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Reasoning and Learning with Analogies: Making Metacognition "Natural"


Duncan Sibley, Center for Research on College Science Teaching and Learning, Michigan State University

By show of hands, roughly 70% of the students in my general education course for non-science majors believe scientists and non-scientists think differently. If students believe that scientific thinking is somehow different from the way they think, learning science must, for them, represent a daunting challenge. Faced with this obstacle, students might rationally choose to attempt to learn science by rote memory, a strategy at odds with most instructors' desire to help students develop higher order thinking skills. If students are provided the opportunity to reason by analogy, they may recognize that everyone thinks like a scientist.

According to linguists and cognitive scientists, the human mind specializes in learning through analogies (Lakoff and Johnson 1980, Hofstadter 2006, Pinker 2007). Children do it (Goswamii 2001). Even chimps draw analogies (Oden et al., 2001). Douglas Hofstadter writes in the introduction to his recent book, I Am A Strange Loop, "the bottom line is, every thought herein could be listed under analogies." Pinker (2007) expresses this in a different way, "to think is to grasp a metaphor". Part of the reason Hofstader, Pinker and many other cognitive scientists (e.g., Gick and Holyoak, 1983, Blanchette and Dunbar 2002, Gentner 2003, Holyoak, 2005) believe analogy is a fundamental cognitive process is that drawing analogies requires some sort of similarity mapping of one concept on another, a process which lies at the heart of learning. As a recent example, many of us have been reading newspapers hoping to learn about the global financial crisis. We've learned that credit default swaps are like insurance policies and that the present global financial crisis is sort of like the Great Depression, but there are important differences. Almost everything we've read about the financial crisis has been cast as analogies.

Geologist reason by analogy (Schumm 1991, Frodeman 1995). When Lyell coined the geologists' mantra, "the present is the key to the past", he tacitly expressed the central importance of drawing analogies in geological reasoning. Walther (1893) stated, "the most satisfying genetic [genesis of] explanations of ancient phenomena were by analogy with modern geologic processes" (quote from Middleton 1973, p. 981). Airy (1855) described the "perfect" analogy between the earth's crust floating on the mantle and a raft of timber floating on water. Analogies remain prevalent in the most up to date geoscience literature as in a recent article, Brazilian Analog for Ancient Marine Environments on Mars (Bridges et al., 2008).

Figure 1. Click image to see a larger version.
I include instruction and practice of analogical reasoning to help students engage in authentic geologic reasoning. We begin with everyday analogies, hopefully convincing students that reasoning by analogy is both familiar and natural. This approach is implicitly metacognitive. It is implicit in that students are asked to recognize the similarity between their everyday analogical reasoning and the assignments I give them to draw analogies between new concepts and their established understanding of similar concepts. The approach is made metacognitively explicit when we breakdown analogical reasoning into parts (Figure 1A) as suggested by Holyoak (2005). Each part is explained with examples from the everyday analogies the students draw. For example, retrieval may be exemplified by noticing the wings on a bat while mapping, the process of comparing similarities and differences, might lead to the conclusion that comparing hair on a bat to the on hair on a mouse is more meaningful than comparing wings on bats and birds. While wings on birds and bats support inferences something about bats, the fact that bats and dogs share hair and, therefore, are both mammals supports many more inferences. We move from students' analogies about the very familiar to students' analogies that will help them learn new concepts. For example, the average amount of time students spend in university is an analog for residence time of water molecules in the oceans. Later in the semester, the water cycle is an analog for the rock cycle. Characteristics of the rock and water cycles can be used to construct a model of the carbon cycle. At this point, students are building a scientific model based on the same elements found in analogies (Figure 1B).

QUESTION COMPONENTS

SCORING RUBRIC

1.Write an analogy for _________*.

You may include a drawing or diagram in your answer.

SCORING RUBRIC: Each analog will be categorized as relational, descriptive, trivial or other. Correct relational or descriptive analogs will be scored 1. The other category includes non-analogs.

2a. Make a list of two significant similarities between the target and the analog.

2b. List two or more significant differences between the analog and target.

