## Tuesday, 21 April 2015

### Math Problem Solving Tips

An Experienced Math Tutor's Tips for Solving Math Word Problems
As a teacher and math tutor, I have seen many students struggle with solving word problems. Who of us doesn't remember being asked questions about 2 trains leaving different stations at different speeds, and being asked to figure out when they will meet? While some of us love these types of problems, many others have great difficulty tackling these sorts of questions. Often we just don't know where to begin, or what strategies we should be using to try to find an answer.

This article is intended to help people who struggle with word problems, by providing them with a strategic approach and a set of tools to use when encountering questions of this sort. Like most writings on Problem solving, this article leans heavily on the ideas and writings of George Polya (1887-1985) a mathematician who refined many of the ideas for problem solving that are in common use today. His classic book 'Solve It' is a must read for the advanced student - a simplified system is provided below:
An Approach to Problem Solving:
Start by being sure that you understand the problem - I can't tell you the number of times that teachers see students turn in copious amounts of work that fails to answer the question that was actually asked. This is often heartbreaking for both the student and the teacher.
Always try to restate the problem in your own words. If you can't rephrase the problem, then there is a good chance that you may not fully understand it.
Be clear on what you need to accomplish. Think about what information you will need. Is there any information missing? Can it be found by using the information that is present?
Make a plan - once you are confident that you know what the question is asking and what data will be needed to answer it, start thinking about how you will tackle the problem
Think about if you have seen a similar question before. If so, how did you solve it?
Solve a simpler problem - if some parts of the problem are not clear try simplifying it and solving what you know. This is a form of 'divide and conquer' - once you have solved a part of the problem it is not uncommon for the answer to the mysterious part to suddenly jump out at you. You can also try simplifying the data - if the numbers are too big and awkward then make them smaller and simpler. This allows you to get clear on the steps and processes involved in solving the problem
Draw a picture - often using a diagram will help to organize the data in a way that allows your brain to create additional connections between the pieces and possibly spark some ideas.
List your data - can you put it in a table? Can you organize it?
Can you spot a pattern?
Do you know a formula? Are there any formulas that you know that could be relevant to the problem? Think about how you could possibly use them in this particular instance.
Can you work backwards? Sometimes approaching a problem in the other direction can cause your mental light bulb to turn on!
Guessing is great! Take a guess if you can and then check if your guess is close. Many of us adults were taught never to guess when we were in school - this is unfortunate as guessing and estimation are powerful problem solving tools.
Carry out your plan - you've got your plan so now it's time to execute it. Use one of the approaches above that you think fit the situation best. Don't be afraid to drop one approach and try another if you don't seem to be making headway.
Look back - is there another method? Could you solve it a different way? Is there a general principle that can be applied?
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### What Are Some Examples of the Singapore Math Method?

What are Some Examples of the Singapore Math Method?
Mathematics can be one of the greatest academic challenges a child can face. By introducing Singapore Maths, Our School has integrated into their curriculum a way to reach all students at all learning levels. Singapore Math is a visual method, using pictorials to describe concepts.

Instead of using numbers to describe a problem, Singapore Math uses pictures. These pictures are presented in stories that can aid in the learning process. A child may see a picture of four birds on a branch and two birds flying towards it, then they will be presented with the problem 4 + 2 =? Another addition problem may illustrate two children with two toys in front of each of them. They will be asked how many toys the children have together and be presented with the problem 2 + 2 =?
A child may see a picture of four birds nests, and each nest may contain four birds. They will be asked to solve the problem: there are (blank) birds in four nests. Being able to see the amount of parts in each whole as an illustration, the child can easily count and solve the problem.
Having experienced this visual style of math, students are then introduced to mental math. The pictures are less descriptive and the problems are more complex, encouraging a student to use their imaginative power to solve the problems. The student may receive three possible answers; three groups of circles with a numerical value in each of them. The student will then be asked to solve what 40 less than 578 is and asked to pick from the three answers available. In order to solve this problem, a mental strategy must be used. Students are encouraged to develop their own mental strategies and share it with others.
As the education process moves on, they will be required to rely on their own mental abilities more and more. The pictures will be replaced with word problems, and ask to solve. A student may see the following problem in words:
125 children participated in a math competition. 54 of them were girls.

