Montessori Math Method

In this video, it is shown how children should be able to count with the presence of material used. Children can see and learn better if the things they learn are tangible. This is parallel with what Piaget has said that children learn best according to their stages. In the pre-operational stage, they need to deal with concrete objects to learn. Thus, it is worth for teachers to consider instigating such materials as number representation in classroom. There are many items that can become representations such as seashells, counters, marbles, etc.





Next, in this video we are introduced with checkered board, a board that helps children to do multiplications of big numbers. Even me myself are impressed of how the material is used to multiply 6425 x 3 in very simple way. Indeed, it takes time but it is effective in the way it can help the children learn Mathematics. However, it is obvious that the students need to master number sense awareness to be able to use this checkered board.






This video tells us how to use objects around us to get our children learn Mathematics. This suits for parents who want to teach pre-number among their children. In fact, teachers can ask their students to bring materials from home in learning Mathematics.


It is interesting to view these videos of Montessori Mathematics Method. Teacher should consider this method to be part of their resources in teaching and learning. After all, teaching Mathematics require teachers to enrich themselves not only with knowledge and skills but also brilliant ideas and suitable materials.

Mathematics in Malaysia: A Reflection.

I started learning Mathematics when I was in Year One, 7 years old. And last time I learned Mathematics was last three ago when I was in Form Five in Upper Secondary School. Mathematics was my obsession throughout my schooling. I always aimed for a good grade in every test or exam or quiz. 

This semester when I am enrolled in Exploration in Mathematics for Early Childhood, I started realizing how different the ‘environment’ of Mathematics classroom in Malaysia and in Australia. I do not have much experiences and exposure to Mathematics classroom in Australia but based on five week interaction in the tutorial I can draw some differences that I found between Malaysia and Australia.

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When I was in the school, I can remember that my teacher never employ games in the classroom. The only time my friends and I played ‘academic’ games such as Monoply and Snake & Ladder was in the library. 

However here, I am exposed to many kinds of mathematical games that are very engaging, interactive and attracting, at the same time very educational. For example, we played games on ‘division’ in which we have to do a division problem to play the games. 


I believe this is an effective way of teaching mathematics in a way it seems to be relaxed and engaging but at the same time give knowledge on mathematical concepts to the students.


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It impressed me when I saw local students in my class are able to tell the strategies they are using in coding mathematical problems. Indeed, anyone would give the correct answer but not all can give the strategy they use to attain the answer. 
Personally, at the beginning it is difficult for me to share how I come to an answer for any mathematical problems. 


This suggests that Australian schools are teaching their students the strategies to settle mathematical problems but in Malaysia we are taught using spoon-feeding. 


For example, from primary school, we are expected to memorize multiplication chart from chart 1 until chart 12. Every morning before coming to the class we have to say the multiplication charts beside the classroom.

I always believe that mathematics should be fun. Learning mathematics should be expanding students’ thinking and knowledge. In spite of the fact that mathematical skill is an important literacy in the real world, that mirrors it as a very serious subject; we should give children an opportunity to learn the subject in more interactive and relaxed way. 


All in all, the opportunity to see and experience mathematic classroom in Australia is very meaningful in the way this can be an initiator for us, future teachers, to bring good idea to be implemented in Malaysia soon. 

Using Songs in Mathematics

Who don't love song? Everyone loves to sing songs. Thus, the idea of using songs in teaching Mathematics should be taken into serious consideration.


This is an example of a song on introducing numbers for beginner students.

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With the advent of internet and computer, resource like songs become available for teachers to use in classroom. Websites such as YouTube and http://www.songsforteaching.com/mathsongs.htm offer variety of songs that can support teachers to achieve the objectives of the lesson.


Why Do We use Songs? 


Simple, students come to school with the knowledge of songs like 'Mary Had A Little lamb' or ' Twinkle Twinkle Little Star'. Imagine if the students come to school with the acquisition of Mathematics concept by all their heart through songs. Can you see the effects songs can bring to students' life?


