Category: Math

How to Succeed at Skipping a Year in Math

Posted on by Chris Loper
Reading Time: 3 minutes

a child jumping over a gap

Long-time readers will know that I generally advise against skipping a year in math. For many reasons, it’s usually a bad idea. Nonetheless, many students continue to make this choice, so let’s talk about how to do it right.

Most people just figure that the school said they were smart enough to jump ahead, so that’s good enough. This approach often leads to serious problems down the road: a snowballing accumulation of knowledge gaps and a growing feeling that you’re not really a “math person,” which ultimately leads to giving up on STEM.

Skipping Ahead in Middle School

The most common version of skipping a year is jumping from 7th-grade math to Algebra 1, effectively skipping over 8th-grade math. If that’s your path, then you should spend this summer learning the course you’re skipping.

Make a Khan Academy account (it’s free) and work your way through their 8th-grade math course. Do every single exercise in every single unit. Watch the videos on topics you don’t know yet and take notes.

Khan Academy's 8th grade math dashboard

If something is hard for you, print worksheets from Kuta Software (also free) and work the problems until you’ve really mastered the topic. Take Khan Academy’s quizzes and the tests. Retake them after more practice if you do poorly. Even if you think you already know the material, prove it by doing the work.

If the math comes easily, great, but learning the math is only part of the reason you should do this. The other part is practicing doing more work than you’re required to do. Succeeding in advanced math doesn’t just require intelligence and math knowledge; it also requires diligence and grit. Skipping ahead usually means more homework and more difficult homework, but it also means you’ll frequently need to study and practice beyond the homework. Doing regular math practice over the summer is a powerful way to build this habit.

All of this is doubly important for those students who skip two years – jumping from 6th-grade math to Algebra 1 in 7th grade.

Skipping Ahead in High School

The other way people skip a year in math is by taking a course over the summer. Most commonly, students take an online Geometry class in order to jump from Algebra 1 to Algebra 2. This is, actually, not a terrible idea. It avoids the “Geometry sandwich” that is often problematic for students, and of all the regular high school math courses, Geometry is the least connected to the others.

(A less common – and far worse idea – is to take Algebra 2 over the summer to skip from Geometry to PreCalc. Algebra 2 is the foundation of higher math, and shortcutting through this course is likely to be disastrous. Math is an upside-down pyramid, and all of the layers are important, but Algebra 2 is uniquely important. It effectively serves as a gateway to higher math.)

a gateway at the bottom of a staircase

If you’re taking an online class over the summer (or retaking a class in summer school), you should keep in mind that you’re cramming a year’s worth of content into a couple of months. This makes it much harder to engage in mastery learning, so you’ll have to do more work on your own. I know that’s a tough sell, since it’s summer vacation, and you’re already doing the work at a faster pace than you would during the school year. But if you want to retain the knowledge, you’re going to have to earn it.

What if it’s too late?

What if you already skipped a year, and you’re starting to feel like you’re drowning? Then it’s time to patch the holes in your math knowledge, so you’re actually ready for what comes next. This investment will pay off enormously during the school year.

Imagine if all those lingering areas of math where you’re unconfident – fractions, long division, factoring – were as easy for you as addition. That can be your reality; you just have to earn it. Oh, and those things that were hard to learn when you were young? They won’t be as hard now. You’re smarter than you used to be.

It Was Never About the Math

Posted on by Chris Loper
Reading Time: 4 minutes

complicated math problems on a blackboard

Most people don’t use math in their careers. Most people rarely use anything other than basic math in their daily lives. So, for most people, learning math is a waste of time, right?

Nope.

Nearly all of the benefits of studying math have nothing to do with math. Math is brain training, pure and simple.

Brain Muscles

The various types of math problems students do are like the various kinds of exercise you do at the gym. Rock climbers, football players, and skiers all lift weights at the gym, not because they do any of the same lifting motions during their sports, but because their athletic performance benefits from having stronger muscles in general.

a cartoon brain lifting weights

As I often say, your brain is like a bunch of muscles that get stronger when you use them. There isn’t a “math muscle” in your brain. Rather, math exercises several important mental muscles that everyone needs.

Logic

Math is sometimes described as “the language of logic” because all math must make sense. Everything in math, from 2+2=4 to the way you calculate a derivative, is something that can be explained and understood logically. None of it is arbitrary.

A common mistake students make is to simply memorize formulas without ever trying to understand them. This might result in a good test score, but it doesn’t give you the benefit of exercising your brain’s logic muscle. Plus, if you focus on understanding the formulas, they’re easier to remember.

