Maths is one of the crucial and necessary subject we have to learn in school. Everyone has to go through it.
Some like it, while some fear it. Have you wonder why?
Actually this fear is not only towards maths. The underlying reasons applies to anything we do.
It could be literature, Chinese language, dancing, or even driving and riding a bicycle.
What we have to do to reduce maths anxiety is to know why the fear occurs.
One of the issue links to the confidence level. This affects the comfort level. With things we are not comfortable, we tend to avoid. Avoiding make us do less of the subject.
We thus lack practices.
Learning maths involves 2 parts, namely:-
1) Procedural skills, and
2) Conceptual understanding.
Different stages / levels in the learning journey entails different focus of these 2 stages.
To have a better understanding, you may go to this maths site to read more.
It is rather enlightening.
Learning anything needs a plan. (Procedure ==> Conceptual ==> Application)
If fear is the barrier, and causes obtrusion to learning, seek out why.
We grow as a result of this process.
Maths is one target in life that we can use to challenge yourself, besides the tools and techniques picked up to solve mathematical problems.
It involves character development as well, if you border to analyse the learning process.
Finally, to motive any maths learners,
just know that "Maths Is Interesting!".
You will then like maths, and anything you set forth to master.
Cheers! :-D.
Showing posts with label Learning maths. Show all posts
Showing posts with label Learning maths. Show all posts
Friday, 17 February 2012
Monday, 22 November 2010
Basic Decimal Conversion
`
Every thing falls back to basic.
If the fundamentals are weak, any maths learners will have a hard time moving forward in their maths learning journey.
Let me quote an example.
How do we change 4.75 to fraction.
We can use 475 / 100 and reduce it through long division. This will give 4 and 3/4.
However, if we know that 4.75 is actually consisting of 4 add to 0.75, the conversion will be simpler.
4 and 0.75 means 4 + (3/4) which leads directly to 4 whole and 3/4. Same as answer of above.
(NOTE: 0.75 is a quarter which equates to 3/4).
Simple isn't it?
Maths is interesting.
:-)
Every thing falls back to basic.
If the fundamentals are weak, any maths learners will have a hard time moving forward in their maths learning journey.
Let me quote an example.
How do we change 4.75 to fraction.
We can use 475 / 100 and reduce it through long division. This will give 4 and 3/4.
However, if we know that 4.75 is actually consisting of 4 add to 0.75, the conversion will be simpler.
4 and 0.75 means 4 + (3/4) which leads directly to 4 whole and 3/4. Same as answer of above.
(NOTE: 0.75 is a quarter which equates to 3/4).
Simple isn't it?
Maths is interesting.
:-)
Sunday, 3 October 2010
Pointers in Teaching, Learning Speed
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At elementary level in maths education, speed is always a challenging topic for learners.
It caught my attention and I started wondering why?
Many mistakes can be made when dealing with these types of questions.
After studying the various mistakes made by learners, I came to a few conclusion that I like to share here.
How to avoid confusion in doing Speed questions in maths:-
1) Speed involves two parameters, namely, distance and time.
This is the key issue. Dealing with one parameter is already a challenge, and dealng with two is always a "headache".
The concept, has thus to be clearly addressed upon, before the ratio of distance and time leading to speed can be fully understood.
What is distance?
What is time?
These 2 items are variable in nature. They change in value.
They causes confusion when lumped together!
Examples of daily activities will help in this case.
Quote cases like running in a race, where the champion came back in the shortest time covering the same distance as all others.
Get the concept of distance versus time into them.
Also FAST and SLOW relation to speed.
2) Error in units:-
Break up the tasks of calculating km, m or cm and sec, hours, minutes separately.
In other words,deal with one item at a time.
Use basic unit if possible to reduce chances of making costly errors.
The learners have to handle the logical part of the question, and also the mechanical part of unit manipulation in speed problems.
Tell them to find one thing at a time, and the need for doing that. Be patience is the message.
3) Draw out a pictorial image of the question.
This method will help some kids to visualise the real issue.
By having drawn the length for distance to be covered (or covered), they will have a better idea of what distance is about in the maths question. They will not have to "keep" this disatnce in their mind together with the problematic "time" condition.
Use the seeing method helps them clear any doubts and can also reduce mistakes in interpreting the question.
There will definitely be more pointers to be added to my three above.
But with these 3 basic issues settled, most of the queries about speed and its maths problems should be clearer.
If you have any other pointers, you may share in the comment space.
Cheers :-)
Maths is interesting, I suppose you cannot agree more.
.
At elementary level in maths education, speed is always a challenging topic for learners.
It caught my attention and I started wondering why?
Many mistakes can be made when dealing with these types of questions.
After studying the various mistakes made by learners, I came to a few conclusion that I like to share here.
How to avoid confusion in doing Speed questions in maths:-
1) Speed involves two parameters, namely, distance and time.
This is the key issue. Dealing with one parameter is already a challenge, and dealng with two is always a "headache".
The concept, has thus to be clearly addressed upon, before the ratio of distance and time leading to speed can be fully understood.
