If one wants to conduct a 1/2 day workshop in Mathematics for 12-16 year old students - how one should go about preparing the workshop

Question

The questions that I want ask are the following:

1. What are the most important and effective topics to conduct a workshop?
2. What fraction of workshop should include lectures, activity, problem solving, etc.
3. What could be the optimal number (roughly) of students in a workshop?
4. What all other parameters one should think while designing a workshop?

Answer 1

Math Circles are one type of "workshop" I'd recommend. Math Circles can take many forms: More students or fewer, more lecture or less. But the idea is that the students do most of the work, and the leaders are there to give helpful nudges. (Perhaps 10 students with one leader, 15 with two, 7 or 8 for each leader if more.)

Good problems are "low floor, high ceiling", easy to get started, and full of rich content. They also can be approached from many directions. You need problems that will intrigue students. Resources include: Tom Davis's page, mathcircles site, National Association of Math Circles, and a few posts on my blog, including this one about doing a math circle with the game Spot It. There are no important topics, only good ones and not so good.

Instead of having all participants working on one problem, you can have a festival of mathematics, like the Julia Robinson Mathematics Festival, with a different problem sheet or puzzle collection at each table (along with a table leader).

Since most math leaders have not been trained in this style of work, it's important that the leaders get experience playing with problems together before leading.

(I see that you are in India. I just now googled "math circles India" and I see a number of promising looking sites. Maybe the people behind those will have some advice for you too.)

Answer 2

Glad you are seeking peer support for this. Leaders' connections to good math friends make their mathematics events shine!

Some suggestions, based on my experiences organizing math events:

1. Know your audience.
2. KNOW YOUR AUDIENCE. Are your students there for goal-oriented work, such as an academic credit or winning a competition, or are they playing and exploring? How does their life experience and identity intersect with their math work? Are the families supportive? What's their past math experience, and how do you know? Are the students well-fed, well-rested, and well-supplied when you meet, or do you need to provide general well-being support and supplies as well? Who finances your endeavor (families, a non-profit, a school system...) and what are their expectations of you? What struggles in the relevant communities are likely to affect your event (poverty, political tensions...)? You may want to include some of that info in your next question about organizing events.
3. What's your setting: physical or virtual venue and what kind, during or after school, how many people (students, teachers, volunteers), what supplies, etc.?
4. Who are you? Workshops are built on personal trust towards people leading them. So are peer networks. You may want to show your face(s) and name(s) to your prospective audience and to the peers whose support you seek.
5. What are hopes and dreams of the members of your organization in regard to your event? If all goes well, what will change for you and yours?
6. What is your organization's big goal, philosophy, manifesto? What change are you trying to cause in mathematics education overall? What is it all about for you? The more specific you can be here, the better it will help to plan your event.

If you do not know your audience and setting, start there. Find a community that needs a math workshop, and adjust your work to THEIR needs. Become community-responsive.

Thank you for sharing your journey!

Answer 3

One tactical suggestion is to do a hands on statistical workshop. Stats is still math, right? I mean, even if lower class, back of the bus math. ;)

I know of one with miniature catapults, that is used for corporate SiX Sigma efforts. But you could look for others that are simpler or just make your own (tossing paper airplanes or the like). It leads to several interesting topics (average, std deviation, sample size, factors, etc.) And it involves some fun moving and doing.

And really, you're not doing any serious investigation of physics/aerodynamics. But using them to explore mathematics. If you will allow me to creep the ghetto of stats into math. Plus just the time duration and the like will fit well into a workshop. And the KEY for workshops is to keep the animals BUSY (working, producing, trying, etc.) not viewing slides and getting unhappy.