How to teach Science & Maths

JBNSTS Science Teachers Training Program

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Ramakrishna Mission Vidyamandira (Ekalavya Model Residential School), Jhargram

Revered Swami Shantimayanandaji Maharaj, Revered Swami Shubhakaranandaji Maharaj, distinguished guests on the stage and learned colleagues: it is a pleasure to be present here amongst you all today and to deliver the keynote address at the JBNSTC Science Teachers Training Program. I came to this school exactly one year ago, just a day before Ramakrishna Mission took over this school from the Government. Today, when I entered the campus, I was wonderstruck at how much it had changed. Indeed, the efforts of Shantanu Maharaj are paying off, and in an incredible manner. Who would have ever imagined seeing this kind of development in this remote school! And that too in so short a time! It will not be an exaggeration to say that Bhagawan Sri Ramakrishna is using Shantanu Maharaj and his team to work up a revolution here in this Ekalavya School at Jhargram.

Today onwards, JBNSTC will be conducting a workshop for the Science and Math teachers. I am given to understand that there are teachers from various schools of Jhargram.

I too have been in this education area for the last decade. I know what problems areas exist for us. I am also aware of how ill-prepared we are for handling those problems. It is a tough job we are doing. In fact, our job is also very dangerous. You know, once George Bernard Shaw was asked about the most dangerous profession in the world. He replied that it was ‘teaching’. His humorous argument was like this: if a lawyer makes a mistake, it hangs six feet above the ground, and then the whole world forgets about it. If a doctor makes a mistake, it is buried six feet underground, then everyone forgets about it and the world moves on. But if a teacher makes a mistake, six hundred years of the country’s history gets damaged!

When I was asked to look after a school in Arunachal Pradesh, I made a special study of the Jesuit philosophy of Education. One particular saying of the Jesuit Father Ignatius Loyala seemed to sum up the entire philosophy of teaching, for me. He said, “If you wish to teach Math to John, you should know Math and you should know John.” Just look at this statement!

We must know our subject very well. After some years of teaching the ‘syllabus’, we become experts, so to speak. We develop the habit of going to classes without any preparation. We are confident of winging it! I remember seeing some books in our Bangalore Ashrama. There was a very revered Swamiji there long back called Swami Yatishwaranandaji. He was a great scholar and a highly venerated monk. Yet, till the last, he would prepare notes for his lectures! Those books had those notes; painstakingly he would write down all the points he would deal with in the class. He naturally had no need to such notes. It was all at his fingertips. Yet…

We should ‘know’ our student. What is meant by this? Is it that we should know about his family background? The problems he faces at home? Those things too matter. But what is more important is that the boy is not a blank slate. He comes with some fund of information in his young mind. Can we understand that? Unless we know that, we can never really teach him effectively. The problem is this – we too were students once upon a time, and we too had struggled with ideas; for a long time, the concepts and principles made no sense for us too. Then, the constant effort we put in bore fruit and connections were made with pre-existing ideas in our brain! And we have forgotten how exactly those connections were made. If only we can recall those moments, we will be able to really ‘know’ our student!

I am sure you all will agree with me that teaching Science and Math is especially challenging. Teaching any subject, for that matter, is a tough job. But more so with these two subjects. Why? Because they are very dry. Consider History or Literature. There are stories, plots, sub-plots, poems, intrigues, heroes and villains; there is always an excitement about what will happen next! That is completely absent with Science & Math. Just lifeless ideas and numbers! Have you wondered why there has been no blockbuster Bollywood movie on Science? Our subjects don’t lend themselves to that kind of treatment.

I wish to place two ideas before you today. Actually I will be sharing these two ideas, which are actually my life-lessons during my stint as a teacher. First, the importance of remembering facts and principles; second, some techniques I picked up on the way.

We must acknowledge the fact that we need two different approaches while teaching Science & Math. The approach we adopt for the students up to secondary level is different from the approach we adopt for teaching the HS students. But, in both cases, we need to emphasize the habit of learning by-heart a whole lot of facts. I am afraid, we don’t do this. Our present examination system is doing away with this habit. And it is working to the detriment of our boys. Unless the boy knows a whole lot of things my memory, he won’t be able to play with ideas. Playing with ideas, calls for a solid fund of facts in the brain. And what is Science & Math teaching-learning if it’s not playing with ideas! Just take a look at the ancient tols in our country. The first few years of the student’s life was spent in rote-learning. If the student could learn by-heart a certain set of books, he could graduate to the higher education. Then would start the most interesting play with the ideas which the boy could recall from memory!

