Mental computation strategy

Computation is related to any type of information processing (Bobis, Mulligan & Lowrie, 2008). In mathematics, computation can be separated into two- computation using tools and mental computation (Origo, 2008). These two type of computations are co-related and need to be developed from the early childhood. Hence, in this entry we will look at how we can implement these computations in teaching early children.

In the previous entry, a good teaching model implement the computation of using tools  through concrete objects. Therefore, representation of concrete object develop an authentic learning experience as children can visualise the problems in their minds. 

In Mathematics, teacher can use tens frame, hundred chart, number line, ice cream sticks or any other things that related with counting in enabling the students to 'picture' the problems. 

Tens Frames

Tens frames use 10 as and indicator in counting. As a first step, teacher can use simple problem of addition and subtraction  under 10. For example, teacher 

can show the quantity of 8 on the tens frames.

In this tens frame, children can see that 8 is less two then 10, or 10 less 2 is 8. From here, teacher can develop knowledge of addition or subtraction using two tens frame. For example, teacher can ask the students how to present 8+7 in the tens frame.

Diagram 1

Diagram 2

In the example above, we can see that in the diagram1 students ordered both of the tens frames according to the question 8+7. However, at the diagram 2, students realised that in order to complete the first tens frames, their need to move two more buttons from the other frame. This is because young children most of the students have an understanding of number 10. Therefore, students' mental computations are developing as they realised that 7 buttons need to be decreased to 5 in order to make the first tens frames up to 10. Simplify, the will get 15 as the answer because the have an indicator that a complete tens frame is 10, plus the other 5 buttons in the next tens frames is equal to 15. This knowledge is called bridge-to ten.

The same knowledge is applied in the hundred chart and number line. The example is shown below.

Hundred chart

Equation: 48-23

steps: 

1) children round up 48 to 50 

2) children jump two rows backward  in the multiplication of ten

(50-20)
3) children take away another 3 

(because it minus 23)

4) children take away another 2 

(because they round up to 48 to 50)

Number Line

As the computation using tools are co-related with the mental computation, teacher can ask question in order the develop students' reasoning and problem solving skills. For example teacher can ask:

 - How do you solve this problem?

 - Did anyone else did the same thing or different ways?

  - How is that different?

 - How is that the same?