Mathematics: Learners and Educators

   What is mathematics?

                          

I have encountered this question several times in my life and answered in many different ways which precisely goes as it is abstract science of number, quantity, and space, measurements, sets and operators.  Yet this is not all what I wanted to cover for this question. So I have my informal way of answering as follows.

Mathematics is an unknown city to be traveled by newly arrived traveler. The guide(teacher) for the traveler speaks in a new language of not so familiar notations, terminologies, diagrams and symbols.

           Why do we learn mathematics?

In order to live a meaningful life in this world one has to learn basics of mathematics. This would allow us to reach a destination in time, to prioritise works to be completed in orderly manner.

At the same time to explore natural and experimental sciences mathematicians introduced advance mathematics courses. To study architecture, design, astronomy one needs to have very good knowledge of mathematics. Hence the  influence of mathematics cannot be avoided, so it has to be learned.

A student who is competent in mathematics.

A competent student (in mathematics)  is someone understands the reasoning, computes proficiently, applies knowledge to tackle new situations and involves himself  in order to explore mathematics. He does not accept what has been offered unless it makes sense to him.

          A teacher who is effective in helping students learn mathematics.

An effective mathematics teacher is one who sees everything from students point of view and who is aware of the background knowledge of his pupil. Teacher becomes effective as he comes across learners. He closely establishes connection with the learner and caters with learners of all abilities through differentiated instructions.

An effective teacher brings essence of the topic to be explained at the start by introducing something which is familiar to the learner. Instead of giving a direct answer he leads to the answer through asking series of guided questions. 

Self-access e-learning

Self-access e-learning is gaining popularity among young minds of today. It is beneficial to all level of learners across the globe in many ways.  With the help of internet (or soft copy, which is portable in today’s electronic devices) it solves the problem of carrying books from one place to another.

E-learning helps the learner to study at his/her own time and pace. By doing so it addresses the issues of learners from different abilities, different nationalities and different background.  E-learning publishers integrate hyperlinks, graphical software and other animated objects in order to help learners in best possible ways.  Any unfamiliar terminology is again linked with detail explanation. It is considered as authentic and acceptable as the content is prepared by experienced educators and modified by experts around the world through continuous feedback from learners.  Educators and facilitators modify and present their work in a better, more acceptable way when they get instant feed backs. Self-evaluation, instant badges, reference links are added advantages for learners as compare to printed books. It has become now modern trends that institutions, companies tie up with e-learning publishers in order to help its learners.

Once the authenticity of the publisher is established one can go ahead with e-learning. Though self-access e-learning content does not answer any direct question that comes in the mind of its reader, it reduces the possibility of raising questions and doubts. Hence the importance of self-access

e-learning is numerous.  Be it educator or be it learner it is win-win situation for both. 

IBDP Math HL Option 8: Statistics and Probability

This morning in my class, we started talking about  pdf and cdf of  discrete probability distributions, continuous probability distribution followed by individual discrete and continuous distribution and their mean and variance.

Probability mass functions(for discrete) probability density functions(for continuous) gave us enormous pleasure when compared  with (minimum) different scenarios. 

(Will be Continued..)