Maths is not about just doing and computing mathematical challenges. It is also not just about planning strategies to solve a problem. It involves more than mentioned.
It includes skill seemingly not related to maths.
What is it then?
It is about presenting the solution and steps in approaching the maths problems.
And presenting them well and in an understandable way.
Example :
3x - 6 = x. Find x.
Solution A:
x = 6 / 2 = 3
Solution B:
3x - x = 6
2x = 6
x = 6 / 2 =3
In your view, which solution has a better presentation?
Which shows the approach better?
My view is Solution B is better. Why?
It showed the thinking that goes on in the learner's mind.
In real life, we need to make clear our thoughts in getting and convincing partners and team-mates to work with us. It is an important skill to present our ideas to others.
By doing and presenting our maths solution, we are actually aligning ourselves to real working life.
Thus performing good presentation in our maths solving helps.
Agree?
Maths is interesting.
.
Showing posts with label attitude. Show all posts
Showing posts with label attitude. Show all posts
Saturday, 9 March 2013
Friday, 17 February 2012
Fear Over Maths
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.
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.
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!
.
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
.
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
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
.
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 :-)
.
Saturday, 9 May 2009
Learning Math Topics in Isolation
Learning encompasses linking with other area and related topics.
Learning thing with disregard for other is alright for the sake of triggering the mind. But does it benefits more if linked to others?
Does indices related to quadratic equation?
Does multiplication relates to addition?
Does complex number relates to algebra?
All the above questions are common in the mind of a math learners.
If you do not have these questions along the learning phase, something is very wrong.
Learning math in isolation is similar to living in an isolated island all by yourself.
You do not know what is happening in the world.
You do not know if there is famine somewhere, or swine flu going round, or a plane crash near you.
Math has to be done with linkage to many other mathematical topics. It cannot be done in isolation.
Math is a tool that solves real-life problems. With mastery of various mathematical concept and relation among them, you will be better prepare to solve more problems.
Many a time, you will come across students who just study topical math without knowing that they can apply what have been taught to them previously.
They start fresh when a new topic is introduced.
Algebra is different from complex number.
The addition in complex number is done differently from that done in algebra. That's what they assumed, since the heading is different!
Interesting learning ways, right?
That is human nature, to be frank. Only when you are told, sometimes, otherwise you will not know it. Adults learn through experience that this assumption is pulling you down.
The ability to link many things together is a very beneficial skill to permanently internalise.
This does not point to math alone. Others apply.
Math can be tough if learned using an improper learning method.
One good technique is the linking technique where you will see yourself happily doing math, being able to apply and solve questions using previous and current taught concepts.
It motivates you.
This is the STARTING point if you are unaware. This is the point where it decides whether you can sustain math learning.
Learn wide and later deep into math. But start with the correct footing. Link as much to previous as possible. It will be a sure way to happy math doing.
:-) I like math!
.
Learning thing with disregard for other is alright for the sake of triggering the mind. But does it benefits more if linked to others?
Does indices related to quadratic equation?
Does multiplication relates to addition?
Does complex number relates to algebra?
All the above questions are common in the mind of a math learners.
If you do not have these questions along the learning phase, something is very wrong.
Learning math in isolation is similar to living in an isolated island all by yourself.
You do not know what is happening in the world.
You do not know if there is famine somewhere, or swine flu going round, or a plane crash near you.
Math has to be done with linkage to many other mathematical topics. It cannot be done in isolation.
Math is a tool that solves real-life problems. With mastery of various mathematical concept and relation among them, you will be better prepare to solve more problems.
Many a time, you will come across students who just study topical math without knowing that they can apply what have been taught to them previously.
They start fresh when a new topic is introduced.
Algebra is different from complex number.
The addition in complex number is done differently from that done in algebra. That's what they assumed, since the heading is different!
Interesting learning ways, right?
That is human nature, to be frank. Only when you are told, sometimes, otherwise you will not know it. Adults learn through experience that this assumption is pulling you down.
The ability to link many things together is a very beneficial skill to permanently internalise.
This does not point to math alone. Others apply.
Math can be tough if learned using an improper learning method.
