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    Is it possible to teach higher mathematics in an interesting manner?


    Are the concepts of higher mathematics difficult to explain as a teacher? What are the possible ways in which it can be taught in a manner which will interest the students?



    Since our childhood, we have heard about many teachers who have taught or are teaching Mathematics in various interesting and innovative manner. Some sing songs to teach multiplication tables, some other draw colourful figures to teach basic arithmetic operations like addition, subtraction, multiplication and division. Some other teachers teach various concepts like fraction, percentage, profit & loss in many other innovative ways.

    But when we start studying higher mathematics like Abstract Algebra, Calculus, Real Analysis, Vector and Tensor, Theory of Equation, LPP and other branches, we enter the realm of a different world which has no relation with the normal world of numbers. Everything is abstract in higher mathematics. There is no way to teach higher mathematics in an innovative manner. Whoever studies higher mathematics, does this due to his love for abstract numbers.

    These students of higher mathematics enter, live and love this abstract world. They don't want to come back to the world of real numbers.
  • #653097
    No there is no different means to teach mathematics in higher classes. Even I didn't study maths in any different style by any teacher in childhood, still, I had special affection with it. I was always a good student in maths. I used to find some tough questions of calculus and use to check my ability to solve them. Everyone in my class used to come to me solve their problem. Maths is a very good subject and if you have understood the basics of it thoroughly then you will not have a problem in higher class.

    I remember in the 9th standard we had a very beautiful teacher of mathematics in school that's the reason I have got interested in the subject and after that my interest multiplied.

    Sanjeev

    " It is better to be hated for what you are than to be loved for what you are not" ... Andre Gide

  • #653098
    Mathematics is an interesting subject only for them who understand it and have got an interest and aptitude for it. It is not the everyone's cup of tea.

    It is a flawless subject. There are no ambiguities in it. The principles are well defined and more and more advance we go more and more complicated and difficult it becomes.

    The most difficult parts in physics and chemistry are dealt with Mathematical formulations. I still remember in our graduation we had a derivation of mass and velocity relation as stipulated by the great scientist Einstein but we had big difficulty in understanding the derivation and those who were not good in Mathematics miserably failed to understand that.

    So higher Mathematics is definitely a tough subject and there are no easy ways to learn it.

    Knowledge is power.

  • #653099
    Any subject, not only mathematics, at higher levels it is very difficult to understand or teach. But some teachers will find out innovative methods to teach the subject. During my post graduation a professor used to take very good examples to explain the electronic configuration of elements. Even after 42 years of completing the course I remember those examples. Like that some Professors in mathematics may also give good examples so that we will remember the subject.

    Mathematics is a very tough subject and advanced mathematics is further complex. So in addition to hearing the classes, one should practice the subject more. Then only one can become thorough in the subject. One should also understand the subject in detail instead of simply practicing it.

    drrao
    always confident

  • #653101
    So, we can say that those who study higher mathematics, do so from their love for abstract numbers which are not found in the real world.
    Beware! I question everything and everybody.

  • #653128

    This thread about teaching/learning Mathematics arises because of the assumption that among different subjects a student studies Mathematics is the difficult one. In most of the cases it may be true. But for a student who likes and follows the classes, it is just like any other class. In my case, from the school classes onwards, I did not feel any difficulty in learning and understanding maths. Very often I got the top position in it in the class. I opted for Maths at the degree class only because of that. I opted Mathematics as the main and Statistics as subsidiary at the degree level. At post graduate level I opted for Statistics.
    Afterwards, I accepted teaching positions in Statistics, to be exact in Bio statistics. I found my students, most of them were having Biology background, were afraid of sitting.iny class, mainly because they were afraid of the subject, biometrics. But when I introduced the subject with necessary examples from their fields of interest, they started showing interest. Some of them took projects from related fields. Some of them after completing PG, went for Ph.D. took problems involving lots of data collection and analysis. Application of Maths and Statistics were there in their works. From among them some got selected as lecturers in the same college. They did several research projects jointly with me and published the results as research papers.
    Such people though were afraid of Maths in the beginning started loving it.


    tmsankaran

  • #653130
    Why not? There are evening classrooms which teach their students the most interesting ways to learn & grasp the things including the mathematics. If you have to some calculation than there are different ways in which this can be done. The easiest to watch & witness these is through YouTube.com & you can even subscribe for those on order to get the updates during the coming times.

