Accelerated maths/rapid mental maths vs logical thinking ability

[dna]

If I let my child learn accelerated math / rapid mental math such as jones geniuses or using abacus, no doubt it will help to stimulate right brain and solve maths problems in a very fast way.

1. In the school system, students have to show the workings and calculation in solving the maths problem (i'm not sure how the schools system in other countries work, but for my school the marks are allocated to my workings shown in the exam paper). This is especially for primary/secondary schools. E.g. if question is 234526+737383, the student can straight away give answer using rapid mental math and write the answer without showing the calculation in vertical format, there will be zero mark (the teacher might think that the student cheated in class).

2. My maths teacher in high school told me before, we must work out step by step calculation/working (e.g. In algebra) towards our answers because maths is a logical subject (it's called deduction?). And if we are able to do maths in such way it will train us to think logically.

My question is: if I teach my children using rapid mental maths, will this cause him/her to lose the ability to show step by step workings in math problems? Or ability to think logically?

Any opinion or advise on this? 

[rd]

I have also been thinking about this.  When I was in school, we got marks for showing the working out, but didn't get full marks if the actual answer was incorrect.  At that time, the graphics calculator (used for graphing on xy plane) was also being introduced and we were allowed to have them for the exams.  Some students just typed the equations into the calculator, and copied the answer straight onto the exam paper, without really knowing how the answer was derived. 

For maths, there is usually not one way of getting to the answer.  For mental maths, I presume there also would be a formula that needs to be followed in order to get to the answer, so maybe this method would be written as the working out.  I don't know if this is correct as I am not familiar with mental maths techniques but I saw an ad for Brainetics where they were teaching multiplication of 3 digit numbers by 3 digits and there was a formula to get the answer in one line.  I would also like to know what others think.

[waterdreamer]

My husband and I were just talking about this. He can do math in his head and he remembers failing a test even though he had all the answers right, just because he did it in his head and failed to "show his work". I remember in Highschool, if I didn't know how to do a question on a test, I would just doddle some numbers like I was working it out just to get a few marks. I'm not sure what the answer is to this, I would rather see my son understand the work and do it in his head, however the school system has different ideas..

[susankhan]

What they do at my childrens school is both ways.  It is true that in the U.S  public schools they must show their work.   At my childrens school the teacher does not care how they get the correct answer as long as they are not cheating and he does teach rapid math, math tricks , vedic math etc... but to help in case the kids go to public schools he teaches them the method of showing work.  Funny though the kids at this school are in the top 1 percent in the world for math and it is such a small school.

Susan Khan

[dna]

Thanks everyone for sharing.

Susankhan, glad to hear that. can you share more about how to teach both? Which one should introduce first? Teach working first then teach rapid math? Or the other way round? Thank you.

[2010BEBES]

...He can do math in his head and he remembers failing a test even though he had all the answers right, just because he did it in his head and failed to "show his work". I remember in Highschool, if I didn't know how to do a question on a test, I would just doddle some numbers like I was working it out just to get a few marks. I'm not sure what the answer is to this, I would rather see my son understand the work and do it in his head, however the school system has different ideas..

I saw the same problem with my daughter that did a lot of work in her head and dislike the fact that she had to write down wherre the answeer came from.
But at the same time i can see the teachers point and imagine it is to avoid copying just the answer.
Nevertheless it is an excellent practice to try working out problems or math operations in your head.

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