What does a math class in high school look like?
It is hard to standardize this image with such a large variety in the quality of education across the United States. But most of us can probably envision whiteboards, equations, formulas, lectures, and a mostly rigid schedule of what happens in a regular class. Perhaps it goes like this: the teacher explains a new concept, gives a few pertinent formulas, does an example problem, then lets the students do problems by themselves. Maybe there's nothing wrong with this: it is efficient enough, it teaches students how to solve problems, and the teacher does not need to be an expert.
But is this the most effective way to teach math in high school? Do students enjoy the process for the sake of learning math, or are their incentives based on grades? As a whole, does the math education system in high school need to change?
It would be meaningless to try to answer these questions myself, a high school student. So instead, I reached out to one of the most famous math communicators on the internet - Grant Sanderson - whose YouTube channel 3Blue1Brown has over 5 million subscribers. According to his channel description, 3Blue1Brown is a "combination of math and entertainment, depending on your disposition." The videos, having amassed more than 350 million cumulative views, are animation-based and break down difficult concepts in an intuitive way.
His video topics range from basic calculus (of which he has an excellent series explaining the essence of calculus) to AI and machine learning, as well as everything in between. I asked Grant both questions about the state of math education, as well as some personal questions about his channel.
3Blue1Brown on Math Education
Straight to the point, the first question I asked Grant was what, if anything, he would change about how math is taught in high school.
"In a word, what's often most lacking is motivation. For a given topic, before a student can really engage with it, they need to have a strong reason why."
Which is true - most students do not learn the use of the math they are learning. According to a study by EdReports, only 41% of high school math teachers engage more than half of their class in applying math to real-world contexts. Grant continues:
"What will this new bit of math let them solve? Is the idea intrinsically beautiful? Is it clear how learning a given subject (like calculus) will unlock future doors of worthy things to learn (like physics/engineering/data science)?"
Clearly, Grant feels as if math classes in high school can and should improve offer students a "why" for what they are learning. The wording here is important: it is the math curriculum that has to improve, not the teachers. Grant states, "I don't think the fault here is with the teachers, by the way - they have a nearly impossible task."
But aside from the motivation, should everyone even learn the level of math education 3Blue1Brown discusses? Of course, there is no inherent truth to this, and the answer is opinion-based. Grant's opinion is that it is not necessary.
"There are lots of worthy things in the world to learn, and there's no need for everyone to pour themselves into the upper echelons of math unless they want to. I do think that everyone should feel like they can learn as much math as they want if they put in the work, and not to feel that any is fundamentally out of reach."
Along the same lines, I asked if 3Blue1Brown thinks his style of teaching should be utilized in high school. His response to this was clear: there is a difference between what he does in his videos, and teaching in the classroom.
"Through the videos I make, I explain things, and I (hopefully) entertain, but teaching is something different. Teaching means mentoring, and eliciting ideas and interest from the students in front of you. It's something that can only be done well face-to-face."
I believe this is one of the more important things Grant says in this interview. His videos are not a substitute for proper math education and they should not be viewed as such. So, though Grant believes improvements can be made to the high school math system, he does not see his videos (or any videos on YouTube in a similar vein) as the solution. Obviously, this does not mean his videos are useless for students:
"If we limit our focus just to explanation, acknowledging that that's just one small part of teaching, there are some principles I aim to employ that high school teachers may benefit from. It seems learners resonate when visual intuition is leveraged as much as possible. Abstract concepts are best explained when preceded by concrete examples. It's worth highlighting how and when the subject can be beautiful, not just when it's useful."
Once again, Grant returns to the point of motivation. He offers "visual intuition" in his content, which can help highlight the elegance and beauty of the subject being discussed. While this does not necessarily teach, it can provide students motivation; which can greatly facilitate their learning.
A natural follow-up to the previous question is how Grant would suggest students utilize his videos to accompany their learning of a topic. The answer went hand in hand with his comments on proper math education versus his videos:
"Hopefully, they can offer some inspiration, and when accompanied by a class they might offer some intuition for specific topics. Often the aim with videos is to offer a mental framework that can be used in the subject, but a student still must do the problem sets and exercises from a class in the subject to actually practice and solidify that mental framework."
This idea of practice is extremely important when students are learning math. It is no mistake that teachers assign so many problems. Grant expanded on this when I asked him how he thinks students can improve their math abilities on their own.
