Creativity break: How can we combine ways of thinking in problem solving? | Algebra 1 | Khan Academy

[Music] One of the newest ways of thinking about problem solving for me is, um, something that my math professor would tell me. Um, he would say, "Don't be afraid to be stuck." And I think that a lot of the time, when we are doing math and we get stuck, it's like sometimes it can be— you can feel like, "Wow, this is a reflection of me and my mathematical abilities. Wow, maybe I shouldn't be doing math." But really, a lot of the time, it's just an indication that you need to spend more time uh doing the math or figuring out what the problem is.

Exactly! If you haven't gotten stuck yet, then I mean, you probably will get stuck at some point. So being stuck is just a part of math. And it's kind of learning how to— what to do when you are stuck is a really big, uh, a big part of being creative in math and being able to um solve problems in the future.

One example um, that I often use um, is I often try to solve problems both in like the traditional um algebraic way, but I also try to visualize problems in 2D and 3D space to solve them more visually. And so I think the more ways that you can figure out how to solve a problem, um, the more ways that you can eventually sort of like save in your toolbox and use later on to solve other problems.

There's lots of different tools and resources, apps, and puzzle games that are going to help you think about problems in new ways and help develop that critical thinking that you need to be able to apply your skills to a lot of different areas. And sometimes even starting at the answer and working backwards through the problem can help you see a different way of getting to the answer.

Students can combine new ways of thinking about problem solving by trying to look at it from different angles. Anytime you approach a problem, if you're just looking at it from your perspective, you're not going to get a holistic view of the solution space. So try to have perspectives and look at the problem from multiple angles to understand all the ways in which it could be viewed. The more holistically you view a problem, the more paths you look at. The more efficient and effective you're going to be at solving it.

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