For instance, in our Aalo School, I had to teach force analysis in Mechanics in Class-XI. I found out that the students had no clear understanding of trigonometry. During those days, trigonometry was taught in Class 9 & 10. So I passed on this feedback to teachers who handled those classes. The next batches became better!

Similarly, once our HS Chemistry had resigned in the middle of a year. So I had to handle Chemistry for Class XII. While teaching the class, I found that the students had trouble working numerical problems in Electrochemistry, especially the ones on Nernst’s Equation, etc. I found out why that was so. The students had to have a conception of logarithms for working these problems. And wonder of wonders, the CBSE in its great wisdom had removed logarithms from the entire school syllabus. Hence it was never taught! So, I sat with my teachers and decided that we would give an introductory class on logarithms to our Class XI students. That too bore great results later on for us.

Remembering facts and numbers must become a passion with students. It must seem rewarding to the students. We need to encourage students to develop their own ‘memory development techniques’. Mnemonics, for instance, could be very helpful.

  • To memorize the colors of therainbow: the phrase ‘Richard Of York Gave Battle In Vain’ – each of the initial letters matches the colors of the rainbow in order (Red, Orange, Yellow, Green, Blue, Indigo, Violet). Other examples are the phrase ‘Run over your granny because it’s violent’ or the imaginary name ‘Roy G. Biv’.
  • To memorize the North AmericanGreat Lakes: the acronym HOMES – matching the letters of the five lakes (Huron, Ontario, Michigan, Erie, and Superior)
  • To memorizecolor codes as they are used in electronics: the phrase “Bill Brown Realized Only Yesterday Good Boys Value Good Work” represents in order the 10 colors and their numerical order: black (0), brown (1), red (2), orange (3), yellow (4), green (5), blue (6), violet or purple (7), grey (8), and white (9).
  • To memorize chemical reactions, such asredox reactions, where it is common to mix up oxidation and reduction, the short phrase ‘LEO (Lose Electron Oxidation) the lion says GER (Gain Electron Reduction)’. An alternate mnemonic is ‘Oil Rig’ can be used – which is an acronym for ‘Oxidation is losing, Reduction is gaining’.
  • To memorize the names of the planets, use theplanetary mnemonic: Each of the initial letters matches the name of the planets in our solar system (Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, [Pluto]).

Mean Very Evil Men Just Shortened Up Nature

Mary’s ‘Virgin’ Explanation Made Joseph Suspect Upstairs Neighbor

My Very Easy Method Just Speeds Up Naming Planets

Many Very Educated Men Justify Stealing Unique Ninth

My Very Educated Mother Just Served Us Nachos

  • Mnemonic phrases or poems can be used to encode numeric sequences by various methods. One common one is to create a new phrase in which the number of letters in each word represents the according digit of pi. For example, the first 15 digits of the mathematical constantpi (3.14159265358979) can be encoded as ‘Now I need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics’; ‘Now’, having 3 letters, represents the first number, 3, and so on. Piphilology is the practice dedicated to creating mnemonics for pi.
  • To remember the order oftaxa in biology

(Domain, Kingdom, Phylum, Class, Order, Family, Genus, Species):

Dear King Philip Come Over For Good Spaghetti/Soup

Do Kings Play Chess On Friday Golf Saturday?

Do Kings Play Chess On Fat Green Stools?

Did King Paul Cry Out For Good Soup?

Do Kings Play Chess On Fine Green Silk?

Dumb Kids Prefer Candy Over Fancy Green Salad

Dumb Kids Playing Catch On Freeway Get Squashed

Do Kids Pass Chemistry Or Flunk General Science?

Does King Phillp Come Over For Grape Soda

Don’t Kill Parrot’s Carrots Or Face Gruesome Sicknesses

  • To remember the lifecycle of cells

(Interphase, Prophase, Metaphase, Anaphase, Telophase, Cytokinesis):

Idiotic Penguins Make Antarctica Too Cold

I Pee More After Tea Consumption

  • To remember the common functional groups

(Hydroxyl, Carbonyl, Carboxyl, Amine, Sulfhydryl, Phosphate, Methyl):

Hair Care Can Always Save People Money

  • To remember the processes that define living things:

MRS GREN: Movement; Respiration; Sensation; Growth; Reproduction; Excretion; Nutrition

  • Metabolism; Response; Homeostasis; Growth; Reproduction; Nutrition:

My Really Hungry Grasshopper Refuses Neglect

  • To remember the roles of reproductive organs in flowers:

Stamen are male; stigma (as in mother) are female

  • To remember the number of humps on types of camels:

D in Dromedary has one hump; B in Bactrian has two

  • To remember the 6 nutrients (Water,Carbohydrates, Proteins, Minerals, Vitamins, Lipids).