"Problems, problems, problems. Learning comes from solving things, and especially from finding your methods of solving things. Lectures, books and videos should be seen as ways of setting up hints that will help you solve problems, and only once you've sat down and worked through some problems have you actually learned."
The last two math-related questions both asked Grant about what he believes to be so important for math students: motivation. If there was one thing you could show to a calculus student to get them to appreciate math more, what would it be?
"If possible, I'd want to tailor it to what that student was interested in. If they like science, I might show how some physics problems can only be solved by understanding calculus, e.g. understanding planets' orbits, or analyzing oscillators. If they like computer games, I might find some examples from graphics or game development where calculus is used, for example, Bezier curves and how they relate to first/second derivatives."
This is in line with Grant's earlier responses, as he believes connecting calculus to a discipline a student is interested in would have a strong impact on their motivation. After all, if a student realizes that what they are learning is used in something they are passionate about, it is only natural for them to be motivated to explore that concept.
But while this may be easier to do in a STEM field, I wondered if it was possible in something related to other disciplines. So I asked 3Blue1Brown: Do you think math could be interwoven with other disciplines, either by showcasing direct applications or by demonstrating more abstract relations (ex: a connection between proofs and persuasive essays)?
"I think that's a great idea. Another good example is how the language/structure Jefferson used in the Declaration of Independence ("We hold these truths to be self-evident...") is somewhat reminiscent of Euclid's elements, and we know that the intellectuals of that time often held up that work as a paragon of rigorous clear thinking."
I think that's pretty neat. Something I had never considered to have any relation to math, the foundation of America, still works with the same axioms that math does. While this topic - the intersection between math and humanities - calls for a deeper look, I like how there are at least elements of math that even an English major can use.
Personal Questions
With an abundance of questions about 3Blue1Brown's opinion on the math system in high school out of the way, here are some more personal questions Grant answered.
I wondered when Grant began to enjoy math, and what his relationship with it was in high school. So I asked, what has been your experience with math education in high school?
"Back when I was a high schooler, I was fortunate enough to already love math. That started much earlier for me. If I'm honest, though, I think a meaningful part of my interest in the subject at that time came from a competitive mindset. In school, we're praised for good grades and doing well on tests, so as an adolescent, it's hard not to be primarily motivated by this race, as opposed to, say, the beauty or usefulness of math."
Again Grant alludes to motivation. He acknowledges he was motivated by competition, not based on an intrinsic love of the subject. Based off of this, perhaps an argument can be made about the grading and testing system in high school - but again, a topic for another time.
Is there a certain math teacher or professor who inspired you, either in terms of starting your channel or appreciating math in general? If not, are there any qualities of a good math educator you try to emulate in your videos?
"I had a particularly killer calculus teacher, Mr. Sakashita, who helped open my eyes to the attraction of math beyond what's shown and praised in school. He introduced me to a math circle regularly held at the University of Utah, he lent me books, and he answered the questions I'd ask him after school. I really do owe a lot to him."
While Grant greatly appreciated this math teacher in high school, he admits that once he was at college, there was no specific math professor that stood out to him. "In college, I think I actually found more pedagogical inspiration from the computer science department. The lecturer Keith Schwartz, for example, was a master of the craft."
How has the success of 3Blue1Brown impacted your life so far, and do you have any future plans for the channel?
"It's afforded me the freedom to explain math for a living, in the way I choose, for which I'm incredibly grateful. My future plans are simply to try my best to explain things people want to understand, and to share topics which may make them love the subject more."
Lastly, I asked Grant if there were any other math communicators or educators he wanted to highlight. Grant was happy to promote several people:
"Matt Parker (Stand-up Maths on YouTube), Philip Legner (Mathigon), Steven Strogatz (many books, columns etc.), James Gleick (perhaps my favorite author)"
While I personally am only familiar with Matt Parker on this list, I plan to check everyone else out, and I suggest others do the same!
As previously stated, 3Blue1Brown is one of the most famous math communicators in the world. This is a testament to his excellence in the craft and his easygoing personality, if his humble yet informative responses in this interview are anything to go off of. 3Blue1Brown has inspired millions of people across the world to study math because of the artistic beauty he expresses in easy-to-understand terms. But most importantly, I think Grant gives these students what he believes is missing in the education system, what is so crucial for their learning, and what requires a true leader to impart: motivation.
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