One good technique is the linking technique where you will see yourself happily doing math, being able to apply and solve questions using previous and current taught concepts.
It motivates you.
This is the STARTING point if you are unaware. This is the point where it decides whether you can sustain math learning.
Learn wide and later deep into math. But start with the correct footing. Link as much to previous as possible. It will be a sure way to happy math doing.
:-) I like math!
.
Monday, 16 March 2009
Not Knowing Maths Is OK
.
Anxiety is caused by not being able to fulfill your desire but strongly wishing for it.
Maths anxiety is likewise. Wanting to master maths but is unable to grasp the concepts.
Don't worry. It is not the end of the world!
Maths is just a tool for you to solve problems easily.
Maths lets you have a systematic approach in solving questions.
But if you do not understand maths, does it mean that you cannot solve problems?
You still can, but maybe only through more guessing (that is, non-systematical).
While learning or doing your maths homework, forgo the idea to quickly master the topic.
Forcing your learning through at a faster pace than you are able to handle does not serve any purpose.
Learning needs time to digest and analyse information. It is just like eating a meal.
Eating too fast will get you indigestion!
Same to learning maths, as well as other subjects.
Just understand that not knowing maths is OK.
Knowing maths is a privilege, a bonus.
With this mindset, you will find maths interesting.
It is a tool only for helping you find answers in an "education" and impressive way.
Life still goes on without you knowing maths.
(In fact, you actually use it, except that you did not know that it is called maths!).
Does this message make you feel better?
Hope it does.
Let maths be your slave.
And not you being the slave to maths.
Cheers! :D
.
Anxiety is caused by not being able to fulfill your desire but strongly wishing for it.
Maths anxiety is likewise. Wanting to master maths but is unable to grasp the concepts.
Don't worry. It is not the end of the world!
Maths is just a tool for you to solve problems easily.
Maths lets you have a systematic approach in solving questions.
But if you do not understand maths, does it mean that you cannot solve problems?
You still can, but maybe only through more guessing (that is, non-systematical).
While learning or doing your maths homework, forgo the idea to quickly master the topic.
Forcing your learning through at a faster pace than you are able to handle does not serve any purpose.
Learning needs time to digest and analyse information. It is just like eating a meal.
Eating too fast will get you indigestion!
Same to learning maths, as well as other subjects.
Just understand that not knowing maths is OK.
Knowing maths is a privilege, a bonus.
With this mindset, you will find maths interesting.
It is a tool only for helping you find answers in an "education" and impressive way.
Life still goes on without you knowing maths.
(In fact, you actually use it, except that you did not know that it is called maths!).
Does this message make you feel better?
Hope it does.
Let maths be your slave.
And not you being the slave to maths.
Cheers! :D
.
Sunday, 15 February 2009
Mathematics Letter S
Using graph and equation, you can create wonders.
Graph does not only mean lines and curves. It can be "letter" too, as seen below.
With creativity and a bit of trying, you can have surprising images formed through graphs.
With mathematics, you are not limited to equation and solving problem. You can have fun and that makes mathematics interesting.
:-)
Graph does not only mean lines and curves. It can be "letter" too, as seen below.
With creativity and a bit of trying, you can have surprising images formed through graphs.
With mathematics, you are not limited to equation and solving problem. You can have fun and that makes mathematics interesting.
:-)
Thursday, 15 January 2009
How Is Maths Interesting ?
Anyone who do a taxing job will detest the job finally.
Anyone who has trouble learning a subject will lose interest ultimately.
Anyone who find a task difficult will not have interest developed for it.
These are threads of a human being and a fact of life.
When you put in effort to rectify the undesired for a good cause, you will find fulfilment gradually.
This gradual increase of satisfaction will arouse your interest for the subject or task.
The interest will develop, if the process is correct, to a liking.
Learning maths is the same.
Put in the appropriate effort and see interest develop.
Finding maths interesting will lead you to like maths finally.
You will find that maths is not that difficult after all. You will start to challenge yourself when faced with testing questions. You will like the thrill.
If you find that thrill, I can safely say that you have succeeded with maths learning.
. .
U SMILE
.
Anyone who has trouble learning a subject will lose interest ultimately.
