Why Study Math? - Functions and Rules

One of the most important concepts in mathematics is that of a function. Although the topic of function can appear abstract, it is nothing more than a specific rule between two sets of mathematical objects. These sets are usually numbers, but they do not have to be restricted to such mundane entities. The sets might consist of more interesting objects, such as matrices or vectors. This notwithstanding, a function is nothing more than a rule that associates with each member of one set another member of the other set. Here we discuss this exciting concept in a little more detail so that the next time you see or hear about it, rather than avert your eyes or go cowering away in fear, you jump right in on the conversation.

Before we introduce the concept of function let us define what we mean by a set. A set is simply a well-defined collection of objects. Sets can be defined by listing their specific elements as in

S = 1, 2, 3 or by definition such as S = n is an integer to define the infinite set of even integers. A function is simply a rule between two sets, such that this rule assigns to each element of the first set, call it set A, a unique element of the second set, call it set B. For example, let set A = 1, 2, 3 and B = 2, 4, 6. We traditionally let the letter f stand for a function. We can define a function f from set A to B such that we associate 1 in A with 2 in B; 2 in A with 4 in B; and 3 in A with 6 in B.

If you have not realized it yet, we are doubling the elements of A. That is the function defined from set A to set B is that which multiplies each element or member in A (which is usually denoted by little "a") by 2 to get each element "b" in set B. That is for each a in A we get b in B equal to 2a. Thus 2 = 2(1); 4 = 2(2); and 6 = 2(3). We write this function as f(a) = 2a. Remember that f(a) produces an element in the second set B.

In mathematics and particularly algebra, we often see the notation y = f(x). Here x in X is the first set, completely analogous with set A above; and y in Y is the second set, completely analogous with set B above. As you may realize now, functions between the letters x and y are common and x and y stand for the axes of the cartesian coordinate plane or x-y system. Depending on the complexity of the function or rule, the function y = f(x) can usually be graphed using graph paper and the pictorial relationship between the two sets X and Y can be seen and studied.

It is common to come across the terms "domain" and "range" when talking about functions. The first set in a functional relationship is called the domain and the second set is called the range. The notation f:X->Y is the symbolism which stands for the function from set X (the domain) to set Y (the range). The letters X and Y are often replaced by other characters, and it is not uncommon to use the letters g, H, and z for functions. As mentioned previously, X and Y are most common in functional notation because of convention in naming the axes in a coordinate plane by using these letters.

Functions occur throughout the realm of mathematics and indeed life. Specific functions model many real world phenomena and help solve many practical problems. For example, the function
s = -16t^2, between s (distance) and t (time) models the distance a body will free fall in time t.

The function P = A(1 + r)^t, between P (principal) and t (time) models the amount of principal accumulated after an initial deposit A at interest rate r.

Functions give us a unique opportunity to observe what we see around us---as in nature---and come up with some kind of rule which helps to explain what we experience. Without this utile concept, we would certainly not understand the world as well as we do. Functions hold the key. So the next time you see y = f(x) or b = f(a), remember you have entered the realm of functions. And oh what an interesting realm it is!

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How to Start a Profitable Home Tutoring Service

Starting a home tutoring service is a small business that does not require much start-up costs or training. Essentially, this service is an excellent business for stay-at-home moms who love to deal with children and make some money on the side. Apart from that, this home business provides time flexibility as the tutor would only need to spend a few hours each day on tutoring. Of course, more classes can also be scheduled according to personal preferences.

In fact, a tutoring business can be conducted either within the comfort of the tutor's home or at the home of the students. This essentially eliminates the need to pay for rental costs of any kind, with the only cost being transportation costs and the time spent on the classes.

Start Up Costs and Financing Sources:
Starting a tutoring business does not require much in start up costs. In fact, the bare essentials that you need to purchase are pencils and paper as well as some books, all of which will cost you less than $20.

Pricing Guidelines for Service:
Tutors normally charge between $15 and $40 an hour for their services. Rates are dependent on the subjects and the levels that are being tutored as well as the location where the services are offered. Naturally, services offered in larger cities will cost more.

Advertising and Marketing:
Advertising and marketing your tutoring service is one of the most crucial steps in order to ensure success in your business. In fact, there are many ways in which tutoring services can be marketed. The first thing that you should do is to create a profile for yourself. List down your credentials, including the details of your degrees as well as any previous tutoring experience that you may have. Apart from that, other teaching related experience such as peer tutoring while at the university may also help in building a strong profile.

Next, think about which area of study that you are interested to teach as well as the specific age group. Most tutors specialize in specific subjects like Arithmetic or History, while others may deal with just elementary students.

Once you have your resume all ready, you are then ready to approach the schools to market yourself. Inform any school teachers that you know about your expertise, experience and the services that you are offering. This is as many parents enquire with school teachers on where they can send their children for tutoring, which makes teachers the best people to promote you. Alternatively you can also approach the school counselor or principal about your services, as they may be constantly seeking tutors to recommend to the parents of children with problems in their studies.

