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The Downward Spiral of Math Avoidance

Okay, so imagine I’m a student who is having a tough time in math. Because I’m having a tough time with the content, doing the homework is a struggle, and that struggle is uncomfortable. Homework is bad enough as it is, but what I’m experiencing is much worse: homework where I don’t know what I’m doing. Hence, I often choose to not do the homework.

So because engaging with math is uncomfortable, I avoid it. Because I’m not practicing, I fall further behind. I never completely understand any of the topics being taught in class, so I’m unprepared for whatever comes next, which means that the next topic will be even more uncomfortable, so I’ll be even more inclined to avoid it.

This only gets worse as time goes on. In class, I feel less and less inclined to engage with what’s being taught, less and less inclined to take notes and ask questions. At home, I conveniently “forget” to do my homework. On tests, I feel like I’m drowning. In other words, I’m experiencing the downward spiral of math avoidance:

This downward spiral leads me to believe that I’m “bad” at math. But because I can’t see this feedback loop – because I don’t understand the pattern – I think that I’m the problem. I think there’s something wrong with me, that I’m “not a math person,” or that I’m simply not smart enough to learn the math.

And because each new math topic is more uncomfortable than the last, I start to really dislike math. I decide that math just isn’t my thing. I don’t recognize that I just don’t like things that I have a hard time with. It’s a natural human tendency to prefer doing things we do well and avoid things that don’t feel good. If I always get praised for the way I sing, I’ll keep on singing. If I crash my bike and get hurt every time I go for a ride, I will quickly decide that I don’t like riding bikes.

This downward spiral of math discomfort and math avoidance sets me up to have fixed-minded beliefs about my relationship with math that actually have nothing to do with my own abilities and everything to do with this feedback loop.

Reversing Course

The good news is that feedback loops can be reversed. If I take notes in class, ask questions, learn techniques, use resources to figure things out, and practice math on a regular basis, I’ll start doing better. This will feel good, making me less inclined to avoid math. As I continue engaging with math, I will find more and more success, and math will be more and more enjoyable.

Thus, the happy opposite of the downward spiral is the following feedback loop:

Reversing course may be simple, but it’s not easy. If I’ve been in the downward spiral for a long time, the behavior pattern will have some serious momentum behind it. It’s always better to intervene early. The further I fall behind, the harder it is to catch up.

The longer I’ve been in the downward spiral, the more toxic my relationship is with math. Once I’m really deep in the pit, I won’t be able to see the light of day, and I’ll lose hope. If I’ve fallen to that depth, I’ll need a great deal of help climbing back out.

I will need a steady stream of growth-mindset reframes from coaches, parents, tutors, and teachers. Because I don’t believe in myself, I will need to hear these people repeatedly express a certainty that I am capable of figuring the math out and capable of getting caught up. But this must be realistic optimism, backed up by concrete support and my own hard work. I might simply need to be reassured that I can, in fact, reverse course and build positive momentum.

I will need content tutoring to support me as I struggle with math concepts. I will need academic coaching to learn techniques to manage cognitive load and form stronger memories, such as making written product and spaced repetition.

I will need to steadily engage with math by paying attention in school, completing my homework, and doing extra practice beyond the homework. This will be very uncomfortable at first, so I might need procrastination coaching to help me get started. I might need help overcoming perfectionism.

Seeing Where You Are

Most students who are caught in the downward spiral of math avoidance are unaware of it, and the few who are aware usually can’t see a way out. Author and YouTube educator John Green said in his TED Talk that “You very rarely go to a place that isn’t on your personal map.” So a student needs to at least know that there’s an alternative if he’s to have any hope of going there.

Students who live in the downward spiral are like hikers stumbling around in the fog without a map and compass. They’re lost, and they don’t know how to get unlost. Our job isn’t just to show them how to do the math, which would be like showing them how to hike, our job is to help them see the territory and navigate it deliberately. Our job is to clear the fog, so they can choose the right direction. We cannot make them walk the path, but we can provide them with the necessary tools and present them with a choice.

Sometimes I have a conversation with a student that goes like this:

Student: “I’m really bad at math.”

Chris: “Oh. Let me ask you something. Aside from the homework they give you, how often do you practice math?”

Student (brow furrowed): “Um, never.”

