As children are immature and excited, they like acknowledgement and appreciation even more.

Even verbal appreciation is a reward. It can get easily more than verbal like an additional pat on the back or more.

Children are in formative stage of their life. Their behaviors can be moulded for better. It is necessary to encourage desirable and discourage undesirable behaviors of a child. Reward and punishment are two opposing methods that may be used for this purpose. When used with a child, rewards and withholding rewards is better than punishment or fear of punishment.

**Parental Association and Role**

Parents are the most important authority and influence for a child. Association between parents and their child is not only psychological but also biological. It is characterized by great love and association.

Parents have a great interest in well being of their children. But others won’t be interested typically. They have their own children to care for.

Parents are both natural providers and up-bringers for their children.

**Social and Family Influences**

Emphasis on studies varies with social and family influences. Highly educated parents who earn based on their high education are likely to be more particular about education of their children. Example of such parents include university professors. School and peer influence are also important. Quality of education in schools varies a lot. A child is also influenced by the company of other children especially if it is regular.

Rewarding can have a positive effect on the behavior of a child. You can use it to improve academic performance of a child.

Parents are in the best position to use such rewarding. Yet, there are some difficulties they may face in doing this.

The rest of this article identifies and mentions such difficulties in some detail.

**1) Number of behaviors to reward at a time**

Don’t use rewards for over one behavior at a time. If parents try to influence many behaviors of their child same time, child may lose motivation and interest towards such changes. Target important behaviors. Try to influence only one behavior at a time by using rewards. Using reward for a desirable behavior change doesn’t mean that you cannot advise your child over other things.

**2) Size of a reward **

Don’t use rewards that are too small or too big. Use both smaller and bigger rewards for study improvement. You may use a smaller reward for study goal of a day and a bigger reward for study goal of a week. The goal may also be like getting a better grade in a test or exam. Reward your child only when he has done the task he is to do.

You may use as simple a reward as a chocolate or ice-cream but only if you know that it will be enough to motivate your child to study more. Chocolate and ice-cream are easy to get. A child may not take them worth his greater effort for his studies.

**3) Identifying rewards **

Your rewards can get mixed with other things that you provide to your child. Keep your rewards separate and distinct from other things that you provide. Rewards can vary and must be things that the child likes especially.

**4) Child may take rewards for granted**

Some parents provide everything that their children ask them for. This makes children take such things for granted. It is best to have a balanced approach. Provide your child with certain things but withhold others for a later time. Deny them a few things altogether. It is important to be both firm and loving in dealing with your child.

**5) Frequency of rewarding**

If you use rewards commonly they may lose their value and influence for a child. Its frequency should not be more than once a day.

**6) Remaining involved with your child’s studies**

For all this to happen properly, you will need to have a close involvement with the studies of your child. Otherwise, you won’t be able to know exactly the effect rewards are having on studies of your child.

]]>In the words of American poet Paul Engle

Poetry is ordinary language raised to the Nth power. Poetry is boned with ideas, nerved and blooded with emotions, all held together by the delicate, tough skin of words

I have included this category in this blog because of my own love and association with poetry.

Another consideration for me is the great importance of poetry in education. Though I am not a poetry teacher and tutor, I have been tutoring English writing, English speech etc.

Here I want to share my experiences of poetry in a way that interests readers and also satisfies my association with it.

Music also has poetry very commonly as songs. This is one reason why there are so many poetry fans.

I am also a big music fan.

I love Twitter because it allows only short sized tweets. It may be a limitation in a way but a very important strength same time. Any person who tweets knows that he has to convey his/her meaning in a very short form. People reading tweets don’t have to read much which is convenient for them.

Shortness in poetry is very common which is like a twitter tweet. Many poems are short. It is one thing I love about poetry.

I find it great to remember short poems, then keep on repeating them in my mind. It is wonderful to know the depth of meaning that they carry.

]]>It is also necessary that you attend to your examination. But never lose sight of the use of deep knowledge in practical life.

Remember knowledge is a pure human endeavor that no other living species on the earth is capable of. Good study habits help gain of true knowledge.

Here are some ways you can help your studies.

**1) Study for short periods and have breaks **

Don’t study for hours without a break. It may affect your concentration and vigilance. While studying, it is good to have a short break after a period like half an hour. Alternatively, you may have a break after studying a certain bit you assign as your goal. For example, a textbook topic or its few pages.

Also have planned extended breaks.

Such breaks will help you refresh yourself.

Give yourself a reward for achieving a significant study goal. Rewards are positive reinforcers that strengthen desirable behaviors. Size of the reward should match with the size of the study goal. You cannot fly out of the city on a vacation after completing study of a day.

**2) Repetition**

Repetition is very important to learning. You will develop better learning of things you often repeat.

**3) Take Notes**

Take notes in the classroom. Also make your own as you study yourself.