Anyone who find a task difficult will not have interest developed for it.
These are threads of a human being and a fact of life.
When you put in effort to rectify the undesired for a good cause, you will find fulfilment gradually.
This gradual increase of satisfaction will arouse your interest for the subject or task.
The interest will develop, if the process is correct, to a liking.
Learning maths is the same.
Put in the appropriate effort and see interest develop.
Finding maths interesting will lead you to like maths finally.
You will find that maths is not that difficult after all. You will start to challenge yourself when faced with testing questions. You will like the thrill.
If you find that thrill, I can safely say that you have succeeded with maths learning.
. .
U SMILE
.
Monday, 8 December 2008
Correct Method over Correct Answer
In math, you do not go for correct answer.
Yes, correct answer motivates. It is the ultimate goal for any math learner.
But is that all to math?
Math calls for more than that.
Read this story before moving on......
You have to ensure that the correct answer is gotten with the correct method and concept or principles.
Many a times, students can obtain correct answers to a math question, if it is not properly though over by the teacher.
If the teacher did not do a scrutiny over the working, the answer may be passed off as correct.
This is disaster.
If the student did not master the concept properly, this sort of happening will also results in learning disaster.
Therefore, seek to learn the correct technique or math method instead of aiming for the answer.
It is better to get wrong answer with the correct method than getting correct answer with wrong technique.
This makes learning math interesting!
.
Yes, correct answer motivates. It is the ultimate goal for any math learner.
But is that all to math?
Math calls for more than that.
Read this story before moving on......
You have to ensure that the correct answer is gotten with the correct method and concept or principles.
Many a times, students can obtain correct answers to a math question, if it is not properly though over by the teacher.
If the teacher did not do a scrutiny over the working, the answer may be passed off as correct.
This is disaster.
If the student did not master the concept properly, this sort of happening will also results in learning disaster.
Therefore, seek to learn the correct technique or math method instead of aiming for the answer.
It is better to get wrong answer with the correct method than getting correct answer with wrong technique.
This makes learning math interesting!
.
Saturday, 29 November 2008
Solving Index expression in Quadratic form
In maths, the solving of indices questions and its quadratic counterparts are a common practice.
Depending on how you approach the solving, you may encounter a tough journey or a smooth-flowing one.
There are, however, simple tools and concepts that can be applied, in order to have fun solving them.
Here you go....
First, let's us take an example.
Example:
(2x)2 + 3(2x) - 4 = 0
To solve this type of quadratic (index) equation, you have to take note of the common mistake in mis-interpreting the second term above.
This is the "3(2x)" term. Refer to this link for explanation on the mistake.
Next, apply the concept of using "let" to the given equation.
This is needed to simplify the mathematical expression visually. Otherwise, it may look intimidating.
To learn about the power of using "Let", click here.
With the above 2 basic steps adhered to, you are ready to move forward into a relax solving environment to handle the given equation with ease.
Simplified equation: (After letting y = 2x)
==> y2 +3y -4 = 0
Applying next, the quadratic formula method, you can see that a = 1, b= 3 and c = -4.
Solving it for y, you will get 2 values shown below. ( Click here to learn how to make use of quadractic formula to solve.)
==> y = (-3 + 5)/2 = 1 and y = (-3-5)/2 = -4
After which, solve for x.
This y is related to x by the "letting" operation you have did in the first place, that is, y = 2x.
y = 1: y = 2x ==> 2x = 1 = 20 ==> x = 0 (Answer), logical comparison.
The other answer of y = -4 will not yield any valid real answer for x here.
( Why? --- see my next post).
So, you have done the solution very easily and without hiccups if you have understood the basic concept. If you have reviewed the working here, you will notice that there is nothing complex with all the steps.
Maths can be solved through a series of mind-blowing steps. But the reverse can also be true. It is up to you to define and choose the desire path.
Do not despair initially, as you need experience to manage this selection of strategy. How to achieve this experience? Simply practice and practice.
:-) ***
Depending on how you approach the solving, you may encounter a tough journey or a smooth-flowing one.
There are, however, simple tools and concepts that can be applied, in order to have fun solving them.
Here you go....
First, let's us take an example.