Chris (happy tone): “Okay, that makes sense. I never practice basketball, so I’m really bad at basketball.”

Student: “So you’re saying I should practice.”

Chris: “Nope. I’m saying you could. You don’t have to, and I won’t be upset if you choose not to, but you could.”

Then we might discuss something they are “good” at, like a sport, a musical instrument, or a video game. And then I map out the downward spiral, so they can see that the issue is structural rather than personal. This pairs well with a discussion of how math is an upside-down pyramid and the mastery path, which are two more structural reasons students struggle with math.

I’ll explain that there is no quick fix, but there is a way forward, and that I would love to support the process if they’re interested.

This applies to more than just math. The downward spiral of discomfort and avoidance shows up in reading, writing, science, the study of foreign languages, and even school as a whole. It’s important that we recognize it and respond to it as soon as possible.

 

Image Credits

Title Image: Creative Commons Public Domain. Courtesy of Pixabay. https://pixabay.com/en/lighthouse-stairs-circular-steps-1069771/#_=_.

Feedback Loops: Loper, Chris. 2018.

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Calculators, Brain Atrophy, and the New SAT

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Disclaimer: I am not anti-calculator. Calculators are genuinely useful and they have an important role to play in academics as well as human progress. Furthermore, for various reasons, such as a dyscalculia diagnosis, some students have been granted an accommodation that allows them to always have access to a calculator for schoolwork, tests, and standardized exams. I am not advocating for these students to abandon the accommodation they are entitled to. I am simply making the case that any student will benefit from regularly practicing math without a calculator.

Math classes have changed during the past few decades. Boring, black-and-white textbooks have been replaced with more colorful ones. Rote memorization has been replaced with exploration and intrigue whenever possible. The newer textbooks favor real-world numbers for which the arithmetic is difficult. Calculators have become more complicated and much more prevalent.

All of this is well and good so long as nothing needs to be memorized and so long as calculators are always allowed. Since we now live in a high-tech world, complete with Google, smartphones, and fancy graphing calculators, it’s easy to see why math classes have shifted in this direction.

But in the spring of 2016, the College Board launched the newest version of the SAT. For over one third of the math questions on the new SAT, no calculators are allowed. Given the direction math classes have gone in recent years, it should come as no surprise that the #1 thing we hear from our students about the new SAT is that the no-calculator section is very hard.

To be fair, this isn’t entirely about calculators. Both of the new SAT’s math sections cover higher-level content than the old SAT did. Students are expected to know nearly everything from Algebra I, Geometry, and Algebra II in addition to the fundamentals from the lower levels of math’s inverted pyramid. In terms of math content, the bar has been raised. The new SAT, in short, is harder.

But it’s especially harder for students who don’t have their math facts memorized. If you have to struggle with arithmetic, the no-calculator section is brutal. After all, the exam isn’t testing arithmetic; it’s testing higher-level math skills and problem-solving. If you have to spend a great deal of mental energy crunching the numbers, you won’t have enough brainpower or time leftover to solve the test’s harder problems. You’ll be slower and less agile because you’re weighed down by excess cognitive load.

You might be surprised how common it is for a student to be doing well in high school math classes but to be simultaneously lacking knowledge of fraction operations, how to set up proportion problems, or how to decode a word problem. To a certain extent, the SAT has always punished students for forgetting these skills. Now it also punishes students for struggling with addition, subtraction, multiplication, and division. Many students have chosen not to memorize their math facts, and now they’re paying for it. Others once had their math facts memorized, but have since forgotten them through lack of practice, in a classic case of use it or lose it.

Because the brain is like a bunch of muscles, any skill we don’t use regularly weakens. If we never use the skill, it atrophies. If you always wear a brace on your wrist, your wrist will become weaker. If you always ride your bike with training wheels, you’ll never develop balance. If you always use a calculator, you’ll forget how to do math without one.

Students who wish to do well on the new SAT will have to go back to basics and put in some time working on the fundamentals. The prospect of devoting time to working on old math is particularly hard to stomach during the schoolyear because there is so much new content to learn, which makes summer the ideal time to work on this goal.

