30 May 2023

How to Understand Complex Math Concepts

Math is a subject where the challenges are constant. No matter how good you think you are, there is always a level above that will stress even the geniuses. For the ordinary student though, there are parabolkas in grade 10, transformation and trig in grade 11, and limits and deriviatives in grade 12. There will always be challenges mainly because math is a subject that is cumulative — there are many parts that stack onto each other, switch with one another, and combine with one another. If you think about it, math is extremely fluid.

You should begin to realize this at an early grade – you can’t simply plug in numbers and get an answer. Much of the stress in schools these days isn’t the correct answer anyways — it’s how you managed to get that answer. There is laways several ways to solve a problem, and yhis is where the malleability comes in.

As we stated before, math is cumulative, meaning that all the parts grow and build upon one another. The skills you learn in grade  will be used in grade 12. Surprised? well fractions are familiar, but you don’t start applyong them to graphs until grade 11. It’s only then taht the confusion sets in.

Three tips to help you through understanding conplex problems are:

  1. Asking why
  2. Organization
  3. Explaining the concept in plain English

Asking Why                                                   

Asking why is the original way to learn about life as a child, adn it has the same effects here in math. Why do the operations function the way they do? Why would the steps flow this way? What does it accomplish? These are questions that will help clear things up.

Simply asking questions will help you understand the underlying mechanics. Here’s an example: In trig, why do we need the CAST rule? It helps you to determine whether a value is positive or negative, depending on where the triangle is located. In his case, you will begin to relate the location of the triangle to the signs of the answer, rather than blindly memorizing the steps.

Asking Why                                                       

Let’s stick with this example for a second. Look at graphs. Most students know that the number in front of the graph determines its vertical stretch and shrink, but have you ever asked why? This is because a trig function gives you a value (y value), and if you multiply that by a number, it will make the value bigger. If you apply that to every single number on the graph, it will make the entire graph bigger, and therefore create a vertical stretch.

If you can understand this, you can now relate what happens to the graphs if you replace that number with a fraction or a negative. Let’s examine the fraction. The fraction will make the value smaller, and therefore create a vertical shrink. How about negative? A negative in front will change the sign of the value. Now if you apply that to every value in the graph, it will flip the graph upside down, and therefore reflect it across the x-axis.

Simply by asking why, you can unlock the reasoning behind all the equations and headaches. Remember, blindly following formulas may help you in the knowledge and understanding portion of the tests when you’re regurgitating facts, but when you need to actually apply the knowledge, you won’t have a clue if you don’t understand it. Make sure you ask why!


Organization is a life skill, not simply one for math. However, even if you aren’t the nearest person, adopting some organization skills for math might not be a bad idea. As you get to know the different parts of a concept, it might help to organize the big picture. The problem is that the teachers and textbooks often teach in scattered parts, only giving snapshots of the whole. What you need to do is try to evaluate the entire concept by putting all the pieces together. How to do this? Garb a sheet of paper and dig into the questions of the textbook.

As you’re going through the questions, start to fill in this idea of the big picture. What happens if a certain value or algebra changes? Is this new to you? If it is, write it down. If you keep going, you’ll end up with a summary sheet containing the different scenarios.

Now you’ll have to categorize these questions into different types. For example, if a question with integers operates differently form one with fractions, write his down. If you encounter a question that is entirely different, make a new category and plop that one down in there. Keep going through all the questions. Now you’ll have a comprehensive package containing all the questions and summaries. By this time, you should have a good understanding of the overall picture of the chapter, along with its parts and scenarios. This will help you tremendously in your tests and exams.

The key is to remember this: high school math is only so difficult. Teachers are restricted by the levels of math they can give you. If you can ace and keep organized the materials in your textbook, you’ll be fine. It all comes down to perseverance!

Expalin Yourself in Plain English                       

They say you learn the most when you can teach someone else. That demonstrates true understanding. So, teach someone! Or at least, pretend to. And to do that, imagine explaining these concepts to a classmate. Can you do it simply enough? If your explanation isn’t simple, then your understanding isn’t good enough.

Can you answer the following questions? What are you trying to do? How are you doing it? Why are certain steps relevant? Don’t be shy and let it all out. If you skimp out on details or hide something, it might change someone’s understanding. If you can’t do this successfully, go back to step  and ask someone else to explain it to you!

The post is originally written by Queen Elizabeth AcademyMath Tutor Mississauga.