Example:
(2x)2 + 3(2x) - 4 = 0
To solve this type of quadratic (index) equation, you have to take note of the common mistake in mis-interpreting the second term above.
This is the "3(2x)" term. Refer to this link for explanation on the mistake.
Next, apply the concept of using "let" to the given equation.
This is needed to simplify the mathematical expression visually. Otherwise, it may look intimidating.
To learn about the power of using "Let", click here.
With the above 2 basic steps adhered to, you are ready to move forward into a relax solving environment to handle the given equation with ease.
Simplified equation: (After letting y = 2x)
==> y2 +3y -4 = 0
Applying next, the quadratic formula method, you can see that a = 1, b= 3 and c = -4.
Solving it for y, you will get 2 values shown below. ( Click here to learn how to make use of quadractic formula to solve.)
==> y = (-3 + 5)/2 = 1 and y = (-3-5)/2 = -4
After which, solve for x.
This y is related to x by the "letting" operation you have did in the first place, that is, y = 2x.
y = 1: y = 2x ==> 2x = 1 = 20 ==> x = 0 (Answer), logical comparison.
The other answer of y = -4 will not yield any valid real answer for x here.
( Why? --- see my next post).
So, you have done the solution very easily and without hiccups if you have understood the basic concept. If you have reviewed the working here, you will notice that there is nothing complex with all the steps.
Maths can be solved through a series of mind-blowing steps. But the reverse can also be true. It is up to you to define and choose the desire path.
Do not despair initially, as you need experience to manage this selection of strategy. How to achieve this experience? Simply practice and practice.
:-) ***
Sunday, 16 November 2008
Logical Comparison in Maths
Given a maths question, most of us will attempt solving it step by step, diligently, using formula and methods we have mastered.
However, there are times when a simpler solution can be done if we are able to see the logical side to the maths problem assigned.
Let me show an example.
Question:
2x = 24, find the value of x.
Solution: (mathematically)
Taking "log" on both sides, ==> x log 2 = 4 log 2 ==> x = 4 (log 2) / (log 2) = 4
Solution: (logically)
Comparing the values of their power, we get x = 4, since their base is the same (=2).
No working is needed!
Thus, maths does not actually just train us to do things systematically, it allows us to have a bit of mental freedom. This freedom is done in terms of the small little "twists" that make use of visual comparison or logical thinking (comparison).
Interesting approach to maths learning, right?
So many ways, mathematically and non-mathematically.
But best is the stretch to our mind to develop it to see things in many angles.
.
However, there are times when a simpler solution can be done if we are able to see the logical side to the maths problem assigned.
Let me show an example.
Question:
2x = 24, find the value of x.
Solution: (mathematically)
Taking "log" on both sides, ==> x log 2 = 4 log 2 ==> x = 4 (log 2) / (log 2) = 4
Solution: (logically)
Comparing the values of their power, we get x = 4, since their base is the same (=2).
No working is needed!
Thus, maths does not actually just train us to do things systematically, it allows us to have a bit of mental freedom. This freedom is done in terms of the small little "twists" that make use of visual comparison or logical thinking (comparison).
Interesting approach to maths learning, right?
So many ways, mathematically and non-mathematically.
But best is the stretch to our mind to develop it to see things in many angles.
.
Saturday, 18 October 2008
Does Math make you clever?
Why do we need to study math?
Is this question a familiar one?
We know that we need math to do some calculations for our daily necessity. But have we to go to the extent of learning logarithm, calculus, and the more complex mathematical techniques?
Math learning also involves some form of drilling to pump in the key steps and concepts. It is also a form of structured and systematic approach to solving problems.
So does this so-called systematic approach tie us to a rigid way of doing thing?
Will math, therefore, make us a more flexible or rigid, straight-only person?
Compare this math learning to literature learning, which has more room for personal expression?
My guess, is that you will say "literature".
Yes, learning subjects, like the literature and languages , do give us the freedom of expression through writing what comes to the mind, filling in beautiful words for descriptions and the like.
Math, on the other hand, forces us to think only in a structure manner. Any deviation from the "laws" will be deemed inappropriate.
Thus, learning math makes us less clever.