In fact, musics and songs get students to partcipate, adding another levels of engagement among students. Obviously, they need to memorize the lyric for them to be able to sing and 'enjoy' the tune. It is fine for them to sing if the teacher ask any questions that need them to recall the yric of the song. For example, if they have memorize a song on number one to ten. Then it is okay for them to sing the song to recall their memory.


However, it is important for teachers to note that the objectives of the lesson are still regarded as the main agenda, using songs as a tool to help the students acquire mathematical concepts. 

100 Charts.. 99 Charts..

100 charts or 99 charts are frequenly used in Mathematic class as a tool for students to count. It can be a good help in counting addition and subtraction problems. There are several basic 'rule' that the students need to acquire to use the chart effectiely.


1)  Horizontal movement represents moving away 10 steps from the first stop. 10 steps backwards if moving up e.g. 23 to 13 and 10 steps forwards if moving down e.g. 56 to 66. 


2)  Vertical movement represents moving 1 step from the first stop. 1 step backwards if moving to the left e.g. 45 to 44 and 1 step forwards if moving to the right e.g. 96 to 97.

Hundred Chart

99 Chart

Mental Computation

When I was in Year 1, 2 and 3, the thing i like the most during Mathematics subject  is when my teacher ask mathematical questions and we have to write down the answer in our book. That might probably due to the fact that the competitive mood created when we were all excited to write the correct answer quickly. This is my little experience engaging in mental computation.

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What is Mental Computation?


When people hear the term "mental computation" many think of the mental arithmetic problems they did at school which focuses on producing correct answers quickly.  In fact, when I was first time introduced to this term, I think of what my teacher did in my early school (which I have described in the first paragraph). While not neglecting the correctness of the answer, mental computation emphasises the mental processes used to achieve the answer.


Studies have found that some students are able to choose from a variety of strategies based on their number sense while others are using mental images of pencil-paper algorithms. 


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Tips For Teachers:


1)  To develop mental computation in the classroom, teachers can encourage students to explain how they arrived at their answers and to compare their strategies with those of other students.


2)  Teach mental computation; don't just test it. Teacher need to emphasize on the way how answers are obtained and don't just put all the focus on the speed of getting the correct answer.


3)  Some strategies can be learned through discussion, sharing, etc. Therefore, teacher should provide opportunity and space for the students acquire other strategies for their peers.

Strategies in Counting

Subitizing 

Recognizing how many in a small group based on their appearance and with no need to count them at all.

For example, when children look at this box, they can recognize that there are 14 boxes with penguins out of 20.

Counting All 

After counting say 3 objects and then counting 2 more when asked how many altogether the whole set is counted from the beginning again. For example, if children are firstly given 3 counters, they will count 1, 2, 3. And then if we give another 3 counters and ask them how many counters they have, they will start counting from 1, 2, 3 until 6.

Counting On 

when the number in one group is known the total of the number in two groups is found by counting on from the first number. For example, if children are firstly given 3 counters, they will count 1, 2, 3. And then if we give another 3 counters, they will just continue to count 4, 5, 6.

Doubles 

children love to learn their doubles to ten and beyond and some will learn them faster than they learn the count on 2s and 3s. For example, they are comfortable to count 4 + 4, 6 + 6 rather 3 + 6 or 7 + 2.

Turnarounds 

When presented with say 2+5 the children will automatically count on 2 from the larger number rather than count on 5 from the smaller number i.e. 5+2 = 5, 6, 7 instead of 5+2 = 2, 3, 4, 5, 6, 7

Near Doubles 

when the children are confidently using doubles they can be introduced to near doubles which are double plus or minus 1. So for 4 + 5 a child can work it out as double 4 plus 1 or by doing double 5 take away 1

Bridge to 10 

Where a number is broken into two parts that enable 10 to be used as a bridge. For example, 7 + 6 = 7 + 3 + 3 = 10 + 3 = 13

Extended Number Facts 

applying any of the above strategies to larger numbers, for instance using knowledge of 3+4 work out 30 + 40 or 13 + 4


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Tips For Teachers:


1)  Students should be exposed to diversified strategies in counting as to provide them opportunity to choose their own strategy that they are comfortable with.


