- Creativity break: How can we combine ways of thinking in problem solving?
- Identifying quadratic patterns
- Factorization with substitution
- Factoring using the perfect square pattern
- Factoring using the difference of squares pattern
- Factor polynomials using structure
Experts share how they combine ways of thinking to solve complex problems. Created by Khan Academy.
(upbeat music) - One of the newest ways of thinking about problem solving for me is something that my math professor would tell me. 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 you can feel like, wow, this is a reflection of me and my mathematical abilities. 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 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 what to do when you are stuck is a really big part of being creative in math and being able to solve problems in the future. - One example that I often use is I often try to solve problems both in the traditional 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, the more ways that you can eventually save in your toolbox and use later on to solve other problems. - There's lots of different tools and resources like apps and puzzle games that are gonna 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 gonna 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 gonna be at solving it.