learning in EAB 023 class over this semester. The contents are parts of my documentation within the course I take for this year. They are mean to be shared with other for education purposes in helping for a better and successful learning experiences for children in Mathematics.The entries in this blog will be provided with evidences of my engagement in the content of this unit over the semester.