WRONG!
Now let's look at learning math in another angle.
Assume you are the civil engineer having to plan the site layout for constructing a building. You are given a boundary with the area within filled with hard rocks beneath.
Another civil engineer is asked to build a similar building but now in a prairie, without any boundary constraint and the soil is marvellous.
Who has a better time?
Who need to be more experience or knowledgeable?
Who need to be better?
You have to be better.
Link this to learning math, where you are given "boundaries" to operate in. The structured approach ties you within the laws, but still requires you to come out with the answers.
Learning subjects, like the English, is equivalent to the other engineer. He has his challenges but in another form (maybe to optimise budget, appearance, etc).
So, does learning math makes you clever?
Maybe. But it will definitely not make you less clever.
Having to operate and think with more constraints requires building, in fact, more flexibilities, for you to overcome any obstacles.
This is the power of learning math, and the very reason why we need to have math in our education since young.
Interesting ironical concept, right?
(Constraints create more flexibilities).
:D
Is this question a familiar one?
We know that we need math to do some calculations for our daily necessity. But have we to go to the extent of learning logarithm, calculus, and the more complex mathematical techniques?
Math learning also involves some form of drilling to pump in the key steps and concepts. It is also a form of structured and systematic approach to solving problems.
So does this so-called systematic approach tie us to a rigid way of doing thing?
Will math, therefore, make us a more flexible or rigid, straight-only person?
Compare this math learning to literature learning, which has more room for personal expression?
My guess, is that you will say "literature".
Yes, learning subjects, like the literature and languages , do give us the freedom of expression through writing what comes to the mind, filling in beautiful words for descriptions and the like.
Math, on the other hand, forces us to think only in a structure manner. Any deviation from the "laws" will be deemed inappropriate.
Thus, learning math makes us less clever.
WRONG!
Now let's look at learning math in another angle.
Assume you are the civil engineer having to plan the site layout for constructing a building. You are given a boundary with the area within filled with hard rocks beneath.
Another civil engineer is asked to build a similar building but now in a prairie, without any boundary constraint and the soil is marvellous.
Who has a better time?
Who need to be more experience or knowledgeable?
Who need to be better?
You have to be better.
Link this to learning math, where you are given "boundaries" to operate in. The structured approach ties you within the laws, but still requires you to come out with the answers.
Learning subjects, like the English, is equivalent to the other engineer. He has his challenges but in another form (maybe to optimise budget, appearance, etc).
So, does learning math makes you clever?
Maybe. But it will definitely not make you less clever.
Having to operate and think with more constraints requires building, in fact, more flexibilities, for you to overcome any obstacles.
This is the power of learning math, and the very reason why we need to have math in our education since young.
Interesting ironical concept, right?
(Constraints create more flexibilities).
:D
Monday, 18 August 2008
Principles of Learning (Mathematics)
Learning? Yes, a simple word, but the implication is far-reaching than the word itself.
Before we start learning anything useful, we need to question ourselves over its purpose.
If the answer to it is sufficient enough for you to strike on, you are in the correct path to a better future.
However, what is the mental approach to learning, before actual content acquisition?
Is the ownership of learning clear?
These are the questions you have to answer before you set out on the bright journey of learning.
The key issue here is OWNERSHIP of learning.
Besides learning the essential principles of mathematics, the crucial principles of learning has to be handled well too. Do note that both go hand-in-hand.
Principle of learning takes into account the idea that learning is the sole ownership of the learner.
The teacher is, just after all, a catalyst to speed up the learning process. He is there to address any questions that may be harder to solve or missing links that may unknowing been left out during the course of lesson delivery.
But to have a fruitful learning outcome, you must know the fact that you are the ultimate target of the process. You have to constantly remind yourself that "I am the one learning".
Whether can the teacher teach well or explain properly, the learning still goes back to you. (Do not blame anyone for failure to learn!). It becomes an excuse to deviate from the proper.
So, the principles of learning has to be clearly understood before principles of mathematics can be effectively captured.
Mathematics learning will then be a wonderful learning journey.
Wonderful here does not mean easy-going though.