SCORING RUBRIC: Correct relational or descriptive similarities and differences will be scored 1. Incorrect relational or descriptive similarities and differences will be scored 0.

3. What questions about the target does the analog raise for you?

SCORING RUBRIC: We are not sure how the students in this study will respond to this question. We will attempt to score it on a basis of 1- has significant questions about the target and 0 - does not have significant questions about the target.

4. State a hypothesis based on one of these questions.

SCORING RUBRIC: We will score this as 0 - no hypothesis or hypothesis not related to the analog or 1 - hypothesis related to analog.

5. Test your hypotheses

SCORING RUBRIC: We will score this as 0 - no test or 1 – a reasonable test.

6. Based on what you know about the analog, what can you infer about the target? In other words, what does your analog tell you about the target?

SCORING RUBRIC: This will be scored as 0- incorrect inference(s), 1- correct

Table 1. Scoring rubric for analogies. Many exercises involve fewer than six components. For example, students might be asked to take a give analogy and complete components 2, 4 and 5 or they might be asked to draw their own analogy and complet3e components 3 and 6.

At the beginning of the semester, students are not proficient at analogical reasoning about science. Quite naturally, they use non-scientific analogs for scientific concepts. For example, two cars crashing is the most common analog students use for subduction. To help students improve, we have to provide lots of practice with feedback. Students write analogies online using our online homework and course management system, LON CAPA. Their responses are downloaded into SPSS Text Analysis which we use to establish the most common answers. We have also developed a rubric for scoring students' analogies (Table 1). We are still in the process of determining the validity and reliability of this rubric. If it is valid and reliable, then we will use it to measure students' ability to reason by analogy. Their reasoning would be determined to be correct when they can draw an analogy, recognize similarities and differences between the analog and target and either test hypotheses or draw inferences using the analogy. Students who can do this would be thinking and reasoning as scientists.

References Cited

Airy, G.B., 1855, On the computation of the effect of the attraction of mountain masses. Philosophical Transactions of the Royal Society of London 145 (1855), pp. 101–104.

Blanchette, I. and Dunbar, K. (2002). Representational change and analogy: How analogical inferences alter target representations. Journal of Experimental Psychology: Learning, Memory, and Cognition, 28, 672-685.

Bridges, N.T., Hook, S.J., Crowley, J.K., Filho, R. deS., Macambira, J.B., Silva, G.,deL.P.,Thomson, B.J., EOS, 89, 329-330.

Frodeman, R. (1995). Geological reasoning: Geology as an interpretive and historical science. Geological Society of America Bulletin, 107, 960-968.

Gentner, D. (2003). Why we're so smart. In D. Gentner and S. Goldin-Meadow (Eds.), Language in mind: Advances in the study of language and thought (pp.195-235). Cambridge, MA: MIT Press.

Gick, M.L. and Holyoak, K.J. (1983). Schema induction and analogical transfer. Cognitive Psychology, 15, 1-38.

Goswami, U. (2001). Analogical Reasoning in Children. In D. Gentner, K.J. Holyoak, and B.N Kokinov (Eds), The Analogical Mind (pp.437-470). Cambridge: MIT Press.

Hofstadter, D. (2007). I am a Strange Loop, NY: Basic Books

Holyoak, K.J. (2005). Analogy In K.J. Holyoak and R.G. Morrison (Eds.), The Cambridge Handbook of Thinking and Reasoning (pp.117-142). Cambridge MA, Cambridge Univ. Press.

Lakoff G. and Johnson, M. (1980). Metaphors We Live By. Chicago, University of Chicago Press.

Middleton, G.V. (1973). Joannes Walther's law of correlation of facies. Geological Society of America Bulletin, 84, 125-142.

Oden, D.L., Thompson, R.K.R., and Premack, D. (2001). Can an ape reason analogically ?, In D. Gentner, K.J. Holyoak, and B.N Kokinov, (Eds.), The Analogical Mind (pp.471-497). Cambridge MA: MIT Press.

Pinker, S., (2007). The Stuff of Thought. NY: Penguin.

Schumm, S.A. (1991). To Interpret the Earth: Ten Ways to be Wrong. NY: Cambridge University Press.


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