Dr.Yeap explained that Mathematics could be in two folds as stated by Richard Skemp, a Mathematician.
1) Instrumental understanding: rote or ‘learn the rule/method/algorithm’ kind of learning (which gives quicker results for the teacher in the short term), e.g. writing 10 would be understood as “This is how we write 10” in instrumental terms.
2) Relational understanding: a more meaningful learning in which the child is able to understand the links and relationships which give mathematics its structure (which is more beneficial in the long term and aids motivation), e.g. writing 10 would be understood as “This is why we write 10 like this (in terms of place value)” in relational terms.
Nowadays children are exposed to relational understandings to get children to be aware of the semantics that answer may be the same but the meaning is different. For example: 3×2=6 and 2×3=6. But 3×2 means 3 baskets of apples and 2×3 means 2 baskets of apples. On the other hand, an example of Multiplication comparison in a problem sum would be : I have 3 cookies. My friend has twice as much. How many cookies does my friend have?
I agree to Dr. Yeap’s saying that it is important for teachers to go through with children the journey to get to the destination and not merely teaching them through rote or rule learning.