Without decent struggle in learning and thinking, retention of knowledge will not last long. This is a well-known fact! (Struggle here means the mental processing of knowledge, past and current).
Study hard (and smart), and know that you are the final gem that any teacher would like to polish, provided you start off with the correct mindset.
Cheers to learning and cheers to you, the mathematics gem.
Maths Is Interesting!
.
Before we start learning anything useful, we need to question ourselves over its purpose.
If the answer to it is sufficient enough for you to strike on, you are in the correct path to a better future.
However, what is the mental approach to learning, before actual content acquisition?
Is the ownership of learning clear?
These are the questions you have to answer before you set out on the bright journey of learning.
The key issue here is OWNERSHIP of learning.
Besides learning the essential principles of mathematics, the crucial principles of learning has to be handled well too. Do note that both go hand-in-hand.
Principle of learning takes into account the idea that learning is the sole ownership of the learner.
The teacher is, just after all, a catalyst to speed up the learning process. He is there to address any questions that may be harder to solve or missing links that may unknowing been left out during the course of lesson delivery.
But to have a fruitful learning outcome, you must know the fact that you are the ultimate target of the process. You have to constantly remind yourself that "I am the one learning".
Whether can the teacher teach well or explain properly, the learning still goes back to you. (Do not blame anyone for failure to learn!). It becomes an excuse to deviate from the proper.
So, the principles of learning has to be clearly understood before principles of mathematics can be effectively captured.
Mathematics learning will then be a wonderful learning journey.
Wonderful here does not mean easy-going though.
Without decent struggle in learning and thinking, retention of knowledge will not last long. This is a well-known fact! (Struggle here means the mental processing of knowledge, past and current).
Study hard (and smart), and know that you are the final gem that any teacher would like to polish, provided you start off with the correct mindset.
Cheers to learning and cheers to you, the mathematics gem.
Maths Is Interesting!
.
Sunday, 17 August 2008
4 Sure Ways To Fail Math
There are ways to pass math, and there are ways to fail math.
Failing math is easy. Just handing up a blank math paper will surely results in failure outright.
But how to fail math gracefully without submitting a blank paper?
Here 4 sure ways are proposed (from compilation of past experiences).
Way ONE:
Ignore the purpose of "equal" symbol (=).
Example:
x + 5 = 8 ==> x = 8 + 5. This will guarantee a cross.
Way TWO:
Ignore the written size of the text.
Example:
2x = 6 ===> 2x = 6.
logx = 5 ===> log x = 5. Two crosses are confirmed!
Way THREE:
Ignore the purpose of the parenthese (or brackets).
Example:
5 (x + 6) = 0 ===> 5x + 6 = 0. Wonderfully incorrect!
Way FOUR:
Treating function name as variables.
Example:
sin x + sin 2x = 0 ===> sin (x + 2x) = 0. Confirm failure!
From the above 4 techniques, you can be reassured a failure for math.
Why?
All the basic principles of mathematics have been violated and they are almost needed for most mathematical computations.
To pass math, therefore, is to reverse the above 4 sure ways to math failure!
(Unless you are challenging the norm!)
.
Failing math is easy. Just handing up a blank math paper will surely results in failure outright.
But how to fail math gracefully without submitting a blank paper?
Here 4 sure ways are proposed (from compilation of past experiences).
Way ONE:
Ignore the purpose of "equal" symbol (=).
Example:
x + 5 = 8 ==> x = 8 + 5. This will guarantee a cross.
Way TWO:
Ignore the written size of the text.
Example:
2x = 6 ===> 2x = 6.
logx = 5 ===> log x = 5. Two crosses are confirmed!
Way THREE:
Ignore the purpose of the parenthese (or brackets).
Example:
5 (x + 6) = 0 ===> 5x + 6 = 0. Wonderfully incorrect!
Way FOUR:
Treating function name as variables.
Example:
sin x + sin 2x = 0 ===> sin (x + 2x) = 0. Confirm failure!
From the above 4 techniques, you can be reassured a failure for math.
Why?
All the basic principles of mathematics have been violated and they are almost needed for most mathematical computations.
To pass math, therefore, is to reverse the above 4 sure ways to math failure!
(Unless you are challenging the norm!)
.
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