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Drawing a logical conclusion from premises, evidence and sometimes assumptions.
In logic, to infer is to make a very specific connection between things, based upon your knowledge about each of them. A classic example used to introduce this idea is the following logical conclusion: "Socrates is a man, all men are mortal, therefore Socrates is mortal."
Halpern (2003, p.157) described a form of this thought with the following taxonomy:
All A are B.
All students are smart.
Some A are B.
Some video games are fun.
No A are B.
No smurfs are pink.
Some A are not B.
Some democrats are not liberals.
From this taxonomy of premises, Halpern demonstrated how to determine the validity of an inference while emphasizing that an inference can be logically valid, but not true (if, for example, one of the premises is untrue). To determine whether a conclusion is logically valid, one only needs two additional pieces of vocabulary:
With these two pieces of vocabulary, we can use the the following algorithm to determine whether a conclusion can be validly drawn from a set of premises (adapted from Halpern, 2003, p.167):
Inferences can also be illustrated using Venn diagrams. The graph below is adapted from Halpern's (2003) visual depiction of logical validity testing, and the interested reader is directed to page 158 for an in-depth discussion of how to represent logical validity tests using diagrams like this.
In the real world, we must make inferences in circumstances where definitions are disputed and premises not always crisply distinct. Inferences are therefore frequently based on our own opinions and assumptions and can therefore vary widely in quality and bias. For this reason, it is important that students learn to scrutinize their own inferences and those made by others. Some teachers slow down the inference process to identify which inferences students can make that are supported by specific observations. Others play games in class that require students collect data and draw inferences from those data.
Research findings indicate that inference appears to be a skill that can be improved with training that requires students to organize or cognitively elaborate upon given material. Constable and Klein (2008) found that when individuals were asked to construct a story with a sequential set of information, they were better able to make explanatory and predictive inferences about the given information. Some teachers put a twist on this method, by having students use the data to tell two different stories.
Some have found that the use of diagrams in conjunction with text supports inference skills as well as reduces errors (Butcher, 2006). McGee and Johnson (2003) increased the inferential accuracy of their students using three techniques: helping them identify key words within a text, helping them generate their own questions about a text, and obscuring part of a text and asking students to predict the obscured section contains. This last technique is similar to problematizing part of a text, which other teachers have also found effective.
Butcher, K.R. (2006). Learning from text with diagrams: Promoting mental model development and inference generation. Journal of Educational Psychology, 98(1). 182-197.
Constabile, K.A., & Klein, S.B. (2008). Understanding and predicting social events: The effects of narrative construction on inference generation. Social Cognition, 26(4), 420-437.
Elder, L., & Paul, R. (2002). Critical thinking: Distinguishing between inferences and assumptions. Journal of Developmental Education, 25(3), 34-35.
Halpern, D.F. (2003). Thought and knowledge: An introduction to critical thinking (4th Edition). Mahwah, NJ: Lawrence Earlbaum.
Lee, H.S., & Holyoak, K.J. (2008). The role of causal models in analogical inference. Journal of Experimental Psychology: Learning, Memory, and Cognition, 34(5), 1111-1122.
McGee, A. & Johnson, H. (2003). The effect of inference training on skilled and less skilled comprehenders. Educational Psychology,23(1). 47-59.
Richards, J.C. & Anderson, N.A. (2003, November). How do you know? A strategy to help emergent readers make inferences. The Reading Teacher, 57(3), 290-292.