The next thing you can do is to stick a small ad on bulletin boards located in stores around town. You can find these boards in laundromats, convenience stores and supermarkets. Some parents may notice your ad and call you up for a tutoring engagement. Apart from that, you can even design a nicely printed flyer, highlighting your services and credentials as well as your contact information and send them out to mail boxes within your area.

Another thing that you could do is to contact a local home school group in your location. Many parents of home schooled children require tutoring in certain subjects and may be seeking tutors for this purpose.
Recommended training, experience, or needed skills:
A tutor does not necessarily need to have a degree in teaching in order to be qualified for tutoring. However, teaching experience will help in building a profile, as parents will be more confident with your abilities. Furthermore, as a tutor, you need to seek out the latest syllabus and texts which are being used in classes so as to ensure that what your teaching is aligned with the current education system.

Additionally, a visit to the library could help in obtaining lists of books specifically on tutoring your areas of focus. Furthermore, you will be able to find a wide variety of material to present to your students in class from within the local library. You may even obtain creative teaching and tutoring ideas that will help draw the attention of your students during class.

Income potential:
The potential earnings from a home tutoring service are really dependent on the efforts and the commitment of the individual. If more time were allocated to tutoring, then more income will be generated.

There have been tutors who have successfully made an annual income of $10,000 to $15,000 tutoring just 20 hours a week from home.

Target market:
Students from Elementary Level up to High School

Success tips:
One of the factors influencing the success of a home tutoring service is the level of education and guidance that has been provided to the students. Usually, this is measured by the results attained by the students. Once a student scores an 'A' in a subject area that he or she has been poor in, your effective tutoring work will travel quickly by word of mouth as parents will make good recommendations to other parents. In fact, word of mouth is the channel that facilitates rapid growth in your business.

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Tutoring Services - 1st Grade Reading Tutoring Exercises

First grade is a great year for students. This is the year that they really get to explore the world of academics. Reading is one subject that first graders are officially introduced to. It is important for first graders to acquire the basics of reading during this grade otherwise they will struggle with all of their subjects. However, while many students learn the basic skills required for reading at grade level and above, many students struggle with reading at first. Fortunately, there are 1st grade reading tutoring exercises that tutoring services and tutors can complete with students to help them develop the reading skills needed to become proficient readers.

Option No. 1: Flash Cards
One of the most effective reading exercises that you can offer first graders is flash card drills. These drill will pair graphics of the word with the written form of the word. Flash cards work well because they use repetition to help the student to quickly associate the written word with a graphic. Flash cards are popular with first graders, their parents and teachers because they are easy to make, inexpensive and easy to store and use.

Option No. 2: Storytime
Introducing first graders to great literary characters is a great way to (1) peak their interest in reading and to (2) develop their reading skills. While they may not be able to read all the words at first in the story books that they select, as they read along with you they will pick up more and more words until they are able to read you the book from cover to cover.

Option No. 3: Composition Drills
Repetition is key to learning how to read and to write. Because of this you can help first graders to develop their literacy skills by having them complete journaling exercises. Their journaling exercises are not going to be elaborate stories, instead they will most likely be lists of vocabulary words and phrases.

Option No. 4: Magnetic Word Exercises
Another fun reading exercise that you can complete is to use magnetic words to put together sentences. This can be a fun project to do with first graders. For example you work with your first graders to write a story or describe a scene using magnetic words on a metal board.

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Where to Get the Best Online Math Tutoring Courses At No Cost - Don't Rely on Internet Marketers

Not long ago, I was reading some articles online written by someone who owned a website peddling math tutoring, and I was taken aback by the advice, and realized that the writer had done nothing more than confuse any student who might have come to that web-article. Part of me wondered if it was even written by a human, it almost looked to me as if it had been written using derivative software, the type that spins an article or content from somewhere else and re-arranges the sentences to make it appear to be genuine unique content.

Indeed, I suppose derivative content generation software might fool some people, some of the time, but I'd say it is a very unwise idea for teaching or tutoring math because it's very hard to describe how to do a math problem using words without symbols.

Now then, I understand that a math tutor might have a hard time writing articles online, because math has a specific set of rules and standards which must be followed and writing proper English is a completely different set of skills some of which must seem very arbitrary, ambiguous, and even bathed in hypocrisy sometimes to a mathematic mind; "it's all wrong they might say," as the rules are so full of holes and exceptions, and then there is writer's prose on top of that, which trumps all.

One great thing about reading articles on mathematics is that for anyone in the field it is quite easy to immediately spot a phony. Of course, the opposite is also true, anyone who isn't an expert, probably will not know the difference. So, to that point, I can see why a gentleman who is an accomplished "internet marketer" is able to survive, perhaps even thrive posting garbage online content. However, it doesn't seem to pass the Rotarian smell test; "Is it fair for all concerned" - because it really isn't you see.

