Invention and discovery in Math

       

        A great discovery solves a great problem, but you can find a grain of discovery in the solution of every problem. You can have a modest problem in front of you; but if it will arouse your curiosity and put into play your faculties of inventiveness, and if you solve that problem by your own without any external help, then you can feel the tension before discovery and you can enjoy the triumph of its creation. Such experiences, at an age where you have maximum receptivity, can create the taste for the intellectual work putting its imprint on the mind and the character for life.
        In these conditions the Math teacher has great possibilities. If he fills his time by reprimanding his students with routine operations, he kills their interest, he hampers their intellectual development and he uses really bad his great possibilities. But if he arouse their curiosity, proposing problems which are proportional with their knowledge and if he helps them to solve the problems by stimulating questions, he can inculcate them a taste for independent thinking and suitably develop their aptitudes.
        The student whose program also includes a math course, has big possibilities. Of course, these possibilities loose themselves, if he considers Math just an object in which he just needs to give a certain number of exams and and that he will forget as soon as possible after the graduation exam. These possibilities also can be lost in the case when the student has
certain natural skills for mathematics, because, just as any other one, he must discover his talents and his tastes; he doesn't know if he likes the pudding with raspberries in case he never tasted before. But he can get to find that a math problem can be just as captivating as solving a crossword puzzle or that a strained intellectual work can represent an exercise so appropriate as a tennis match. After he has tasted the pleasure of mathematics, he will never forget it easily and exists then big chances that mathematics may come to mean something to him: an amateur concern, an instrument in his profession, maybe even his profession or a big ambition.
        When I was a student I was eager to understand a little bit of Math and Physics. I was listening to lectures, reading books, I was searching to assimilate solutions and facts that were presented to me, but there was a question which always troubled me: " Yes, the solution seems to work, makes the impression that is correct; but how can be invented such a solution? Yes, this experiment seems to achieve his goal, it shows like a fact; but how can people discover such facts? And how can I invent or discover myself this kind of things? ". I imagine or hope that some of the students with more thirst for knowledge put themselves similar questions and, for this reason, I am trying to satisfy their curiosity. Searching to understand the solution of such and such problems, also the motivation for the solution found and the processes by which it was obtained, I can explain to others also my findings. The interest to discover or invent seems more widely spread than at first glance. The space that the newspapers and the magazines for the general public give to crossword puzzles and other games seems to show that people spend some time to solve problems without practical value. At the base of this wish to solve different problems which do not give material advantages can stay a more profound curiosity, a desire to understand the ways and meanings, themotivations and solution procedures. Thank you

Teaching math in the classroom

          

       1. Let's help the student. One of the most important tasks for a teacher is to help his students in the right way. This task is not so easy as it seems; it requires time, experience, dedication and healthy principles. The student must gain a larger independently work experience. If he is let alone with his problem, hot helped or helped partially and insufficient, he might not progress at all. If the teacher helps too much, the student has nothing left to do. The teacher must help, but not too much and not too less, so that the student to have a rational part of work for himself also. Mo matter if the concerned student is not able to do a big deal, the teacher must give him the illusion that he works independently. To realize this, the teacher must help his student in a discrete, not annoying way. The best is that the student to be helped in a natural way. The teacher must place himself in the student position, to see his learning difficulties, to try to understand what happens in his mind and to put him a question or to show him one step that he could also had in mind.
        2. Questions, recommendations, intellectual operations. Seeking to help the student in an efficient way, but in a natural and discrete way, the teacher is headed to put always the same question and to show the same steps. This way, in countless problems, we need to ask: "Which is the unknown in our problem?". We can change the words and ask the same thing in a different way than before: What is required? What do we want to find? What do we need to search? The goal of these questions is to concentrate the attention of the student over the unknown. Sometimes we get the same effect in a more natural way by a recommendation like: "Let's check the unknown!" The question and the recommendation follow the same result; they tend to trigger the same mental operation. It is useful to gather and group the questions and recommendations typical worthy for the student when a problem is discussed with him. The list we need to study contains questions and recommendations of this kind, chosen and ordered carefully; they are just as useful for someone who solve problems working individually. The list enumerate, not in a direct way, intellectual operations typical helpful in solving problems. These operations are passed in the list according in the order they occur most frequently.
        3. The generality it's an important characteristic of the questions and recommendations which are in our list. Let's take the following questions: "Which is the unknown in our problem we need to find? What are the data we know in our problem that we can use? Which is the condition in our problem we need to respect? " . These questions have a general application, we can formulate them with good results in any kind of problems. Their benefit is not limited by the subject of the problem. We can have an algebra or geometry problem, mathematical or not, theoretical or practical, a serious problem or just simply a game; no matter its state, these questions keep their sense and can help us solve the problem. It's true that there is a restriction or limitation, but it has nothing to do with the subject of the problem. Some questions and recommendations from the list are applicable only for the problems in which we need to find something and not for the problems in which we need to prove something. If we have a problem of the last kind, we must take in consideration other questions. We will continue. Thank you

