Calculus is one of the most challenging subjects students may take. Some students may find that learning calculus in a classroom may be overwhelming or impossible to understand. Due to its difficulty level, finding a private calculus tutor can be crucial for ensuring academic success.
Here are a few of the reasons why students struggle with calculus:
Students attempt calculus before they have grasped previous concepts
More than any other subject we learn at school, maths requires us to build off of existing knowledge and skills. We ought to be fluent in basic maths before we can progress. Unfortunately, this frequently doesn’t happen. Due to large class sizes and the need to move quickly through a packed syllabus, teachers move ahead before all of their students are fully comfortable with a topic. In maths, this is disaster. It is why so many students feel they do not “get” maths. They are working on difficult problems before they have got to grips with the tools needed to tackle them.
It is abstract
Basic arithmetic, geometry and algebra are all easily explainable with references to the real world. As a calculus tutor helping students who struggle with maths, I can draw upon examples of apples and oranges, of how much things cost, or of real life shapes on a page. This helps students contextualise concepts. However, there is no such analogy to help with ideas of “derivative”, “rate of change”, or “limit” when teaching calculus. It seems like a lot of rules with no relation to anything real.
It is non-intuitive
Before we learn calculus, concepts we cover in maths are mostly intuitive. Once you get your head around the idea that xis just a number, it follows that 2xis double that number, or x+1 is one more than it. With calculus, this is not the case. Why should it be that when you differentiate x2 you should get 2x? Why does integrating give us the area between the curve and the x-axis? It doesn’t seem to make sense.
Students have been taught rules but not reasons
A quick fix for students struggling with maths is to learn rules to solve specific problems. But this is akin to papering over cracks in order to sell a house. As time goes on, those cracks are going to cause big issues. Students need to understand what they’re actually doing. With particular regard to calculus, many students don’t know what a function really is. They think of it as just another equation instead of an “input-output machine”. This means when we introduce calculus as a way of describing how functions behave, the student has no idea how to interpret that. A function can behave?!
The good news is that this can all be fixed. If you are struggling with calculus there are simple steps you can take:
Fill in previous gaps
Make sure you fully understand all the calculus concepts you have covered in previous years. Even if you passed your exam that year, take the time to go back and make sure you really understand what’s going on and why. A calculus tutor can help you with this.
Speed up your basics
Calculus draws on many different areas of maths and the problems can take time. They can be overwhelming. If you can speed through the easier aspects of solving a problem, the brain power required to solve calculus problems is reduced dramatically. Go back and practice easier questions and methods until you can do them in your sleep.
Practice calculus problems
Calculus can be hard. It’s not that intuitive at first and there’s a lot to get your head around. But maths is like a musical instrument or a language – you get better with practice. If your basics are solid, but you still can’t do calculus problems, just keep practicing them. Every day if you can! With time they will start to flow and become natural to you.