Okay so, rather than settling for bad online math articles, I recommend that you search online; "The Khan Institute" and start watching all the math videos posted. I completely guarantee you, that if you watch each and every one of those videos 10-times each giving them you full attention, while sitting with a pad of paper and a pencil, trying it as you go, that once you are done, you will be in the top 1/10 TH of 1% of the math experts in this entire nation. And don't worry they are free.

Indeed, I hope you will consider all this and be careful from whom you take advice online. Meanwhile after you are half-way through with the assignment of watching all those videos 10-times each, let me know what you think.

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How to Start Your Successful Tutoring Business!

Starting your own tutoring business not only means developing an amazing income, it also benefits you in many other ways.

Tutoring allows you to be your own boss and set your own schedule leaving more time for family and friends. It allows you to choose whom you want to work with and when you want to work. Being a tutor also means you get paid to learn new things yourself! Wouldn't it be nice to have a job that you enjoy everyday and allows you to work with children of all ages?

Can you imagine starting your own business with very little expenses and overhead costs while immediately profiting from each hour you teach? Tutoring allows people of all types to do this! Many don't realize that they have amazing skills that are valuable in the marketplace! Many folks believe that they need a Bachelor's or Master's Degree to qualify as a tutor. This is a common misconception. However, if you are not knowledgeable in the subject you are tutoring, chances are you will not be tutoring for very long.

Even though many tutoring franchises have been developing and starting throughout the US & Europe, I believe tutoring works best when the relationship is directly between the student, parent and the tutor and doesn't pass through the third party or tutoring company.

Often times the tutoring company takes a hefty cut of the tutor's pay and the prices are inflated due to this cut. It is pretty simple to get your own clients and referrals from tutoring and starting your own business is easy and satisfying!

Also, if any issues arise between a student or parent and the tutor it is much easier to resolve itself if you are dealing directly with one another rather than going through a third party.

Tutors are being called on to help with MANY subjects. For example it is common nowadays to be hired to tutor for the basic subjects (Math, English, Sciences, Reading) as well as Study Skills, Time Management, Computer Courses, Driver's Ed and even sports development.

Tutoring lends itself to be a part time or a full time position depending on how much you want to do! Many tutors start out only tutoring as a hobby and for a little extra money on the side only to find out that it is a great full time job.

Many students have study halls during their school day making it even easier to tutor during the morning and early afternoon as well as the evenings and weekends. Also, many tutors are offering online tutoring through the development of web cameras and new computer software.
It has never been easier to start your own home based business with little to no start up costs and start earning money for skills you already have!

If you are a great tutor, you may even find that it doesn't even feel like a job but more of a fun hobby!

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Figuring Out How To Tutor A Child In Math

Kids all learn at various levels and in different ways. With so many kids using their own learning methods, it can make tutoring that more complex. When someone wants to know how to tutor a child in math, they will first need to assess the person's learning ability and style. When it becomes clear how the student figures out their math, then a program can be designed for them in mind.

When an adult or older child first sits down with a student, they may ask them to do some simple math questions. If a child is in a certain grade level, then asking them to do some work from a previous grade could help to give a great starting point. When a child struggles with the previous year's work then continue going back until it begins to make sense for the them. Finding a base line to start with may assist a teacher with their lesson planning.

If a person struggles with subtracting double digits for example, the teacher may wonder if they can subtract single digits. If the person cannot, then it may be determined how they are going about finding their answers. The methods that are currently being used may not be effective for that particular child.

In some cases what works for one student may not work for another. Everyone sees ideas differently and some people get ideas quickly and others do not. There are many ways that students can learn various math points. A teacher can simple pick one idea first to see if it helps. For subtraction help, the teacher could start with a touch math program. If that idea seems to hard to grasp, the adult could choose another math aid to help.

There are a few teaching aids that are used for adding and subtraction. Finding the one that is the most useful may be helpful in the child's learning. When the student figures out how to use the aid that works for them, it may help them to figure out how to get the homework done.

As a child begins to get one aspect of math, it could be a good idea to phase out the aid over time. Eventually the homework needs to get done without special aids, and knowing when to take them away is essential in their learning achievements.

Most sessions between an adult and student are an hour. Time can either pass by quickly or slowly depending on the student and the amount of homework that needs to get done. Careful planning and time management can be used to help pass the time. A session could contain some easy math games to start using concepts that are already known. Then there may be some one on one time, followed by another concept game. The games may help to break up the time while still teaching important lessons.

When how to tutor a child in math is the center of an idea, there are many concepts to use. Finding ways to fill the time slot are essential. Learning about the child and how they learn the best will also increase the level of their skill learning. All kids learn differently and assessing those issues and needs may be helpful.

