Friday, 29 January 2010

Maths Solution Presentation

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".

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!


Friday, 8 January 2010

Proper Way Of Writing Maths Expression

Maths expression tells certain message. When it is not written properly, or written in such a way that it causes wrong interpretation, then you will expect marks to be deducted.


1)     y = cos (A + B)
2)    g = x + log K
3)    y / x + 2

Let's look at the above examples one by one.

Example 1:
If the brackets are taken out, y = cos A + B.
Does it also mean B + cos A?

Example 2:
If the sequence is swapped, y = log K + x
Does it mean y = log (K + x)?

Example 3:
Is the denominator just x or (x + 2)?
Or is the correct expression 2 + (y /x) ?

From the above 3 maths expressions, you will observe and sense that something will go wrong when you did not write "properly".

This need practice and does need some "maths" sense to go along with the practice.
You need to know the different form of expression and its implications.

Questions like:
- one term or two terms in the desired expression?
- which is the actual denominator?
- will anyone mis-interpret the logging of term?
- If the words or symbols are too small, will they be able to see clearly?

To save time and marks, write with the reader or marker at heart.
Write as though they are reading them.
Think and write like they will be.

Maths is afterall, a language that has to be shared and used to solve certain objectives.
Do write clearly and appropriately.

The practice and skill mastered will do you and everyone one good.
Strive to make less unnecessary mistakes and reduce the chance of your marks being subtracted off through improper writing.

Cheers!   ^.^