Why tutor math online with Skype

       Why teach math online these days? Well is not difficult to answer to this question: teaching math today is very simple, but with one condition: to know math. This doesn't mean you need to be a mathematician, but you need to know the stuff you are teaching. If someone asks you to teach him/her some concepts in any of the math fields out there then you need to be able to do that.
       Becoming a math tutor was never been more easy if you know your stuff. You have so many tools for tutoring math online these days. First you need to decide at what level you want to teach math. This is very important because this way you know what people to target for your marketing campaign. Deciding the level is not hard if you know very well your strength in the math field. Certifications and online math tests are also helpful for you to decide what level suits you best. After you decide this you can set up a Skype account, a Paypal account and your good to go. Then you need to market yourself and your math talent.
       First you can start making accounts on some websites which offer math online tutoring services. The ones I have tried so far are fiverr.com, slader.com, freelancer.com, upwork.com, algebra.com and onmatu.com. On all these websites I have an active account and I use them to gain potential clients and also to promote myself and my blog. But there are many more websites like these with a simple google search. You just need to take action. After you get some contacts to get starting with, you can make your own blog or website. This is the easier part: you can use the most popular blog platforms which are available now which are Blogger and Wordpress. Wordpress is for websites as well. Be careful about the content you put there: has to be original. This is the most important rule when you make your website or blog: to write true original content inspired from your own experience. If your main subject for your blog is tutoring math online then you should write about this on most of your articles.  You can get a lot of ideas for the articles if you think about what are the challenges of tutoring math online. You may do this in the beginning just to gain some money to pay the bills, to survive financially or to help your family and friends. No matter what is the reason you need to be very serious about this and about the way you teach math online. After a while, you will get to do this with all your heart if you have inclinations on mathematics.
       Think about the process of teaching math online very well: all that you need is a good internet connection, knowledge and you are all set up. You can do it from everywhere if you have these, you can decide your schedule, how many hours do you want to do in a certain amount of time so you have full flexibility as well. So what are you waiting? Take action now!

What math means in our daily life

      

       You should tutor math online and real time only if you know about it. You can't afford to teach people bad things or habits especially in the math field. Learning math means to organize better your thoughts, your ideas, your activities, your life.
       Learning math the good way means to solve better and more wisely your problems, to take action step-by-step, each step with its own results, to think cold when dealing with hot problems, to think simple when dealing with tough problems. This is why I tutor math real time and online. I really like it and what I described above is the most important part: do not make the mistake to avoid this when teaching people math. They will realize this and they will give up on you.
       The better you understand and know the math concepts yourself, the better you will explain them to others. The more you exercise the math principles and concepts with exercises and problems, the more you will develop your imagination towards math. The richer the imagination, the better math tutoring process will become. You have a huge responsibility when teaching math, you can make people's life better or worse. All around me I see people complaining about their poor financial state, some of them being broke, some of them borrowing money from banks and friends, some of them buying more than they can earn. All this by ignoring doing some simple math with their money and after that becoming sad because of their situation. Of course money are not the most important thing in our life, but they do give you some confidence and maintain our happiness.
       When tutor people math keep this in mind: as long as it will be a financial system ruled by the money and the world being rules by this financial system, math knowledge will be always welcomed and vital. If you want to defend people's hard-earned money, then you need to teach them good math as well. If you want people to think more clearly, to be more rational about their problems and life, teach them good math. Do it in a responsible way. Let's take in consideration a fact for this: of the 30 fastest growing occupations through 2016, 16 will require substantial mathematics and science preparation. If students choose to ignore Math, or if they not take it seriously in high school, they will destroy many future career opportunities that they could have. More than half of the job market will not be for them. I know that the vast majority of the university degrees require math. The importance of math for the potential future jobs cannot be more highlighted here in a few words.
      You would be wise if you enter university with a good background in math. It is shown from experience that students who come to university with a bad grade in Math (or if they choose to skip math in high school) have difficulties in the disciplines they have chosen to major in. So learn math for your future, for your life. Thank you

The power of math

     