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Why Finland's Education System Works

Not too long ago, Finland's education system was comparable to that in the U.S. How they changed their system is interesting, because by having "less" school they are achieving greater results. In the U.S., the system of "doing what you hate longer and harder" seems to be the prevailing logic driving the "scientific test-results" orientation to achievement. Both systems are multi-cultural and multi-lingual and have special populations served in the general education setting.

U.S. Approach To Reform
Children must enroll in school (kindergarten or first grade) at age 5. Many children have had preschool experiences because parents work or they are qualified for Head Start, Early Start, Even Start and other programs. Preschool standards involve readiness skills (standards directed), but not all children receive such instruction. Direct reading (decoding) instruction begins in kindergarten and ends in second grade. State (and federal) standards direct what instruction children receive from kindergarten through high school and in higher education settings (technical/vocational schools and colleges/universities). Children must remain in school until they reach the age of dropping out (varies by state but usually between 16 and 18 years of age) or they graduate by meeting all their state's requirements. Standards, formal testing and statistics drive decision making by central administrators not in contact with students.

Finnish Approach To Reform
Children enroll in school at age 7, but they are given several years of preschool experiences which focus on language and physical development. The schools tend to be small because population centers are few; usually the schools have 300-400 students. Local teachers control their schools and curricula; they spend some of their work day developing and/or preparing materials to be used. Their school day is shorter than in the U.S. and they spend a lot of time outdoors, either in play or in applied "work" in the outdoor setting. Students attend elementary schools for 5-7 years, at which point they attend either a vocational schools or a higher education schools. Student skills and interests drive local decision making by teachers working with students.

What Are The Critical Differences?
The critical differences are:
· Preschool experiences are different: the U.S. focus on readiness (cognitive) skills development for reading and math, the Finnish focus on developmental skills in language and physical development. This translates into developmental readiness for instruction (Finland) or struggle to achieve (U.S.).
· School sizes differ: The U.S. consolidates and usually has 500+/school, the Finnish have few students so everyone receives attention. This translates into emotional security (Finland) or insecurity (U.S.).
· Children start reading instruction at different ages: the U.S. at age 5, the Finnish at age 7. This translates into being neurologically ready for instruction (Finland) or compensating with taxed memory skills (U.S.).
· Vocational schools are options for education in early adolescence. This translates into motivation (Finland) or non-motivational (U.S.).
· Decisions are based on testing/statistics (U.S.) or motivation and interests (Finland).

Conclusions
Focusing on behaviors and achievements for guiding change eliminates the humanness of education: interest, motivation, purpose. No matter how anyone looks at it, the U.S. system is a failure. Perhaps those making the decisions should relinquish the controls and let teachers who work with students and know what they need and want to learn make the decisions. Instead of rushing children to early achievement, maybe those who know about what happens to children developmentally will start driving the reforms.

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Teach Math to Kids Using These Tips

Math has been one of the most important subjects that every child must have a good foundation with. Sadly, many kids nowadays do not show interest in math because they find it boring and hard to understand.

However, math is counted as one of the subjects that you must pass in order to proceed to the next level of your education. So this problem must be solved and conquered. Here are 5 tips to teach math so that kids do not get bored.

1. Age and relevant things to teach.

Keep in mind that "slow and steady wins the race". There is no need to rush into things because kids take in things fast, but it will also confuse them if they take in information too fast and do not understand it. Be sure that what you are teaching is understandable by the kid.
2. Use different teaching methods.

Every individual has a different learning style. There is no one-guarantee way to ensure everyone understands. So it is important for you to have a few teaching methods. Examples: Teach them in a way where they can relate to things around them. Let's say teaching fractions, you can actually get a pizza and cut it into whatever fractions you are teaching. This makes learning much more fun.
3. Games.

Kids love to play games. Use games to cultivate their interest for math, it helps. Through playing games like board games or online math games, kids learn that math can be applied through games and not only in school. It gives them a more meaningful purpose to learn math.
4. Recall.

Math relies a lot on recalling skills and also mental calculations. Therefore, exercising the brain will be very important. Giving your child assessments on mental calculation and timetable will help them improve their memory skill.

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Effective E-Mail Math Tutoring

When people think of additional school help for their child who is struggling in math, they usually think of one-on-one private tutoring. Private tutoring is a great way to get help for your struggling child. As mentioned in my article on effective math tutoring, the knowledge that a tutor brings to the table is not so important as his ability to relate well to your child and to identify with their source of difficulty. Even though private tutoring is the way parents think they need to go, there are alternatives such as email tutoring that can be a welcome help to your child.

