Believe me, I knew my algebra, the rational (and the irrational) numbers and how to find the hypotenuse!
Nevertheless, herein lays the problem for me at school. Why on earth was I working so hard at my algebra? I could never understand for the life of me the purpose of learning the algebraic identities, the rational number sequences etc. Why does one need to know by rote the properties of rational numbers?
My issue was that Students need the Teacher to explain to them the use of such techniques and bridge the gap between the textbook and the real life. (AC)^2 = (AB)^2 + (BC)^2 by itself just did not work then, at least not for me.
Our Mathematical questions did have some practical connotation "If a rope of length so and so is laid alongside a wall of length...etc" but believe me; these problems were taught in a mechanical fashion like "If the word problem contains length of a rope or a shadow, use the Pythagoras formula to solve the problem..."
Here is some more. CBSE pedagogy prescribed the deduction of a "half a mark" for not writing the abbreviation "Ans" at the last line. Likewise for the letters "QED" at the end of the theorems. My teacher would warn us that the Board would deduct such marks and we should be careful about it.
I am sure all here will reflect on this ludicrous emphasis that the Board put, in order to ensure that we have this clerical mentality and penchant for the silliest and the most insignificant details on earth. It is this attitude that reduced Mathematics to a rote.
A word now, for my Math teachers. I perfectly understood, later, that it was impossible for them to do what I thought they should be doing. The number of students, course syllabus, CBSE rules and rituals, etc., binds the teachers.
So, as much as I would like to absolve my teachers, Mathematics and the CBSE still deserve every invective for the way the subject was designed in the 1970s!
Yes, Mathematics still needs to grow up and solve its own problems. If it needs our assistance, then it better make efforts to convince us that it shares a symbiotic relationship with us students! (He He)
I have a copy of a text book on mathematics for Grade 8 by Orient Blackswan. I will write for here, word for word, the manner in which it introduces the topic on rational numbers
"There is a need to extend the number system to find answers to problems like 1/3 - 1/2 or 5 divided by 3. Just as we extended the whole number system to the left of 0 to get negative integers, we now extend the number system to so as to include all fractions. In this number system, corresponding to every positive fraction to the right of Zero, there is a corresponding negative fraction to the left of Zero. Thus:
-1/3 corresponds to + 1/3 and so on. We call this the rational number system."
There is nothing wrong with what is written above except that it is as boring as steamed rice.
The text mentions, "there is a need to extend the number system..." This is an assertion, which can sound unconvincing to Grade 8 students. I am sure somebody can do a better job of making the use of this subject matter more interesting for students.
Now, for a little bit of my experience with mathematics in USA. My Professor was from Russia. When he taught us mathematics, he made it clear that he is not interested in "Mathematical Regurgitation" (He actually had another word for "regurgitation" but it would be inappropriate for me to use it on this forum). He was of the opinion that "Mathematical Regurgitation" is something Asian students love to do.
He insisted that all problems are to be solved to a simple level and not to its simplest level. This meant that once we had reached an answer (say) 3 + 2, we were advised to stop working on this problem and move ahead to another problem as the answer 3 + 2 is simple enough. There is no need to total it to 5. And here is the best part - He said that he would deduct a mark for writing 5 as the answer as we would be wasting time and not adding any meaning to what was already simplified as 3 + 2.
This system is markedly different from our Indian counterpart. In my opinion, the Indian draconian system of marks allocation, for every significant and insignificant step of the mathematical problem, is more an extension of the latent desire for power and domination that many in the education department and government harbor (apart from imparting a petty and clerical mentality on students).
The math class in USA eventually prepared us for a level where we understood the implications of calculus on financial statements, how algebra is a must for a newspaper layout editor etc.
Therefore, the point is that the system in USA put a great deal of emphasis on "knowing the subject at hand and enhancing one's ability to solve one's problems by using mathematics".
I consistently use Calculus for my management accounting and financial reporting work. However, one can argue that this is all at graduate school level. However, I am sure, similar simple practical uses can be demonstrated to students in primary and secondary schools so that students clearly understand their own need to study mathematics.
© Nitesh Kotecha