What is distance?
What is time?
These 2 items are variable in nature. They change in value.
They causes confusion when lumped together!
Examples of daily activities will help in this case.
Quote cases like running in a race, where the champion came back in the shortest time covering the same distance as all others.
Get the concept of distance versus time into them.
Also FAST and SLOW relation to speed.
2) Error in units:-
Break up the tasks of calculating km, m or cm and sec, hours, minutes separately.
In other words,deal with one item at a time.
Use basic unit if possible to reduce chances of making costly errors.
The learners have to handle the logical part of the question, and also the mechanical part of unit manipulation in speed problems.
Tell them to find one thing at a time, and the need for doing that. Be patience is the message.
3) Draw out a pictorial image of the question.
This method will help some kids to visualise the real issue.
By having drawn the length for distance to be covered (or covered), they will have a better idea of what distance is about in the maths question. They will not have to "keep" this disatnce in their mind together with the problematic "time" condition.
Use the seeing method helps them clear any doubts and can also reduce mistakes in interpreting the question.
There will definitely be more pointers to be added to my three above.
But with these 3 basic issues settled, most of the queries about speed and its maths problems should be clearer.
If you have any other pointers, you may share in the comment space.
Cheers :-)
Maths is interesting, I suppose you cannot agree more.
.
Wednesday, 2 June 2010
Model versus Variable Technique
'
In using Model method of solving maths question, we are using visual blocks to scope our thinking. This is followed by analysis through the models.
Models become a link to our thinking process.
The demerit is when we did not create the Model properly, or miss out some details that cause the model to be represented wrongly.
The merit is that it can be simple and straight forward when drawn properly. It reflects outright the relationship between many unknowns.
Less workings is thus needed, as visual que sets in.
For algebraic variable technique, the unknowns are pre-defined and booked as "letters". A space, mentally, has been reserved for the answer.
The working is just simply to accept that the answer is already there but only not numerical. Following through the working steps will ultimately reveal the letter of its numerical data which is what we want.
Variable as letter is good in the sense that we need less analysis, but just mechanically following the rules and steps leading to the final step, of course with some logic and mathematical strategy.
Each has its own advantages and weakness. It is up to us to make use of them in the correct way.
Experience is the only way to overcome the proper selection of which technique.
Thus practice to gain experience in maths is one good way to master maths.
Skiving is a no-no.
Through practice, you will sooner or later find that maths is interesting.
:-)
In using Model method of solving maths question, we are using visual blocks to scope our thinking. This is followed by analysis through the models.
Models become a link to our thinking process.
The demerit is when we did not create the Model properly, or miss out some details that cause the model to be represented wrongly.
The merit is that it can be simple and straight forward when drawn properly. It reflects outright the relationship between many unknowns.
Less workings is thus needed, as visual que sets in.
For algebraic variable technique, the unknowns are pre-defined and booked as "letters". A space, mentally, has been reserved for the answer.
The working is just simply to accept that the answer is already there but only not numerical. Following through the working steps will ultimately reveal the letter of its numerical data which is what we want.
Variable as letter is good in the sense that we need less analysis, but just mechanically following the rules and steps leading to the final step, of course with some logic and mathematical strategy.
Each has its own advantages and weakness. It is up to us to make use of them in the correct way.
Experience is the only way to overcome the proper selection of which technique.
Thus practice to gain experience in maths is one good way to master maths.
Skiving is a no-no.
Through practice, you will sooner or later find that maths is interesting.
:-)
Saturday, 27 March 2010
Area Displacement Theory
.
Maths is not all about calculation.
There are always more to it than meet the eyes.
This is especially true when you are doing geometrical questions where you are involved with area, perimeter and so on.
Displacement theory or its equivalent is always done without the knowledge of many people.
What is this theory about?
Let's look at one example below.
In the diagram above, you will see a path (white coloured) going across a blue platform.
If you are asked to find the area of this path, what can you do to obtain this area?
If no data of dimension is given, it is definitely not possible.
Now if the width of the path and the vertical length of the blue platform is given, can you compute the answer?
Again , this need a bit of thinking.
Displacement theory kicks in here. Look at the diagram on the right.
It is the displaced or closed up portion of the blue platform that does the trick.
Here you will notice the dashed line forming a white rectangluar area on the right-most side of the white blue platform.
Are you able to find the area of this white rectangular piece?
The width of this rectangle piece is ACTUAL the width of the white path!
You should now be able to calculate the area of this rectangular piece since the path width and length of the rectangular block is known or deduced now.
How this is possibe is through the "hidden" clue or step of closing up the path revealing the simpler rectangular area that any decent maths student can calculate.
Hence, maths is wonderful in that it tests you not only about applcations of maths tools, but your other "intelligence".
Having known displacement theory here, I believe you are really for the Math Challenge 23.
Go there and answer the question, and be quick before others grap the position one ...
:-D
.
Maths is not all about calculation.
There are always more to it than meet the eyes.
This is especially true when you are doing geometrical questions where you are involved with area, perimeter and so on.
