References

References 


Clements, D., & Sarama, J. (2000).  The earliest geometry. 
  Teaching Children Mathematics,  7(October), 82-86.


Hannibal, M.A. (1999). Young children’s developing understanding of geometric shapes. Teaching
   Children Mathematics, 5(3), 353-357.


Warren, E., and Cooper, T. (2006). Using repeating pattern to explore functional thinking. Australia
   Primary Mathematics Classroom, 11 (1), 9-14.

Picture references

Bee-Bot. Focus Educational Software Ltd [image]. Retrieved October 22, 2011, from http://www.focuseducational.com/category/item/6

Bee-Bot. (2011). Bee-Bots at CPS [image]. Retrieved October 22, 2011, from http://beebotsatcps.wordpress.com/

Bee-Bot activity. (2011). Youtube [video]. Retreived October 22, 2011, from http://www.youtube.com/watch?v=p4EPfC04URk

Measurement: Making a measuring device ( volume)

·         Making a measuring device - using an empty box to make a measuring device.
     
      Using utensils such as cups and spoons, one will help to introduce volume. In order to fill the empty container, children can use corn seeds or marbles. 
    
   An example can be seen below of a simple way in which volume can be put into play in classroom.

Picture 1: A plastic spoon and empty box

   Picture 2:
This picture shows how much volume is taken up when one plastic spoon worth of corn is added.

     

   Later, teachers can ask questions to further the students' understanding of this topic. 

     

   Q:  What is the non-standard measurement used? 

A:     Plastic spoon.  

   Q: How many plastic spoon does the container hold?  

   A:  4. 

     Q: What is the volume of the container? 

     A: The volume of the container is 4 plastic spoons. 

   Then, teachers can set task for children by asking them to use their measuring device (Picture 2) to find out other volume of different container. Teachers could ask this possible questions to help children with their finding. For example:

   T: How many container is needed to fill up the pyramid container?   

   S: 2.

   T: Then, how many plastic spoon is needed to fill the same pyramid container?

   S: 8.

   The below picture shows a poor example of how to teach volume within a classroom. 

                                                   

   Each of the marks have to be numbered so children can see how much of the corn is added with each separate  spoon. 

   

   Another mistake that must be avoid is to write the total or overall result of corn seeds. The reason being that children cannot see how much of the corn was added with each separate spoon.

Here, children can only see the overall result  written on it.

Measurement : Non-standard units

     Using non-standard units before using standard units will help children form a better understanding of the topic and will often help them in comparing and comprehending. Children must understand few rules when come into measurement. 
   
   The rules are no gaps, no overlaps, consistency, and understanding units must be as close as possible in size.

   Children can use all sort of material to measure any length that they want. Teacher can ask them to use their part of body such as arm, fingers and foot to measure other objects. Apart from that, they also can try to use paper clips, ice-cream sticks, and paper rolls.

Picture 1: Paper clips and paper roll.

Picture 2: Ice-cream stick.

   Picture 1 and 2 show two different materials that children can use as non-standard unit measurement.

    One particular activity that children can work on in the class is by measuring body parts (see pictures below). As this is using non-standard units of measurement it is easier for the children to comprehend.

Picture 3: Blue - Neck, Green - Arm and Red - Leg.

   After they have finished with measuring their own body parts, they can compare them with other friends and sorting them into categories.

Picture 4

   Teachers can ask questions to help extend on the idea of  length such as:

   T: Who fore arm is the longest?

   T: Can you order the size of the pinky from the shortest to longest?

    Later, children can use their non-standard unit measurement to measure the length of objects and people in the class. 

Picture 3: Measuring the length of book with paper clips.

      The above picture (Picture 3) shows how children can demonstrate of their understanding in measuring with non-standard unit. Then, they can do the indirect comparison by using the measuring tape (standard unit).

   Teachers can help to strengthen their understanding by prompting questions. For example:

        T: How much paper clips is needed to measure the  

            length of this book?

        S: 9 paper clips.

Picture 4: Measuring the length of table with paper clips.

    

Geometry: Location and direction

·   
   Teachers can teach direction to children by using the Bee-Bot.

