Chapter 1. Nine-Dot Problem

1.1 Introduction

Problems are called problems for a reason: their solutions are not obvious. Psychologists have long studied what it is about problems that make them easier or harder to solve. What are the cognitive mechanisms that help us or hinder us in solving problems? In this task, you will be presented with a classic laboratory problem. After you try to solve the problem, the results will be presented, and we will examine what it is about this problem that tends to make it difficult.

1.2 Experiment Setup

1.3 Instructions

In this experiment, you will be asked to connect dots by drawing multiple connected lines. To draw these lines, click the mouse to indicate one end point. The computer will then display a line going from the location of your click to where your mouse is currently. When you are at the end of the line that you want, click the mouse again. Since you will need to draw multiple connected lines, this second click will also indicate the beginning of the next line. When you have drawn all the lines allowed, the mouse will stop drawing lines. Clicking again will clear the screen and either allow you to start again or, if you have done the task correctly, end the task. There is also a “Start Over” button that you can use to begin drawing again.

There are two steps in this experiment. First, you will be given a training exercise for the task, and then you will be asked to solve the actual problem. The instructions will be almost identical and will be presented on the screen with each problem.

1.4 Experiment

1.5 Results

1.6 Debriefing

The nine-dot problem is a classic ill-defined problem. An ill-defined problem is a problem where not all of the facets of the problem are clear. The problem statement might not be clear, how to solve the problem might not be clear, or what the solution would look like might not be clear. In addition, the nine-dot problem is called an insight problem. Insight problems are objectively simple in that the problem statements are short, don’t seem to have a lot of elements to the problem, and the solutions require few steps, like the four lines of the nine-dot problems. Yet, they are difficult to solve and their solutions seem to come suddenly (Kershaw & Ohlsson, 2004).

There are several factors that seem to cause the difficulty in solving the nine-dot problem. First, the nine dots form the clear perception of a square. They form what psychologists call a gestalt. You do not see the nine-dots so much as you see them all as part of a whole, which is a square. This perception tends to make it difficult for you to draw outside of the square. This difficulty of the nine-dot problem explains one of the practice conditions that you might have been exposed to. If you had the practice condition where you had to make a turn that is not on a dot, it can help you to break the gestalt and more likely to solve the problem. In addition to this perceptual factor, there are prior learning and experience, and even the ways we search for solutions, that all make this problem hard to solve for us. One feature of the way we attempt to solve this problem is the tendency to use prior learning and problem solving approaches even when they do not work in the current situation. This rigidity of processing approaches caused by prior learning is referred to as functional fixedness (Dunker, 1945).

References:

Duncker, K. (1945). On problem solving. Psychological Monographs, 58(5), Whole No. 270).

Kershaw, T. C., & Ohlsson, S. (2004). Multiple causes of difficulty in insight: the case of the nine-dot problem. Journal of Experimental Psychology: Learning, Memory, and Cognition, 30(1), 3-13.

Maier, N. R. F. (1930). Reasoning in humans: I. On direction. Journal of Comparative Psychology, 10, 115-143.

1.7 Quiz