[MUSIC] So in the last lesson, we looked at four of the seven categories of problems. To quickly recap, according to Robinson, these were knowledge of lean problems, which need little prior information to solve them. Knowledge-rich problems, where a lot of prior knowledge is needed. Well-defined problems, where all the information needed to solve the problem can be inferred, or it's explicitly stated. And finally, ill-defined problems, where some aspect of the problem, such as what you are supposed to do, is only vaguely stated. In this lesson, we'll look at the last three categories of problems, semantically lean problems, semantically rich problems and insight problems. According to Robertson, semantically rich problems are problems where the solver has had a lot of practice with the problem type. Take the following simple maths problem. What is the sum of 333 + 334? It is relatively simple to figure out that the answer is 667, even if you had to check a calculator. This is because we know the process of how to do this problem. On the other hand, Robertson points out that we also have semantically lean problems, which are types of problems that the solver has not encountered before. For example, the average four year old might struggle with the simple addition of 4 + 3, not because they don't know what 3 and 4 are, but because they do not have the knowledge of how to do addition to answer it. Addition, in this example, is the unknown problem type. Thus, semantic problems are entirely solver-dependent. For a four year old, an addition problem is semantically lean, where for you or I, this kind of problem is semantically rich. This is the reason we do homework problems and practice exams. Not because the answers are important but to develop semantic knowledge of particular problem types. Then, when we encounter these kinds of problems in the future, we have a better chance of solving them. Universities aim to bring students from being semantically lean to semantically rich in their fields of study. Lastly, we have insight problems. These problems are by far the most difficult to define. These problem types can be a subset of any of the previous six types of problems that we have discussed. What characterizes insight problems is that as Dow and Meyer described, the problem appears to have a particular solution path, but actually requires the solver to take a new approach to solve the problem. Often, this happens as a flash of insight, where the answer according to Robertson suddenly becomes obvious. There are many classic insight problems that look like math problems but require a different approach that is deceptively simple. For example, the water lily problem. Water lilies double in area every 24 hours. At the beginning of summer, there is one water lily on a lake. It takes 60 days for the lake to become completely covered with water lilies. On which day is the lake half covered? The answer is day 59. On first reading, it may be tempting to start by working through the number of lilies that would be on each day, starting from day one. Or it may seem that if we divide the number of days in half, we'll know when the lake was half-covered. However, we don't actually know the area of the lake, nor the number of lilies that it would take to cover it. Instead, if we go back to the premise that lilies double every 24 hours, and work backward from the completely covered lake on day 60, logic follows that the lake would be half covered on day 59. So now we have covered seven types of problems that you'll encounter at university and in everyday life. Knowledge-lean and rich problems. Well and ill-defined problems, semantically lean and rich problems, and insight problems. [MUSIC]
