Saturday, 25 July 2009

Meaning of "Average"

I managed to see a word problem shown below:

" Mary obtained an average of 80 marks for 2 tests. What marks has she to get for an average of 80 marks for 3 tests?"

If a maths student understand the meaning of "average", she can do this without even working out the mathematical steps.

The first statement in the question stated that Mary scored on both tests an average of 80 marks. This implied that for one test, she obtained 80 marks. Same as for the second test.

For the next test (the third one), to get an average of again 80 marks, it meant that all the test she has to get 80 marks each. This is the power of "average". That is to say, all the test can be concluded as the same score.

The actual differences between the individual marks can be offset from each other to achieve a final "average" of same marks (here, 80 marks).

The maths problem is to test the understanding of the word "average" in maths, and its concept.

Thus, knowing concepts do help in solving maths questions.
It does not mean working out the mechanical computation steps to get answers.

With strong maths concept, anyone can solve simple problems without doing working.
But that is maths also (in the brain, the step-less way).

Interesting. Maths is so. Fear not.


Saturday, 18 July 2009

Maths Is Just Another Language

"I don't understand maths!"

Does this sound familiar?

This statement is not only from young learners, but from adults too.

What actually happened?

Maths is interestingly unique. This is so because it represents a different way of presenting messages.

Maths is a "short form" of written langauge.

It is like the short-hand symbols that many people use to note down minutes of meeting.

What is 1 + 3 = 4?
In the common English language, it simply means "one added to three equals four".
Nothing different.
However, visually, the maths equation is encoded with symbols.

What is this "+" and "="?
If you do not understand the meaning and usage of these two symbols, then you are lost.
Thetefore, learning and understanding maths is knowing the unique symbols presenting the "message".

How about 3y = 24. What is "y"?

The question is finding "y" given the relationship above.
The equation in English means "When we multiply "y" by 3, it gives 24".

The solution, thus, it English, is: If I divide this 24 by 3, I will get the answer that is 24/3 = 8.
In maths concept: 3y = 24 ===> y = 24/3 = 8.

It is the interpretation of the maths symbol and its communication with the learners that is key to doing maths.

It is not difficult if you understand the language of maths.

Maths is interesting!


Friday, 10 July 2009

Amazing Trigonometric Art

Maths does wonders when presented in graphical form.

This is provided the mathematical equation makes it so.

Using the trigonometric relation, x sin x = y cos y, the artistic effect of this equation is shown below.

You can now see that, though maths can be boring at times, it can reflect its beauty through other means.

Don't you agree?

Maths is Interesting! Watch out for it!

.. :D

Monday, 6 July 2009

Application of Boolean OR operation

Besides the Boolean AND operation and its application, Boolean OR operation also serves a special application.

For the AND operation, which is equivalent to the maths multiplication, the use is for it to pull any untied input to a system to zero state.

For the OR operation, the concept is similar, except that now it is the maths addition.
Instead of pulling the untied input to the system to zero, you can set it to the other Boolean state, which is the "1".

In base 2 number system (Boolean), if the input is 000101, and you need the data to be all 1, just OR the input with 111111.

What you will get after this OR (adding) operation is 111111.

This is so due to the fact that 1 + 0 = 1.

Here you will see that option to set the untied input to 0 or 1 can be done using either the AND or OR operation of the Boolean system.

This is maths, if you are aware.
This is the application of maths after understanding the principles of maths operation.

Any comment?


Sunday, 5 July 2009

Boolean OR operation | Special Maths Addition

Boolean means 2-state operation.

OR means any one state that is valid will result in a positive outcome.

Example: When James or Mary come, the show will be start.

In maths, this translates to ADD, except only 2 states can occur (that is, on or off only).
1 = on, 0 = off (or vice versa).

What do I mean?

0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 1

From the above addition, you will notice that as long as one state is ON, the result will be ON.
The operation is that of an "add".

Note: Since the operation is Boolean, it cannot go above 1 or 2 and above cannot exist. Only base 2 number (0, 1) can happen.

This field of maths is known as Boolean Algebra, a special maths operation used in digital electronics.

If you are using this Boolean process, make it clear that the number base system is 2, otherwise 1 + 1 = 2!

1 + 1 = 2 in Boolean means that you go over the ceiling!

Another interesting maths concept, right?

Maths is interesting!