Many articles and research reports have been published on the importance of mental math for children. Many educators also advocate not let children use calculator until after grade 7. Many theories and methods teach children do fast calculation and call those calculation tips mental math. So just how much mental math do children need to acquire so they will not be at disadvantage? I have been closely watching my private students on how they do calculations and at what points they seem to be at disadvantage since the lack of their mental math ability has hampered their math ability and their marks.
My observations have been an educational experience for me since most of these so called mental math seem to have directed children into wrong ways of doing math.
I have discovered that many times children seem to run into problems is because they can not see patterns, so the math IQ training is not really just to discover quick calculation tips (and memorizing these rules.) rather it is more helpful to them to train how to be sensitive to number patterns. For example some math weak students can not see how to do (125) to the power of 2/3 when doing this problem by hand. The calculator will not give them the answer of 5 to the power 3 is 125, so the student needs to know the power 3 of 5 is 125. Clearly the training here is to train the reverse thinking that is to train students to know that 125 has factor of 5 and then 25 has another of factor of 5.
Reversing calculations training seems to be far more important than the training of knowing some speedy math tips of multiplying 23 times 19 since student can get the product by using a calculator. For example, the square root of 48, some students can not do or see 48 is a product of 3 times 16 so the answer is 4 root 3. Again here the student needs to know quickly if 48 has a perfect number factor and then use it.
It is also strange that high school students can not see 3 times (-2/3), the answer is 2. The normal way for them to understand is to multiply 2 integers or 2 proper fractions multiplied together but when a integer multiplied by a fraction then they get confused. Again, this has nothing to do with any mental speedy calculation but just different ways of multiplying rational numbers. The training of having students to be familiar with cross manipulation or vertical manipulation is very important.
Form above observations, we can see that mental math is not limited to scope of being a human calculator of doing some calculations in lighting speed. To acquire the mental math skills so it truly benefit students, the students must learn the skill of reversing calculating like how to get factors of a number, how to quickly find prime factor of a number, how to find if a number has perfect factor, how to not only do calculation in linear fashion, but also know how to do calculations in cross or vertical way quickly and be able to see patterns.
To increase one's math ability, to train mental math alone is not the key but to also train math IQ such that the students know number, symbols or figure pattern, logic relation between numbers, reversing calculations, and different formats of calculations can truly increase a student's thinking skills and math ability.
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A nice article on illustrating on how mental math affects children's math ability by giving examples and how children can increase their mantal math ability.
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