With the omnipresence of the computer and with online internet service as ubiquitous as the telephone, email tutoring is something that has come of age. Combine email tutoring with the telephone, and you can now become a virtual tutor capable of working with anyone across the country. Effective email tutoring is the result of clearly defined questions responded to with easy-to-understand answers. Critical to effective email tutoring is a tutor with very strong written communication skills. This is one area which I have worked hard on throughout the years, and I attribute a lot of my success in tutoring students--whether in person, on the telephone, or via email--to my strong written and verbal communication skills. Knowing one's field is one thing; being able to communicate that knowledge to a struggling student is another.

Some might think that math tutoring has to be done one-on-one, teacher sitting beside student ready to respond to his every need. Admittedly, the one-on-one scenario does have advantages; however, a competent tutor with strong communication skills can effectively remediate most problems as though he were sitting next to the student. A student who is struggling with quadratic equations, for example, can get his problem fixed via email, provided the tutor is competent at communicating this topic. With several problems worked out methodically, showing step-by-step procedures, a tutor can get the student back on the road to health in a short time.

Because I have worked on the various modalities of tutoring--in-person, telephone, email, and combinations of these--and have proven successful with each one of them, I wanted to make my tutoring techniques available to the student who might not live in central New Jersey, and thus be geographically "untutorable." Remember good tutoring does not have to be only in-person.

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Math Is Not Hard!

As a math tutor for 15 years, I have tutored hundreds of students from all the grade levels. I found most of the students were not comfortable with mathematics. More than 80% of them said, "the mathematics is very hard." Why do most of the students find mathematics a hard subject and try to avoid it?

The answer for the above question is hidden in a simple example. I always give the example of stairs to my students, and giving the same example in this article. I compare the steps of a staircase to the concepts in mathematics. As this is very hard to reach higher floors of a building without stairs (or elevators these days), same way learn higher concepts in mathematics without learning basic concepts is very hard.

People have to start from the ground, then first step, second, third and so on to reach their destination floor. Exactly the same way students have to start from Kindergarten, then grade one, grade two and three and so on to reach their math destination. Also, if some of the steps are broken in the staircase, it is still hard to reach the desired floor using those steps. Same way, if you are missing some of the basic concepts from elementary grades, math for you is still hard.

Now, the kindergarten, first grade and second grade are like first couple of the steps of the stairs. You can learn this level of math easily, as you can jump enough to take yourself to second or third step of the stairs easily. As it is very hard to reach sixth or seventh step of a stairs by jumping from the ground, exactly the same way to learn grade five or higher grade math is very hard (or impossible) without having the good knowledge of the kindergarten to grade three or grade four math.

Now, consider one person is jumping on the ground to reach the third floor of a building. Can this person make it? Never, if he is not Spiderman. For this person, to reach the third floor by jumping is impossible or very hard and finally he gave up saying that it was very hard to reach third floor.

But another person used the stairs to reach the same floor. This person found it very easy and reach there with little effort. Compare this person to a student who knows all the basic concepts learned in elementary grades. To learn grade six or grade seven math for this student will be easy. But there is another student in grade six and doesn't know the lower grade math concepts such as, times tables, factors or number system. This student is in the same situation as the person, who is jumping to reach third floor from the ground level.

From the example it is very clear that mathematics in each grade have the same importance. So, you need to be focused on math in all the grades on all the basic concepts. Ask your teachers lots of questions. Keep asking until you are not clear about the concepts or topics you are working on.

Each grade act as a step in the whole staircase to the mathematics high-rise building. Performing poor in math in any grade is like breaking some steps in the whole staircase. As broken steps make the whole staircase risky or scary to use in the future, incomplete math competencies in lower grades make math very hard in the high school.

So, what it takes to be smart in mathematics? My answer is; stay focused on math in each and every level of your studies. Participate in your class math practice sessions. Ask your teacher lots of questions until you are not clear about any concept. Mathematics is a subject of solving the problems on paper by hand rather than only to read them. As in case of Social Studies taking more readings make you smart, in math practicing lots of problems and solving them by hand makes you smart.

To practice mathematics, math workbooks are the good source. You learn a concept in a workbook, then in the same booklet there are more problems on the same concept for practice. Another good method to practice mathematical concepts is using math worksheets and you can print math worksheets free of charge from the web.

Finally, choice is yours. You can choose the jumping method to reach your math destination or you can use right and proven path to reach your math destination.

The right and proven path to math destination has the following steps:

* Start learning math as soon as you start your kindergarten

* Focus in your math classes and listen to your teacher

* Ask your teacher lots of question until you are not clear about the concept, you are learning

* Practice, practice and practice. For this you can use math worksheets or math workbooks.

If you take the proven path, one day you might say, "Math is not hard."

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Review of Free Math Apps for the Surface 2 - November Edition

There are so many tablets out on the market now and hundreds upon hundreds of educational apps to go right along with them. Sifting through these apps to choose ones that are actually worthwhile for you and your students can be a daunting task. I am here to make that part of your life a little easier by reviewing some of the free Windows-based math apps for you! This is the first article in a series that aims to find meaningful (and free!) math apps for the classroom.

