Do you agree with the necessity of the sequencing E - L - P - S for learning? If not, then what do you suggest as an alternative path for understanding and internalising mathematical concepts?

Previously you read that primary school children are at the concrete operational stage of development. To help your learner proceed to the next stage, you would need to emphasise the links between the concrete and the formal.

You may feel that once a child has understood a particular abstract concept or process, henceforth she does not need concrete learning experiences to grasp other concepts or processes. But this is not true. Even after becoming capable of doing mental and formal arithmetic successfully, children may need to check their understanding of concepts, operations, problems, etc., by using actual objects. This spiral nature of their development is characteristic of mathematics learning.

For example, children need to understand 'place value', first when double digit numbers are introduced. For this, they would need a lot of concrete experiences of grouping, and so on (see Unit 6). This would help them to slowly progress towards an understanding of 'tens' and 'ones'. After this they would be ready to learn how to formally multiply and divide small numbers. And then, they would again need to be exposed to a variety of concrete learning situations for developing an understanding of 'place value' in the context of larger numbers.

This way of dealing with the concept in the context of smaller numbers first, and then with larger numbers, also gives children a chance of developing a better understanding of the concept. For example, consider a child who is grappling with a new concept like commutatively of addition. To start with she only needs to see how the property works in the context of small numbers, which she is already familiar with. At this stage she can do without the extra burden of handling large numbers, which she is not comfortable with.