High School Academics: Math

Each month, our team of tutors will introduce you to a key academic subject and offer you a guide to what to expect. Once you start high school, you’ll take a mix of required courses and electives spanning STEM (math, science, and technology), the humanities and social sciences (including English, history, geography, economics, and psychology), foreign languages, music and art, and health and physical education. You will also have all sorts of extracurriculars to choose from, some of which will allow you to explore these topics in a more relaxed setting. Our series will help you get up to speed and hit the ground running on Day 1! Today, read on about math…

“I wish that I remembered how to do this!” This is the most uttered phrase in my Calculus classroom. My students often tell me that they feel confident with new Calculus ideas but not with the combination of fractions or simplification using exponent rules or something else from earlier in their math careers. And the same thing happens in my Statistics classroom! And in my Precalculus classroom, and even in my Algebra 2 classroom.

This brings up a big question. Why is our prior math knowledge often not what it needs to be?

In your middle school math years, your goal in a math problem is typically to get an answer — to find the area of a circle, to add fractions together, to simplify a square root. If you have taken an SSAT or HSPT or another standardized test, where your goal was to quickly figure out which letter to choose, you know this very well!

This way of thinking about math favors working quickly, showing little work, and thinking about each question individually. It also, unfortunately, makes it really easy to forget everything as soon as the test is over. And two, three, or four years from now, you’ll be sitting in a math classroom wishing that you remembered these concepts and tools.

Contrary to how it may seem in your current math classes or test prep, math is not a disconnected set of ideas full of quick and easy steps to get nice, pretty answers. Math is a language. And just like with any language —English, Spanish, Arabic, even Java (!) — the point of math is to learn how to draw connections and communicate logically and effectively. The math that you are working on now is the foundation of this language and is giving you the building blocks to form the sentences and paragraphs and stories of higher-level math. Just like you need to learn how to conjugate verbs in Spanish, identify root letters in Arabic, or figure out the proper notation in Java, you need to know the foundational aspects of the language of math, like how to simplify expressions, how to graph on a coordinate plane, and how to solve an equation.

Now, we know that the point of learning how to conjugate a verb in Spanish, for instance, is not just to conjugate a verb quickly on a test and never do it again. The point of learning how to conjugate a verb in Spanish is to ultimately be able to converse in Spanish, to get to the point where you can conjugate verbs and pick vocabulary words and form clearly structured sentences as effortlessly as you do in your first language. The same is true for math. The point of learning your foundational skills right now is to be able to use and combine them easily in your higher-level thought processes, not to quickly use them right now and never think about them again.

So, I encourage you to shift your thinking about your goals in your math classroom. While right now, you are learning ideas that may seem straight-forward or disconnected from each other, keep in mind that you are really learning the building blocks of the language of math. They will be an integral part of future courses! Continuously tell yourself that the point is not to quickly get an answer and move on, but rather, it is to understand why a process works so that you can use it later. Continuously tell yourself that you are starting to learn a new language and think about your math practice in a similar way to your practice of another language. The more that you tell yourself that the answer is not really the point, the better you’ll get at focusing on your work, your thinking, and your conceptual understanding. And the more that you do this, the more it will stick — the more you will be able to make connections and remember key concepts as you move through classes, and you will not have to say, “I wish that I remembered how to do this” as you sit in your Calculus class.