Displacement theory or its equivalent is always done without the knowledge of many people.
What is this theory about?
Let's look at one example below.
In the diagram above, you will see a path (white coloured) going across a blue platform.
If you are asked to find the area of this path, what can you do to obtain this area?
If no data of dimension is given, it is definitely not possible.
Now if the width of the path and the vertical length of the blue platform is given, can you compute the answer?
Again , this need a bit of thinking.
Displacement theory kicks in here. Look at the diagram on the right.
It is the displaced or closed up portion of the blue platform that does the trick.
Here you will notice the dashed line forming a white rectangluar area on the right-most side of the white blue platform.
Are you able to find the area of this white rectangular piece?
The width of this rectangle piece is ACTUAL the width of the white path!
You should now be able to calculate the area of this rectangular piece since the path width and length of the rectangular block is known or deduced now.
How this is possibe is through the "hidden" clue or step of closing up the path revealing the simpler rectangular area that any decent maths student can calculate.
Hence, maths is wonderful in that it tests you not only about applcations of maths tools, but your other "intelligence".
Having known displacement theory here, I believe you are really for the Math Challenge 23.
Go there and answer the question, and be quick before others grap the position one ...
:-D
.
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".
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!
.
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!
.
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.
Examples:
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! ^.^
.
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.
Examples:
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! ^.^
.
Monday, 26 October 2009
What Does "of" Means In Mathematics?
*
Reading maths question is a critical skill to learn.
Without understanding the question, you will not be able to solve the challenge correctly.
A typical maths problem uses the word "of" to express ratio.
What really does this simple word means?
To an adult this is the understanding of English.
But to a kid, this is not English but a maths question!
What then is "of" in maths?
Answer: It means MULTIPLY.
Examples:
half of the time ==> 0.5 x time
2/3 of the class ==> (2/3) x (class total)
If 40% of the apples are rotten, how many are left? ==> 0.4 x apples are rotten
Learn English well to handle maths.
This simple word "of" may make you happy or sad.
The choice is yours.
But remember, "Maths Is Interesting!".
So despair not, enjoy your maths.
Cheers :-D
.
Reading maths question is a critical skill to learn.
Without understanding the question, you will not be able to solve the challenge correctly.
A typical maths problem uses the word "of" to express ratio.
What really does this simple word means?
To an adult this is the understanding of English.
But to a kid, this is not English but a maths question!
What then is "of" in maths?
Answer: It means MULTIPLY.
Examples:
half of the time ==> 0.5 x time
2/3 of the class ==> (2/3) x (class total)
If 40% of the apples are rotten, how many are left? ==> 0.4 x apples are rotten
Learn English well to handle maths.
This simple word "of" may make you happy or sad.
The choice is yours.
But remember, "Maths Is Interesting!".
So despair not, enjoy your maths.
Cheers :-D
.
Saturday, 17 October 2009
Solving Maths Visually
.
Maths is interesting!
There are many exciting concepts and techniques one can apply.
Read on ...
There are many ways to solve a maths question.
Normally it involves taking many steps with related sequence.
However, there are also simple ways to handle a maths problem.
One such solving method is simply through visual steps.
This has no working at all.
What do I mean?
Let's look at an example.
Example:
Determine the angle B from the diagram below. Angle A is 40 degree.
Angle B is same as angle A = 40 degree.
There is no working at all. Just the visual determination.
Concept of this trigonometrical question in geometry:
When 2 straight lines cross and meet at an angle to each other, the angle opposite to any one is the same.
As such, angle C is also equal to angle D.
This is visual maths.
Interesting?
:-D
Maths is interesting!
There are many exciting concepts and techniques one can apply.
Read on ...
There are many ways to solve a maths question.
Normally it involves taking many steps with related sequence.
However, there are also simple ways to handle a maths problem.
One such solving method is simply through visual steps.
This has no working at all.
What do I mean?
Let's look at an example.
Example:
Determine the angle B from the diagram below. Angle A is 40 degree.
Solution:
There is no working at all. Just the visual determination.
Concept of this trigonometrical question in geometry:
When 2 straight lines cross and meet at an angle to each other, the angle opposite to any one is the same.
As such, angle C is also equal to angle D.
This is visual maths.
Interesting?
:-D
Tuesday, 6 October 2009
Time Mathematics | Tips On Avoiding Mistakes
Dealing with time and its calculation can be a bit tricky sometimes.
There are the hours, the minutes and the seconds to handle.
We can add or subtract them.
We do not operate in the hundreds, or ones, like any simple arithmetric.
We are calculating in terms of sixties.
1 hour = 60 minutes
1 minute = 60 seconds
Hence when given a maths question on subtracting two times, how do we go about to avoid mistakes?
Let's take an example to illustrate.
Question:
John start his journey to the market at 09:15am. If he arrived at the market at 10:05am, how long did he travelled?
Approach 1:
We can use the conventional method of carrying back 60 to the minutes, since the ending minute is smaller than the starting minute. And reducing the 10 to 9 (hour).