   
       Well the financial system which rules this world is entirely based on math and from here we get the conclusion that this science of numbers governs fully this financial apparatus and from here again we take the conclusion that math rules the world. And all of this by making a simple logic reasoning. But this is not available just for the money. Can you imagine any industry without math? What about the technology? We so easily forget that so many things have applied math in them, that we are taking all for granted. We don't completely realize and sometimes not at all the importance of this science in our lives.
       We can't imagine our lives now without computers, television, internet, mobile phones and tablets, cars and so on, but they have all applied math in them. Now there is mathematical physics, mathematical biology or biomathematics, mathematical genetics, mathematical geology and even mathematical philosophy. But they are so many more. So why bother learning some math? Why bother learning this universal language and the language of the Universe? And the most important question: why bother learning just a small part of it? Why? Well they figured out that too. Statistically speaking people who know math are happier than the others and they live better lives and make better decisions, they have also more chances of being financially independent. Now why?
       Math organizes your mind, helps you make connections between notions, to analyze, to compare, to select, to find the optimal solution in the shortest time possible. Success will come only with hard work on a long-term basis. You need to learn some math first of all for you to survive financially and to remain free. Learn the game of numbers and you will not borrow money from your friends or even worse, get in the hands of the banking or non-banking institutions. But learn the science of numbers also to defend yourself against all kind marketing offers, risky investments, gambling, lottery and so many other money traps which are not what they seem to be. All of them imply pure math, but much more complex and which if you don't handle it then you will be manipulated, tricked and you will lose your hard-earned money. I am not saying this to scare you or something, but this is the truth and I am talking from my own experience as well. The best example for this is the global economic crisis which started at the end of 2008.  
       The beauty of math comes from its purity. It's very precise as a science and everything is a clear notion of an absolute truth. I am not sure if I can say the same thing concerning the other sciences. The best way you can learn math is by solving a lot of problems. This means that if you have an hypothesis and a conclusion, then you need to find a solution, a way to solve the problem by starting with what is given and finishing with what you need to find. Here it comes the research, the imagination, the attempts to find a solution and the process of selecting the optimal one. The intellectual effort of overcoming the obstacles when you solve math problems develops a feeling of deep satisfaction and understanding in you. And this is by far the most important gain when learning this science. These are also the reasons why I tutor math in real life and online through Skype.

Learn math for a better life

     

     
       Recognize that math is everywhere and this is not bad at all! Have you ever thought what means for a science to be used in almost everything? The biggest consequence of this is that if you learn this marvelous science, then you can apply it everywhere for solving your problems in life and from here more chances of succeeding. Everything around us is math whether if you like it or not. You meet the numbers and the relations between them like every day. You must learn to handle the numbers and you don't want to do any mistakes because these will cost you for sure time and money.
       Now let's discuss some simple examples to prove to you this. Every day you probably buy something and you need to know how much money to give and how much to receive back. What about going with your friends at a restaurant, a bar or something for some food or drinks? Usually, but not always, you want to leave a tip which can be between 10% and 20% from the total bill. What about if nobody from the group do know how to find the correct tip or a fair estimation of it ? How would solve this problem if you do want to leave a tip? And if you are young you do often go out with some friends so similar situations like these happen a lot through life so you need to learn how to handle the numbers. But these are basic math skills for solving the basic needs. You usually learn these in the fourth grade so you can say that you already know this stuff so why bother learning more. Now let's talk about something more serious.
       When I am thinking to my financial situation I am thinking to numbers because I know I need to calculate how much money i spend every day on food and stuff so that at the end of the month to not be in debt. Otherwise, I have to borrow money from my friends if I am in urgent need but this is the best case. Think about what math you need to know if you get a credit line from a bank, how many variables you need to take in consideration in order to respect the terms of service from the contractual agreement. How many details you need to analyze and pay attention for if don't want to get robbed by the bank. This is of course in the case you read the contract, but how many of us do that? What way will you take after all being said about these circumstances: the easier way in which you keep under control your spending related with the income you have by doing not very complicated math operations? Or the unpredictable and dangerous way, the risky strategy of borrowing some money from the bank and after that paying all kind of interests and commissions? Do you wish to have your hard-earned money in the hands of the banks without knowing a little math, no matter now if you are borrowing or make some deposits there? It's already known the fact that banks use special math in financial instruments which most of the time are against people's money? Why getting in their hands with your money earned by hard work when with just a little math you can be your own master?
       These are some of the reasons of why I teach math in real life and online through Skype. And when I tutor people I always make time and tell them about these motives because the things have changed and the world has changed dramatically as well. These days you are not learning math just because you have to or for a career or for a job, degree, pleasure or for whatever. You learn it to defend yourself , to make your life easier and without too much pain.  
                   

Why you should learn math

            

      There are many reasons of why you should learn math, but I believe these are the most important when dealing with the queen of sciences: the first one and the most important is the problem solving skill that mathematics develops in you by practice and practice and practice. This way it will force you to think logically and to solve a lot of problems using that skill, many of them maybe which are not related with numbers, but need strong logic and a step-by-step process to find solutions.             
      Do you know that of the 30 fastest growing occupations through 2016, will require substantial mathematics or science preparation? Math is required everywhere, anywhere and every time like in: engineering, medicine, banking and finance sector, business and constructions and the most important use is definitely for "personal day to day work". We are faced with math and science every day of our life and these two encourages critical thinking skills in the 21st century education.             
      You use math in most any job and without good math skills, it will make it harder to graduate from high school or college. This will make it very difficult to get a good job. What about spending your money wisely? When you are older you will need good math skills in order to make a budget. You use math to make sure you don't spend more money than you have! Or what about cooking? You have to measure ingredients, cut recipes in half, or make a double batch. This all involves math.   
       Math really is important for your daily life, no matter what you want to do it's true that not everything you learn will be needed later, but you never know what you will want to do, and the more you know and have to build on, the better off you will be. In reality math is the basic language of the world, for everyone uses math in most everything they do (often without realizing it).             
      If you are having trouble in math do not wait until you are behind. Seek help or find a tutor. Maybe you are missing a single step and not getting the answer right the first time.  Take a moment to stop and ask for help! This is almost as good as calling 911 for help!