Problem Solving

In this video I introduce several concepts related to problem-solving. I begin with mental set, which refers to our tendency to rely on approaches that have worked in the past. Similarly, functional fixedness refers to our tendency to think of tools as having single fixed uses and this may cause us to overlook novel uses for them. Convergent thinking refers to approaches leading to a single solution, while divergent thinking refers to coming up with many possible solutions which may not be related to one another.

 

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Video Transcript:

Hi, I’m Michael Corayer and this is Psych Exam Review. In this video I want to introduce some ideas related to problem solving.

So how do we solve problems? Well, sometimes the way that we solve problems is that we don’t actually have to solve them. We have a memory for a solution and we simply need to bring it to mind.

For instance, if I ask you to solve two plus two you can immediately tell me that the answer is four and you don’t really have to go through any problem-solving steps. Whereas at some point in the past you did actually have to solve this problem, you had to work at it and find the solution and you

probably did this by physically representing the problem, you know, on your fingers and then counting one two three four. Ok, two plus two is four and now you have that solution and you memorize it and you can bring it to mind later when you need it and it’s not going to change.

So sometimes we simply call on our memory for how we’ve solved the problem in the past. Now this can lead us to a problem in that sometimes we call upon old solutions that aren’t going to work for new problems and this brings us to what’s called mental set.

So mental set is the idea that we use a problem-solving approach that has worked in the past but it might not necessarily work for a new problem but it’s sort of the first thing that we go to. So for instance if you’ve had problems with your computer in the past and you’ve solved these problems simply by restarting your computer and that’s resolved the issue then if you have a new problem with your computer you’re likely to try restarting your computer to solve this problem, even if that solution isn’t necessarily going to work. That would be a demonstration of your mental set. You have an approach to solving computer problems which is to restart the computer and you try that with a new problem even though you don’t know if it’s going to work and it may not resolve the issue that you’re having.

Now we also have this tendency to rely on past solutions when it comes to how we use tools because we tend to think of the usefulness of tools in terms of how we’ve used them before or how they’re generally used and so when we’re referring to tools we call this functional fixedness and this is the idea that the functions of tools are seen as fixed, they don’t change. We use a tool for a particular purpose and that purpose only.

So for instance if you were trying to hang a picture on your wall and you need to hammer a nail into the wall you might go and get your tool box and then you open it up and you remember that you lent your hammer to a friend last weekend and you forgot to get it back. Now you might think well “I guess I can’t hang up the picture today” instead of realizing that there’s a wrench in front of you and you could use the wrench to drive a nail into the wall and in this case that would pretty much work just as well as a hammer. You might overlook this because of functional fixedness. You think of hammers are for hammering things wrenches are for wrenching things and you fail to see that you could use the wrench as a hammer.

This functional fixedness is often described as an error in problem-solving but I don’t really think it’s an error because a lot of the time functional fixedness is a good thing. It keeps us from damaging our tools and ruining their ability to perform their special task that they’re designed for. So we don’t always want to think of all the possible uses for something. I mean sure you could use your cell phone to hammer a nail into a wall that would probably work. It would get the job done but in doing that you destroy the functions that your cell phone is specifically designed to perform. In that case functional fixedness isn’t really an error. Sure you don’t think of using your cell phone as a hammer but most of the time that’s probably a good thing.

Ok, so thinking about the different uses for tools brings us to consider the difference between convergent thinking and divergent thinking. So what do these refer to?

Convergent thinking is when we have a problem that has a single solution and so all the steps that we take, all the approaches that we have should all point us to this one solution. Think of it as we have a single solution and everything we do should point us toward that solution.

For instance, if you’re solving an algebra equation and you’re solving for X and there’s one answer that X can be, then each of the steps that you take in solving this problem should get you closer to finding that answer of what is X, right? So we have many approaches that all point us to a single solution. This is convergent thinking. Everything converges onto one solution.

In contrast, we also have what’s called divergent thinking and in divergent thinking we diverge from a single point. We have a starting point and then we have multiple solutions and these solutions sort of go off in different directions and by that I mean they may not be related to one another at all. So this is a bit more creative, right? We have to come up with new unrelated ideas for maybe how we could use a particular tool. That would be an example of divergent thinking.

So if you took your hammer and you said “what are all the possible things that I could use a hammer for?”, you’re going to come up with many different answers and they’re not going to be related to one another. So you say “okay I could use a hammer as a paperweight or I could use it to help me reach something that’s just out of reach. If I had a hammer and then I’d get a little a little bit longer reach and maybe I could you know knock something off the shelf” or you could say “well maybe I could use it to prop a door open so I don’t get stuck outside or, you know, I could use it as a weapon if I needed to or maybe I could use it as a clock, in which case it’s always hammer time”.

But anyway this shows us that we have multiple different solutions to a problem and they’re not related to one another and so this creativity comes from this divergent thinking; trying to come up with new unrelated solutions and this is something we might not do as often as convergent thinking where we’re focused on finding a single solution to a single problem.

Ok, so that’s mental set and functional fixedness and the difference between convergent and divergent thinking. I hope you found this helpful, if so, please like the video and subscribe to the channel for more.

Thanks for watching!