Creativity in algebra | Algebra 1 | Khan Academy

[Music] [Music] Hi folks, Sal Khan here, and all I have to say is that algebra is perhaps the most pure way of expressing human thought. And like everything dealing with human thought, it's incredibly creative. But you don't have to take my word for it; we have some of my good friends to better draw that link between algebra and creativity.

[Music] It's all about solving problems. It's not about, like maybe in previous years, you've done a multiplication table memorization. It's not like memorizing how to solve problems; it's learning the tools of how to solve problems and then using them, um, and building them up in creative ways. So it's kind of like—it really does remind me of art because if you are doing like a painting or something, you have like specific tools about, like maybe paint brushes or different techniques you can use, um, to create something bigger.

Um, so I feel like algebra is really all about combining things that you already know how to do, um, into something bigger. So the word algebra comes from the Arabic word "al-jabr" that literally translates to "reunion of broken parts." This is breaking a part of mathematical representations and putting it back together in the form of balanced equations; that's the essence of algebra.

And the beautiful thing is that this balancing and solving of equations can be done in many different ways, which is where creativity comes in. So if you're trying to communicate a complex topic such as mathematics or a mathematical problem to the general public, who might not be familiar with the specifics behind that problem, there are many different ways to help you get that concept across.

And one of the ways that we do this in Mathematicals is to use videos and things that are visually appealing to people. So by using lots of visual aids—so bright colors and cartoons and word prompts on your screen—you can engage and capture the audience in different ways that you might not be able to do if you're just speaking in terms of equations and mathematics.

When we're more creative about how we present and how we talk about math, it makes it more relatable to people from a variety of backgrounds and cultures and experiences. When we are creative in how we explain or how we relate mathematical concepts, we can use things from sports, entertainment, or real-world occurrences to help really ground the principles that we're learning and the theories that we're learning to something relatable.

So the more creative we can be in explaining how math is related to the world around us, how it's related to things that we are invested in, the more likely it is to resonate with the people around us. As soon as a problem is posed, our instinct is to find the solution. But remember, often there's more than one solution, and usually, there's more than one path to it.

One day my family was building this fence around my chicken coop because there were problems with raccoons, and we wanted to make sure that, like, the perimeter of the fence was like twice the length of the, uh, of the width. And I remember thinking this is exactly like my algebra class—like I'm actually doing things that are useful. And actually, like, algebra wasn't just something that you do on paper; it's something that, like, it was actually protecting the lives of my chickens.

So I felt like that was a moment for me where, like, math is useful to the world, and we're solving real problems with it, and it's really powerful. So I realized that I first liked algebra and just math in general my first year in college. It was a little bit of a late bloomer in realizing the importance of math. I was taking an early statistics course for my psychology degree, and I really began to understand how the concepts that I was learning, um, could help me understand the world around me better in a more concrete, um, fluid, and rich way.

And so being able to make that connection from these things that I'm learning in the classroom out into the real world so I can understand different phenomena, I can understand, um, how various things in our culture work and progress, really helped me and made me feel like I had a deeper understanding for the importance of math and algebra. And from that point, I've really been in love.

In order to get more creative, I would encourage young people to be not afraid of making mistakes. It's okay to fail while exploring a new trail of thought. Know that usually, there is more than one solution to the problem. Math is as much about posing problems as problem-solving, and at that point, creativity is noticing where there is something worthwhile investigating.

As a student in math, I think it's important to remember that math isn't just like random symbols on paper; like, math can mean something, and it's pretty powerful that you, as a student, can build something that uses math. Creativity in math isn't just about being able to pluck numbers from the air and like, "Oh yes, I know the solution." It's about being able to use problems that help with your daily life.