In a new series aimed at closing the gap between research and practice, Usable Knowledge is partnering with Digital Promise on a project that collects real questions from educators across the country and poses them to faculty members at the Harvard Graduate School of Education. The series, called Ask a Researcher, offers evidence-based guidance to classroom dilemmas in the areas of literacy, mathematics, and English language learning, giving teachers credible strategies to enhance student learning. (Questions are gathered from educators in Ditigal Promise's League of Innovative Schools; plans are developing to solicit questions more broadly.)
Here, we share an excerpt of questions and answers in mathematics, with links to the full series.
Q: For struggling math learners, how can teachers fill in the gaps and teach on grade level, all in one year?
Keep these two goals separate, advises Jon Star. Devote instructional time daily to filling gaps by giving students opportunities to revisit past content. Then consider ways to modify the complexity of new content, by using “easier” numbers, fewer fractions, and more straightforward problems. "This way, struggling students can begin to grasp the important ideas of the new material without being handicapped by their fragile understanding of the 'old,'" Star says. Read Star's full answer.
Q: How do you build students' math confidence?
Recognize, and work to counteract, the prevailing binary narrative about math, says Noah Heller: Either you're good at it or you're not good at it. "If students have received negative feedback on assessments, if they’ve been placed in lower math tracks, or if they misunderstand the content, then oftentimes, they think they’re bad at math," Heller says. "One way to change this assumption is to create a classroom culture where errors become learning opportunities." Also: try to de-emphasize answers and spend more time on reasoning, making math class more discursive, less about coming to a single answer. Read Heller's complete answer.
Q: What assessment strategies are most effective for improving math learning?
Based on the paucity of rigorous evidence showing the impact of formative assessment, "I’m not optimistic about teachers studying formal student data, and, if I were a principal, I’d put my eggs in another basket," says Heather Hill. "For instance, I’d probably think about coaching teachers to be more aware of students’ in-classroom work product and cues." The answer to improved learning probably lies in a package of pedagogical techniques, one that includes formative assessment strategies but also new tasks and student-centered teaching methods, including time spent on open-ended, cognitively complex problems. Read Hill's full answer.
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Noah Heller is lecturer on education and a master teacher in residence in mathematics for the Harvard Teacher Fellows (HTF) Program. His past research focused on ninth-grade students identification with mathematics in regard to how they see themselves as math persons.
Heather C. Hill's primary work focuses on teacher and teaching quality and the effects of policies aimed at improving both. She is known for developing instruments for measuring teachers mathematical knowledge for teaching (MKT) and the mathematical quality of instruction (MQI) within classrooms.
Jon Star is an educational psychologist who studies children's learning of mathematics in middle and high school, particularly algebra. Star's current research explores the development of flexibility in mathematical problem solving.