It is possible, however, to make significant progress on the basics while you’re learning higher-level content. You simply have to find opportunities to practice the basics while you’re doing your homework. Essentially, this means choosing to do problems the hard way. Not necessarily every time, but whenever you could do a problem without a calculator, that’s an opportunity to practice the basics. It will make your math homework take slightly longer, but you’ll be killing two birds with one stone. Do it the hard way.

The SAT isn’t likely to change again for many years, and it will take a long time for the school system to shift in such a way that helps students tackle the new exam. So that leaves you. You’ll have to change. You’ll have to choose to help yourself.

 

Image Credit

Title Image: Creative Commons Public Domain. Courtesy of Pixabay. https://pixabay.com/en/calculator-math-mathematics-988017/. Text added.

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Math Facts

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7+5=12

15-9=6

8×6=48

24÷8=3

72=49

¼=0.25=25%

These are math facts. They are simple, mathematical truths that all students are made to learn. At first glance, math facts are just like everything else students learn in school, but there is a difference between learning your math facts and, say, learning to write an essay. Math facts are meant to be memorized.

Now, you don’t have to memorize them. You can, through very slow methods, calculate the answers to each of the problems I just listed. But as you move up in the world of math, you’ll be increasingly expected to have them memorized, and for good reason. If you don’t memorize your math facts, you’ll spend your entire math career weighed down by excess cognitive load.

Solving higher-level math problems takes brainpower. Because the brain is like a bunch of muscles, your brainpower at any given moment is limited. Any mental energy you spend calculating a non-memorized math fact is energy that is not available for the more difficult math you’re trying to do. If, instead, you have your math facts deeply memorized, then you’ll expend no brainpower whatsoever to access them, leaving plenty leftover to think about the problem at hand.

Automaticity is the goal. When your math facts are deeply memorized, you see questions like 7×8 and react instinctively, instantly, and without thought. When it comes to knowing your math facts, understanding is not enough; you have to master them. Walk the mastery path. It’s worth it.

Remember, math is an upside-down pyramid. The simple topics at the bottom form a narrow foundation that supports a top-heavy structure containing all of the upper-level math content:

math pyramid

Because math facts are at the bottom of this inverted pyramid, you can’t afford to have weakness there. Start at the bottom and work your way up.

It’s never too late to memorize your math facts. Even if you’re taking AP Calculus or preparing for the SAT, you need your math facts. Both of those exams contain no-calculator sections, so you’ll be penalized if you don’t know them.

So how do you memorize your math facts?

The best method is to simply work with them on a regular basis. Devote two minutes each day to memorizing your math facts. Even though it would be more total time, doing 20 minutes once a week would be less effective because it would fail to utilize spaced repetition. You can work with your math facts on paper, with flashcards, on Khan Academy, or anywhere, anytime, using mental recall.

One neat trick is to stick a set of flashcards in between the salt and pepper shakers on your dinner table. At the beginning of one of your meals each day, do a two-minute drill with the flashcards. This method helps bring structure and routine into the effort, which is critical because you want the drills to become an automatic habit.

Self-development expert James Clear calls this method of attaching a new habit to a preexisting one “habit stacking,” and argues that it increases the likelihood of having the behavior stick.1 Other examples of habit stacking include flossing immediately after brushing your teeth, meditating right after you have your morning coffee, and writing in a gratitude journal as soon as you go to bed.

I would also like to point out that two minutes is just 0.2% of your waking hours. It’s hard to say you don’t have time for something that takes only two minutes. And I’m certain that you’ll wind up saving a great deal more time on your math homework. Memorizing your math facts is an investment that can pay enormous dividends.

Once you reach middle school, there are so many other concerns that memorizing your math facts will probably never seem urgent. Therefore, you’ll easily find justifications for putting it off or never doing it at all. Just please recognize that you could choose to memorize your math facts, and if you did, you’d be doing yourself a huge favor.

 

Works Cited

1 Clear, James. “Habit Stacking: How to Build New Habits by Taking Advantage of Old Ones.” http://jamesclear.com/habit-stacking.

Image Credits

Title Image: Creative Commons Public Domain. Courtesy of Pixabay. https://pixabay.com/en/maths-mathematics-maths-symbols-1426891/. Text added.

Math Pyramid: Loper, Chris. “Math is an Upside-Down Pyramid.” 2016.