Next, we can then subtract with the new numbers.
That is 9:65 - 9:15 = 50 minutes.
This answer is fine.
Approach 2:
Change all the times to mintes.
10:05 ==> (10 x 60) + 5 = 605
09:15 ==> ( 9 x 60) + 15 = 555
Subtracting the two new numbers gives 50 minutes directly.
And that is the answer!
Remarks:
Comparing approach 1 with approach 2, you would notice that the latter seems to be simpler.
Why so?
This is because we have simplified the mixture of hours and minutes to only one dimension, that is, the minutes.
Thus, subtracting the newly created numbers involved only the minutes, avoiding the distraction of handling the hours.
To do maths, clear the mind of the unnecessary.
In the example above, we have removed the "hours" factor to focus purely on the "minutes".
Maths is interesting in that it is up to us to "play" with the techniques.
We can work with it or go against it.
The choice is up to us to select.
Hope you pick up some tips to make maths interesting.
Cheers!
:-D
There are the hours, the minutes and the seconds to handle.
We can add or subtract them.
We do not operate in the hundreds, or ones, like any simple arithmetric.
We are calculating in terms of sixties.
1 hour = 60 minutes
1 minute = 60 seconds
Hence when given a maths question on subtracting two times, how do we go about to avoid mistakes?
Let's take an example to illustrate.
Question:
John start his journey to the market at 09:15am. If he arrived at the market at 10:05am, how long did he travelled?
Approach 1:
We can use the conventional method of carrying back 60 to the minutes, since the ending minute is smaller than the starting minute. And reducing the 10 to 9 (hour).
Next, we can then subtract with the new numbers.
That is 9:65 - 9:15 = 50 minutes.
This answer is fine.
Approach 2:
Change all the times to mintes.
10:05 ==> (10 x 60) + 5 = 605
09:15 ==> ( 9 x 60) + 15 = 555
Subtracting the two new numbers gives 50 minutes directly.
And that is the answer!
Remarks:
Comparing approach 1 with approach 2, you would notice that the latter seems to be simpler.
Why so?
This is because we have simplified the mixture of hours and minutes to only one dimension, that is, the minutes.
Thus, subtracting the newly created numbers involved only the minutes, avoiding the distraction of handling the hours.
To do maths, clear the mind of the unnecessary.
In the example above, we have removed the "hours" factor to focus purely on the "minutes".
Maths is interesting in that it is up to us to "play" with the techniques.
We can work with it or go against it.
The choice is up to us to select.
Hope you pick up some tips to make maths interesting.
Cheers!
:-D
Wednesday, 30 September 2009
A Simple Way To Reduce Maths Errors
Anyone doing maths will know that making maths errors is very frustrating as the results obtained will definitely be wrong.
Just a simple slip-of-the-mind type of error can cause havoc.
Once a step is incorrect, the following steps will make use of the wrong numbers to "accumulate" the errors.
If the maths teacher is merciful, she will look for the application of concepts instead of hard numbers or the final outcome.
But maths is maths.
Numbers are always there.
Techniques and systematic approach are almost a must in handling maths questions.
So can we avoid making maths errors if every step is important?
Yes, if you try hard. But note, we are human. Thus to completely eliminate errors everytime is calling for being an angel!
One simple way to reduce maths mistakes is to stay focus.
Being focus and understanding the maths probem is one of the easy method to solve making careless mistakes.
Pay attention to ever steps you write and know the purpose of each working.
Every expression must have a meaning. Otherwise what for write it down as a working.
Simply focus and do not be distracted by the surrounding. This is one of the main cause of making errors.
If you are working in front of the television, switch it off or re-locate to another pleasant place.
If there is too many people around and talking aloud, move away if you do not have any ear plugs.
Just stay away from areas or surroundings that are dysfunctional to your maths learning (and in fact to any learning).
Apply what I wrote and you will find a different.
Happy maths learning and do not forget that "Maths Is Interesting!"
:-)
Just a simple slip-of-the-mind type of error can cause havoc.
Once a step is incorrect, the following steps will make use of the wrong numbers to "accumulate" the errors.
If the maths teacher is merciful, she will look for the application of concepts instead of hard numbers or the final outcome.
But maths is maths.
Numbers are always there.
Techniques and systematic approach are almost a must in handling maths questions.
So can we avoid making maths errors if every step is important?
Yes, if you try hard. But note, we are human. Thus to completely eliminate errors everytime is calling for being an angel!
One simple way to reduce maths mistakes is to stay focus.
Being focus and understanding the maths probem is one of the easy method to solve making careless mistakes.
Pay attention to ever steps you write and know the purpose of each working.
Every expression must have a meaning. Otherwise what for write it down as a working.
Simply focus and do not be distracted by the surrounding. This is one of the main cause of making errors.
If you are working in front of the television, switch it off or re-locate to another pleasant place.
If there is too many people around and talking aloud, move away if you do not have any ear plugs.
Just stay away from areas or surroundings that are dysfunctional to your maths learning (and in fact to any learning).
Apply what I wrote and you will find a different.
