Is 2/7ths larger than 4/11ths?
That’s the question the middle school class was struggling to answer. Fractions hadn’t really connected with the students, says John Barclay, a teacher in Richmond Public Schools in Virginia. The concept just wasn’t intuitive.
But one student piped up: She’d noticed that if you figure out how much you’d have to add to the numerator to get a whole number, then you can tell which fraction is larger.
That really wasn’t the rule that she was being taught. But Barclay — a former Virginia math educator of the year — thought back to his own experience with a discouraging middle school teacher and decided to think through what the student was saying rather than dismiss it. The student’s rule brought her to the right answer: 4/11ths is larger. “I was like, ‘Oh, shit. Is that brilliant?’” Barclay says.
The student’s shortcut turned out to be unreliable and could have sent her to the wrong answer in some cases. But that wasn’t immediately clear. It takes critical thinking and a sense for the numbers to even understand how or why a student’s approach might be wrong, Barclay says.
This isn’t unusual: Students often get weird concepts of math, developing logical-seeming routes for answering questions, Barclay says. It can be tempting to fall back on procedural rules, particularly since students’ strange alternative rules can be time-consuming to explore. But thinking through many of students’ alternative thought patterns, so crucial to relaying math concepts, is becoming more difficult, according to Barclay. He feels like he’s given increasingly less leeway in how to implement the curricula he receives from his district, even when students are not fully understanding key concepts.
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