     The Bee-Bot is a small bug looking electronic device which has four differing directional buttons; forward, back, left and right. The buttons allow the user to control the direction that the Bee-Bot moves and also the distance it moves in each direction. 

   

   The major focus of this activity is drawing on the geometrical aspects of direction. Therefore, it is essential for children to understand and know how to use the specific words.  

      The Bee-Bot activity.  

    First, children have to build their own city. Below is an example of a city that can be make in the classroom.

Picture of city that children can build.

    The Bee-Bot has the ability to do a full 360 degree movement, but it can only do it in motions of 90 degrees. Therefore, the shape of the city must cater the aspect of the Bee-Bot movement. 

    Upon completing the city, the required movements have to be recorded in order to program the Bee-Bot to accurately move through the city. The recorded movements are as follows: 

    

•     Forward x 2
•     Right x 1
•     Forward x 1
•     Right x 1
•     Forward x 1
•     Backward x 1
•     Right x 1
•     Forward x 1
•     Left x 1
•     Forward x 2

       

   These movements are programmed into the Bee-Bot and the final product of the activity can be viewed in the video below.

Bee-Bot activity.

Geometry : Shape

·       Clements & Sarama (2000) claim that young children have developed their understanding about shapes 
   before they enter school. These children may acquire this knowledge from their home environment such as the shape of the door or windows.  

      In the classroom setting, there are many activities that can be done to help children to understand the concept of shape. 
       
      Hannibal (1999) suggested activities such as 
     - Looking at puzzles, books and so on and discussing 
      attributes of the shapes (do rectangle vary in size, right 
      angles, obtuse, isosceles triangles etc)
    - Include the concept and study of shape in not only maths
      but other areas of the curriculum too
    - Feely bag activities
    - Finding shapes from different angles
    - Working with tessellations
    - Cooking activities involving shape
    - Shape bingo, and the list goes on...
    
    All these activities can help children to recognize and   distinguish shape. Teachers have to scaffold children by asking them to visualize it. Allow time for children to explore shapes kinaesthetically and describe the shapes.
   
   Activity 1 : Describe the attribute of a shape.  

    Let's the children explore their surrounding and ask them to describe the shape that their have found. Besides, teachers also could provide them with wooden blocks that have different shapes (Picture 2). Then, we could ask them if any of the blocks have similarities to one and another; cube and cuboid or pyramid and cone. 

Picture 1: Discussing the attributes of the shape by using objects in class.

.

Picture 2: Wooden block.

    Apart from that, teachers also can show a picture of the shape and asks children to tell the attribute of the shape. For example;

Q  Can you name this shape and some of the features

    that it has?
A  It is a triangle. It has 3 sides, 3 points, 3 angles, all
    the sides are straight and all the lines are connected.

      

    Activity 2 : Looking shape at different angles. 

Picture 2 and 3 are examples of finding shapes from different angle.

Picture 3

T: If we look at this picture from this angle what shape do we
    see?
S: A circle.

Picture 4

          T: Now, if we look at this picture from this angle what shape
       do we see?
   S: A cylinder.


   
   Activity 3: Ordering/grouping the shape based on their 
                  attribute.


   Another activities that can be done in a class is by asking the children to order the shapes based on their attribute. First, teachers have to provide them with a paper that have pictures with different shapes (Picture 5). Then, children have to cut out the shapes and begin to order them based on their interest. For example Picture 6 and 7. As for teachers, we should ask questions to them to check on their understanding in this area such as 'How do you order your shape?' or 'Can you explain the attribute each of the group?'

Picture 5

Picture 6: 

Ordering the shapes based on different side: acute, isosceles, and obtuse triangle.

Picture 7:
Ordering the shapes based on different angles.

Activity 4: Geoboard.

   Another activities that children can do is by asking them to create a shape by listening to the specific instruction from the teacher.

Picture 8

Picture 8 at the above shows an activity where children have to create shapes by using a rubber band on a geoboard. They have to listen carefully for the teacher instruction or description of the specific shape. Here is an example description that a teacher can use in this activity.


T:  I want you to make a shape that has 3 sides, 3 points, 3 angles, all the sides are straight and
     all the lines are connected. 