Happy maths learning and do not forget that "Maths Is Interesting!"
:-)
Sunday, 27 September 2009
Maths Symbols versus Real life Applications| Teaching style
'
Is maths interesting and is easy to learn or teach?
There are always argument over how to really capture maths students' attention and make them understand the principles and concepts in maths.
One school of thought is to approach the real life case studies.
Here actual applications are taught to make aware the usefulness of maths.
Problem-based case studies are planned into the curriculum to allow the learners to learn maths.
Another approach that is conventional is to pump in concepts and techniques using symbols and hard formulae.
Here students learn maths consists of symbols and their true meaning in the workings.
No real life indication is mentioned or just skimmed through. The focus is purely the use of maths tools to solve questions.
What are the advantages and disadvantages?
1) For real life approach, there are chances that the learners may couple their maths learning to only that particular application.
If train speed is mentioned or used, the students may only understand that the maths tools apply to train and not areoplane. The scope of aplication is a factor and serve to be a disadvantage.
The advantage is that the learners can relate to the usefulness of maths and will pay more attention and feel more fulfilled.
2) The advantage of pure symbolic approach in the conventional teaching method is that scope of the maths tools are wide. No tying down of the maths techniques to any specific area enables fredom of use.
The disadvantage, of course, is that the students may take a longer time to see that actual useulness of the maths tools and principles.
So what is the best method to learn maths?
I suppose the answer lies with the type of students and the topics to be taught.
No one way is best.
It has to be customised to suit the students or majority of them
Flexibility is thus the best methods and getting a good maths teacher who can read the minds of the students is the better choice.
If the classroom teacher is not up to expectation or has some constraints, it will be good to look for private tutors to brush up the maths learning. Note, classroom teaching does not cater for individual needs and this is a fact.
Happy maths learning.
Maths is interesting!
Don't forget it.
:-)
Is maths interesting and is easy to learn or teach?
There are always argument over how to really capture maths students' attention and make them understand the principles and concepts in maths.
One school of thought is to approach the real life case studies.
Here actual applications are taught to make aware the usefulness of maths.
Problem-based case studies are planned into the curriculum to allow the learners to learn maths.
Another approach that is conventional is to pump in concepts and techniques using symbols and hard formulae.
Here students learn maths consists of symbols and their true meaning in the workings.
No real life indication is mentioned or just skimmed through. The focus is purely the use of maths tools to solve questions.
What are the advantages and disadvantages?
1) For real life approach, there are chances that the learners may couple their maths learning to only that particular application.
If train speed is mentioned or used, the students may only understand that the maths tools apply to train and not areoplane. The scope of aplication is a factor and serve to be a disadvantage.
The advantage is that the learners can relate to the usefulness of maths and will pay more attention and feel more fulfilled.
2) The advantage of pure symbolic approach in the conventional teaching method is that scope of the maths tools are wide. No tying down of the maths techniques to any specific area enables fredom of use.
The disadvantage, of course, is that the students may take a longer time to see that actual useulness of the maths tools and principles.
So what is the best method to learn maths?
I suppose the answer lies with the type of students and the topics to be taught.
No one way is best.
It has to be customised to suit the students or majority of them
Flexibility is thus the best methods and getting a good maths teacher who can read the minds of the students is the better choice.
If the classroom teacher is not up to expectation or has some constraints, it will be good to look for private tutors to brush up the maths learning. Note, classroom teaching does not cater for individual needs and this is a fact.
Happy maths learning.
Maths is interesting!
Don't forget it.
:-)
Sunday, 13 September 2009
Graph | Length of line
'
In graph plotting, something we need to know the length of a segment of the line plotted.
This may be for the distance to be travelled (like in a field trip).
Or it may be for checking the material to be used in building a slanted pole / support.
Let's take an example to illustrate.
From the plot, if we are to calculate the length of the line between the two red crosses, we can use the well-known Pythagoras' Theorem.
However, we need to know the co0ordinates for the crosses or markres first, to check their positions.
For the lower cross, we will have x1 = 2, and y1 = 3.
For the upper cross, x2 = 6 and y2 = 5.
This allows us to determine that the length in the x-axis direction is 6 - 2 = 4 units.
The length in the y-axis direction will be 5 - 3 = 2 units up.
Using then Pythagoras' Theorem, lenght of targetted line segment will be given as sqrt(42 + 22) = 4.472 units.
From graph and its application with other maths theorem, you can find answers easily.
It is the choosing of the appropriate maths tools that is is key to having a solution in a proper way.
Many a times, you may find answers or solutions through different techniques and methods. But the number of steps are more. But it is still correct.
It is through practice and gaining experience in maths problem-solving that helps you reach a level that let you handle maths with mental ease and confidence.
Everyone can achieve that. It is the attitude. Do not fear maths. It is just a tools to solve problems.
Maths is interesting! Love maths !
Cheers! :D
In graph plotting, something we need to know the length of a segment of the line plotted.
This may be for the distance to be travelled (like in a field trip).
Or it may be for checking the material to be used in building a slanted pole / support.
