How Children Learn Mathematics

Children perceive things around them very differently than adults around them. Children usually learn from the visual inputs i.e., through seeing things. Somehow they rely more on their photographic memory. This is particularly seen in case of mathematics.

• We might have observed that when we teach numbers and increment one number at a time will only confuse them more. Instead, we ask them to count on their fingers. This is because of their photographic memory.
• It is this practical sense that will help them learn math. After teaching them how to count on their fingers we can go further and teach them how to avoid fingers and start counting in their mind. This is the hard part which is easier said than done. This transition period is a little hard for children. Give them some time to coup up with the new technique. Not all children learn and perform the same way.
• Tell them how mathematics is used in everyday life by giving them practical examples. Take them to a store and teach them math there. Give them a ruler to and show them how the numbers progress. They will definitely understand practical part of it. Tell them how fun it is with math around. Tell them that math is not a scary animal but a friendly pet.
• After the counting, additions and subtractions are completed, now comes the hardest part yet. The Multiplication tables. Instead of asking them to by heart the tables, teach them how multiplication tables are formed. Tell them the basis for multiplication is addition and how it works. It is sure to work.
• Follow a similar route while dealing with fractions as well. Fractions are a little more complicated than multiplications. The parents or the teachers can use their imagination while teaching mathematics to children. This small act will make them rethink their notion about mathematics.
• Try math-games. Math-games are one of the best methods to teach friendly math to children. Teach them measurements like pound, foot, mile, etc. Talk about time as well. Of course only after they understand multiplication.

Remember that mathematics is a practical subject and look for the appropriate examples which you think will help them understand math more clearly. The key to all these things is patience and while dealing with children who are learning mathematics, patience is that you will need to see any positive result.

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Mathematics! This subject gives nightmares to many students and some students are really bored by the student. Often many teachers and parents complain that children do not score well in mathematics apart from being good in other subjects. Some children are really afraid of the subject that they do not want to talk about it, even casually.

Many teachers complain lack of attention in mathematics class. This is due to the fact that one teacher has to teach a class of 20-30 students. It is a very low chance that all the children have identical or similar abilities of grasping subjects, especially mathematics. This makes the class even more challenging for the teacher. So, they are not able to concentrate on all the children in the same way and give equal importance to all students. Only some students can grab the attention of the teacher and some cannot. This is more or less the same situation in a regular tutoring institution. One tutor teaches a group of say 10 students. Even here, the weak students try desperately to grab the tutor’s attention and they fail ending up with many doubts in subjects, especially mathematics. This can only mean one thing; those students find it hard to move forward in their education and careers.

A best alternative to this situation is the online tutoring. Online tutoring unlike conventional tutoring sessions, hold their classes online and we all know that. The best thing about the online tutoring is the advantage the weak students get is that, there is a tutor who will listen and solve only their doubts for a whole one hour.

It is not only about weak students. But also students well-performing students also need tutoring to prepare themselves ahead of next year. There are many students who take entrance exams in order to join elite institutions. One other words online tutoring is helpful for all kinds of students. Online tutors cover the most important concepts in mathematics depending upon their grade and the student’s capability.

Online tutoring sessions begin with internet, a webcam, a writing pad, a headset and a digital whiteboard. The software required is very simple and is available for free on the internet.

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Algebraic Topology is that branch of Mathematics which uses the algebra to study topological problems. The goal is to find algebraic invariants that classify topological spaces up to homeomorphism. In many situtations this is too much to hope for and it is more prudent to aim for a modest goal, classification up to homotopy equivalance.

The algebraic tools used in topology include various cohomology theories, homology theories, homotopy groups, and groups of maps. These in turn have necessitated the development of more complex algebraic tools such as derived functors and spectral sequences; the machinery mostly derived from homological algebra is powerful if rather daunting.

The value of algebraic topology is measured by the extent to which it answers questions which arise more geometrically. These classical topics were, before the development of the full algebraic tools, often treated as questions involving numbers. For example, the dimension of a real vector space is a topological invariant say, R^n is not homeomorphic to R^m if n > m, but this was not easy to prove for m > 1. Likewise, many questions about maps between n-dimensional spaces could be resolved with an appeal to the degree of the map, an extension of the winding number from complex analysis, due to Brouwer-- the Fundamental Theorem of Algebra and the Hairy Ball Theorem are two well-known examples. Other questions of a geometric nature which can be addressed with an appeal to the algebra include fixed-point theorems. For example, Lefschetz's theorem guarantees a fixed point if a certain calculated number is nonzero; Smith theory studies the regularity of fixed points under self-homeomorphisms of finite order.

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