A total of 6 free Windows- based math apps were reviewed:

1. Math (3 out of 5 stars)

2. Math Operators (2 out of 5 stars)

3. Elementary Math Flashcards (4 out of 5 stars)

4. Math Flash - Subtraction (2 out of 5 stars)

5. Math Flash - Multiplication (2 out of 5 stars)

6. Flash Cards (4 out of 5 stars)

The November Windows Math App winner is a tie!

Flash Cards (4 out of 5 stars)

Pros:

This app has available quizzes for all four math operations and it allows students to focus on one of these operations or a combination of operations. I liked that the app gives the quiz score in a percentage and that you can adjust how many questions are in a quiz (default is 30 questions) along with the digits that are used for the questions. There are user friendly buttons present, such as skip ahead, skip back and view cards. There are also play and home buttons in the hidden section of the Surface tablet menu bar (at the bottom). I also found it helpful that you can save a quiz as a favorite to come back to later. I think that students will like seeing their best score, and best speed, along with the average seconds per question. That information could lead to some excellent self-monitoring and goal creation.

Cons:

When playing this game, I purposely got a question wrong, but the app did not correct me. It simply had me continue guessing and never stepped in to give the answer. I think that this could be extremely frustrating to students who are not strong in their basic facts or strategy work. I had 13 incorrect responses and the program still had not advanced me to the next question.

Elementary Math Flashcards (4 out of 5 stars)

Pros:

This app offers all four operations and the choice of adjusting the number of questions asked in a set (5,10,25). Students can enter their name before starting to play and the program wishes them "good luck", which is always a great way to start a game that can be stressful for students. With a plain blue screen, large numbers, and white lettering, the graphics are very easy on the eyes. There are distinct buttons for students to help with navigating the app, including a green arrow button to advance to the next screen. When students get a problem incorrect, a red "x" is placed over the option and then students have the chance to pick another option. At the end of the review, the game results are given, including the students score out of the total number. The program also ends on a positive note by telling the student "good work " while displaying the back button to start over.

Cons:

The main con for this app was in the graphics. This is a very basic design and it seems that students might get very bored with the lack of bright colors and the true interactive gaming feeling that is so prevalent in their lives. Nevertheless, this app still delivers a great review and quick practice for basic computation.

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Montessori Preschool Math Education - Here's Why it Works So Well

After 15 years as a math educator, and parent of five children, I actually saw something new (to me) in math education this past year, that really impressed me.

My (then four-year-old) son attended a Montessori preschool class and learned math concepts in a way that I had never used myself in the classroom, nor had any of my three older children learned before.

The Montessori Approach to Math
The Montessori math education concept is based on going from concrete to more abstract lessons, referred to in Montessori lingo as "works," which are really just manipulatives.

These well-designed, highly specialized manipulatives for each "math work" make the abstract ideas much more accessible to a child.

Each new work is introduced to the student only via a one-on-one lesson with the teacher.

Thanks to this individualized instruction, the teacher can wait until each student is ready for the next level of abstraction before introducing it.

Step-by-Step Progress
Some children in my son's (mixed age) preschool class were still learning to count to twenty, while others were learning place value and addition and subtraction. But, even those younger children doing the early math works understood that they needed to master counting and one-to-one relationships in order to do the place value and addition and subtraction works.

This is an extremely important concept for children to remember. There can be no "skipping" lessons in the Montessori preschool math curriculum, (and there shouldn't be "skipping" in any math curriculum, in my humble opinion.) My son's classmates understand that mastering each lesson is a means to an end in competency in math. It is a wonderful approach to preschool math education!

Math Lessons Are Fun!
From my son's perspective, the "works" he used to learn math were almost like toys. He got to play with them in the way the teacher showed him and then he came away with mastery of a math concept. In reality, those works are just really well-designed math education manipulatives that teach one highly focused math concept.

There are works that teach key math education skills such as; measurement, counting, number order, number formation, one-to-one relationships, addition and subtraction, and even higher math concepts. Every time the teacher introduced a new math "work" the kids who were ready for that next math concept were excited and energized to learn a new math skill. They watch and help each other complete the tasks of the work and learn from their peers in that way. This is a great way to have group math work!

Montessori Works as Toys
Some of these math manipulatives would make wonderful toys and "kitchen table" lessons for parents to do with their children when introducing math concepts at home. I was very pleased with my son's progress in math using the Montessori preschool-math education method, of course he had an exceptionally talented teacher, but I think many children could benefit from using the Montessori math manipulatives at home,too.