2)  Learning Mathematics is not only about getting the answer correct but teachers should be aware of how the students attained the correct answer. 


3)  The use of teaching aids and materials to help students in their counting is meaningful. 

Pre-number Mathematics

Many children can parrot the words 'one', 'two', 'three', 'four', 'five' etc. However, rarely do they understand that the number refers to an item or a set of items. At this stage, children do not have 'number conservation'. Normally children enjoy making comparison using words such as 'more than', 'bigger than' or 'higher than'. In addition, we often observe their misconception. 

 For example, they always think that they have 'more water' if their glass is higher than others.

How Do We Clarify Their Misconception?

Get the children involved with activities that promote matching, sorting, ordering and patterning using objects around them.

Matching get them to match one object to another object of the same numbers. For example, match their pencil with counters. If they have five pencils, they will need five counters. This activity will get them to use counting skills (even though they have not acquired the skills).

Sorting get them to classify many objects into several group of the same attributes. The meaning of 'sort' is 'to put into groups'. The groups can be varied. For example, attributes of color, attribute of shape, attributes of size, etc. Teacher can use the students themselves, for instance. Ask the students to sort themselves into groups of height, month of birth, size or gender. 

Ordering involves arranging objects from first to last according to certain attributes the same as the attributes in sorting activities. For example, ordering students' book from big to small, ordering the students from tall to short, etc. Obviously, teachers can bring any objects into classroom for the students to order such as counters, marbles, stones, etc.

Patterning to arrange objects in some forms of regularity. Again, attributes of the objects are used to patterning. The pattern can be represented by alphabet like rhymes such as ABCABCABCABC, DYDYDYDYDY, FEEDFEEDFEEDFEED, etc.

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Tips For Teachers:


1)  It is important for teachers to clarify children's misconception about numbers, values and measurement before it becomes their beliefs.


2)  It is interesting to use things or objects around them, or even the students themselves, in conducting matching, sorting, ordering and patterning activities. However, teacher should be aware of sensitive issue such as weight and height.


3)  The teachers should first recognize what the chidren perceive about numbers, values and measurement. This is important as to know to which extent the children are misunderstood.  

Number Line

I am sure that most of us have encountered number line during our primary or secondary school in Mathematics class. Basically, number line is useful for children to do an addiction or subtraction problem. 


Addition Problem

This picture explains us how to do 5 = 4 using number line. First, start counting five from zero (0) and you will reach at number 5. Then jump four number afterward and you will reach at number 9. 


Subtraction Problem

This picture meanwhile explain us how to do 6-2 using number line. First, start at number 6 and move backwards 4 until you reach number 2. The gap between 6 and 2 is the answer which is 4.

Getting Children to Use a Number Line

Use ruler as a tool to represent number line. This is effective for less than ten problem.

Or else, use bigger number ruler like this one. Or else, just use pencil and paper! Draw a line horizontally, and start your number.

This is a video from Youtube about number line use in addition problem.

Strategies on Doing Multiplication Problem

Today, I would like to share some strategies on doing multiplication problem dealing with number 9 and 5, which I find it very easy and useful for children.

Use Finger for Nine

Number your ten fingers from 1 to 10.

To start multiplying, on your fingers (starting with your thumb) count the number you are multiplying by and hold down that finger. 

The number of fingers before the finger held down is the first digit of the answer and the number of finger after the finger held down is the second digit of the answer.

For example, 

If you want to multiply 9 and 4, hold down your forth finger. The number of finger before the forth finger is 3 and after that is 6. Therefore, the answer is 36. 

NOW...

Can you do 8 x 9 using your finger?

...

...

...

Can you get 72? 

Well done!

Use Clock for Five

Generally, this strategy implies the concept of minutes in clock that every number carries five minutes. For example, if the long indicator is at number 5, it means 25 minutes. Therefore, children can use a clock to do five multiplication.

Big Number Subtraction

When I was in primary school, this is the way that my teacher taught me. And I believe that till today, many teachers still teach their students to do a subtraction using this strategy. 

Indeed, we are here dealing with big number which means prior to this stage, children are introduced to an array of subtraction strategies with small numbers.