Furthermore, the geoboard also a good tool for students to explore the concept of perimeter and area.


Click this link: Geoboard, for fun and interactive activity by using virtual geoboard to explore geometric concepts of area and perimeter. 

Algebra: Function

Function is where children are aspect to recognize and identify how "thing" is change in relation to each other.


Here, children have to know which is the input and output of the function.

Circle is the input, triangle is the output.

Q: What will the circle change into?

Also, function is focusing on children to describe the change and rule that show how the thing is change.

Figure 1: Concept of function

     

For example:

T: Look at the Function Machine and tell me how does it operate based on the input and output of the machine.

S: The function machine that should go in the space is (X 4).

Besides from the example above, teacher can test children by asking them to find the input and output of the Function Machine.

Below is an example of question that can be used to find the output of Function Machine.

T: Look at the Function Machine and tell me how does it operate based on the input and output of the machine.

S: The output for 26 is 130 as the relation is (input x 5) 

Click here for more fun activities about function: Function game and Function machine

Algebra: Repeating pattern

Repeating patterns are "patterns where a group of elements repeat themselves as the pattern extends" (Warren and Cooper, 2006). It can lead to the early development of functional thinking, that is, relationships between two data sets.

Figure 1: Repeating pattern; ABCABC

By using this sample repeating pattern, children are able to expand their learning experience in understanding the concept of pattern. Below are the steps that can be done in class to extend the concept of pattern.

Copying the pattern
First, the teacher can ask children to copy the pattern (Figure 1). This will help them to be familiarized with the pattern.
  

Continuing the pattern
Then, the children should able to continue the next pattern. Here, the teacher has to ensure that they realise repeating pattern can continue in both direction. Teacher could prompt questions to integer children understanding. For example; "What shape comes after yellow circle? What shape comes before triangle?

Identifying the pattern
Here, teacher encourages children to say the pattern out loud (green triangle, red rectangular, yellow circle, green triangle, red rectangular, yellow circle). Children have to identify the part of the pattern that repeated (core).

Complete pattern
Teacher encourages students to complete the pattern. 


Creating own pattern
Once children understand the concept of repeating pattern, teacher should encourage them to create their own repeating pattern. Teacher can ask questions for checking their understanding. For example; "Why this is a repeating pattern?" "Which part is repeated?"



Translating the patterns
In this stage, teacher is testing children understanding of pattern by asking them to replace the pattern (Picture 2) with other form of pattern.


Teacher: What can you replace these shapes with?
Students: Jump! Clap!Stomp!

Picture 2: Clap, Stomp, Jump, Clap, Stomp, Jump.

References

Biggs, E. S. (1983). Teaching Mathematics 5 to 9. England: Mcgraw - Hill Book Company (UK) Limited.

Bobis, J., Mulligan, J., & and Lowrie, T. (2008). Chapter 9: Promoting Number Sense: Beyond   

     Computation. In J. Bobis, J. Mulligan, & T. and Lowrie, Mathematics for children (pp. 215 - 242).  

     NSW: Pearson Education Australia. Retrieved from Queensland University of Technology Course 

     Materials  

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 

Irons, R. (1999). Numeracy in Early Childhood. Educating Young Children: Learning and Teaching in 

   Early Childhood , 5 (3), 26-32. Retrieved from Queensland University of Technology Course 

   Materials 

Kirbes-Zaleta, C. & Bradshaw, D. (2003). Play is children’s work: Principles and standards for 

    school mathematics. Teaching Children Mathematics, 9(7), 397-399.

Thompson, I. (2010). The principal counting principles. Retrieved August 20, 2011, from 
    https://www.ncetm.org.uk/public/files/712850/The+principal+counting+principles.pd


References for pictures

Quest 3D.  Cone shape [Image]. Retrieved August 18, 2011, from 

     http://support.quest3d.com/index.php?title=Newton_Collision_Primitive

Bowers, A. (2011).How to Teach Mathematics to Homeschooled Children.

    Boy and abacus   Image]. Retrieved August 18, 2011, from                                                                                                             http://education.more4kids.info/57/how-to-teach-mathematics-to-homeschooled-children/ 

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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