Should You Skip a Year in Math?

Many parents, mostly of middle-school aged students, express a desire to see their child skip a year in math. Many students share the same desire. Sometimes they see it as a way to get ahead because it will mean they can start taking college calculus while still in high school. Others want to jump up a year in math because some of their peers have, and they want to keep up with the Joneses. Some even equate being on the standard math track with being “dumb” even though it really just means you’re progressing at the normal pace.

So much of our culture and our academic systems are built on comparisons. We compare ourselves to our peers. We compare grades and test scores. We compare our children to other people’s children. While understandable and difficult to avoid entirely, deriving our sense of self-worth from such comparisons is unhealthy. We want to shift away from this sort of dependent self-esteem and toward healthier, independent self-esteem.

It’s Not About Intelligence

Usually, the belief that one’s son or daughter should be allowed to skip a year in math is born out of the belief that the child is “smart” enough to do so. But this reflects a deep misunderstanding about math, intelligence, and school in general. It turns out that being smart has almost nothing to do with whether or not you should skip a year.

You could legitimately skip a year in math when you are a full year ahead in both your knowledge and your skills. This is very different from having a high IQ. One can easily have a high IQ and gain math knowledge very quickly without ever practicing math skills outside of schoolwork, leaving those skills underdeveloped. One can easily have a high IQ and have many knowledge gaps. And those gaps matter. They weaken the foundation of math’s upside down pyramid, setting the child up for difficulties in the future.

Being able to skip a year in math is something that students earn through independent study and extra practice. We often see students who believe that they are entitled to be in an advanced math class but who are completely unwilling to do this extra work.

If, as a 7th grader, you already know everything they’re going to teach in 8th grade, and you’ve practiced it all enough to have it fairly well mastered, then yes, you could jump into Algebra 1. But if you haven’t, then to skip a year would be a mistake.

A Well-Built House

If you were building a house, would you begin construction on the first floor before laying a foundation? Or would you add the second floor before you finish framing the first floor? Of course not. But, as Khan Academy founder Sal Khan points out in this TED Talk, this is precisely what we do with math students. Math is always built on what came before. We move kids through the curriculum, year to year, whether or not they’re really ready to advance.

If you earned a 70% in this year’s math class, you get to advance. But next year, you’ll be expected to not only remember the 70% you did know – some of which you’ll forget – you’ll also be expected to know the 30% you didn’t learn this year. In other words, you get to build next year’s curriculum on top of an incomplete foundation. Likewise, a student who thinks they’re ready to skip 8th grade math but only knows 70% of the 8th grade curriculum is not ready for the jump.

Or course, in either case, the student could make good use of summer and fill in those knowledge gaps, but how many students are willing to do that?

It’s Also Not Entirely About Content

As my rhetorical question makes clear, being “ready” to move ahead in math is about much more than just knowing the content.  It’s also about work ethic and the willingness to regularly practice math when no one is making you. Moving forward in math requires an eagerness to learn strategy and the willingness to use helpful techniques instead of taking shortcuts.

This turns out to be particularly problematic for the very group of students who are most often encouraged to skip a year. Students for whom elementary and middle school math comes easily often run into trouble in Algebra 1 because, up until now, they’ve gotten away with doing problems in their heads. They’ve never learned to engage with pencil-and-paper techniques that reduce cognitive load, so when the math demands that they show their work, they often get stuck, or they make so many mistakes that they get frustrated and start to dislike math.

Furthermore, students for whom math comes easily at a young age are often disinclined to practice. They’ve been told they’re smart, and one way to prove they’re smart is to succeed without hard work. Discovering that they actually need to put in some work to succeed in math is such an unpleasant wake-up call for these students that many ignore it. Every student who has breezed through math with ease will eventually hit the wall. It might not happen during Algebra 1, or even during high school, but it will happen.

It’s one thing to be a year ahead in math ability and content knowledge; it’s another thing entirely to be a year ahead in character development. Skipping ahead successfully requires both. And I’ve just been talking about skipping one year. Many students are encouraged to skip two!

“But I’m bored!”

Boredom is often a reason folks think skipping a year in math is a good idea. The student reports being bored in math class, and this is taken to mean that the class is too easy for him. And although this does sometimes happen, it’s actually very rare.

