3 things I've learnt; 2 questions I still have.

3 things I've learnt:

1. Logic lies in the 'noun'. 
Addition can only take place within items of the same noun, e.g. 1 flower and 4 flowers. One cannot add 1 flower and 2 pots- it does not make sense. Along the same line, when teaching fractions, avoid calling 3/4 'three out of/over four'. Instead, say 'three-fourths'. Why? Calling 3/4 'three-fourths' helps children to see it as a whole unit, and not as to separate units. This is necessary when the child learns to add fractions because then he who can add 1 flower to 4 flowers can add 'three-fourths' to 'one-fourth'. (The noun is significant because it aids logical understanding of the concept.)
The child who can add 1/2 to 2/4 and obtain 3/6 for his answer shows that he obviously does not understand the concept of fractions. One half and two fourths cannot add up because addition is only possible when the nouns of the addends are common!

2. A sound foundation in number bonds is a strategy.
How are number bonds- the very rudiments of Math education- useful knowledge for tackling bigger problems? Take this for instance: 9 x 5. If a child suddenly blanks out at this problem, he can summon his knowledge of number bonds to his aid. Number bonds will help him see that 9 is made up of, say, 4 and 5. And so if he knows the times tables for 4x5 and 5x5, finding out the answers for both and then adding them up can help him obtain the solution for 9x5. Alternatively, he can use 3x5 and 6x5 as well. Helping a child gain a strong foundation in number bonds is equipping him with a strategy that he can use in solving difficult problems in future math exercises.

3. The beginning of 'Measurement'.
The first step to mastering measurement is to teach children to compare lengths, sizes, weight, etc. Comparing comes before measuring. There are two stages in getting children to do comparisons. The first stage is 'direct comparison'- when two objects are placed side by side and are compared that way. After this is established, the teacher and learner can then go on to 'indirect comparison'- when the objects compared are objects that cannot be brought together (e.g. the length of a whale vs the length of a sea lion).

Once indirect comparison is established, children may begin measuring with non-standard units. Then again, there are also 2 stages in this phase. The first phase is to measure with many non-standard units e.g. measuring the length of a shoe with paperclips. Once that is understood, the second phase is then to measure with one non-standard unit e.g. how many toothpicks long is this table?

Some children are unable to reconcile or associate the number of non-standard units with the length of the object measured. They get confused thinking that counting the number of units is a separate activity from measuring the length of the object and are not able to make the connection between the number of units and the length. The way to help them make that association is to ensure that the language that we as teachers use when verbalizing the measurements, is complete. So for instance we can say, "Yes, the length of this table is 12 toothpicks long," or "This table is as long as 12 toothpicks." As we take note to always say the number of the non-standard unit with the length of the object measured, children will learn to associate the number of units with the length over time.

2 Questions I have:


1. If the society is headed so stubbornly in the direction of 'accelerated' learning, won't 'enrichment' learning give my child less of a competitive edge amongst his peers, albeit him understanding each topic taught more thoroughly?

2. Using strategies such as number bonds and breaking problems down into manageable portions help a child to tackle problems more ably. However, it may also result in a slower working process. When is a child expected to be able to use more efficient methods to solve problems?