Let's take an example to illustrate.
From the plot, if we are to calculate the length of the line between the two red crosses, we can use the well-known Pythagoras' Theorem.
However, we need to know the co0ordinates for the crosses or markres first, to check their positions.
For the lower cross, we will have x1 = 2, and y1 = 3.
For the upper cross, x2 = 6 and y2 = 5.
This allows us to determine that the length in the x-axis direction is 6 - 2 = 4 units.
The length in the y-axis direction will be 5 - 3 = 2 units up.
Using then Pythagoras' Theorem, lenght of targetted line segment will be given as sqrt(42 + 22) = 4.472 units.
From graph and its application with other maths theorem, you can find answers easily.
It is the choosing of the appropriate maths tools that is is key to having a solution in a proper way.
Many a times, you may find answers or solutions through different techniques and methods. But the number of steps are more. But it is still correct.
It is through practice and gaining experience in maths problem-solving that helps you reach a level that let you handle maths with mental ease and confidence.
Everyone can achieve that. It is the attitude. Do not fear maths. It is just a tools to solve problems.
Maths is interesting! Love maths !
Cheers! :D
Wednesday, 26 August 2009
Usage of Percentage
'
In maths learning, every learners will come across the terms "percent" or "percentage".
Percentage is a ratio.
It is a ratio between two numbers.
The denominator is normally the total of an item.
The unit used is %.
The above may be common knowledge for anyone doing percent maths problems.
However, what is the presentation of the solution that is appropriate?
Let's us do an example.
Example:
Class A has 30 students. If 40% of them are girls, how many are boys?
Solution:
Number of boys in the class = 30 - 40%
Now, is this "30 - 40%" correct?
The idea may be there, but someting is amiss.
What is this "40%"?
Can we just write 40% as it is?
The answer is NO!
Percentage is a ratio of the total (the class size of 30).
We cannot simply write 40% if we want to know the actual number.
The correct way is to present the step or working as: (40/100) x 30 = 12 students
We cannot simply write : 30 - 40%.
The correct way has to be 30 - (40/100) x 30 = 30 - 12 = 28 students.
2 mistakes, in concept, were made:
1) Number cannot subtract a percentage. Their units are different.
2) Percentage is a ratio, an indication of the proportion of a piece to the total. It is a relative term, not an absolute number. Thus, an absolute number cannot operate with a relative term.
Understanding this concept of "percent" and "percentage" will be handy and avoid the unnecessary trouble and anxiety of doing maths.
Tips:
Thinks of a slice of cake when doing "Percent". It has meaning only when compared to the whole cake.
Remember: Maths Is Interesting! And it WILL be get more interesting.
:D
In maths learning, every learners will come across the terms "percent" or "percentage".
Percentage is a ratio.
It is a ratio between two numbers.
The denominator is normally the total of an item.
The unit used is %.
The above may be common knowledge for anyone doing percent maths problems.
However, what is the presentation of the solution that is appropriate?
Let's us do an example.
Example:
Class A has 30 students. If 40% of them are girls, how many are boys?
Solution:
Number of boys in the class = 30 - 40%
Now, is this "30 - 40%" correct?
The idea may be there, but someting is amiss.
What is this "40%"?
Can we just write 40% as it is?
The answer is NO!
Percentage is a ratio of the total (the class size of 30).
We cannot simply write 40% if we want to know the actual number.
The correct way is to present the step or working as: (40/100) x 30 = 12 students
We cannot simply write : 30 - 40%.
The correct way has to be 30 - (40/100) x 30 = 30 - 12 = 28 students.
2 mistakes, in concept, were made:
1) Number cannot subtract a percentage. Their units are different.
2) Percentage is a ratio, an indication of the proportion of a piece to the total. It is a relative term, not an absolute number. Thus, an absolute number cannot operate with a relative term.
Understanding this concept of "percent" and "percentage" will be handy and avoid the unnecessary trouble and anxiety of doing maths.
Tips:
Thinks of a slice of cake when doing "Percent". It has meaning only when compared to the whole cake.
Remember: Maths Is Interesting! And it WILL be get more interesting.
:D
Thursday, 6 August 2009
Character of A Person Revealed Through Maths
'
There are many ways to dig into the true character of a person.
One way is through maths.
By being in a classroom of maths learners, which I suppose everyone went through or is in one, you will notice many types of characters and behaviours.
Some are strong and stubborn, the never-say-die doer.
Some are the "can do, then do" type.
Some are the easy surrenders of maths.
Some cannot even be bordered to try!
Those who attempted the maths question, also revealed some weakness also.
The careless type and the long-winded type.
They made all sort of mistakes due poor handwriting or not reading the questions properly. They may miss a few variable or maths operators in an equation.
They may indirectly simplified the problems given through seeing or copying wrongly.
Those long-winded are the "better" lot with the will to stay on track.
They do and do, even when applying the wrong technique. They, however, do get the result through their hardworking attitude.
Some are the intelligent type who spot the trick just by reading the maths question.
They are the "flexible" ones.