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Special Learning Strategies For Elementary Mathematics

Many children experience anxiety related to mathematics to a certain extent, and this may begin as early as kindergarten. This anxiety can result in poor academic performance in math, many misunderstandings in math content and procedures, and negative attitudes toward math. Obtaining a math tutor may be helpful for many students, but often, parents who have a general understanding of learning strategies for mathematics can provide equally effective help. The following information can help parents, teachers, and tutors provide a basis for mathematics learning for elementary school students.

Understanding the Learning Progression

First, we need to consider how children best learn. Think about very early learning for children and the idea of "cat". When toddlers see a cat, their parent says, "cat", and pats it, to give the child the name for that object. Soon, the toddler knows what a cat is, from seeing it, touching it, and hearing the name for it. Later, the child draws a picture, points to it, and says "cat". Eventually, as a child grows, he is able to associate the spoken word "cat" with a mental picture of the animal. This learning progression, from concrete (the real cat) to semi-concrete (the picture) to abstract (the spoken word) is an example of how children learn mathematics as well. To teach a child about triangles, first they need to interact with real triangles - touch them, trace them, see them. This is where manipulatives play a large part in mathematics instruction. Children use hands-on manipulatives to learn the characteristics of math concepts (like a triangle), or use them to show procedures (like adding 4 blocks and 3 blocks). The first learning strategy to use when teaching children new mathematics content, therefore, is to go to the manipulatives.

Learning the Underlying Rules

A second strategy that is helpful for students when learning mathematics is to memorize necessary facts, vocabulary, and rules. Much time is spent in the 1st and 2nd grade with students learning addition and subtraction facts, and an equivalent amount of time is spent in the 3rd and 4th grade with learning multiplication and division facts. Even with this practice time at school, many students have difficulty committing these facts to memory. It is critically important that students memorize these, however, as most later mathematics learning is dependent upon the quick and accurate recall of math facts. Think how difficult it would be for children to add 358 to 472 if they did not have a firm grasp of addition facts? Likewise, how would a student find a common denominator for two fractions if they could not recall basic multiplication facts? There are many, many ways that these facts can be practiced. One way is the "tried and true" flash cards. A variation of traditional flash cards is 3-sided flash cards. When studying multiplication facts, for example, write one factor in one corner, one factor in another corner, and the product in the final corner. When using these flash cards, cover up the product with your finger, so that the child can see the two factors, and practice multiplying them together. When studying division facts, put your finger over one of the smaller numbers, so they can see the large number and one of the smaller numbers. They have to divide to determine which number is covered. For example:

On your triangle, write 2, 3, and 6 - one number in each corner. When practicing multiplication, cover the 6, so that the child sees 2 and 3, and multiplies them together to get the answer of 6. When practicing division, cover the 2, so that the child calculates 6 divided by 3, to determine the answer of 2.

Helpful Shortcuts

Another strategy that is effective is teaching students the steps of a procedure by using mnemonics. For example, the first letters of Please Excuse My Dear Aunt Sally stand for the steps of the order of operations (parentheses, exponents, multiply, divide, add, subtract). The "family list" of Daddy, Mother, Sister, Brother, Cousins, Relatives indicates the steps for long division (divide, multiply, subtract, bring down, compare, repeat or remainder). Strategies such as these help students remember procedural steps so that they can perform them consistently.

For conceptual learning, like "What is an equilateral triangle?", children learn through the processes of explain, elaborate, illustrate. In this situation, a child should define the equilateral triangle (explain), tell what that means in his own words (elaborate), and draw a picture of it (illustrate).

As with any other type of learning, mathematics strategies can only be learned through consistent application and multiple opportunities to practice. You will know that children have become proficient in the use of the strategies when they are able to independently apply them to mathematics problems they encounter in school.

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Changes in Mathematics Teaching

The Minister in the United Kingdom government responsible for education recently announced that all children should know their multiplication tables by the age of 9. As with any statement by a politician, this is obviously more wishful thinking than a command. However, it did wake up a few ideas in me. What happens to children who cannot learn their tables? How do they feel about not succeeding? What experience does this minister, or others who set educational goals, have of the real world of schools and their pupils? What is so special about the age of nine? What is so special about multiplication tables? I knew my tables when I was nine, but that was over 60 years ago, and I later went on to get a mathematics degree. Has the world changed since then?

When I think back to my three years as an undergraduate, I have memories of sitting for hours in lecture theatres, failing to understand a word of what was going on. That cannot be a true remembrance or the University of Bristol would not have given me a degree, but it has left me with sympathy for school children who fail to grasp basic ideas of mathematics - or anything else. Because progress in mathematics is easy to assess, so is a pupil's success - and failure. Set a tables test of 20 questions. Well done, those who get 19 or 20 correct, but how do children feel if they score 5 or 6 or 7? There is a saying in the UK: "nothing succeeds like success," but I have not heard one which says "nothing depresses like failure" - something which is equally true in my opinion.

