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!"
:-)
Wednesday, 30 September 2009
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.
:-)
Monday, 21 September 2009
Simple Tricky Maths Pattern
.
Maths forms interesting patterns if you care to look around.
One such example is highlighted below:
12 11 10 09 08 07 06 <== row 1 (decreasing by 1)
01 02 03 04 05 06 07 <== row 2 (increasing by 1)
If you add the numbers in row 1 to that in row 2, you will get, surprisingly, the same answer throughout!
13 13 13 13 13 13 13
Why is it so?
It is a simple trick to the unwaries, actually.
Maths is not that difficult, to start off.
The answers to the above additions seem to be accidental in having the same number.
It is actually not accidental if you think abit.
The answers were intended to be 13 to begin with.
13 = 12 + 1
13 = 11 + 2
13 = 10 + 3 .... and so on.
Though the additions seems magical with one row in ascending mode while the other row in descending mode, it is the visual maths trick that corrupts and confuses the mind.
If your principles of mathematics is good and strong, you will break through this simple trick in no time.
To excite young minds, this is a good one to try on them.
Happy playing with maths.
Maths is interesting!
:D
Maths forms interesting patterns if you care to look around.
One such example is highlighted below:
12 11 10 09 08 07 06 <== row 1 (decreasing by 1)
01 02 03 04 05 06 07 <== row 2 (increasing by 1)
If you add the numbers in row 1 to that in row 2, you will get, surprisingly, the same answer throughout!
13 13 13 13 13 13 13
Why is it so?
It is a simple trick to the unwaries, actually.
Maths is not that difficult, to start off.
The answers to the above additions seem to be accidental in having the same number.
It is actually not accidental if you think abit.
The answers were intended to be 13 to begin with.
13 = 12 + 1
13 = 11 + 2
13 = 10 + 3 .... and so on.
Though the additions seems magical with one row in ascending mode while the other row in descending mode, it is the visual maths trick that corrupts and confuses the mind.
If your principles of mathematics is good and strong, you will break through this simple trick in no time.
To excite young minds, this is a good one to try on them.
Happy playing with maths.
Maths is interesting!
:D
Wednesday, 16 September 2009
Purpose of Graph
.
What is the purpose of graph?
This may be the question every learners first ask when they were exposed to this maths topic.
When do we use graph as opposed to using, for example, Argand diagram or vectors sketch?
Graph by nature is a graphical presentation of data that collectively form into information that reflects the trend of some parameters.
It shows the past, current and possibly the future (prediction).
Graph is a relative as well as an absolute maths tool for people using it.
An example of graph application is that in stock market data prediction.
Using past records, people tends to forecast the future through looking at the graph.
Another example is in engineering work.
Collecting data of a certain electrical system behaviour, engineers can predict the failure or potential life of its operation.
A simple graph is plotted with normally 2 parameters.
But this is not always true.
Graph may come in 3 dimensional. The x, y and z direction.
Knowing graph is an alternative problem solving skill or prediction skill.
It allows users to see an overview of the relation between specific targets.
Graph is wonderful if you let it be.
Enjoy it.
:D
What is the purpose of graph?
This may be the question every learners first ask when they were exposed to this maths topic.
When do we use graph as opposed to using, for example, Argand diagram or vectors sketch?
Graph by nature is a graphical presentation of data that collectively form into information that reflects the trend of some parameters.
It shows the past, current and possibly the future (prediction).
Graph is a relative as well as an absolute maths tool for people using it.
An example of graph application is that in stock market data prediction.
Using past records, people tends to forecast the future through looking at the graph.
Another example is in engineering work.
Collecting data of a certain electrical system behaviour, engineers can predict the failure or potential life of its operation.
A simple graph is plotted with normally 2 parameters.
But this is not always true.
Graph may come in 3 dimensional. The x, y and z direction.
Knowing graph is an alternative problem solving skill or prediction skill.
It allows users to see an overview of the relation between specific targets.
Graph is wonderful if you let it be.
Enjoy it.
:D
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
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