Teaching Logic

When I was a sophomore in high school, taking Integrated Math, I hated proofs.  For some reason, I just couldn't see the value in outlining the logic of a solution step-by-step.  To me, it seemed redundant--like a waste of time: if a conclusion was obvious to me, why on earth would I need to explain the reasoning?

Fast-forward 16 years: as a teacher, I never thought to teach logic.  As far as I was concerned, if students had a good enough grasp on a concept or theme, they would be able to arrive at logical conclusions about the topic at hand.

Here's what I have realized, though:
1) Being intelligent does not guarantee that one will arrive at logical conclusions.
2) The ability to arrive at logical conclusions does not necessarily mean that one is thinking logically.

In other words, the process of logic needs to be taught and practiced, even for students who consistently arrive at logical conclusions.

I have set aside time on Mondays and Tuesdays each week to study rhetoric in my Humanities class, and the past month has been dedicated to an in-depth study of logos--an appeal to logic.

We spent some time on syllogistic reasoning, the classical example being:
Major premise: All men are mortal.
Minor premise: Socrates is a man.
Conclusion: Socrates is mortal.

We then looked at enthymemes, which condense syllogisms into a single statement, typically leaving out the major premise.  For example, "Socrates is mortal because he is a man" (the unstated assumption being that all men are mortal).

I had the students practice converting syllogisms into enthymemes and vice versa, the main purpose being to root out and explicitly identify the major premise inherent within each claim.  I also had the students practice evaluating each syllogism for its validity (whether or not it followed a logical form) and its truth (whether or not its premises were true).

This was where we observed the limitations of syllogistic reasoning: for a syllogism to be sound, it not only needs to follow a logical pattern, but it also needs to start from categorically true premises.  Most debates in real life are far messier, resting on premises and assumptions that are, themselves, controversial.

This was where the Toulmin model came into play.  Stephen Toulmin was a British philosopher who created a model for argumentation that he believed would fit the messiness and ambiguity of day-to-day discussion and debate.  The Toulmin model is comprised of six parts:

I. Claim (The proposal made by the speaker or writer)
II. Reasons/Evidence (Their reasons for making the proposal and the evidence supporting the reason)
III. Warrant (The underlying assumption connecting the reasons and evidence to the claim)
IV. Backing (Evidence in support of the warrant)
V. Rebuttal (Anticipating and responding to potential counter-arguments)
VI. Qualifiers (Words and phrases that qualify and limit the claim in order to avoid sweeping generalizations such as "every", "all", "always", "never", "none", etc)

We spent a day going over these terms together, and since this was my first time teaching it, I decided I'd try assessing the students right away.  I gave them a short, two-paragraph write-up arguing in defense of a proposal for a tax on sugary drinks and junk food and asked them to analyze it according to the Toulmin model.

A few students immediately identified each part of the Toulmin model correctly, but most students struggled, particularly with the warrant, and distinguishing the backing from the reasons and evidence behind the claim itself, not to mention identifying qualifiers.

So, we spent a class period reviewing and analyzing that passage together.  The next day, I offered another chance to analyze a passage, this time, arguing for a ban on smoking in public places.  The improvement was astounding: all but a few of the students correctly identified the warrant and the backing.  The greatest area of difficulty lay in the qualifiers: while many students did identify qualifying words such as "if", "few" or "sometimes" during the passage, they failed to identify how the writer qualified the claim itself.

Still, it was incredibly exciting to see something as complex as warrants and backing click with the students--the students now understand the importance of examining, identifying and defending their own assumptions as they make arguments, and identifying and critiquing the assumptions in arguments that they encounter.

This is a part of my curriculum that I hope to develop and deepen in coming years, and I regret that I did not recognize the importance of teaching logic and argument structures sooner.  As the debate season starts up in the next week or two, I am looking forward to seeing how my 11th graders on the team apply what they've learned!