Mathematic Practice Standard #8 states students should, “Look for and express regularity in repeated reasoning.” The criteria in this standard suggests that “mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts.”
Driving home tonight, I heard a story on NPR on our human appreciation for repetition in math and in other areas as well, specifically music. Reporter Alix Spiegel researched why repetition is “seductive to humans” in her audio-story Play It Again And Again, Sam that explores the research of music psychologist Elizabeth Margulis who notes that humans are drawn to repetition.
“Musical repetitiveness isn’t really an idiosyncratic feature of music that’s arisen over the past few hundred years in the West,” she says. “It seems to be a cultural universal. Not only does every known human culture make music, but also, every known human culture makes music [in which] repetition is a defining element.”
Margulis has studies the mere exposure effect where repeated exposure to anything increases our acceptance, and helps us develop a positive attitude.
“Let’s say you’ve heard a little tune before, but you don’t even knowthat you’ve heard it, and then you hear it again. The second time you hear it you know what to expect to a certain extent, even if you don’t know you know,” Maugulis says. “You are just better able to handle that sequence of sounds. And what it seems like [your mind is saying] is just, ‘Oh I like this! This is a good tune!’ But that’s a misattribution.”
Familiarity helps to develop acceptance, and the eight mathematic practice standards should become familiar to every teacher. They offer strategies that can be used by teachers in every discipline. Especially if these standards become part of a repeated practice…just as Mathematical Practice Standard #8 suggests.