Trig was not hard; How you were taught is to blame!
Ask any Indian high-school student, many will answer trigonometry as one of the hardest things to master they have come across till date. But was it really that hard?
Think about your high school days? Did you find trigonometry too hard? You are not alone.
Our method of teaching is broken
It has been said before, yet I state again — Our method of teaching is broken. Instead of making students understand the basics of how things work, our examination pattern has been designed in a manner that forces rigorous rote-learning, even in Maths.
Yes Maths! I personally remember having to sit nights to remember some dozen score trigonometry formulas, and number of chemical formulas that would overflow a signed-byte worth of computer memory (A signed byte in a computer can store a number up to 127), and what not, without knowing why the obscure formulas the way they are. Why sin² + cos² = 1? Why Ethyne was C₂H₂ and not simply CH? No one answered!
Just a fortnight ago, a colleague once asked me about electronic configuration of Iron — something her eighth grader son was stuck with. While I solved it, the trick I used is not taught till 11th grade. Until then, you simply remember it as an exception to the simple 2n² rule.
A Study by Homi Bhabha Centre For Science Education, TIFR, Mumbai highlights this fact. The study clearly shows that subjects such as History, Geography, Language — which involved a lot of rote-learning was particularly perceived as boring and hard by students. In context of mathematics, 29% of students put maths as their hardest subject, with the majority reason also being “hard to learn by-heart”. This clearly shows that instead of practicing and understanding the logic behind the subjects, students blindly opt for rote-learning.
What they could have done
Consider this simple explanation of sine using the unit circle theory:
Let a line through the origin, making an angle of θ with the positive half of the x-axis, intersect the unit circle. The x- and y-coordinates of this point of intersection are equal to cos(θ) and sin(θ), respectively. The point’s distance from the origin is always 1.
Simplifying a bit — it is the x-intercept of any point on the unit circle.
Lines and intercepts are a part of the mathematics syllabus for 8th grade. With a similar definition of the Cosine function, it is trivial to show “sin² + cos² = 1” with a bit of Pythagoras theorem and the radius of the unit circle. Easy to remember and most importantly easy to visualize. Numerous studies have already shown that visualizing is the best way to understand things.
No, don’t throw away the exams
I strongly believe that exams to good. They bring a sense of urgency by imposing a deadline which is effective. But I don’t necessarily agree with the way they are implemented. What we need is a set of exams that test the understanding, craft and creativity and not how well can someone memorize square-root of 42.
Make them modular
Students (myself included) took too much stress during our board (graduation) exams. In addition to lot of content to cover, the marks also determined whether I would be eligible to take courses of my choice. What I believe is smaller modular exams, probably in more frequent intervals could easy out the anxiety and stress in students.
The much longed flexibility
Making the subjects and streams flexible would help students study what they enjoy. I sincerely wished to take up papers on English literature whilst I pursued my degree in Computer Science.
Progressively enhancing courses
One thing I always liked about my (ICSE) curriculum that they always try to introduce concepts slowly, first as a teaser and then in the following years more in-depth study, instead of introducing everything in a bang. This helps to solidify understandings of many concepts.
Though the teaching aids have become somewhat smart, the method is still archaic. Our teachers, if you are reading this, please think of yourself as a student in the equivalent grade, how much could you answer? And please don’t expect your students to be “Sherlock Holmes” and solve “mysteries” of chemical elements all by themselves without any logical explanation. Peace!