We teachers learn early on that exams should reflect what students have learned. They should attempt to measure what was taught, to capture student understanding in a way that helps drive future instruction.

But lately, I’ve been asking myself, *what if I included material on exams that students haven’t explicitly learned? What if I expected them to stretch what they did learn to apply it in a new way?*

Specifically, I’m thinking that 10% of each exam would be stuff that students have never seen in class or homework. It would be unknown to the kids before they saw it on an exam. This 10% would push students to expand and enrich what they did learn. It would allow me to bridge pre- and post-exam content and possibly preassess things to come. It would trigger meaningful reflection afterward which, I hope, would cause students to genuinely learn something new. It would also help me measure how far their understanding of the mathematics will take them into uncharted territory — which is probably worth it in and of itself. And besides, the oh-so-high-stakes Regents exam in June is filled with problems that neither they nor I could have predicted…so why not prepare them for this all throughout the year?

All that sounds great. But what scares me is the unethical nature of it all. This is where my preservice days haunt me. How could I possibly hold my kids accountable for material they’ve never interacted with? Is that fair? This unpredictability for the students is making me second guess myself.

Although, I am only thinking about what’s expected now — which is that exams will follow suit with the problems they’ve already done. But what if this unknown 10% was a norm that was baked into our classroom culture from jump? What if it was something students understood and acknowledged going into every exam, an inherent challenge I placed on them to demonstrate their mathematical abilities to new ways?

bp