How many more boys than girls were there?
Instead of being shown the two steps used to complete the problem, the student must determine what they are. Students are encouraged to refrain from drawing pictorial models and use equations to solve the problem.
The country of Singapore has placed in the top three of when tested in mathematics for years for various. This method has been proven by the test of time to provide a strategy for math that works for all students.

## Monday, 20 April 2015

### Help With How to Solve Math Problems

How to solve math problems can be a particularly daunting task for many students. Are huge number of people have a lot of difficulty with math although there are a number of ways which you can get round the main problems and if you keep positive and dedicated, you should certainly be able to do quite well.

Firstly, it is important not to be afraid to ask questions and write down anything that you're not sure of. The difficulty that many people have with mathematics, is that they have to be a hundred percent focused. This can be difficult and if you lose your concentration for a moment, you will often have to start over again.
This can be really frustrating and can severely hinder the learning process. This is where it is extremely important to keep notes at all times. As soon as something comes to your head, write it down. It is always a big mistake to only right down the answers when they come to you, if they come to you. You need to be able to study the problem intensely and when you have the first clue of how you might be able to solve it, you should write down their clue as clearly as possible.
You should also spend a considerable amount of time practicing. This does not mean that you have to spend several hours in one time; quite the contrary. You should spend maybe half an hour a day or even less but as long as it is on a regular basis, revising over what you have learned.

This will help program it into your mind and you will better be able to cope with the problems that arise in tests and exams. Having regular that short revision sessions are essential to any learning process.

A word of caution here. Don't punish your child when they initially struggle with the activity, nor should you or others say to them, "That's wrong." Instead, try using phrases like, "Are you sure? Let's look at that again." Keep trying until the child gets it right, then clap and make a big deal out of the correct identification just like you did (or may be doing) with potty training. The idea is to build links in the brain, not create more barriers, which negative language can cause. Soon your little one will be marching around telling everyone they know that they are a big girl/boy because they can put on their own shoes! As a parent, you may never know which small accomplishment will provide the breakthrough that your child needs to stop complaining and start getting excited about learning.
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## Thursday, 16 April 2015

### Mathematics Lessons - Find Them Online and Get Your Problems Solved

Mathematics is a subject that people use throughout their lives and most often unknowingly. As a kid many people were afraid of the mathematics lessons and this continues till date. Kids fear the calculations and therefore get low grades in their respective classes. Most of the lessons and concepts in mathematics is not understood or conceived by kids just because they fear doing them. Today, learning mathematics is different and the main reason is that the style of teaching has been changed so that more and more students are able to conceive the concepts and grasp them in a better way.

Most of the schools give stress on the pattern of teaching so that more and more students enjoy learning mathematics and other subjects. Many have left the traditional way of teaching as there are many drawbacks of that system. The teachers are being trained in that way and learning is more related to activities rather than giving lectures to the students. As an adult, every person has to face mathematics every now and then in life. It is not just that you used the calculator or believed the salesman at the shopping mall and paid whatever was asked.

If you will analyze the facts you will understand that you need mathematics to sustain in life from day to night. In fact, this keeps us disciplined and helps doing a lot of work on time and helps us get some rest as well. Learning mathematics is important at work and business. We do plenty of calculations daily and we cannot ignore the omnipresence of mathematics no matter to what post we belong. If you think about anything in life, you will not find it free from calculations.

From business transactions to money making, from counting burgers you ate to calculating and managing things in your limited salary, you need mathematics in every aspect of life. So, if you find that you are poor at calculations, you can easily opt for learning mathematics by joining classes online. Remember, there is nothing to be ashamed of because you should not feel pity for the person who cannot count but for the one who refuses to count.

So, learn and practice problem solving maths from the time you are in school so that you do not have to face embarrassment afterwards in life. The most remarkable thing about today is that though math is vital in life, there are many ways in which you can master things nowadays.

### Online Maths Tutoring - Get To Know Its Benefits

With the development of the internet technology and with the increasing number of people using this technology, nowadays, everything is done online and this is applicable to the field of education as well. Since the internet has the capability to shrink the world into a small room, many websites are offering online maths coaching service these days. As most of us know, mathematics is the toughest subject, but when its concepts are understood, it is the easiest subject to score good marks as compared to any other subjects. So, if a kid is struggling in this subject, if he is made to understand the subject clearly with the help of tutors, parents can enable the kid to get good marks in this subject, which has so far been a nightmare for their child.

