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Teaching Reasoning in Mathematics

Posted by Jonathan Martin under

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Washington Post wrote yesterday about new NCTM principles “emphasizing that “reasoning” and “sense-making” should be at the center of all lessons.” This is great to see; the argument here on this site is that we need to emphasize these things all the way across the curriculum.

The council “says a fresh emphasis on the goal is necessary after a half-decade of high-stakes testing has taken spontaneity from many math discussions. Multiple choice tests leave little room for expansive thought.”

Engagement is a constant theme here, and the concern is that much of mathematics instruction, abstracted from any linkage to the real world and devoid of any relevance, creates too great a distance for students. particularly in middle and high school: “teenagers are more autonomous thinkers… Younger students are more willing to work at something because they are told to; teens need a reason to care. They need to be *engaged*.”

Engagement is best when students feel they are tackling problems first, and then seeking the tools, the formulas, the techniques they need to solve those problems. Too often, I fear, we introduce the techniques first, and drill for following the rules, and only then set students upon their problems. One teacher cited in the article explains her exemplary approach:

“Math is not a set of rules to memorize. It is problem-solving,” she said. “If our students don’t have a chance to do that in a math classroom, how will they ever know what math is?” After a week of talking about slope and the notion of “rate of change” through word problems, patterns in tables and points on graphs, Nichols introduced a formula for slope. The relief in the classroom was visible. Some students sitting back reluctantly in their chairs leaned forward, piped up and started plugging in numbers. But quickly, they became confused. Which numbers in the problem work for X, and which ones work for Y? “Can you see?” Nichols asked them. “Formulas aren’t so great if you don’t know what they are talking about.”

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