The best thing about online communities (IMO), is the emergence of artefacts from the collected actions of many people. The online math education community (known as the MTBoS) has seen many of these collections throughout the years, most of which are aimed at supporting imaginative mathematics instruction in grade school. Personally, I have felt the community around Fraction Talks explode right under my nose, and it has been a joy to see how the prompts have sponsored amazing student reasoning. A few months ago, I had another idea for a task structure–that I dubbed #MenuMath–and began to collect examples from engaged math teachers. Since then, the collection has grown and become bilingual thanks to the translation work of Joce Dagenais. I love hearing about student and teacher creations, and you are encouraged to submit menus via my contact page if you feel inspired to do so.
At the very least, head on over to the Menu Math page and check out some of the tasks, or read the post where I introduced them to the MTBoS. I mean, the rest of this post won’t make much sense without familiarizing yourself with the structure, but I am not about to tell you how to live your life.
I have enjoyed watching the contributions come in from all grade levels; however, some of the contributions to a collective idea are not intentional, and this post is about just that: How a Menu Math interaction sponsored an idea that I have come to like very much. It began after a Canadian math educator from Alberta, Stephanie Gower, submitted a Menu Math task on polynomial functions. She tweeted me some of her actions with her students:
Normally, students are presented with all the required constraints when satisfying a Menu Math task. Until this moment, I had focused task creation on assembling groups of constraints that intersected in interesting ways in the hopes of sponsoring reasoning that was off the beaten path. Any extensions to the activity came in the form of added constraints (which Stephanie hints at), asking students to satisfy with fewer objects, or in asking students to build a “super object”–one that satisfies as many constraints as possible. Stephanie, however, provides an amazing alternative: What if instead of extending student action by adding constraints or asking students to change their objects in broad daylight, they were required to satisfy a “secret” constraint without knowing what it was?
I have since dubbed this constraint: The Easter Egg.
The idea is so simple, as many elegant ideas are. I choose one of the constraints in the Menu Math prompt and “hide” it. (You can also build an additional constraint not listed in the original menu). Then, after students satisfy the all the constraints, I reveal two pieces of information:
- Whether or not they’ve satisfied the Easter Egg.
- How many times they’ve satisfied the Easter Egg.
It is then their job to determine what the Easter Egg might be. The best part about this extension is they are free to alter their objects and ask for the same two pieces of information. Of course, a shift in objects still needs to satisfy all the constraints in the visible menu at least once. This allows students to dive back into the creation and contrast of objects with a new purpose, rather than going back into the task to simply “do it another way”. In the end, it is very possible that students arrive at different identities for the Easter Egg, all of which are equally defensible. This, to me, is a utopian scenario; after all, it is the justification of a solution that I am after.
If this post hints at a proof of anything, it’s that serendipitous phenomena occur when teachers meaningfully interact around issues of their practice. A huge thanks is owed to Steph–in particular–for uncovering this neat extension activity, and–in general– for reminding me of the power of the collective.