Learning By Doing
Fast forward a few hundred years. You are now a world-class oncologist, and you are working with a new technology to treat cancer. It's called a "gamma knife" because it uses gamma rays to kill cancerous cells. At high energy levels, a gamma ray will destroy healthy tissue. At low energy levels, it can't knock out the cancer. How can you use the gamma knife to destroy the cancerous cells, without harming the surrounding tissue?
Did you solve each of the problems? If so, how did you solve them? (Note: the image for this blog was meant to serve as a hint.) Did you notice a similarity between the two scenarios? Did the second scenario help with the first (or vice versa)? This famous analogical problem was originally stated by Mary Gick and Keith Holyoak in 1980 [1].
Nucleus : Sun :: Electrons : Planets
Much of our problem solving is done analogically. We see a problem, and when we're lucky, it might remind us of a similar problem we've solved in the past. If a true relationship exists, then we can extrapolate from the past to the current problem. The history of science contains several illuminating examples of this process.Take, for instance, Ernest Rutherford's model of the atom that he proposed in 1911 [2]. Knowing that the atom was made up of protons, neutrons, and electrons, he took what he knew about the solar system (i.e., the base), and applied the same logic to the structure of the atom (i.e., the target). The proton and neutron were found at the center of the atom, much like the sun sits at the center of the solar system. The electrons revolved around the nucleus in a manner similar to the planets revolving around the sun. In other words, Rutherford saw a mapping between the atomic nucleus and the sun and the electrons and planets (see Figure 1).
Figure 1: The analogical mapping between the solar system and the atom
Notice, however, that there are some properties of the solar system that he did not map onto the atomic structure. For instance, the sun gives off an intense amount of heat and might be considered "yellow." Nowhere in this theorizing did Rutherford claim that the nucleus gave off heat or is "yellow." That means Rutherford was sensitive to the properties and relationships between the two systems. He knew that some of the properties of the base domain (i.e., the solar system) should not map onto the target domain (i.e., the atom).
"Hey! That thing gotta hemi?"
To better understand the psychological processes used during analogical reasoning, Dedre Genter and her colleagues built a computational model called The Stucture Mapping Engine (SME) [3]. One of the key features of the SME is the emphasis that it places on relations instead of features.Let's take electricity for example. In the early days, when scientists were trying to make sense of the concept of electricity, they likened it to something they understood quite well: the flow of water. The analogy is that electrons are like water and they move from one location to another. A battery is like a reservoir, and gravity is like the difference in electrical potential. The SME looks for alignments between the relations in the base and target domains. For example, it sees a commonality between two different types of FORCES (i.e., gravity vs. electrical potential) and two different types of ENTITIES (i.e., water vs. electrons).
It necessarily throws out the surface-level features that are irrelevant to understanding how electricity works. For example, one feature of water is that it is blue. Since this is a feature and not a relation, the SME does not transfer the features water is blue or water is wet onto electrons.
The S.T.E.M. Connection
There are several learning studies that explicitly instruct students to do their own analogical comparisons between two sources of information. For example, my friend and collaborator, Tim Nokes-Malach and Dan Belenky, explicitly trained students in a physics class to compare worked-out examples of rotational kinematics problems. The students had to answer questions such as:- What is similar and what is different across the two problems?
- Are there differences in what the two problems ask for in terms of acceleration? If so, what are they?
This kind of intervention could be done for many topics. The goal, of course, is to show how relations in the base domain map onto the target domain. It's also relevant to talk about how the features of the base and target domains don't necessarily have to align.
Analogical reasoning is extremely powerful because it can extend the knowledge that we have into the unknown. It can help us draw upon the knowledge we have from previous problems we've solved and apply that knowledge to problems we've never seen before. That's pretty cool (analogically speaking, of course).
Share and Enjoy!
Dr. Bob
Going Beyond the Information Given
[1] Gick, M. L., & Holyoak, K. J. (1980). Analogical problem solving. Cognitive psychology, 12(3), 306-355.[2] Allain, R. (Sept. 9, 2009) The development of the atomic model. Retrieved from https://www.wired.com/2009/09/the-development-of-the-atomic-model.
[3] No, the structure mapping engine doesn't gotta hemi, but it does a pretty good job modeling the analogical processes that humans use! Check out their original paper: Falkenhainer, B., Forbus, K. D., & Gentner, D. (1989). The structure-mapping engine: Algorithm and examples. Artificial intelligence, 41(1), 1-63.
[4] Nokes-Malach, T. J., VanLehn, K., Belenky, D. M., Lichtenstein, M., & Cox, G. (2013). Coordinating principles and examples through analogy and self-explanation. European Journal of Psychology of Education, 28(4), 1237-1263.
