Challenges in the American Public School System

By the time kids graduate from high school in the U.S., only 37% are proficient in basic math skills.

Quick caveat here: this statistic is based off of NAEP (National Assessment of Educational Progress) scores which, like all standardized tests, is not a particularly accurate measure of a person’s “intelligence” and has faced its fair share of criticisms. However, it is the only independent measurement that compares an even cross section of America and does deserve a reasonable degree of merit. Further, despite its flaws, the fact that such a low percentage of kids achieve proficiency indicates there are far deeper problems than inaccurate measurement.

It’s not that students aren’t understanding advanced courses such as calculus, the NAEP tests areas such as reading a graph, basic algebra, geometry, numerical manipulation, and logic. These aren’t skills that are crammed in right before the assessment, these are skills that should be taught, understood, and become second nature well before senior year.

Sample question for 12th graders, only 7% got this correct and 15% got this partially correct
Sample 12th grade question, only 40% got this correct
Sample 4th grade question, only 35% got this correct (they were provided a unit conversion sheet)

Clearly the problem begins far earlier than high school. It goes back to some fundamental misunderstandings from elementary school; it goes back to the fear instilled in many children from a young age. And that’s reflected in the test results as well: only 41% of 4th graders and 34% of 8th graders were proficient. And 31% of 8th graders were at a below basic level.

If it’s not concerning enough simply that the majority of students enter adulthood with no real grasp on math and with a visceral fear of numbers, lack of math competency hurts people in areas like finding a job or financial planning. Everyday life requires basic math skills from calculating a 15% tip, to determining the better value peanut butter jar, to figuring out what interest rates mean.

To deconstruct how, we have to look at what currently goes on in schools and how far from the ideal we are.

What makes a good teacher?

  1. Knowledge of the subject
  2. Passion for their field
  3. Knowledge of the student(s)

Knowledge of the subject:

At the core, many teachers aren’t equipped to help a student truly understand the material. For example, in one study, over 50% of elementary school teachers couldn’t conceptually explain why/how multi-digit multiplication worked. In another, over half of 4–6th grade teachers couldn’t name a value between 3.1 and 3.11. It’s no wonder kids aren’t learning.

The best teachers really understand what they’re teaching. The best diagnostic of a person’s math teaching ability is not how many math classes they’ve taken, but how well they can break down and explain concepts, how well they can understand and correct students’ misconceptions. Teachers should be able to explain how and why an answer is correct. They should be able to address questions students have that aren’t directly specified in the textbook. They bridge connections between units.

Passion for their field:

You make kids excited about something simply by being excited by it yourself. Kids look to the adults around them to figure out how to act, so it’s important that their role models show that it’s okay to like math.

However, the fact remains that because elementary teachers generally go in wanting to work with kids, not do math, and yet they are still responsible for teaching it. The majority of elementary school teachers are afraid of math, afraid of numbers. And that attitude is subconsciously transmitted to students. Many elementary school teachers disliked math as a kid and so they talk about math like it’s an unfortunately necessary, but painful part of the day.

In addition, much of the recent major rebranding (specifically around math) can unintentionally have negative impacts on students’ attitudes towards math. On the one hand, all of the focus on turning phrases like “I don’t get math” to “I don’t get math yet” is immensely valuable. It teaches kids to persevere and keep an open mind. However subconsciously it also teaches that “everyone” struggles with math, that math is something to struggle with. Nowhere on the growth mindset posters does it say anything about seeing the beauty of math. Nowhere in the teaching of fractions do you learn to see numbers as a way to explain and make sense of the world, to look forward to math class.

And further, there’s a difference between doing math and properly going through the formulas, and thinking in numbers, seeing math all around you, and finding the joy in it.

As a silly example, last weekend my family got a new board game and the first thing we all did was figure out the resource to monster point conversion formula and determine whether it scaled linearly, exponentially, etc. The game came with three dice (four sides with 0, one with 1, and one with 2), and instead of telling my younger brother what the average role for three dice was, we did an experiment. We rolled the dice several times to determine the distribution and calculate the percentage. Then he thought about how to calculate the probability of each sum numerically and compared to the experimental results. That’s just how we work. It’s instinctual. It’s not a math problem, or “homework,” or to teach, it’s just another activity or thing to think about during dinner.