Above all, in the present circumstances, parents are so busy in their work so they do not get time to teach or assist their child in his/her studies and this has also made the importance of online tutoring.
This method of teaching is highly suitable for children due to its flexible time schedule and here are the other benefits offered by this method:

Convenience: Convenience is the biggest benefit of online method of tutoring as the students can take their lessons right at the comfort of their home and they need not carry their books or notebooks to a tuition center located at a distance place after returning from school. They can just sit in front of their system and can visit the website of the tutor and can get their doubts in maths clarified.

Flexible timings: Generally online maths coaching centers offer coaching to the students on their convenient timing and this has made this method more popular among the students and their parents as well. Due to this flexible timing, students can concentrate on other subjects as well. This will enable them to score well not only in mathematics, but also in other subjects as well.

Global location: When it comes to online tutoring, students belonging to any country can learn from any tutor offering coaching from any part of the world and this is the greatest benefit that can be enjoyed by students.

Cheaper: Online tutoring is cheaper as compared to regular tuition centers since with the former method, children can save on traveling expenses and also on coaching fee as well. Online tutors charge lesser as compared to regular tutors as they have lesser overhead cost.

## Wednesday, 15 April 2015

### Advantages of Primary School Maths for Students

These days, maths has become one of those subject that everyone can be seen to be going for since it not only allows individuals to acquire enhanced learning but it also is the best way for them to have a bright future. While the subject may be dull and sometimes quite technical, it still must be studied at all costs as it truly has a wide range of many benefits to offer in both the short as well as the long run. Primary school maths has been labeled as the best way for children to actually have a bright future later on. Studying the subject at primary school level has a lot of advantages, all of which are unique in their own way.

New Subject to Learn
One prominent reason for giving a lot of attention to primary school maths is the fact that it enables students to have a good introduction towards the subject. This is due to the fact that at this point, only the basics of the subject are covered, which are quite fun to learn and study on a day to day basis. Since the subject is not as difficult at this stage, students can actually develop a lot of fondness for it right from the very beginning. This tends to help them in the process of opting for the subject when they reach high school and later on, within universities.

Enhanced Knowledge of the Subject
Studying mathematics right from the beginning, which is in primary school and before that too, is the best way for students to know all there is about mathematical concepts. This is what maths is based upon and in order to do well in the subject, it is highly important for them to see how these concepts work and what they are all about. Primary school maths tends to lay out all mathematical concepts as well as theories and everything as such in brief detail, which is enough for students to be able to understand the extensive part of the subject later on in their lives.

Enhanced Reasoning Power
Students get to learn many things by studying maths at primary school level. One of these exclusive things includes enhanced logic and reasoning skills. The subject is known to be an immensely practical one, which is why it is given so much importance in the first place. Students can use their knowledge of the subject in order to enhance their understanding of logic and also go on to improve their reasoning skills which eventually will help them in a lot of situations throughout their lives in the future.

High End Career Options
On the other hand, learning maths at this stage allows students to be aware of all that the subject has to offer in the short and the long run, most importantly. In the future, mathematics is the kind of subject that has various career options and that means more choice and ultimately success for an individual. Hence, studying the subject from such a level is something that enables students to see all that the subject has to offer. It is through this subject that children can realize that they have a shot at a bright future that allows them to enter fields related to maths, IT as well as science for that matter.

Primary School Maths – The Conclusion
For all that it has to offer, studying mathematics at primary school level is definitely worth it, especially when it has so many short term and long term advantages to offer. Teachers should give students special attention while teaching this subject as it can be complex at times and parents must see to the fact that their children can learn the subject and everything related to it right from the beginning as it will definitely be worth it later on.