What Car Protects My Vital Lips?

Order of mathematical operations

PEMDAS- Parenthesis, Exponents, Multiplication & Division, Addition & Subtraction can be remembered by the phrase: ‘Please excuse my dear Aunt Sally’.

BEDMAS – Brackets (parenthesis), Exponents, Division & Multiplication, Addition & Subtraction

BIDMAS – Brackets, Indices (exponents), Division, Multiplication, Addition, Subtraction

Trigonometry

ASTC stands for All Students Take Calculus, as well as the more simplified mnemonic Add Sugar To Coffee, which represents the trigonometric functions that are positive in each quadrant, beginning with the top right and continuing counterclockwise: All, sine, tangent, cosine – All Science Teachers Are Crazy – All Silver Tea Cups – Annie Spewed Terrible Curses

Remembering the definitions of sine, cosine, and tangent can be done by memorizing SOHCAHTOA, which helps to encode Sine = Opposite over Hypotenuse, Cosine = Adjacent over Hypotenuse, and Tangent = Opposite over Adjacent. These mnemonics are more useful if they can be recited in three groups of three words.

Other ways to remember SOHCAHTOA are:

Some Old Horses Can Always Hear Their Owner Approaching

Some Old Horse Came A-Hoppin’ Through Our Alley

Silly Old Henry Can’t Add Hundreds, Tens Or Anything

Some Old Hags Can’t Always Hide Their Old Age

Some Old Hippie Caught Another Hippie Tripping On Acid

SPH-CBH-TPB (sine = perpendicular/hypotenuse, cosine = base/hypotenuse, tangent = perpendicular/base)

Some People Have Curly Brown Hair Through Proper Brushing

Some People Have Curly Brown Hair Turned Permanently Black

Another odd permutation:

Oranges Have Segments, Apples Have Cores, Oranges Are Tangy

In Hindi, there is a funny mnemonic — Sona Chandi Tole Pandit Badri Prasad Har Har Bole, where:

Sona = Pandit / Har (sine = perpendicular/hypotenuse)

Chandi = Badri / Har (cosine = base/hypotenuse)

Tole = Prasad / Bole (tangent = perpendicular/base)

Let us remember that if we initiate our students into this interesting game of forming mnemonics, they will later on formulate creative ways by themselves. And that will go a long way in enabling effective teaching-learning in the higher classes. It is like building a large vocabulary when it comes to speaking a language. If you don’t have a good fat fund of words, what will you speak?

So, this is the first idea I wanted to share with you. The second idea I want to share with you all is – I have picked up some important techniques which I have used to great advantage with my students. I will explain them one by one.

We must try to provide a physical manifestation of the concepts we teach. For instance, while teaching fractions; consider we have to teach the concept of 2/7. Take a long stick and divide it into 7 parts. Place all the parts on the table and show how it can be called 7/7. If you take 2 parts away, then the arrangement would be called 2/7. A child who sees this demonstration will develop a new insight into numbers, which will blossom into something wonderful in the higher classes.

Why can’t we provide a rationale for the concept that is being taught? What do we do? We take up some idea like differential calculus. We open a standard text book, start dealing with the rules and then proceed to working out the numerical problems. Of course, our Indian boys and girls are really good at picking up unrelated bits of ideas and living their entire lives with those bits of nonsense running riot in their brains! I once read in a book how to introduce the students to the concept of Limits that forms the basis of differential calculus.

We all know the famous story of the hare and the tortoise. Let us assume that the tortoise is given a head start. After the tortoise runs for 1 hour, let us allow the hare to start running. Let us assume that in 1 hour, the tortoise has covered 100 meters. Let us assume that the hare covers this distance in 1 minute. Did the hare catch up with the tortoise? No. Why? Because in that 1 minute, the tortoise would have moved 1 inch more. Let the hare cover that 1 inch in say 1 second. Did the hare now catch up with the tortoise? No. Why? Because in that 1 second, the tortoise would have moved 1mm. Let the hare cover that distance in 1/100th of a second. Again, our linear logic tells us that the hare will never catch up with the tortoise. So, the four operations on numbers – addition, subtraction, multiplication & division – are incapable of analyzing this problem for us. We need a new operation now. And that is Calculus. When the time and distance divisions become smaller and smaller so that they approach the limit of zero, the hare will finally overtake the tortoise! Thus, in this case, the real world and mathematics will match only if we adopt this new tool called calculus.

