See the big picture

There is an old Indian parable about six blind men who only heard about elephants, but had no idea what they were. Villagers wanted them to understand what elephants were so they got an elephant and allowed the men to touch the elephant in order to get an understanding of what this being actually was. The first man touched the side of the elephant and concluded that it’s like a huge wall. The second touched the trunk and said it is a big snake. The third on the other hand touched the tusk of the elephant and said it is a spear. The fourth touched one of the elephants four legs and said it is a large cow. The fifth touched its ear and said it’s like huge fan. And finally the sixth touched its tail and concluded that it’s a rope.

It is clear that none of the blind men got a grasp of what an elephant is, because they were unable to see the big picture. They were focused on certain details – and as we say – they got lost in the details.

As a teacher of mathematics I am constantly thinking of the big picture as it relates to the content I want to impart to my students. I know that if I get them to see the big picture (the main idea of what the piece of content is about) then they won’t have to overly stress about the details. Take a simple concept like gradient/slope (which is merely a measure of steepness). If we try to understand it in a broad and general sense, we would see that it describes how one variable increases or decreases with a unit increase of another. This big picture understanding would make it easy for students to transfer this understanding to other domains of knowledge. For example, students would understand that the exchange rate is the gradient of the line when one currency is plotted against another. Also, in a distance-time graph the gradient gives us speed. This simple concept known as gradient forms the basis for differential calculus (a topic that many find challenging). And so it is with many so called complex topics, they have simple underlying concepts on which they stand. When we get skillful at recognizing these simple underlying concepts we become aware of the fact that things only appear complex when simplicity eludes you.

When you understand the big picture it helps you to see how the details fit into the grand scheme of things. It also helps you to get a deeper understanding of a given topic. There is a myth that is prevalent in the world of mathematics education that excessively practicing mathematics is what makes a student good at the subject. This is only partially true. Quite often students practice math without knowing how what they are doing fits into the larger scheme of things. Consequently, when they are required to solve an unfamiliar problem, they lack the tools necessary to do this. Understanding the big picture leads to a more flexible and fluid understanding of the subject. A student who has an understanding of the big idea within a topic can more easily apply this general understanding to more novel problems.

When learning something new, it is imperative to always ask yourself, what is it that I am really learning? What is the one thing I need to understand that makes everything else easy? If you are unable to come up with a general construct, then ask your teacher to help you. Having an overarching view of a topic prevents you from getting lost in the details and equips you to aptly apply this broader understanding to problems that don’t fall into the proverbial ‘box’.