## Monday, 13 April 2015

### Teaching Kindergarten and Preschool Math

The way math is presented to children makes a tremendous difference in their success as learners, as well as your success as an educator. Children need to take part in activities that encourage them to experiment, to investigate, and to record their observations.
Preschool and kindergarten students always need to have things to move around or manipulate in order to make sense of math concepts. In the education world these are called "manipulatives" and there are a great assortment of these available, such as blocks, counters and pattern blocks. Give children ample time to play with the manipulatives in order to satisfy their curiosity about the materials before attempting to use them to teach a math concept. Introduce new math vocabulary as the children play, as this will help them when they participate in teacher led experiences.
Keep structured lessons short to begin with and do not assume the children understand your expectations. Spend a week teaching proper use of materials and proper cleanup. Teach the children to use mats to identify and define their work area.
The following steps work well when teaching young children. First, demonstrate the math activity two or three times before you give the children materials. You will quickly lose the children's attention if you pass the materials out first. Second, give materials to the children and ask them to try the activity. Check to see all have understood the concept and are experiencing success. Assist children that are having difficulty.
After a few days of the same or similar lessons, record your math experience as the children observe. Keep it simple. For example, after a lesson making repeating patterns print the words, I made a pattern. Say, "I used a red block, a blue block, a red block, a blue block." Draw the pattern and color the blocks. Pass out paper and have the children draw what they did and record words using their knowledge of letters and letter sounds. Recording the activity gives children an opportunity to share and solidify their knowledge.
Visit my kindergarten site for ideas, activities, tips, games and skills lists about teaching preschool and kindergarten maths.

### Suggestions in Solving Math Problems

Mathematical problem solving are number problems. It is all about injecting the right strategy and process in arriving at an answer. It has two stages - the problem execution and the problem representation.

Define the problem first and set a strategy on how to solve it. Be analytical.
Suggestions to Help Solve Math Problems:

- Pay attention in class. Avoid unnecessary distractions that will take your concentration away from the lesson. Confer with classmates at the end of the period, not during class lectures.

- Repeat in your mind the things a professor says.

- Taking notes is often not good while a lecture is ongoing. It divides your attention. Focus on the lecture first, and jot down the important points later.

- Solve as many similar problems about a subject for mastery.

- Some problem solving maths have more than one method of solving. Learn all the methods and see what is least complicated for you.

- Get a copy of the solution of a problem you find difficult to solve. Study the solution carefully.

- Solve many problems. It is the only way to practice.

- Understand and master basic principles and ideas. These are the foundation of even the most complex problems.

- Understanding the logic behind helps in memorizing various formulas and theories.

- Never hesitate to ask a teacher. They are ready to help.

- Ask help from friends and classmates.

- Get a tutor if needed.

- Read supplements about the subject. Do not rely on class lectures alone.

- Hints are sometimes better than giving up immediately.

Mathematics is fun to learn. Do not be easily scared at the sight of numbers. Mathematical problems all require simple logic and analysis. Do not be pressured too much to excel in the subject immediately. Do not be easily discouraged. Devise ways to make studying math a fun learning experience rather than a tedious task to do. When you begin to stop thinking about grades, true learning begins.

### Why Preschool Math Counts!

One of the most critical mathematical concepts is cardinality: the ability to understand quantity. Research suggests that cardinality is innate; infants are born being able to subitize, which means to visually distinguish between different amounts.

How do we prove what infants know? Apparently, it's all in the eye movements. In 1992, Nature magazine published a study that showed 5 month old infants could recognize the consequences of adding and subtracting objects. Similar studies have replicated the results. Regardless of whether you accept the premise that infants grasp cardinality, you have anecdotal evidence that your preschool child does. Your child demonstrated an appreciation for cardinality the first time he or she looked up at you and asked for more!

All this is well and good, but how do we turn the toddler asking for more stories, more ice cream or more glitter into a successful math student? Here are a few preschool maths activities that you can build into everyday routines to develop and practice critical early math concepts.

Count things your child can hold or touch
So many excellent online preschool math games, parents sometimes forget the importance of manipulative. The ability to make the one-to-one correspondence in more advanced cardinality (okay, counting) is strengthened by a child's ability to hold and manipulate the items being counted. Research shows that much of a toddler's learning is tactile and kinetic, so while technology is an outstanding asset in early learning, it can only augment, not replace, manipulative and kinetic experience. Work counting in whenever possible: count books with your child as you put them on the shelf; count blocks as your child stacks them; count snack pieces as you hand them out. Remember, a toddler learns with his or her whole body: you can also count as your child climbs stairs, hops or claps. That being said, preschool math games online can engage children through sound as well as sight. When you use technology, choose games that reinforce counting with music or sound effects.

