Friday, 29 January 2010

Maths Solution Presentation

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To get good marks for a maths test requires understanding of how teacher marks the paper.

"Why do I not get full marks when I have the correct numerical answers?".
This is a common question at the back of any maths students when they see marks deducted "illogically".

Explanation:
When maths teacher give a maths question, she will like to know how is the answer obtained.
She wants to know whether the "thinking" part of solving the problem existed.

With the objectives in mind, the marking schemes are sometimes created to have marks for every steps involved in getting the answer.
Thus getting the answer without the required steps, even though it is mental, is a no-no.

Let me give an example.

Solve (x + 1)(x - 4) = 0

Solution A:
x = -1
x = 4

Solution B:
x + 1 = 0   ===>  x = 1
x  - 4 = 0  ===>  x = 4

Comparing the two solutions presented above, you will notice clearly that Solution B is a better presented solution with proper steps reflecting the "thinking" process of the students.

Though the student of Solution A has the answer correct, he did not reveal the steps and demonstrate his understanding.

With that lack of presentation, he lost precious marks.

However, do note that not every time, we need to write down every steps.
It depends on which educational level you are in.

For the above example of presentation, the level is that of elementary, where foundational understanding is a necessity.

Upon graduating to high school, less detailed steps are needed. This is because it is assumed that the students had obtained a certain level of mathematical computing skill to that level of studies.

As such, reflection of the internal thinking to show minor details can be ignored and "by-passed" to shorten solution time.
However, the marks will still be given for steps needed at high-school level.

This goes for university level too.
By then the marking scheme will access advance thinking steps rather the minor calculations.
When errors do occurs in the calculations, it will normally be taken as "human" error as opposed to conceptual error.

In summary, do know the necessary solution steps to present during test or important assignment.  Do understand the requirement and objectives of the test.
Do know what is being tested.

Writing too little can be detrimental at a lower educational level.
And writing too much can be disastrous at higher level, since you will be left with little time to complete the paper.

Hence doing maths is not simply completing the paper and getting correct answers.
It is a total strategic plan involving a lot of soft skills besides the computational abilities.

Cheers to maths, and
Cheers to it being interesting!

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1 comment:

Education Tay said...

Deciding to write all the steps or not in the presentation of the work depends where you require to hand in the mathematics. Clearly at school, as a previous teacher of mathematics, full workings should be written down and marks are awarded for workings out.

Competitions or your own research you can practice ways of shortening the method of the calculation.