  • #653188
    Mr. Anand: The thread is little bit different. I want to say that in higher mathematics, the complex concepts can't be explained by quoting examples from the real world.
    Beware! I question everything and everybody.

  • #653210
    Hmm..it depends on what level one is to truly understand what higher level mathematics is. Calculus isn't that hard. Trigonometry was one of the easiest things I ever learnt.
    I don't think mathematics can ever come up with something that doesn't apply to real world, except imaginary numbers. Maths has a reputation of being the universal language. Well even imaginary numbers and irrational numbers can be explained by drawing nature's analogies. Pi can be found in every thing that is round. The imaginary number i is the hardest thing to explain though.

    But when we forget all that we remember about maths, take a moment, do you understand the negative numbers of integers? Integers are no where the higher order maths. But we hardly think about numbers like -5. They make sense in operations but as individual numbers they don't make such sense. In comes direction. Minus indicates opposite direction to the normal here. -5 is five steps away from zero in the left and +5 is five steps forward. But problem comes when you multiply two negatives. It will yield a positive right? -5*-5=25. But did we ever ask why? Here opposite to opposite leads to the right of zero. So we go five five steps to right of zero. I think in similar fashion any real number concerning math can be explained. Imaginary numbers though require an imaginary approach.

    The stronger a light shines the darker are the shadows around it.

  • #653212
    Mr. Aditya Mohan: It is not the question of discussing different branches of Mathematics. We are discussing whether problems of higher Mathematics can be explained by real-life examples, or not.

    Mr. Sankaran has given examples from his own work experience. I find that he has mentioned about Applied Mathematics and Statistics (Biostatistics). I admit that these branches can be made interesting by very good professors. But Pure Mathematics! No real-life example is possible.

    Beware! I question everything and everybody.

  • #653213

    It is true that Bio Statistics is relatively not so tough. However, it's application in actual situation becomes difficult if not explained with examples from real situations. This is true with every field of mathematics. I had the difficulty in the Modern Algebra, Measure theory classes, where the concerned teacher was not giving necessary examples. That guided me, when myself became a teacher, to introduce any new topic with suitable practical examples, from the related fields.
    Even pure mathematics can be clubbed with suitable examples.


    tmsankaran

  • #653215
    "Even pure mathematics can be clubbed with suitable examples."................... I would like to have some examples to be convinced on this point.
    Beware! I question everything and everybody.

  • #653221
    I was always at my wits end with Maths and I do not think that there is an easier way to learn it except hard work.

    Students aspiring for science stream and engineering career or research in science topics must have a good grip of Maths otherwise they will not be able to stand in this competitive arena.

    Thoughts exchanged is knowledge gained.

  • #653280
    Pure mathematics refer to abstract science of numbers, quantities, distances, etc. as concepts. However, this become clear when expressed in understandable forms. That is how the numerals came into being. The counting numbers were introduced in different forms in different places. The concept of operations like addition, subtraction, etc. became clear with the practical examples.
    The concept of straight line is abstract. But if expressed in the simple formula " y= a+ bx" and the meaning of these alphabets explained it becomes clear. x and y are varying while the alphabets a and b remain constants for a given straight line.
    Using these methods one can show how the relationship between length and weight of an animal like fish.

    tmsankaran

  • #653284
    I was discussing about integers and irrational numbers Partha. How are they "branches" of maths? They are the building blocks. No matter what kind of maths you apply, these fundamentals stay the same. So I thought discussing them would be apt. A commerce student wouldn't need calculus. A scientist won't need statistics. An engineer on other hand needs them all.
    That is the reason why I say "higher level maths" depends on what kind of maths a person applies. It's not easily definable.

    The stronger a light shines the darker are the shadows around it.


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