Don't be in a rush to move to formal addition and subtraction. However, you can lay the groundwork by adding items to a set or taking some away and saying, "Now how many?" A child with a strong foundation in the mechanics of addition and subtraction will make a smooth transition to the more formal mathematic expressions of it.

Most importantly, remain patient and low-key. As toddlers learn to talk, we guide them to correct pronunciation and syntax; we don't sit them down for "talking class."  Similarly, if you "speak math" in the course of daily activities, your child will, over time, build a foundation that will add up to math success in school.

## Wednesday, 8 April 2015

### Kindergarten Activities - Creative Kids Math

How do you identify creative kids?

1. They are imaginative, resourceful and uninhibited.
2. They are open to new ideas and see things in a different way.
4. They are independent in thinking and social behavior.
5. They are inventive and good at solving problems.
6. They love challenges and are easily bored with routine and mundane tasks.

Kindergarten activities which develop creative maths thinking encourage the kids to think critically, using their existing knowledge to explore new ways of thinking. We can incorporate language, music or math into these activities and for this article we will discuss on using math to develop creativity.
Whenever the word math is mentioned, numbers and formulas come into the picture. Math is more than just number crunching but when it is being introduced to kids creatively, can improve skills like reasoning, logic and problem solving and also widen the kids understanding of Math to a wider scope as listed below:

1. To enable the kids to sort objects in a logical series according to size, shape or any other characteristic.Find objects of different shapes like a book, a clock, a piece of sandwich or pizza, a photo frame, a ball, a pencil case. Put them together and ask the child to group them according to their size. For example a book is a rectangle, what other objects here are rectangle shapes.

You can invent different kindergarten activities by finding objects of different sizes or talk about animals and ask them what animals are big and small.

2. To enable the kids to understand the concept of numbers by letting them have direct experience with objects as the kids will discover that numbers are not just digits but extend to our everyday lives.
Kindergarten activities which kids under five need are songs, rhymes and finger plays that include numbers like Little Indian Boys/Girls, while singing, finger play with them, show your fingers while singing One Little, Two Little, Three Little Indians and so on.

You can also ask questions like - Mummy bought 5 apples and put them in the refrigerator yesterday. You ate one apple and Daddy ate two, so how many apples are in the refrigerator now? Allow the kids to answer and ask them to check the refrigerator to see whether they are correct.

3. To develop their spatial skills by discovering how to fit things together, take things apart, rearrange things and navigation.

Kids with well developed spatial skills are very creative, dramatic, artistic and musical. Some kindergarten activities which encourage spatial skills are playing with Lego, tangram, mazes, play dough and chess.

Engage your kids in creative thinking activities the whole day while you are preparing your meals, gardening or clearing your laundry by asking open-ended questions which are worded in such a way that there is no one correct answer. An example is while clearing your groceries asks your kids what they can do with this tomato. Open-ended questions like this engage the kids in divergent or creative thinking to come up with a whole range of brilliant and imaginative ideas.