Let’s assume the class is being taught at grade level and at a pace that is reasonably challenging for the average student. For a student to be academically bored by such a class, he would have to be cognitively far ahead of his peers and already know the content being taught.

Far more common is that the “boredom” is really a normal and natural aversion to paying attention to lectures, taking notes, and doing homework. Math homework that forms strong memories and strong skills generally involves tedious, repetitive problem solving. Math will, for most students, always seem boring compared to video games, television, playing with friends, and sports. Nobody ever said the mastery path would be thrilling every step of the way.

And sometimes this boredom occurs when a class is moving more slowly than it should for the grade level. The fact that this year’s math class is abnormally easy does not mean next year’s math class will be. In fact, if this is what’s going on, next year’s math class will seem abnormally hard because this year’s class isn’t adequately preparing the students.

Repeating a Year

The flip side of jumping ahead is retaking a year in math.

We allow students to “pass” and move forward in math if they earn a 60% or higher. But, as I pointed out earlier, if you learned less than 70% of the material, you’re probably going to have a hard time next year. Sadly, our system is set up such that many students get sent forward when they’re not ready. And, though they may survive whatever comes next year, they won’t feel very good about it. Year after year, they fall further and further behind, and math becomes more and more unpleasant. These students are the ones most likely to fall into the downward spiral of math avoidance.

And that’s a shame. If we allowed more students to proceed through math slowly, making sure that they build mastery at each level before moving on, I think a great many more students would feel capable of pursuing careers in fields that require math. Instead, we rush students through, always moving forward and making it shameful to be “held back,” even though, sometimes, the wiser choice is repeating a class.

And what if your child skipped a year back in middle school and is now struggling as a sophomore? Few people consider this, but it can be a good choice to drop back to grade level by repeating a class.

When a student repeats a year in math, either by requirement or by choice, the family is wading into tricky emotional waters. It is essential that parents use growth-mindset language, expressing certainty about the student’s potential for growth, praising effort and strategy, and avoiding comparing the student to his peers. If you’re in this position, Greg would love to discuss how best to navigate these waters.

Can vs. Should

One way to frame this conversation is to consider the distinction between “can” and “should.” Just because you can move ahead doesn’t mean you should. Just because a teacher is allowing or even encouraging it doesn’t mean it’s a good idea. You can move forward with a D or a C in a math class, but you should consider retaking the class, even though you technically don’t have to.

Choosing not to skip ahead in math or repeating a class might feel like a setback or a loss this year, but it’s likely to be a win in the long run. If the goal is merely to look smart now, then by all means, skip ahead. But if the goal is long-term success, take it slow.

 

About the Author

Chris Loper has been an academic coach for Northwest Educational Services since 2014. He also writes the popular self-improvement blog Becoming Better, so if you liked this article, head on over to becomingbetter.org and check out his other work. Chris also offers behavioral change coachinghelping busy adults with habit formation and productivity. He lives in Seattle, WA.

 

Image Credits

Title Image: Creative Commons Public Domain. Courtesy of Pixabay. https://pixabay.com/en/parkour-performance-movement-jump-643694/.

House: Creative Commons Public Domain. Courtesy of Pixabay. https://pixabay.com/en/cottage-upside-down-house-928979/.

Bored: Creative Commons Public Domain. Courtesy of Pixabay. https://pixabay.com/en/bored-female-girl-people-school-16811/.

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.

 

About the Author

Chris Loper has been an academic coach for Northwest Educational Services since 2014. He also writes the popular self-improvement blog Becoming Better, so if you liked this article, head on over to becomingbetter.org and check out his other work. Chris also offers behavioral change coachinghelping busy adults with habit formation and productivity. He lives in Seattle, WA.

 

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.

Calculators, Brain Atrophy, and the New SAT

calculators-brain-atrophy-and-the-new-sat-title-image

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.

 

About the Author

Chris Loper has been an academic coach for Northwest Educational Services since 2014. He also writes the popular self-improvement blog Becoming Better, so if you liked this article, head on over to becomingbetter.org and check out his other work. Chris also offers behavioral change coachinghelping busy adults with habit formation and productivity. He lives in Seattle, WA.

 

Image Credit

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