Doing Math (SC 507)

Ultimately, the goal of making math material is for you to make it material for people other than yourself. You now have practice seeing mathematical ideas in play in the world around us, and with creating physical items that embody a mathematical topic. This assignment gives you the opportunity to use those skills to illuminate and engage others concerning a mathematical topic of interest to you. One of the tremendous advantages of building physical realizations of mathematical ideas is that other people then can see, touch, and -- most importantly for this assignment -- interact with the object(s) you've created to form their own impressions, views, and understanding of the ideas you develop. This assignment emphasizes interactivity because that's a key aspect of an exhibit that promotes engagement with, time spent considering, and effort toward thinking through the item you've created.

Thus, in short, this assignment is to create a hands-on/interactive physical exhibit of a mathematical idea for a general audience: in short, something that would work at a hands-on science or math museum, or (in our particular case) the Cambridge Science Festival.

In greater detail: first, choose a topic. Then begin to brainstorm ways you could elucidate that topic, which would benefit from the participant interacting physically with objects you create. As you narrow down the design of the physical item you will create, so too should you become very specific and concrete with your goals concerning what benefits the participant will glean from the interaction. Are you trying to teach a specific mathematical concept, fact, or technique? If so, specifically which one or ones? Are you trying to challenge the participant's potentially incorrect understanding or intuition of a mathematical idea or problem and solution? Are you trying to interest the participant in an area of math s/he may not have seen before? If so, what followup are you hoping to induce (e.g., reading about the topic at home) and how will you support that? Are you trying to expand the participant's concept of what mathematics comprises? You must be clear about your goals for the exhibit in order to optimize its design to meet those goals.

As you head toward a specific design for your exhibit, you should model what you plan to build in software so that you can be sure the structure you imagine for your exhibit fits together properly and embodies the mathematical ideas you mean to convey.

As the model heads toward completion, you should plan the execution of the design. What materials and methods will you use for fabrication? How will you ensure attractive finishes for the exhibit? Visual appeal is an important aspect of engaging visitors; there are many possible styles for an exhibit, but there should be something that catches the potential participant's eye and draws them in. Lettering and other labeling should be neat and large enough to be easily readable; mounting printed texts rather than hand-writing them is strongly recommended. You should plan to make your exhibit durable enough to withstand repeated use by many different participants.

You should prototype your exhibit. This may mean a simplified version made with easy-to-use but perhaps less-accurate materials, or it may mean you make the core of the exhibit and test it for functionality before you apply final finishes, labeling, etc.

Finally, you should execute the final fabrication of your exhibit, creating the production copy that participants will use. The last stage is creation of explanatory texts and labels. These fall into two categories: basic guides on how to use/what to do with the exhibit, and expository material clarifying what mathematical ideas are being shown. In creating these, you should be aware that museum studies show that under 10% of visitors read expository texts in hands-on museum settings, and that they only read short, simple guide texts. So keep your guide texts to the minimum level that will enable a visitor to enjoy what you've produced (completely self-explanatory apparatus that participants can use and obtain productive experiences from without any guiding text is the ideal in the hands-on exhibit world, but it is rarely achieved; do not hesitate to include short guiding texts, especially if they will mean the difference between a participant remaining puzzled and not able to interact with your exhibit and a participant having a positive interaction). You should then also have an explanatory text for the curious, but keep it brief, non-technical, and catchy; often you may want to include a link to further information so that participants whose curiosity you've inspired can find out more.

Bring your finished exhibit to the course open house in Science Center 507 at the final exam time (9:00 on Dec 13) ready to engage with visitors from outside the course, facilitate their interaction with the exhibit, and observe their reactions and experiences. (If we had more time, we would include a component of evaluating the performance of the exhibit and adjusting its design to improve its performance toward goal, but that aspect unfortunately remains outside the scope of this course.)

Time line

There is one month remaining until the course open house. That schedule provides a compact period of time for the production of a hands-on exhibit. Therefore, it is important to stick to a disciplined production schedule in order to produce a high-quality exhibit. Here are the milestones you are expected to meet en route to the final due date:

by Monday, Nov 26th: submit an exhibit proposal. The proposal should include the name or names of the students working on the project, a brief description of the mathematical topic, a brief description (and sketch, if helpful) of what you will build, a description of how participants will interact with the exhibit, and an account of what you see as the primary execution challenges and how you plan to meet them. This must be done in writing, although the quality of that writing will not be assessed as part of this assignment (beyond, of course, that you need to ensure I can understand what you are proposing.) That said, I am happy to meet to discuss your project and ideas prior to the due date of the proposal; if my existing office hours do not serve, make a specific appointment for this purpose. I will respond to each written submission within 24 hours of receiving it, with feedback/ideas for your project and my approval, provisional approval (pending some changes in plan), or withheld approval. Note: you must have an approved exhibit plan in place by Wednesday, Nov 28. You are welcome to submit your exhibit proposal to me at any time between now and the 26th; you may want to discharge this requirement early to maximize the time you have for further design and execution of your exhibit.

by Friday, Nov 30th: Submit a construction plan. This should be a brief summary of materials and methods for executing your exhibit, along with a description of what aspects of it you will prototype, and how. It does not need to be a detailed step-by-step building plan, and again, the writing quality of this will not be assessed, but you need to convince me that you can actually carry out the fabrication of the exhibit.