There are children who have great difficulty in learning things which do not interest them. After several years of 5 out of 20 in tables tests, their toes must curl at the thought of repeating their failure time and time again. No wonder many children hate school, and mathematics in particular. Such children, of course, do not go on to become Ministers of the Crown, nor do they sit on "important" committees.

Although I have retired from teaching, I still work as a volunteer in my local school, helping in mathematics classes for 9, 10 and 11 year olds. The school is very good with an overwhelming proportion of hard-working children. I have helped five teachers, all of whom are as good as you could get for this age range. The internet is "on tap," and lessons, exercises and games in mathematics can be downloaded and projected on to the whiteboard. Even under these favourable circumstances there are still children who cannot rattle off their tables.

When I first started teaching 50 years ago, I taught "Old Math." Euclidian Geometry had been around for 2300 years; logarithms (if you're under 45 you may not know that they were used for doing difficult calculations!) had been around for almost 400 years, and a good facility in arithmetic was necessary because there was no alternative.

Things changed after October 1957 when the Russians were first to put a man in space. The story goes that the content of mathematics in USA schools changed within 2 years to New Math. Whether or not this story is true, schools' mathematics did change in countries around the world. In the UK, the changes were far reaching, but by the end of the 20th century, the pendulum had swung back some way towards the older content and a balanced curriculum.

However, thanks to the wide use of electronic calculators, logarithms are no longer needed for difficult calculations, and Euclid's geometry has finally vanished; we are now allowed to acknowledge the existence of symmetry! Algebra, by that I mean arithmetic algebra, remains important.

So, events and inventions - sputniks, calculators, computers - have led to changes in the content of schools' mathematics, but children are still expected to learn their multiplication tables by the age of 9, just as I did 60 years ago.

If we really do want our children to learn their tables, we must abandon a 9-years-of-age finishing post and motivate them. If you watch a darts match, you will see complicated arithmetic dispatched in the blink of an eye because it is important to the game. What we need is a similar game for youngsters which depends on their ability to multiply.

Any ideas?

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Mathematics Success - Common Mistakes in Mathematics

This math article is going to be an effective mathematics guide that most math course materials have not supplied for sometime now. It is going to talk about an important problem that has made students not to perform at their best in mathematics.

Mathematics today as a subject occupies a prime position in the world of education. It is one of the core subjects that are needed for any human being to attain any height in life. Right from the early days of a child, he or she is expected to master the art of counting and adding. How well he or she does this at this early stage can go along way to determine how good he or she will be as a math student later on in life. Most students who are not doing very well presently in math must have had bad background training and as a result, they find it difficult coping with the subject as they grow. They only struggle from one stage of their academic life to another building on a poor foundation. We all know what the result of this venture will be - a poor math result in their final examinations.

It is a common thing to see students making many foundational errors whenever they solve questions in higher classes. Some students in the examination classes cannot even use the BODMAS rule to solve questions- Yes this is how bad it is! Here are some common mistakes by our students in math and the solutions provided. I hope this will be useful to you or your child. I have provided the likely wrong solutions by students and what should be the right solutions. Comments have also been included under each. Please enjoy them.

QUESTION 1: Simplify - 6 - 5

Wrong solution:
-6 -5
= +30

Right solution:
- 6 -5
= -11

COMMENT: Some students of mathematics still solve this type of question above as - 6 x -5, which is equal to + 30, because - multiply by - = + and 6 x 5 = 30. However, the question above does not involve multiplication, it is simple addition. The solution to the problem can be approached this way; if we use the idea of owing money (-) and having money (+). Owing is taken as a negative (-) thing, while having is taken as a positive (+) thing.

Let us now use this idea to solve the question above and other subsequent questions involving operations on directed numbers. -6 imply I owe six quantities, -5 also imply I owe five quantities. So therefore, I owe eleven quantities altogether i.e. -11 (it is negative eleven because I still owe).

Here is another one:

QUESTION 2: Simplify -1 + 5 - 2 - 3

Right solution:
-1 + 5 - 2 - 3
= -1

COMMENT: Using the "Owing and having rule". I owed one quantity (-) and I have five quantities (+5), when I pay back the one quantity I owe, I will have four quantities (+4) left. I owe a further two quantities (-2) and a further three quantities (-3) which equals five quantities (-5). So, when I pay back four quantities (which I already have), I'll be owing one more quantity (-1). So therefore, the result is -1.

Here is another one:

QUESTION 3: Simplify -3 x -2 x +2

Wrong solution:
-3 x -2 x +2
= -12

Right solution:
-3 x - 2 x + 2
= +12

COMMENT: This problem involves multiplication and the rule of signs must apply. It is necessary to simplify the signs first before the numbers (figures). - x -= +, the resultant + sign multiplied by the last + sign = +. Now to the figures, 3 x 2 x 2 = 12. Therefore, the result is +12.

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