They are the ones that seemed to enjoy most of the maths lessons.
Whatever, the type you are, maths is still an important life-long subject.
It is a practical module that serves us till we leave this world.
Love maths, and maths will love you, whatever your character and feeling towards maths.
Maths is interesting! You have a choice for that.
Cheers.
:D
There are many ways to dig into the true character of a person.
One way is through maths.
By being in a classroom of maths learners, which I suppose everyone went through or is in one, you will notice many types of characters and behaviours.
Some are strong and stubborn, the never-say-die doer.
Some are the "can do, then do" type.
Some are the easy surrenders of maths.
Some cannot even be bordered to try!
Those who attempted the maths question, also revealed some weakness also.
The careless type and the long-winded type.
They made all sort of mistakes due poor handwriting or not reading the questions properly. They may miss a few variable or maths operators in an equation.
They may indirectly simplified the problems given through seeing or copying wrongly.
Those long-winded are the "better" lot with the will to stay on track.
They do and do, even when applying the wrong technique. They, however, do get the result through their hardworking attitude.
Some are the intelligent type who spot the trick just by reading the maths question.
They are the "flexible" ones.
They are the ones that seemed to enjoy most of the maths lessons.
Whatever, the type you are, maths is still an important life-long subject.
It is a practical module that serves us till we leave this world.
Love maths, and maths will love you, whatever your character and feeling towards maths.
Maths is interesting! You have a choice for that.
Cheers.
:D
Sunday, 2 August 2009
Is Maths Really Interesting?
'
One question those who detest maths will ask is "Is maths really interesting?".
It is a very subjective question.
Everyone has likes and dislikes.
However, in the case of maths, it is the gain versus the lack.
Maths is a necessary life skill to have.
Knowing it makes a whole lot of different.
It will speed up your solving to some daily questions.
"What is the time needed if I drive at 60 km/h for a distance of 90km?"
"What is the area of the metal sheet needed to cover this pillar?"
We are weak in maths due to many reasons.
If you do not arrest these reasons, or reduces the obstacles to it, you will always fear maths.
This will create a mental block to your maths learning.
Practice and practice to reveal your weakness. Learn through mistakes.
You will feel the confidence of handling maths problems after that phase.
Like what Mark Twain said "Action speaks louder than words".
I would like to tweet it in the context of maths.
Instead of pure saying that you cannot do maths or you hate maths, practice (action) on it.
You will feel the difference.
You will get the hang of doing maths.
You will realise that maths is not that difficult.
You will find that it is your mindset that is the block, not maths!
Practice.
Do it.
Practice speaks louder than words.
Maths is interesting.
That will be your final conclusion if you take action and do hands-on practice.
Cheers! :D
.
One question those who detest maths will ask is "Is maths really interesting?".
It is a very subjective question.
Everyone has likes and dislikes.
However, in the case of maths, it is the gain versus the lack.
Maths is a necessary life skill to have.
Knowing it makes a whole lot of different.
It will speed up your solving to some daily questions.
"What is the time needed if I drive at 60 km/h for a distance of 90km?"
"What is the area of the metal sheet needed to cover this pillar?"
We are weak in maths due to many reasons.
If you do not arrest these reasons, or reduces the obstacles to it, you will always fear maths.
This will create a mental block to your maths learning.
Practice and practice to reveal your weakness. Learn through mistakes.
You will feel the confidence of handling maths problems after that phase.
Like what Mark Twain said "Action speaks louder than words".
I would like to tweet it in the context of maths.
Instead of pure saying that you cannot do maths or you hate maths, practice (action) on it.
You will feel the difference.
You will get the hang of doing maths.
You will realise that maths is not that difficult.
You will find that it is your mindset that is the block, not maths!
Practice.
Do it.
Practice speaks louder than words.
Maths is interesting.
That will be your final conclusion if you take action and do hands-on practice.
Cheers! :D
.
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!
:D
"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!
:D
Tuesday, 23 June 2009
Percentage Humor
.
Father: How many marks did you get for your math test?
Son: I obtained 100 marks!
Father: Great! You have done me proud. You deserve an ice-cream.
Son: Thanks Dad!
Son to brother: Actually my math test is over a total of 200 marks. I almost failed the test! Luckily dad did not master percentage, otherwise I would not get my free ice-cream.
(To understand percentage, click this link).
..
Father: How many marks did you get for your math test?
Son: I obtained 100 marks!
Father: Great! You have done me proud. You deserve an ice-cream.
Son: Thanks Dad!
Son to brother: Actually my math test is over a total of 200 marks. I almost failed the test! Luckily dad did not master percentage, otherwise I would not get my free ice-cream.
(To understand percentage, click this link).
..
Tuesday, 16 June 2009
What is Percentage?
'
Many people do understand what percentage is about.
If you see a sales offer with 50% discount, you will know that it is cheaper by half.
If the offer is with 40% less, you will also realise that is a good deal since it is almost half the original price.
But what is this percentage in detail?
A mark of 4 / 5 is reflected as a fraction.
