Problem-posing project

Goal: To see mathematics as a creative endeavour by creating (or significantly modifying) an interesting mathematical problem. This problem and its solution will be presented during Math Retreat.

Tasks:

  1. Work in team (2-4 people)
  2. Problem creation
  3. Proposals
  4. Sign up for Math Retreat
  5. Present selected problem to fellow students
  6. Submit paper solutions for the problem

Teams

A presentation team may consist of 2-4 students. Teams of 2-3 students are expected to present for 20 minutes, whereas a team of 4 presents for 50 minutes.

Problem creation

Once your team has been formed, search resources for problems or puzzles or games that would engage other students. These problems must be well-defined, which means there is a definitive answer for the problem. "What is the best movie?" is an example of an ill-defined problem.

Possible resources:

Reminder that Crossing the River with Dogs cannot be used! This includes problems that are planned for later in the semester so I recommend doing a quick search for your problem in our book.

Proposals

Recall that your team will propose two problems (that are different types) that you are considering for your presentation. Not all details of the problems need to be worked out at this stage, but please provide enough information for the instructor to understand the intentions of the problems. These problems cannot be exact duplicates of existing problems and instead must be created from scratch or significantly modified from existing problems.

For each potential problem, please submit a typed proposal that addresses the items below:

  1. Identify your team
  2. State the "new" problem. Again, not all details need to be figured out.
  3. Include problem(s) used for inspiration and their source(s).
  4. Teams of 4: Identify a possible warm-up to start with or an extension in case students finish early. This is recommended, but optional, for smaller teams.

Finally, indicate which problem is your first choice. Problems will be chosen by the instructor based on appropriateness for other students and originality.

Submission

Proposals may be submitted on paper on the due date or as a PDF to Canvas.

Sign-up for Math Retreat

Create your own abstract or use the following boilerplate and feel free to liven it up!

We will discuss a problem involving _____________. This problem is suitable for _____________ students and will be solved together. Specifically, the presentation will introduce the problem, provide thinking time, and give hints where needed. A detailed solution to the problem will be provided near the end of presentation time.

Submission

This will be done during class time.

Presentation

Present your problem to fellow students by: having an introduction, giving time to work on the problem while provide help/hints, presenting a solution to the problem as needed.

Presenters are expected to:

For more details see the scoring guide below.

Paper solutions

Solutions for the presentation problem will be due in class shortly after presentations completed.

Also include discuss for the originality of the problem.

Submission

Bring paper copies of solutions to class on the due date.


Scoring guide 24 MP

In general, the group members receive the same scores except where noted.

Presentation

Requirements

Handout

States problem and gives space for student work. 2 MP
Note: Teams of 4 also need a warm or extension problem.

Comments

Paper solutions

Originality

Solutions

Presentation problem is scored using the usual guidelines. 5 MP

Comments

Collaboration (individual score)

Collaboration score (individual)

This is based on instructor observations, share of presentation responsibilities, and group feedback. Individual presentations automatically receive full credit. 4 MP

Points: 0