**4) Do at least one other thing you love**

This may be playing a physical sport like soccer, listening to music, chatting with friends, etc. Such desirable and forceful distraction will help you come back to your studies in force and spirit. But be careful to save enough time for your studies. Also make sure you do not attend to many such activities giving insufficient time to each.

**5) Discuss with others**

These may include your teachers or your fellow students. It will help you both academically and socially.

**6) Manage distracting or anxious thoughts**

Distracting and anxious thoughts are associated with studies commonly. Try to be opposite. Have related interesting and relaxed thoughts instead.

Discussing such negative thoughts with those close to you can be of help.

Try to broaden and deepen your perspective. For example, observe motion carefully to understand its laws. That was how great Isaac Newton could discover them.

See how the apparent is explained by the things that may not be obvious. This will help you relate your observation and experience to deeper underlying realities.

Internet is also a wonderful resource to help you learn how to polish your study skills. Knowing about them can be of much help to you.

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It has enabled me to use focused methods that suit the one student that I tutor at a time. In a classroom, on the other hand, consideration is to use methods that help best possible learning of all in a group of significant size. So the methods used are mixed and the focus of a teacher’s attention is all students in a classroom.

In terms of student learning, results of my classroom teaching were always mixed despite my best efforts.

My teaching job ended in 2010. Since then, I have been only a tutor. Initially I thought that tutoring without teaching would restrict not just my career but also my experience of making others learn.

However, experience has shown that there is a bright side to individual handling of students in tutoring.

I certainly miss the learning community of a school. But what tutoring especially helps is also the most important goal of a school i.e. to take care of a student’s learning in detail and in depth.

The number of students I teach has certainly gone down. But the quality of learning of my fewer students has improved.

Most of my students also attend a school. So I am required to build on what they learn at their school.

Lack of group support in tutoring can be compensated by group support at school. I often tell my students how they can make their group interactions at school more effective.

Tutoring is personal and close. It may mean a lot in personal care, support, positive influence, counseling and mentoring – all intended to improve learning. How positive human emotions can be and should be enhanced by learning and its love. Tutoring is human interaction and relationship at its best.

]]>In a two boy race, one who runs slower is given a head start say of 10 meters. But how the one who runs faster can ever catch up with him. When the fast runner gets to the point where the slow runner started, the slow runner has moved ahead though by less than 10 meters. When the fast runner gets to this new position of the slow runner, he is ahead again by this time. In this way, the gap continues to narrow but always remains.

The reasoning here seems sound but it is against a very common real world experience. Anything that travels faster can bypass and get ahead of another that travels slower.

This paradox was proposed by a Greek Zeno of Elea (495BCE – 430BCE). It is well known by the name ‘Achilles and the tortoise’. Basic idea of the paradox is presented in differing ways by books and websites.

However, seeming validity of the argument would not effect applying mathematics to a situation like the one here.

If some of the variables are known, the exact time or distance when the two runners are together can be easily calculated using simple algebra.

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He had been good at math up to grade 5. Once in middle school in grade 6, he developed problems with math. His grades started going down.

I noticed two things in solution to math problems he carried out. He wrote solutions to math problems in a large letter size which lessened space between the successive lines in his work. This made his work look congested. Even worse, while writing with an ink pen, he cut his errors repeatedly and untidily.

Both these things apparently may not look to be that important.

I advised him to change these two things. I asked him to reduce the letter size of his handwritten numbers and words to leave more space. I also asked him to use an ink eraser instead of cutting errors.

He was one of those learners who believed in making an active effort. In his case, even this kind of rather distant change proved to be important.

He made effort and I helped him on his way to improvement. He took some time in overcoming his problems.

Human beings are naturally at home with cleanliness and tidiness.

Math is thinking that is naturally very clean and neat.

Math solution to a problem has a logical flow. A clear mention and understanding of every step to the solution is important.

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The figure below is a graph of a straight line. Let us see how to find out the specific algebraic equation for this line.

First the gradient or slope of the line needs to be determined. Only two points on the line are needed for this.

Any two points on the line may be used for the purpose. I will use the two points that are marked on the line. (1.5,0) is the x-intercept and (0,–3) is the y-intercept.

Using the gradient formula for two points

m = (*y*_{2 }– *y*_{1})/(*x*_{2 }– *x*_{1})

m = (–3 – 0)/(0 – 1.5)

m = –3 / –1.5

m = 2

Gradient can also be known by observing the line. As the given line rises from left to right, its gradient is positive. The two marked points clearly show that there is a vertical rise of 3 for a horizontal run of 1.5. This is shown in blue dashes lines. Gradient is obtained by dividing rise by run.

m = rise/run

m = 3/1.5

m = 2

Gradient for a straight line is constant. It remains same and never changes. P(x,y) represents any point on the line. Using gradient formula again with points (1.5,0) and (x,y).

m = (*y* – 0)/(*x* – 1.5)

2 = *y*/(*x* – 1.5)

2(*x* – 1.5) = *y*

2*x* – 3 = *y*

2*x* – *y* = 3

2*x* – *y* = 3 is equation of the given straight line.

