The key of success is the ability to solve problems- this may be a perfect phrase for the most difficult and necessary subject Mathematics. In the present era of technology, a student need both conceptual and practical exposure of Mathematics. For this purpose the teachers (instructors) has a great role. The subject is compulsory up to class X, and after that, it is optional. However, for today’s world every technological, scientific, venture needs the idea of Mathematics a lot.
For this subject many concepts are needed and a student can easily handle this concept if we, the instructors are able to provide some real world phenomena to them based on that concept. This concept has to be given in the beginner level so that students will used to the situation and they can upgrade their thinking capability and cognitive mind. In college / university level, some open problems and classic results can be introduced to the students, which will motivate not only the student but also the teacher. Future teachers of Mathematics are students now. Hence, action learning or real life problems can be introduced to all levels of students from their higher secondary level. Probably this will grow some craze of Mathematics among them.
Some facts:
For the purely theory oriented subject Mathematics, Some of the following facts are very useful. There is a controversy about the teaching of Mathematics. Some teachers follow the conceptual approach with purely theory oriented teaching and after that the application. Some may try to teach theory based on applications. In any case, the basic idea is to trigger
the cognitive mind of the young students to generate a passion for the subject.
Curiosity– This is the main criteria. Regardless the age of the learner, if
curiosity is there, then learning a subject is very pleasant experience. Normally we have seen the child in primary level is more curious rather that an adult now a days.
Motivation– The curiosity will turn into motivation and this help to grow
people as a high quality professional. Teacher has a great role to motivate students. Especially for an engineering or non-math major student, only teacher can motivatehim/her. Initially the motivation will be technology or some real life facts. How Mathematics play a role for the real life problems, if we can able to make a student understand, that may be enough for motivation. Motivation is a bit more in adult learners rather than primary
level due to the lack of visualization of the future of the topic. For example, teacher can motivate a student for differential equation by introducing a real life problem “Vibration of a string” or “Population scenario”.
Deep Learning– For a motivated student, reward does not matter. Sometimes they work for the sake of their passion towards the subject. Students through deep learning try to get the complete knowledge for Mathematics. This will reduce the anxiety among them related to the topic. This can be done through asking questions, drawing diagrams, preparing charts etc.
Real life problems– The common question from student is that “What is the
application in real world?” This question is valid also. For some of the topics in Mathematics (Pure Mathematics), giving a practical example is a challenge. However, for remaining part of Mathematics, we can give some real life problems easily and justify the concept. For example, we can give a pry-predator situation from biological aspect and easily generate some simplified model using differential equation. In optimization we can give the example of work of a delivery boy in a day and how to optimize that properly which leads us to travelling salesman problems in LPP.
Software/ Practical– Now a days, many software are available in the market
to do our job easier. Using MATLAB, MATHEMATICA finding eigen value, characteristic equations, graph generations are very easy and students will be attached to the subject through this. Even in mobiles, we can have various apps of Mathematics, which will make the subject easier for student. Situation of Mathematics in India: Manjul Bhargava, mathematics professor at Princeton University and winner of the Fields Medal(2014), one of the highest honors in math, says India can’t hope to lead the fourth
industrial revolution, “If we don’t have strong mathematical talent coming up very soon”
(Source-https://economictimes.indiatimes.com/jobs/mathematics-is-on-decline-in-india-reasonexcessive-focus-on-engineering/articleshow/69938324.cms?from=mdr) .
“Without the math, the procedures may be just experimental, may work sometimes, sometimes not. Only mathematics will tell you under what circumstances it would work,”- Srinivasa Varadhan, mathematics professor at New York University. (Sourcehttps://economictimes.indiatimes.com/jobs/mathematics-is-on-decline-in-india-reason-excessivefocus-on-engineering/articleshow/69938324.cms?from=mdr)
Both these statements are regarding the two very popular topic of modern era, AI (Artificial Intelligence) and ML (Machine Learning) which is the future all over the world as well as in India. There are various problems I education of Mathematics in India. Specially the ideology of Pure and Applied Math. This divides the whole scenario of Mathematics in India though actually these two topics are not separated. They are very much interlinked and stand together. The study of higher mathematics will be incomplete without the help of research, which is missing in this part of the world. Here we consider teaching and research are two separate quantity.
Action Learning: For these problems, Action Learning may give a ray of hope. This is a problem solving approach, which emphasize on a particular problem and that will reflect on the result. The probable best method is to initially focus on particular topics of the attraction of the students.
Action learning is used traditionally in business management, social science, research based problems. However, this can be introduced to teach Mathematics also. Through this action learning, teacher may be able to find the creativity of the student, which was hidden. It will be the job of the teacher to find the hidden talent through this action learning.
The problems in Mathematics is that it’s language is very abstract and in the higher education it is much more complicated, abstract and it has been taught by create a distance with real world problems. Hence, people are unable to visualize mathematics in real life.
For example, 2? = 4 implies ? = 2, because we divide both side by 2 . Actually, this is a concept of field theory. According to field theory as 2 ≠ 0, so it’s inverse exist and we multiply both side by the inverse, which is 1/2.
When some non math major subjects are taught, the applications of Mathematics in their particular fields need to be discussed, which will attract the students towards it. For non major students, Mathematics need to be taught through action learning and then concepts will be developed based on the applications. So we have to follow “middle of the road” policy.
Hence, finally we can say that Action Learning and Conceptual Mathematics is not different and they will be always together. However, probably we need to fix the order for most of the cases. Without concept, there is no progress. Concepts can be gained through action learning and that will remain with us for a long time.
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