Think aloud at the board, mistakes included

Expert thinking is mostly invisible: the false start you discard, the check you run halfway, the reason you picked this method over that one. Cognitive apprenticeship research made the case decades ago that learners need the master's process made audible, not just the product made visible (Collins, Brown & Newman, 1989), and modelling with narration is one of Rosenshine's (2012) core principles. A think-aloud costs nothing but the willingness to sound less polished.

In practice

• Narrate decisions, not steps: "I'm choosing substitution here because I can see a lonely x", not "now I substitute."
• Leave one genuine wobble in: consider the wrong path aloud, notice why it's wrong, back out. That recovery move is the most transferable thing you'll model all lesson.
• Then flip it: a student thinks aloud at the board while you hold the pen. Their narration is checking-for-understanding gold.