Removing The Fear Of Calculus In Maths – One Concept At A Time

You may have already heard from several mathematics experts that,

“Calculus is to understand;not memorise."

But the fact is, many students in Singapore or elsewhere actually don’t have the idea how to understand calculus. They don’t want to memorise it, but they don't have any other way, as they cannot get a grip on it through logical understanding.

As a result, it remains that uncharted territory that they want to get rid of, as soon as possible.

But it shouldn't be. Calculus can be real fun if you know the basics.

Beyond Secondary 4 and JC level in Singapore, it begins to show its true colors, in subjects like physics, engineering, economics, computer science and data analysis. From rates of change and optimization to accumulation, calculus keeps reappearing often without the label.

So, it’s essential that you have a strong foundation without fear.

At Miracle Learning Centre, our maths tuition classes specifically aim to make calculus as interesting as it can be for students, who are struggling with the concepts of differentiation and integration.

Identifying The Source Of Calculus ‘Fear’

Sometimes, we notice that even the students, who have scored really well in O-Level maths, are struggling with calculus. The reason isn’t their incompetence, but mostly the way the topic is introduced to them.

One thing that you need to know for starters is,

Calculus is not a set of rules to memorise but a way of understanding how quantities change and how values accumulate over time.

So the next time you encounter problems like:

• Differentiate this.
• Integrate that.
• Apply this formula.
• Substitute into that equation.

Don’t get shaken up. And don’t try to copy stuff to speed up.

Understand first. Ask questions.

Only then calculus will feel like a strong foundation and not a house of cards by the end of the season.

Understand What Calculus Is Trying To Say

To simplify the entire world of calculus, you need to understand two core principles -

• Differentiation - How fast something is changing at any given moment
• Integration - How much something has built up over the time passed

But trust us, we know how difficult it can be if you start solving equations only after knowing this. You need to go step-by-step, like:

Step 1: First observe and understand what the problem says. Is it talking about something increasing or decreasing? Also, is it about speed, area, growth or accumulation?

Step 2: Understand the type of change being asked for, like the rate of change or how much change has happened.

Step 3: Now it’s time to translate the situation into a mathematical solution. Use equations, graphs, whatever seems apt.

Step 4: Apply the right method after careful consideration. And voila! You have solved it.

If you don’t rush and attempt each step properly, there will come a time when just seeing the problem will give you the right direction without panic.

And that’s what we teach every student in our maths and Secondary maths tuition classes in Singapore. That Calculus starts to be meaningful when you engage with the ideas behind it and not rush to solve it right away.

Differentiation That Describes Change

Let’s consider a car moving along the road. And a graph shows distance on the vertical axis and time on the horizontal one.

Now,

Slope of the graph = speed

Steep slope = fast movement

Flat slope = no movement

Derivative = dy/dx

This derivative tells us about the slope of the graph at a definite point.

If y = x², dy/dx = 2x at x = 3 and hence, the slope is = 6

It means that the rate of change of y with respect to x at that particular point is 6.

Now let’s connect this to physics.

Velocity = derivative of distance

Acceleration = derivative of velocity

So you see that differentiation is just finding the slope of a graph at a specific point, i.e. the instantaneous change at any given moment.

Integration That Accumulates The Change

Now, integration is no new evil; it’s just the lifelong partner of differentiation.

It’s simple actually. While differentiation breaks things up into micro units, integration builds them up.

Mathematically,

∫ f(x) dx

Let’s consider an example

Calculating the area under a curve.

y = x²

When we draw the graph, it becomes a curve.

Now imagine we want to find the area between the curve and the x-axis, from x = 0 to x = a.

As the graph is curved, we divide the area into multiple thin vertical strips, instead of rectangles or triangles.

Each strip has:

• a small width
• a height given by the value of the function x²

When we add the areas of all these tiny strips together, we get the total area by, you’re right, integration.

Mathematically, we write:

∫₀ᵃ x² dx = a³ / 3

This means that the area under the curve y = x² from 0 to a is equal to a³ divided by 3.

Building Confidence In Calculus Through Proper Clarity

In our maths tuition classes in Singapore, the most frequent change that we see in students is the shift from fear to curiosity.

• What change is being talked about in this problem?
• Why is the graph behaving this way?
• What’s the slope telling at this moment?
• What happens if I move slightly left or right on the graph?
• What are they asking beyond the formula?

They start tweaking graphs to observe the change in values, and confidence starts growing with each guess coming right. Soon, we see students, who once panicked at the utterance of ‘calculus’, getting obsessed over it.

And that’s where our real victory lies.

If your child is facing the same issues regarding calculus, give us a chance to transform their fear into passion and ultimately an unflinching confidence that takes them ahead.

Enrol in our maths tuition today!