Dr. Christian Klaue

One morning a number of years ago, I forgot to erase a completed problem on the whiteboard from the previous math class before my next group of 7th graders came in. To my surprise, instead of barreling in loudly as usual, the new class glanced at the left-over problem and quietly took their seats, evidently thinking this was a continuation of the “silent teaching” strategy I had been using with them recently. “I get this!” one of the students suddenly exclaimed, and others soon followed suit. A follow-up practice problem proved that they indeed 𝘥𝘪𝘥 get it - without me even saying a word. I had accidentally discovered the power of pre-worked examples. I had been working through examples with my students for a number of years by this point, both with commentary and silently, and I thought I had taken John Sweller’s concept of 𝘸𝘰𝘳𝘬𝘦𝘥 𝘦𝘹𝘢𝘮𝘱𝘭𝘦𝘴 as far as it could go. In an instant I found I had merely been scratching the surface; it had never occurred to me that the students could and would work through the examples on their own. In the years since that day, I’ve incorporated pre-worked examples into practically everything I do as a math teacher - from classroom instruction to the creation of the 𝘠𝘰𝘶 𝘛𝘦𝘢𝘤𝘩 𝘠𝘰𝘶 book series - and I’ve had plenty of opportunities to reflect on what makes them so powerful and useful. Here are some of my conclusions: 1/13