with mathematical ideas can engage students’ thinking and
help them learn to persevere in problem solving (National
Council of Teachers of Mathematics, 2014). Emerging from
the growth mindset research of Carol Dweck (2007), we
now know that an individual’s brain grows when he or she
struggles in a productive way with something difficult—like
a challenging math problem (Boaler, 2015).
More and more teachers are confirming that students can
benefit from wrestling with problems they haven’t specifically been taught how to solve. In the process, students learn
about the power of effort and persistence, become more confident problem solvers, and even grow their intelligence.
Upside-Down Teaching in Action
Unlike the traditional teacher-centered classroom based on
lecture, an upside-down classroom is teacher-structured,
but centered on students’ thinking. The goal of the lesson
isn’t simply for students to get the answer to a problem, but
rather for students to learn the intended mathematics of
the lesson using the problem as the basis for thinking and
discussion. After selecting a problem to start the lesson,
the teacher’s job becomes orchestrating the discourse of
the classroom—how students will share their thinking
in ways that lead to the mathematical outcome of the
lesson—and helping students connect the discussion to
the mathematical goal. As the teacher circulates through
the classroom, she generally asks questions to help stu-
dents clarify their thinking or take it to the next level.
While doing so, the teacher is also making decisions in the
moment about which students will share their work with
the whole class and in what order they will be called on.
Sometimes students’ discussion will lead directly to the
mathematical connection the teacher wants to make—as in
a 2nd grade lesson involving subtraction that I’ll describe