Introduction
For some, making mathematics explicit for struggling students means telling
them what to do. The literature is replete with step-by-step directions for al-
gorithms and mnemonic devices designed to foster recall of specific proce-
dures. Although these techniques might be useful in certain circumstances,
an exclusive emphasis on memory results in passive learning. When students
then encounter unfamiliar situations, they are often at a loss for how to ap-
ply the procedures they’ve memorized (Boaler 2008). A more useful way of
being explicit is to make visible the assumptions and processes involved in
problem solving that lead to successful solution strategies. Teachers who do
this kind of explicit teaching create a “learning environment where students
learn about themselves as learners and develop strategies for success” (Asera
2006).
These essays and videos focus on being explicit to help students make
sense of mathematics. Students who struggle with a particular mathematical
idea or struggle to develop useful strategies to solve mathematical problems
often need help seeing the mathematics that underlies an activity, making
mathematical connections among different activities, or figuring out what
to look for as they solve a problem. The teachers featured here use a series
of strategies to reach their struggling students: choosing a mathematically
rich problem, carefully sequencing questions that build appropriate skills
and orientations, and incorporating prompts to support students who are ex-
periencing difficulty (Sullivan, Mousley, and Zevenbergen 2006).