Not everyone thinks like that, but there are immense benefits from just being around a person like that who can point out the math around you. There’s so much fun you can show kids like Pascal’s Triangle or the Map Problem, or any of a number of things even at the elementary level that just makes math a richer field.

Knowledge of the student:

Many teachers are exceptional, selfless humans who encourage their students, inspire them to do things they never thought possible, and make their subject come alive. Even the teachers who may not have the technical knowledge of their subject are often incredibly devoted to their students. After all, you don’t go into teaching for the money.

Teaching requires a mix of compassion, general social skills, an understanding of developmental psychology, etc. Of these things, connection is the first step to teaching. Framing a problem is what makes the difference for the many kids who can list off an incredible number of sports statistics and tell you exactly what they mean, but who freezes up upon seeing a ratio in another context.

(And unfortunately, the stereotype about STEM people being more socially awkward does tend to be true, which I have to imagine is at least partly a reason for why fewer STEM oriented people end up being elementary school teachers).

Understanding developmental psychology enables teachers to predict common student mistakes and address the root causes behind these misconceptions. For instance, many kids view the = sign as a signal to do an action as opposed to a symbol meaning equating. Problems start out as 2+2=? in which the distinction doesn’t matter and so is often ignored. When algebra begins to be introduced though, problems are written as 2+2=?+1 and kids will incorrectly write 4 in the “?” spot. Without understanding the thought process behind the mistake, teachers can’t clarify errors and students will continue to be confused, blindly abiding by arbitrary rules and formulas they don’t understand.

How to change

Education is about teaching kids necessary life skills and giving them the confidence to navigate the world. (In this case in a math context, but arguably school doesn’t do a great job of this in general). And helping more of them find enjoyment math so they can have more of those moments when the lightbulb turns on, more of the moments of wonderment as all the puzzle pieces click into place.

Better professional development training and curriculum design won’t be enough, because removing fear and sparking passion is near impossible in already entrenched adults. I believe we need different types of people to become interested in a career in education, and teachers with a passion for their field almost inherently bring with them improved teaching methodologies. Currently, teaching falls mainly to those who enjoy working with kids, and less so to people super interested in their own thing who happen to also want to share their excitement with kids. And sometimes just being an incredibly caring, devoted person is not enough (or at least, shouldn’t be the only teacher in the classroom and the only type of teacher for 6+ years of school).

There’s extreme resistance to change and little incentive to at least monetarily. One has to make sure to consider all of the complex cogs in the system and work to not unintentionally exacerbate existing inequalities. There’s a lack of concrete studies and data because there are a near infinite number of confounding variables. It would require sorting through the giant bureaucratic machine that is government on all levels. And we can’t forget that this isn’t any change won’t be some inconsequential scenario, it will shape the next generation, and we can never truly know the impactsout until 20+ years later.

So perhaps that begs the question why bother? Is the current system really so bad? How much better can we realistically get?

Maybe you didn’t have many of those “joy-or-learning” moments, didn’t enjoy school or see the point, were too focused on grades or bombarded with stress to realize the stuff you’re learning is actually fascinating and there’s so much in this world to be explored. And if you don’t understand the feeling I’m trying to convey, it means the education system has failed you and robbed you of those experiences. That’s why you might not see that our public education system is so very broken. That’s why you’re not appalled upon learning the status of our schools or feel righteous indignation every time a well meaning policy moves us further away from a school system in which everyone can learn to their fullest potential. As a country built on the ideal of an educated populace we owe this to the next generation of kids.

Hi, and thanks for reading! If you’re also interested education and pedagogy or if you’re working to solve problems in the field and have some thoughts, it’d be great to hear from you! Feel free to send me an email at kiranamak [at]

At 17 years old, I love learning and am interested in materials science, education, and environmental sustainability.