Table Leaders Guideline

Overview:

You will be “leading” a table that runs an activity. There will be two of you at each of those tables. Students will circulate throughout the room until they find an activity that interests them. Feel free to tout your activity! The activities are designed to be easy to start (low threshold), but most of them get very deep (high ceiling)—hard enough that the activity designers don’t know the answers to the final questions.

You own investigation

We will give your activity team a tub containing your activity, instructions, and materials/manipulatives. Dive in! If something is unclear to you, then ask away! We may or may not help you at first. We do need to know if something about the instructions is unclear or if there are missing materials/manipulatives. And...no devices (for you or the students at your table)! There is nothing here that requires them, and they are counterproductive.

How to be a table leader

Your role is not to teach anything at all!

Whoa. Even though you will have explored the activity in your training session, you will likely feel unprepared to teach it. So no worries. That is your ideal condition.A big part of your job is to help students both stay engaged and to have a good time. Our overall goal is to keep students “productively stuck” on the activity, rather than to get them through the activity and to whatever answers they can come up with as quickly as possible. If they are engaged, you have very little to do—a good thing. If they are stuck or frustrated, your job is to get them moving again without giving away too much. And to help them see the puzzle as a chance to play. Remind them that problem solving need not be a solitary game—enlist your tablemates. Suggestions for how to do all this are in the next section.

Your motto: Be less helpful!!

During the festival, should your table be well-covered by your team, feel free to take a break and visit other activity tables. If it seems appropriate, consider asking the students to explain what their activity is and what they have discovered.

Asking students good mathematical questions

The Julia Robinson Math Festival session leader Guide provides some great points about this... The kind of communication you do depends a lot on the kid. For some, you'll be helping them read and understand the questions. For a more advanced student, you'll be reminding them of key strategies like

o Can you try a simpler example?

o Can you do a related problem?

o Draw a picture

Maybe they already solved the problem, and you want to guide them toward a different way of looking at it. Generally, try to be the one asking questions more than answering them.

o Can you explain that to me?

o Why does that have to be so?

o Can you show me an example?

It is also good to be prepared with some questions to ask when kids make a mistake or get something completely wrong.

o Try to say "Why?" with the same tone whether they have it right or wrong --make them explain it to you and uncover their own error.

o Talk about ways they can check their answer, again whether it is right or wrong.

If you hear another kid putting someone down for not knowing an answer or for getting something wrong, be prepared with a remark that suits you. I like to remind them that we're here to explore and learn, and it would be boring if we already knew how to do all the problems.

Teach students how to ask good mathematical questions

From Sam Vandervelde’s Circle in a Box:

Students almost never have the opportunity to ask, “What if . . . ?” types of questions at any point during their secondary school careers. They have no idea that one of the most crucial skills acquired by a professional mathematician is the ability to ask productive questions; the sorts of questions that lead to new areas of research. All of their training suggests that mathematics is synonymous with solving problems; very few of them stop to wonder where the problems come from. Moreover, working on problems can become tiresome or frustrating. But contemplating new directions to explore, free from the burden of needing to answer all the questions that might arise (at least for the time being), is a marvelous, creative endeavor. Every student should be given the chance to practice this process.

So take a few minutes after wrapping up a nice problem to point out that the book is not yet closed on this particular idea, and ask students where it might lead. At first, students may need a lot of coaxing. What happens if one uses different numbers or shapes? Is there an analogous result in higher dimensions? What if we allowed three people to play this game, how would that look? Encourage any ideas or attempts; quite often once the first question or two is tentatively offered the floodgates are opened. Help students refine vague ideas into well-formulated questions. This activity can be as rewarding for the leader as for the students— it is exciting to see what they come up with, and invariably everyone leaves with new ideas to pursue.

And again...Don’t try to teach!

Enjoy seeing how quickly young minds play with new activities and go off in all sorts of crazy directions. As adults, we often try to channel these wild speculations, but who knows where they may lead an inquisitive young mathematician. I have often found middle schoolers to be faster at gaining insights or in finding surprising lateral directions to explore than older kids or adults.