The following is excerpted from the Introduction of the new book by Robert Kaplinsky, Open Middle Math: Problems That Unlock Student Thinking, Grades 6–12. Find out what your classroom can look like by incorporating the ideas from this book into your math instruction.
The bell rings and lunch ends. Sweaty students gather outside your classroom and slowly shuffle in, finding their seats. As the chatting softens and class begins, they look at you and the math problem you’ve written on the board. You’re trying something new today and are cautiously optimistic about how this unfamiliar experience will be received. The problem looks different from what they’re used to, and they wait for you to explain what to do.
As you describe the problem, you hear the groans and whispered resistance. Too many of your students believe that math is something where the teacher tells them what to do and then they repeat those steps dozens of times. This problem doesn’t follow that pattern, and they’re not sure what to make of it. Once you’re done explaining the instructions, students begin working on the problem. They don’t solve it on their first attempt, and the lesson begins to feel like many others you’ve taught. It’s what happens next, though, that surprises you. Strangely, many of the students who often give up instead start trying the problem again. The familiar clink of pencils dropping onto the table as students check out is much fainter than usual. Slowly you start to notice a different energy taking over the room. Kids seem to be on a quest to figure out the answer.
Many students begin placing themselves in self-imposed friendly competitions against each other, struggling to see if they can improve upon their previous work. Those you frequently find daydreaming are actually excited to figure out how to get the best answer. Students who have felt comfortable with years of following the steps in their notes are unsure of what to make of the experience and have not fully bought in, but you’re optimistic that they’re on a path toward making sense of mathematics instead of just getting the answer. All you can see from students who normally finish assignments quickly and complain about being bored is the back of their heads and their furiously moving hands. Kids start chatting, going back and forth. Initially it sounds like they might be off task, but you realize that they’re talking about the problem, whose answer is better, and how they got it. In fact, they’re sharing math discoveries with each other like they’re the first people to realize them, even though you’ve been telling them those same things for weeks.
Minutes fly by, and the time you’d normally spend keeping kids on task is spent guiding students who need help and facilitating powerful classroom conversations around problem-solving strategies. Students still have plenty of misconceptions, but you see them more easily than you ever have before, and they give you a clearer picture as to how you’ll want to adjust future instruction.
Eventually the bell rings, but almost no one leaves. Instead, they beg you for a little more time to work on the problem. It feels like you’re being pranked, because this can’t possibly be happening. You remind them that they’ll be late to their next class and have to leave. There’s more groaning and whispered resistance, but this time it’s for an entirely different reason. Slowly they get up, telling you that they loved this problem and hope to do another one tomorrow.
Some students are in fact late to their next class, and you get a call from their teacher to verify the outlandish excuse they gave. They said that the reason they were late was because they were working on a math problem in your class and didn’t want to stop. Laughing to yourself, you confirm their reason and explain that it won’t happen again. The other teacher hangs up in disbelief, and you stand there feeling the same way. You had hoped this was possible, but it wasn’t until you saw it happen that you were able to believe it.
To find out what is inside Robert Kaplinsky’s new book, Open Middle Math that you can use to create the classroom environment he describes, read the rest of the Introduction here, or buy the book here and get started right away!