I highly recommend you read Anna Blinstein’s account of a math problem that went wrong in one class and right in another. The makeover she applied between classes is available to you no matter what classes or students you teach.
Blinstein notes that “the sheer wordiness and immediate jumping into very abstract ideas was a huge turn-off for many students.”
She describes the makeover as asking students “to try things, engage, take guesses, get a foot in the door, and progress towards increasing abstraction and formality at their own pace.”
Blinstein also notes that she “started with a story.” This is significant! Cognitive scientist Daniel Willingham describes “the privileged status of story.” Stories are often more interesting to people than expository texts and students often learn more from them.
It’s my birthday, but I’m really, really obsessed with all things square. My entire party has a square theme. Of course, I demand a square cake and that all pieces served to guests are perfect squares too.
Of course this isn’t real. No one, not even the spoiled princesses on My Super Sweet 16, has ever asked for such a party. But none of her students cares about that for the same reason that no one cares that the universe of Harry Potter isn’t real:
Blinstein’s students aren’t just reading a story. She’s made them a part of the story.
Crucial to Blinstein’s success here, in my view, is that she has deleted elements of the problem so that she could re-introduce them with her students’ participation. (Also that she has developed an enormous professional community online she could ask for help between classes.)
Her story deepens my conviction that the most productive and interesting problems aren’t assigned on paper, but co-developed by teachers and students in conversation with one another.
Agreed, but it’s interesting to me how few “story problems” contain any of the elements of stories that people enjoy: heroism, conflicts, rising action, resolution, etc.