Education System & its relationship with memorization

With this post I hope to explore a question that has for long troubled me.

What exactly is the place of memorization in our current education system?

And more importantly,

What should be the place of memorization in an ideal education system?

The second question is one that we should keep in mind as we strive to improve our current education system. Because it's best that we openly admit our current failings. Any attempt to look away from our faults just makes it harder for us to improve ourselves.

There are many reasons why seem to hold on to the current method of education which made a lot of sense during the Industrial age when human resources were mainly valued as machines which performed tasks efficiently without room for creativity.

In those times, an employee taking initiative would usually ruin the plans laid down. So the emphasis was on remembering instructions and performing them without question.

But now with the advent of machines, any task which can be done in a mechanical fashion has been automated. As we move into the Information Age, its imperative that the education system stays updated.

I believe that the education system is still playing catch-up, and many other people have their own views - John Baker, The Big Picture, Naveen Jain, Justin Marquis, Shifting thinking just to name a few. I feel that Sir Ken Robinson’s ideas especially resonated with me. But its also important to read the other side of the argument.

Now I will be the first to admit I am biased, its evident to me that I am no good at remembering things I don’t understand and some even that I understand. So I could be suffering from a really strong case of sour grapes.

But it strikes me again and again at various points in my life that,

We should be studying to understand the concepts, not just to perform well in exams!

Most people seem to have forgotten how exams are supposed to be checkpoints, just things which help us reflect on how our pursuit of understanding is progressing.

Now it has turned into a goal by itself, with people trying to beat the system which evaluates them (i.e. the exam). This is plainly not good, because the way I see it the education system is structured in such a way that students (who are young, full of energy, filled with so much potential) are driven to develop ways to crack an artificial problem (the exam).

How does learning how to “score marks” help you? does it add value to society?

Now for that, I guess its possible that it improves our problem solving skills. After all even solving artificial problems should give us some practise. As sometimes it requires the student to analyse the teacher and what questions will come. Manage the limited time in a efficient manner. Even sharpen memory skills. But here another important point arises.

It’s not only about the pros we can find, rather it’s does the cons that exist outweigh the pros?
that is something each one of us should decide, and we do that everyday with our day to day decisions. Is achieving X worth the sacrifice of Y?

I would argue that most students forget the formula’s that they memorizes soon after the need for it vanishes, as many teachers have noted memorization often comes in the way of learning. Also until recent years remembering important “things” was a useful trait given that it was really tedious to find what you needed in a library of books. But with the advent of the internet, Wikipedia, and really smart search engines. Now it’s actually dangerous to rely solely on our human memory with which we are prone to mis-remembering some things.

So then why concepts? why do we need to remember concepts when even those can be found online! Here the thing is, we can’t search for something really specific if we don’t know it exists. So learning various concepts helps you become an actual problem solver. Where we use formulas only as tools to solve the problem. These tools were traditionally kept in our memory hence the reason for the traditional emphasis on rote memorization.

It’s a vicious cycle

Many students are left with almost no choice because society (companies, colleges) need some way of judging (when they have a large pool of applicants) students and exams are one such criteria.

Parents want the best for their child and from their point of view they fuel this greed for marks in order to ensure that their children have a secure future. The students themselfs suffer from loss of self confidence if they fail to get good marks.

Solutions? One of the important things is that a lot of exams are not properly set. Its actually really hard to develop a proper question paper which is hard to game. Therefore paper’s should be set under very strict standards keeping in mind that the objective is to test the student’s understanding of the subject rather than his short term memory.

Also society (parents, teachers, students) should develop awareness on what exams actually are and how they are not always an accurate measuring system. Its when the focus shifts to exams that students start to look for easy ways to score marks.

Its remembering something that you don’t understand for the sole purpose of scoring marks that I am against

even I memorized that the roots of the equation $ax^2+bx+c$ is $$\frac{-b \pm \sqrt{b^2-4ac}}{2a}$$
But just knowing it and not knowing how it came to be, just being able to use it and solve problems isn’t something that should be encouraged or applauded!

I don’t know what’s the matter with people: they don’t learn by understanding; they learn by some other way — by rote or something. Their knowledge is so fragile! - Richard Feynman

I haven’t covered all the points, or completely answered the 2 questions I asked at the beginning but I don’t want to make this too long. So in conclusion,

The main point I am trying to put across is that we should all think about this and if it makes sense, start admitting this problem is very real. We need discussion, we need people to worry about this. Then we can expect that in time some sort of improvement will come.

I am not naive enough to think we will all suddenly change the way we do things, but when I don’t see people actively discussing these things then I wonder. Are my arguments flawed? maybe I am missing some important points.

Or is the education system not worth worrying about? Isn’t it obvious that as long we don’t fix the education system, the future generation won’t know any better and any plans to improve the system gets delayed by a whole generation atleast!

Now you might be wondering why did I write about this now? well I got the motivation to actually sit down and write about this as I was overwhelmed while watching this series The Master of Study. Read more about that on my blog post on The Master of Study - not Learning.

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Position Invariant

I don’t know all the places where you might have come across this term, but I encountered it when studying image processing. They told me that the degradation function (used in image restoration) other than having the property of being “linear” also was “position invariant”.

Now I want to try to give a explanation of what that means, because most engineering students are pretty comfortable with the idea of what Linear functions are as they are used a lot in a lot of the courses.

Consider a image we have described spatially as $f(x,y)$, say that the image is transformed by a function $H$. This means that the function H takes the image $f(x,y)$ as input and gives a “degraded” image $g(x,y)$ as output.

$$H[f(x,y)] = g(x,y)$$

One mistake I initially made was that I thought of $H$ as a function from a image to a different image, its actually a collection of pixel-pixel mappings. For a particular value of $(x,y)$ we get relationship between the pixel intensities.

Why do we care about this degraded function? because the best way of reversing the effect of degradation is to first model it, then find a way to reverse engineer the image before this function was applied. Read more about that in Image Restoration.

but coming to the function $H$, they say that it is postion invariant if

$$H[f(x-\alpha,y-\beta)] = g(x-\alpha,x-\beta)]$$

where $$H[f(x,y)] = g(x,y)$$

now, here a geometrical interpretation that I would like to present for this is that of two 2D planes, one with the domain of $f$ (lets call that the F plane) and the other with the domain of $g$ (lets call that the G plane).

Note that the plane is actually the image itself, with both x and y axis used to position each pixel in $f$ and $g$.

Now $H$ can be thought of as lines starting from points in the F plane and ending up on some point on the G plane. For different $H$ functions, these lines will just move around and establish different relationships between the 2 planes.

In the above picture the red line represents the result of applying $H$ on a single pixel, when you apply $H$ on a image like $f$, then $H$ will be a collection of such lines connecting all the points in $f$.

Now the equation for position invariance makes a lot of sense! what the equation says is that if you take any of the lines connecting 2 points between the two planes; here as a example I consider the line (thick red line) starting from $(x_0,y_0)$ to the $(x_1,y_1)$.

So now if I move a known distance away from this point, (in this case $\alpha$ in negative $x$ direction and $\beta$ in the negative $y$ direction - shown by the yellow lines).

Then the mapping line will also move the exact same distance!

That is; if the mapping $H$ is position invariant then this new pixel at $(x_0-\alpha,y_0-\beta)$ will map to the point $(x_1-\alpha,y_1-\beta)$.

You can sort of imagine it as the red line being fixed to the starting point in the F plane, so when you move the starting point around in the F plane your mapping function $H$ stays stiff and moves along with you.

That wraps that up.

Let me know your feedback and thanks for reading!

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