Use indepth geometric visualization to improve your math learning. Geometry is highly imaginative and coordinate geometry is where geometry meets algebra. It is a relationship that is both interesting and amusing. It is your gateway into the territory of higher math.

There are alternative ways of finding out the equation of a straight line. Read an excellent and colorful article on MathsIsFun to learn more

Click to View Related Article on MathsIsFun

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Math is logical thinking about numbers and shapes. So to improve your math, you should improve your general thinking skills. Improve at things like asking questions and answering them, problem solving, organizing information and evaluating ideas.

Improve your problem solving skills in all subjects that you study. Remember that you are mature enough and all such problems at school level are short and not that difficult. This also applies to math. Also learn to cope with the psychological side of your problems in learning math. Think positive, be well-organized and don’t lose hope.

It is necessary to practice math regularly. Practicing solution to math word problems can be of much help. See the related article entitled How to Make your Math Learning Effective.

Read simple money and everyday math word problems and try to find solutions to them in your head. Working on math in your head repeatedly for short periods of time can be very helpful. You can even think of creating simple math word problems of your own.

Focus on non-word problems. They relate openly to math theory and concepts. Learn math concepts, their organization and their interconnections. Improve your handling of pure math symbols and logic.

Know what math concepts are and don’t mix them with math applications. Math concepts are much less compared to its applications. You are required to learn and memorize math concepts only. They are then used to solve variety of a very large number of math problems.

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“The essence of math is not to make simple things complicated, but to make complicated things simple”.

Math started as a problem solver and it is a great way of viewing school math. See the article entitled How Math Began.

Math is of enormous practical use. Living without math in prehistoric times was uncivilized, thoughtless and savage. It developed naturally as a necessity as living became more and more civilized.

Math provides solution to problems from everyday to business to scientific.

Word problems in school math cover lot of everyday uses of math. Some simple business and scientific uses of math are also covered in school math. This shows how greatly useful math symbols and its logic are. Examples of math symbols are number symbols such as 1, 1.5 etc. and operation symbols such as +, –, × etc. Without math, solutions to such problems would be either impossible or very hard.

Many math learners are good at thinking and reasoning skills but they have problems with math symbols and its subtle reasoning.

Is the nature around us simple? In many situations, it is far from simple even to probe the nature for scientific knowledge. Costly laboratories and equipment may be needed for scientific experiments.

Math has no laboratory or experiment.

Word problems have similar solutions. Many of them are solved using same logic of simple algebra equations.

While solving such problems, appreciate how simple number logic and shape logic rescue the situation so perfectly and so gracefully.

Here is another quote to end this article. It is by John von Neumann – a Hungarian-American mathematician

“If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is”.

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**Example **

A new small business bakes and sells biscuits. The fixed costs of the business are $400. The cost of making each biscuit is $1. The business plans to sell each biscuit at $1.5. Using graphical method find out the following:

- Loss to business if 300 biscuits are sold;
- The exact number of biscuits that the business needs to sell to cover full cost;
- Profit made by the business if 1200 biscuits are sold.

**Solution**

Expenses = Fixed Costs + Cost of Number of Biscuits Made

So total cost* y* for *x* biscuits made is the equation

*y* = 400 + *x*

Income = 1.5 × Number of Biscuits Sold

Expressed in equation form

*y* = 1.5*x*

*y* represents money in dollars whether it is expenses or income. *x* represents number of biscuits.

Both equations above are linear and their graphs are straight lines.

Cost of making 500 biscuits = $400 + $500 = $900

Cost of making 1000 biscuits = $400 + $1000= $1400

This provides coordinates for two points on the graph of the expenses equation. Since cost is dependent on (or function of ) number of biscuits made, number of biscuits is taken as the first of the two coordinates. Coordinates of two points obtained are (500, 900) and (1000, 1400).

Income when 500 biscuits are sold = 1.5 × $500 = $750

Income when 1000 biscuits are sold = 1.5 × $1000 = $1500

So the two points on income equation graph are (500, 750) and (1000, 1500).

All four points are shown as red dots in the graph below.

The black solid line represents expenses and the red solid line represents income.

The two lines meet at C where income equals expenses. Number of biscuits at C is 800. This is the number of biscuits that the business needs to produce and sell to cover full cost.

At 300 biscuits, income is lower than expenses by 250. This is shown by the purple dashed lines. So the business has a loss of $250.

At 1200 biscuits, income is greater than expenses by 200. This is shown by the blue dashed lines. So the business has a profit of $200.

Click the link below to view some excellent videos at KhanAcademy. They teach solution to word problem using graphs.

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