Wednesday, Dec 5th, 1:30 PM: Bring your prototype to the (last) section meeting for the class. We will hold a prototype session in which you can see how others interact with your exhibit (and try out the things that others are developing). This is a vital opportunity to obtain feedback, and observe people experiencing your prototype. The information you gain can be critical for improving the final design of what you submit.

Thursday, Dec 13th, 9:00 AM: Bring your final exhibit to the course open house (location TBA). The public portion of the open house will be advertised to begin at 9:30 so that you have time to set up your exhibit. Be ready to welcome visitors, show them what you've built, facilitate their interaction with the exhibit, and discuss what your exhibit is about, its mathematical meaning and significance, and so on.

Required Materials

Here is the complete list of items you must submit or accomplish for this exhibit:

1. The completed exhibit itself, together with guide and explanatory texts (which might be physically integrated with the exhibit, or might be on separate panels).
2. A transcript of the guide and explanatory texts, submitted electronically.
3. A two-page essay (or longer if you prefer) setting forth your goals for the participant's experience with your exhibit (see the third paragraph of the assignment description) and how your design for the exhibit attempts to accomplish those goals.
4. A brief exposition of the mathematical context of the exhibit and the particular mathematical structure or idea your exhibit displays.
5. The software model of your exhibit.
6. You must have an approved exhibit plan by Nov 28.
7. You must have submitted an adequate construction plan by Nov 30.
8. You must set up your exhibit at the course open house in Science Center 507 on Dec 13th at 9:00 AM, and facilitate visitors' experiences with your exhibit, and discuss/answer questions about the exhibit. We will keep the open house open until 11:30 AM, at which point we will pack up the exhibits and transfer them to my office. Thus, we should wrap up by noon.
9. If you do not consent to your exhibit being shown at the Cambridge Science Festival, you must inform me. Note that unless I receive such a notification, I will keep your finished exhibit through the time of the Festival.

Choosing a topic

For this final project, the responsibility of topic selection rests primarily with you. Some (not necessarily new) advice: Choose a topic you're personally interested in; your enthusiasm will show through. A critical criterion for this project is the capacity to build something that allows viewers to engage in a meaningful experience. So make sure participants are able to build something, measure something, attempt to solve a puzzle or other challenge, play a game, guess/identify/match up items, manipulate something to discover it acts in unexpected ways, fit things together in unusual ways, use a mathematical mechanism, perform an experiment, or ... this list is not meant to be exhaustive, but merely to inspire.

You can look at prior suggestion lists, old Math Mondays columns in Make: Online, "Do the Math" columns in Math Horizons magazine, old Martin Gardner columns from Scientific American, or popular books such as "Things to Make and Do in the Fourth Dimension" by Matt Parker (there are many other titles)  for inspiration. Look back at your Seeing Math essay (or even other students'). Or you can just make your own idea based on a topic from a course you've taken, or a book you've read, or just something you're interested in. Just looking over the list of possible interactions listed above, I am reminded of hinged dissections, polyhedral honeycombs, surfaces of constant diameter with a mechanism for demonstrating that the diameter really is constant, a tic-tac-toe "machine" that learns as it plays, non-circular gears that still fit together and turn smoothly, pentominoes or other sets of tiles, harmonographs, and planimeters. So there are many possibilities, these just scratch the surface; if you want to brainstorm options, just arrange to meet.

You may be wondering if you can build on an earlier project. The answer is yes, you can, but there are some guidelines. First, earlier assignments did not have an interaction requirement. Therefore, be careful that your earlier project can be adapted to provide a meaningful hands-on experience for a participant or participants. Second, since it is public-facing, this project must have the highest standards of finish and quality of construction of any in the course. And finally, you must go beyond what you have already turned in, in terms of mathematical content; don't turn in a more polished but otherwise exact copy of something you have already done and expect to receive an optimal grade. Extend what you have already done in some mathematically meaningful way.

Basis for grading

The following aspects of your project will be considered/evaluated in determining your overall grade on this assignment:

• Writing mechanics of items 2-4.
• Style and effectiveness of communication in items 2-4.
• Correctness, significance, and clarity of mathematical exposition in item 4.
• Organization, relevance, and correctness of software model in item 5.
• Quality of the mathematical connection between the topic and the built item, and the degree to which the built item illuminates the mathematical topic or a specific idea relevant to the topic.
• The quality of the construction submitted for item 1. The standards on this item will generally be somewhat higher than for Making Math.
• The quality of visitor experiences, and your facilitation of them, at the open house on Dec 13.

Enjoy creating your exhibit!