We teachers have to provide a perspective for the concept we teach. We seldom do that. The ideas we teach are obvious to us. They need not be so obvious to our students. I recall; I was once teaching the concept of coefficient of thermal efficiency to Class IX students in Aalo. I used the standard example of the railway track, as given in the NCERT textbook. At the end of the class, I saw blank expressions in the eyes of my students. I delved inside their minds to find out where the disconnect had happened. Why hadn’t they understood what was to me a very simple concept? Do you know what I found out? Those students hadn’t ever seen a real railway track! The only tracks they had seen were in TV and movies. You never get to see the gap in the tracks in the movies or TV, you see.

How about making the students aware of multiple approaches to same problem? Many of us have the habit of teaching according to the ‘syllabuses’. Then there are the five-year or ten-year question papers. A lot of today’s education is governed by these two – syllabus & past question papers. I once overheard one of my teachers; a boy had asked him something; this sage replied, ‘Hey, that is not in your syllabus; they will never ask that in the Exam; don’t bother!’ And, we all worry – why don’t the students of the present generation respect us anymore?! Anyway, we need to make students aware of more than one method of approaching the same problem. Take the example of Factorization. Let us say, we need to find the factors of (x2+5x+6). This is exactly of the [x2+(a+b)x+ab] = (x+a)(x+b) form. With a=2 and b=3, we can factorize this expression as (x+2)(x+3). Well, that is one way of doing it. If we make the students work out many problems of this type,

Then there is another way too. Suppose we need to factorize (x2+5x+7). The students cannot do this with the technique we taught them. They will need another technique for this. Hence we will teach them about roots of the quadratic equation. : . Now, the original expression itself will be seen in a different form, not the [x2+(a+b)x+ab] form, but as (ax2+bx+c). Then we teach the students that these two forms of the quadratic equation are indeed one and the same, interchangeable.

Another important technique I learnt about teaching Science to students is to explain the historical background for those concepts. Take for instance thermodynamics. We know that there is the Zeroth Law of Thermodynamics. Now, how can someone name a law as the Zeroth Law? It is unimaginable. Listen to a story.

There was a numismatic exhibition. Many famous coin-collectors had put up their collections on exhibition. There was a prize for the rarest coin. The prize went to a person who had exhibited a coin which mentioned ‘53 BC’! Now, how can someone print BC on a coin? BC means before Christ. How the hell did the people at that time know that they were 53 years before the birth of Christ?! That coin was fake!

Similarly, with this Zeroth Law! How could anyone know that this was the Zeroth Law? Any sane person would have named it the First Law of Thermodynamics. What actually happened was this: the 1st, 2nd & 3rd Laws of Thermodynamics were enunciated long ago. Then, sometime in the 1930s, there was a British Science teacher called Fowler who was teaching Thermodynamics from a book written by two Indians Saha & Srivastava. In this book, on the 1st page itself, the two authors have mentioned the principle of equivalence of temperatures. Fowler realized that if the three known laws of thermodynamics have to stand, then this equivalence principle was fundamental. Hence, he couldn’t name it as the fourth law of thermodynamics and was constrained to name it the Zeroth Law! That is how it happened.

Lastly, I wish to emphasize the idea of teaching students to imagine vividly, in pictures. We have to understand this world around us. We need a language to do that. Mathematics evolved as that language. However, we can still think quite clearly about everything in this world without resorting to Math. This habit has to develop. After sufficient failure in dealing with this world purely in pictures, we will be forced to resort to Math; not before! The mistake we do is to introduce Math to students without allowing them to struggle with the situation purely armed with their imagination. For instance, take this problem[1]:

A boat carrying a large stone is floating on a lake. The stone is thrown overboard and sinks. The water in the lake, with respect to the shore

  1. Rises
  2. Drops
  3. Remains the same.

It is possible to imagine what happens here. The answer can be arrived at by purely imagination. Math is not required to answer this question. However, if we need to find out how much the boat will rise after the stone is thrown, we will need to use numbers, not until then.

So, I have shared some of my ideas about teaching Science & Math with you all. I believe I have set the tenor for the workshop. I hope the next three days will be profitable to all of you. I pray to Bhagawan Sri Ramakrishna to shower His blessings on you all and on this EMRS Jhargram School.

***************

[1] These problems are called “Mazur’s Concept tests”.

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Author: Swami Vedatitananda

Monk of the Ramakrishna Order

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