As part of a periodic series in The Debatifier on argument and math, today’s post backs up a step from Conor Cameron’s previous post on ‘Sometimes, Always, Never’ questioning in Algebra as a form of argument-making, and examines the broad and now well-established move in K-12 mathematics education toward thinking and reasoning skills at the base of mathematical formulas, procedures, and algorithms. The clear implication of this pedagogical direction is that students should be regularly engaging in argumentation in the classroom, as the articulation and performance of this thinking and reasoning.
Mathematics is constructed on a foundation of logical reasoning, and the National Council of the Teachers of Mathematics (NCTM) has been calling for an elevation of reasoning and argumentation in math education since at least 2000. Formal logic and the mathematical proof share an origin story, and the most influential figure in argument studies over the past 60 years, Stephen Toulmin (creator of the ‘Claim – Data/Evidence – Warrant/Reasoning’ argument model), had as his primary objective to expand the role and influence of informal logic.
By Conor Cameron
The Common Core State Standards demand that students of mathematics, “Construct viable arguments and critique the reasoning of others.” In a vacuum, that requirement probably seems more descriptive of what might occur in an English or social studies classroom. Many math teachers probably think to themselves, “Students may do that sort of work in their Geometry classes, not so much in mine.”
“But My Students Don’t Know Enough Yet to Engage in Debates!” Christopher Lasch on the Argument vs. Information Confusion
By Gerald Graff
“Hey, I’m all for teaching argument and debate,” my colleague assured me after viewing the ACE website. “But students have to know something about a topic before they can usefully debate it, and students these days just don’t.”
It’s one of the most familiar objections to organizing school and college curricula around debatable issues: until students know enough of the relevant information—as today’s students rarely do—they aren’t ready to debate such issues. And it’s certainly true up to a point: it’s hard to enter a debate about whether income inequality is a problem or not if you lack information about what’s been happening to income distribution over the last generation.
What this way of thinking ignores, however, is its circularity: yes, students need some economic knowledge to intelligibly debate the pros and cons of income inequality, but unless they are exposed to the debate they may not see the point of acquiring that data in the first place.
Named for Socrates (469 – 399 B.C.E.), one of the founders of Western philosophy, the Socratic Seminar is a formalized classroom discussion activity that emphasizes reflective thinking about big questions and the use of evidence to support responses. According to Elfie Israel, in Inquiry and the Literary Text (NCTE, 2002):
The Socratic seminar is a formal discussion, based on a text, in which the leader asks open-ended questions. Within the context of the discussion, students listen closely to the comments of others, thinking critically for themselves, and articulate their own thoughts and their responses to the thoughts of others. They learn to work cooperatively and to question intelligently and civilly.
Northern Illinois University’s College of Business and Department of Communication were brought together several years ago over the common goal of developing student’s critical thinking skills. The connection nurtured a mutually beneficial relationship for both NIU departments, and all of the educators and students taking part. My involvement in the collaboration has grown throughout its development. It began with providing example debates as a senior undergraduate member of NIU’S debate team; then I provided more extensive support as a graduate intern; and now I am integrally involved with the project as its professional consultant.