## Tuesday, 7 April 2015

### Best Paying Careers to Pursue after learning a lot of Concept Maths

Those who study humanities subjects end up making a lot of money as they mature up in their careers. However, early on they do not find a very high paying job due to softer skill set. This can be better understood with an example of an engineer and an admin officer. The engineer grows old to become a senior engineer perhaps whereas the other person becomes a manager and possibly an even senior chair holder. Learning math is a tough thing to do and as compared to the scarce math skilled labor in the market, the skill’s demand is huge. This makes every person who knows math well a well demanded individual. Here are a few occupations that pay handsomely if chosen.
Actuary:
Actuary firms hire actuaries and are responsible for making calculations and analyses of data based on national and international levels. For instance, these firms tell the governments how many people are going to die in a certain country in a certain year. In addition to governments, the clients can be corporations. An actuary can make an average of \$70,000 each year that is a good enough pay.
Aerospace:
A person with good concept maths skills, can become an aerospace engineer. This field requires exceptional calculation skills and hence any person who has them can go on to become an engineer. Additionally, knowledge of physics is also a requirement in their field. On average, an aerospace engineer makes more than \$100,000 every year.
Statisticians:
Basics of statistics are easy, but as the level rises, it becomes more and more complex. Statistics is used not only in the calculation of numeric fields but also in the most theoretical of subjects. For example, the entire process of research, in almost every field is dependent upon the statistical analyses of data received from samples. Statistics teachers are needed for service on all levels of education, from the kindergarten all the way up to the doctoral level. In addition to that, governments and research firms hire statisticians for calculations and quantitative analyses. An average salary is about \$75,000 per year for statisticians.
Mathematicians:
It is strange to know that mathematicians are employed more elsewhere than in educational institutes. Having said that; they are employed in large numbers at audit firms and in brokerage houses due to their exceptional skills of making calculations and analyses of the data received as output. A mathematician makes an average of \$90,000 a year. However, if one’s concept maths is very good, they can get certified by accounting and auditing bodies to become financial analysts. Yes, chartered accountants are amongst the highest paid workers. Basically they too are math experts who develop a specialty of dealing with numbers related to asset valuations, liability calculations, and interest and so on. A financial analyst has one of the most important jobs in any corporation and for that matter, gets paid an average of \$75,000 a year.
It is very clear that no skill goes un granted and unrewarded. Learning math is very beneficial and in the world of today where competition is high and jobs are very few, it is better to develop an interest in fields that pay higher instead of following low paying “interesting” careers. Being good at something very few people are is beneficial as it puts an individual a class apart from others. It does a world of good to the wallet and also benefits a person as he goes on to mature up in his career. From teaching to serving in a corporate or a government agency, math skills always benefit big time.

## Saturday, 4 April 2015

### Some Habits to Adopt – Teach Math Enrichment Classes Efficiently

Teaching math is not all that easy. Other, more theoretical subjects are relatively easier to teach as compared to the highly calculative and numerical subject of mathematics. Teachers always try their best to convey their message in the best possible manner, since it affects both their career goals and their sense of accomplishment of their goals as teachers. While teaching any number based subject is tough, here are a few habits that one can develop and then expect them to groom them as teacher.
Letting the Concepts Make Sense:
Math cannot be crammed and needs to be very clear concept wise. Ever wonder why the concepts in this subject keep coming again and again each following year in the text books as the student goes on to get promoted to the next classes. The reason for this is that it takes several years to grasp a concept; hence, the curriculum of this subject is made such that it gradually clarifies the mind of students. The key is not to just focus on the “how” something works in this subject but to also focus on the “why” does it. With this comes care of the level of students under consideration. Being a teacher, it is an absolute crime to simply blindly trust the text book or a help book especially when it comes to calculations. Each question needs to be solved so that if any student has ambiguity in any question, there is a ready solution of it with the teacher.
Make a Goal:
What should the goal of a teacher be? Should it be to simply finish the course up by the end of the school year, or should it be to teach their students valuable things that would benefit them in the years to come in study and in career. There is nothing wrong in having the former as one’s goal with an exception that the teacher does not forget the duties that he or she has. However having the later as goal makes a teacher worth gems. The best teachers always make a long term plan for their students and stick to it for one reason only, that their students are better able to deal with every day complexities of the world. A teacher of math must become a building block in the academic structure of students helping students build their further studies up on the knowledge given to them.
What Tools to Use?
Those who teach maths enrichment classes make a lot of money, they really do. But their effectiveness is confined to the type of tools that they use in the process. Math cannot be taught on presentation slides, it is a board dependent subject that requires thorough practice. For geometry teaching, bigger compass, D and scales are available that are used for accurate drawing on bigger boards. A good teacher is to always keep along a register to note and solve questions and calculations that are not being solved by the students.
Making Math a Living:
Teaching maths enrichment classes can make a person very rich over time especially when it comes to teaching poor calculation skilled individuals. But to really cash in, one needs to love math to its core and should never feel tired of it. It is all about exploring new formulas and methods for solving the same questions over and over again. Doing this keeps the excitement alive and also equips the teacher with wider knowledge base and experience. Going through a number of math books is also essential in case a person wishes to make a publication in the field.

### Why Attend Maths Tuition Class

Studying mathematics is one of the biggest challenges that exist these days. As the subject is complex, students have been highly recommended to remain a lot more focused on it than any other subject out there. Due to this, they should give more time to the subject in order to understand it well. However, a lot of times, students come across many other problems which they may not be able to solve alone. In such cases, attending maths tuition class becomes rather necessary for everyone. These classes are definitely the best way for gaining more knowledge regarding the subject and have been proven to provide positive results for many students worldwide.