A learned maths person will understand that it is (4 /5) x 100 = 80%
If you tell a student that he achieved 50 marks. Is that enough?
The information will not be enough as the total score is not known (unless using the default told before hand).
Thus a mark of 50 upon 50, and a mark of 50 upon 100 means different story altogether.
I believe you will agree totally!
A percentage will always reflect better information since 80% means 80 / 100.
The base of 100 is taken as the default.
The actual base number is immaterial in this matter.
An information of 50 marks compared to 50% showed the power of using percentage.
For absolute marks, you need to tell the total marks to form a complete message.
Using percentage, the fraction part of the calculation can be ignored.
Percentage and fraction are related. But percentage used a common base number (100) to commonise the value.
For comparison sake, percentage, thus stand a more proper way to tell the result.
Example:
Is it easy to tell the closeness between 49 / 56 and 46 / 56,
or is it easier to tell between 78% and 81% ?
The answer is obvious, I hope.
Maths is interesting, and mastering simple concept makes maths learning even more interesting.
Happy learning.
Cheers! :D
Many people do understand what percentage is about.
If you see a sales offer with 50% discount, you will know that it is cheaper by half.
If the offer is with 40% less, you will also realise that is a good deal since it is almost half the original price.
But what is this percentage in detail?
A mark of 4 / 5 is reflected as a fraction.
A learned maths person will understand that it is (4 /5) x 100 = 80%
If you tell a student that he achieved 50 marks. Is that enough?
The information will not be enough as the total score is not known (unless using the default told before hand).
Thus a mark of 50 upon 50, and a mark of 50 upon 100 means different story altogether.
I believe you will agree totally!
A percentage will always reflect better information since 80% means 80 / 100.
The base of 100 is taken as the default.
The actual base number is immaterial in this matter.
An information of 50 marks compared to 50% showed the power of using percentage.
For absolute marks, you need to tell the total marks to form a complete message.
Using percentage, the fraction part of the calculation can be ignored.
Percentage and fraction are related. But percentage used a common base number (100) to commonise the value.
For comparison sake, percentage, thus stand a more proper way to tell the result.
Example:
Is it easy to tell the closeness between 49 / 56 and 46 / 56,
or is it easier to tell between 78% and 81% ?
The answer is obvious, I hope.
Maths is interesting, and mastering simple concept makes maths learning even more interesting.
Happy learning.
Cheers! :D
Sunday, 31 May 2009
Power Law of Logarithm Explained
Logarithm study has a few formulae that are important and key to solving math questions.
By remembering them , you will be in line to solve logarithmic problems and, maybe, fast too.
However, what if you forget them?
Does it mean that you are not able to solve the question regardless of speed?
Do not despair.
As long as you are able to manage the 2 basic laws in logarithm, you are safe.
The product law and the quotient law are must for any students.
Why do I say that?
Let us take the Power Law and do a review.
n log x = log X n
Why is it so? What if you forget this law? Any problem?
These are the very queries any new learners exposed to logarithm will ask.
First allow me to go through the product law of logarithm.
log (XY) = log X + log Y
meaning, 4 log Y = log Y4.
You see that you did not utilise the Power Law here,and yet is able to form this formula!
Amazing isn't it.
What is the message here?
The message is that, when you have the basic understanding in logarithmic principles, you will be able to twist and turn any given problems to come out a solution.
You had used the basic product law to discover this unique Power Law.
It is similar to other laws and also can be expanded to cover other maths topics too.
Do enjoy maths.
Do discover more exciting twists it presents wwith a bit of thinking.
Happy learning :-)
.
By remembering them , you will be in line to solve logarithmic problems and, maybe, fast too.
However, what if you forget them?
Does it mean that you are not able to solve the question regardless of speed?
Do not despair.
As long as you are able to manage the 2 basic laws in logarithm, you are safe.
The product law and the quotient law are must for any students.
Why do I say that?
Let us take the Power Law and do a review.
n log x = log X n
Why is it so? What if you forget this law? Any problem?
These are the very queries any new learners exposed to logarithm will ask.
First allow me to go through the product law of logarithm.
log (XY) = log X + log Y
Here you see that the product of "X" and "Y" in logarithmic operation, becomes a "sum"of the individual logarithms.
4 log Y = log Y + log Y + log Y + log Y (adding up 4 of the log Y)
Using product law, you know that these 4 terms can be combined to log (Y x Y x Y x Y).
log (Y x Y x Y x Y) = log Y4
Now, you see, through the product law, you are able to equate the 4 log Y into log Y4 ,meaning, 4 log Y = log Y4.
You see that you did not utilise the Power Law here,and yet is able to form this formula!
Amazing isn't it.
What is the message here?
The message is that, when you have the basic understanding in logarithmic principles, you will be able to twist and turn any given problems to come out a solution.
You had used the basic product law to discover this unique Power Law.
It is similar to other laws and also can be expanded to cover other maths topics too.
Do enjoy maths.
Do discover more exciting twists it presents wwith a bit of thinking.
Happy learning :-)
.
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