Problem-Solving

Another critical skill that math strengthens is problem-solving. Math trains you to wrestle with complicated, multi-step problems where the correct path forward is not obvious. Life is full of problems like that.

an electrician problem-solving

When you solve a word problem in math, you’re forced to do the following:

  • Account for what you know
  • Determine what you don’t know that would be helpful to know
  • Discard useless or distracting information
  • Set aside information that you’ll need later but don’t need right now
  • Assess what resources you have available (formulas, methods, etc.)
  • Sort out how to get where you want to go
  • Adapt that plan of action as you work the problem, if you discover it needs to change

That’s what word problems in math are all about, and it’s also what problem-solving in general is all about. You could be remodeling a kitchen, planning a vacation, or designing a website, and the essential skills of problem-solving would be the same.

Flexibility

a very flexible man with his body contorted

Lastly, math is an excellent way to develop greater mental flexibility.

Many areas of mathematics, such as quadratics or integrals, have numerous methods that you could use for any given problem. As you learn them, you accumulate a toolkit. Your job as a math student is to flexibly switch from one tool to another as needed.

Many students express frustration that there isn’t one way to solve all such problems – one tool that you always use. It would be easier if you always knew which method to use, but that wouldn’t help you learn how to solve problems in the real world.

In just about any career, you’ll be faced with novel challenges every day: new problems to solve with the toolkit you’ve acquired through college, on-the-job training, and experience. If the problems were easy and simple to solve, you wouldn’t be getting paid good money to solve them. The work would be outsourced to a cheaper labor source, an algorithm, or an AI.

Whether you’re an electrician, a doctor, an engineer, a project manager, or a carpenter, your job is to solve hard problems by drawing upon your knowledge and grabbing the right tools at the right times. Many branches of mathematics train your brain to do exactly that.

a bunch of tools on the wall of a workshop

It’s Never Been About the Math

Whenever math students are asked to learn something esoteric, someone will complain, “But when are we ever going to use this?”

The correct answer to this question is, “Probably never. But also, always.”

You’ll most likely never use this specific piece of mathematics for anything practical, but you will certainly use the mental muscles and general skills you’re developing by learning it.

Remember, the point of school is not the specific things you learn, but who you become through the learning.

Why Do Students Give Up on STEM?

Posted on by Chris Loper
Reading Time: 3 minutes

a student asleep on their math homework

STEM careers are persistently among the most in-demand and high-paying professions out there, and many children dream of becoming scientists, engineers, or doctors because the jobs sound interesting. But as they go through school, many of these students ultimately give up on STEM.

There are many reasons for this, but the one I’ve never seen discussed is the lack of mastery learning in schools.

The kids who are interested in STEM careers are often the ones seen as smart enough to skip ahead in math. So in middle school, they skip 8th grade math and jump into Algebra 1. Or they skip both 7th and 8th grade math to take Algebra 1 and Geometry. Even for very bright students, this is usually a bad idea. They don’t develop a strong foundation for their math knowledge, and their knowledge gaps come back to haunt them later.

a frustrated student struggling with math homework

Plus, whether or not they skip ahead, the way math classes are taught discourages deep learning. Students are not given enough practice problems to walk the mastery path. Essential learning practices like spaced repetition and interleaving aren’t baked into the curriculum. As a result, most students gain only a shallow understanding of each concept, which they quickly forget.

Furthermore, schools advance students to the next math class as long as they pass this year’s class. But if you earn a 75% in this year’s class, then you’re missing 25% of the knowledge – knowledge that you’ll need to do well in next year’s math class. And, of course, you’ll forget some of what you learned over the summer because hardly anyone practices math on summer vacation, so the amount of missing knowledge is more like 50%.

Eventually, this comes to a head, and students hit a wall. They encounter a math class that they can’t handle. Sometimes it’s Algebra 2. Sometimes it’s Calculus. And the saddest thing is that when they hit that wall, they don’t know the real reasons why, so they conclude that they’re not smart enough.

a student at a desk looking ready to give up

So students often give up on STEM because they mistakenly think that they’re not bright enough to handle the difficult classes, when really the problem is structural. They are smart enough. But schools aren’t teaching STEM strategically, and students aren’t taking matters into their own hands by studying STEM strategically.

So if you’re a student who’s finding your STEM classes too difficult, remember, the problem is not you. These classes are supposed to be hard. And that means you have to engage with them using smart learning strategies and effective study techniques. You’ll probably have to patch the holes in your math knowledge. And you’ll certainly have to do more than they’re asking you to do.

I wish schools would provide you with better structure for success in STEM, but until they do, you’ll have to be proactive and go out of your way to truly, deeply learn the content.

If you’re a parent whose child wants to pursue a STEM career, help guide them. Facilitate summer math practice. Normalize the techniques of mastery learning in your household. (Actively model these strategies with whatever you’re learning.) And don’t push them to skip ahead in math because going far usually requires going slowly.