Learning and Teaching Project

This project explores learning and teaching from two perspectives. How can you embed the mathematics that you learn in your classroom? Does there exist a relationship between how well you understand the mathematics, how much you enjoy the mathematics, and how successful you can be as a teacher of mathematics?

Find something we have done this semester that 1) you found especially interesting and 2) you think you could adapt to be a lesson for your students. Prepare a lesson in which you share this mathematics with your students (or a subset of them). Make sure that in your lesson you convey to the students ways in which mathematics is used in the real world and that your students really do some mathematics as part of the lesson. The process of adapting an applied mathematics problem so that it is appropriate for your students can sometimes be very challenging. For example, in order for me to adapt the smallpox problem to the right level for this class (which I hopefully did), I had to understand the original paper well and then come up with a simpler scenario in which we could use a similar method. It will require a deep understanding and a lot of creativity to show your students how mathematics is used in the real world and to do that in a way that they can really appreciate. You can pick any aspect of any project, or something from the February Workshop, to present to your students- anything that you enjoyed, that you think they would also enjoy, and that would convince them that mathematics is really useful.

Once you have chosen a promising topic, you will have to think hard about how to adapt it to the knowledge and skills possessed by your students or how to teach your students the knowledge and skills they need. As you try to develop a topic, you may find that it just doesn’t work and you have to scrap it and try something else (this happened to me several times in developing this class). Once you have settled on something, make sure that you are clear about what skills or ideas you want your students to learn during the lesson. Develop a way to assess whether or not they learned those skills or ideas.

If you plan to include a demonstration or experiment as part of your lesson, make sure you try it out yourself ahead of time.

Here are some questions that might help get you started once you have chosen a potential topic:

How will you present this task to the group with whom you will work?
How will you set the stage for the students to gain an understanding of this problem?
Will pictures, graphs, manipulatives, etc. help the students’ exploration?
What real world examples will you present to motivate the problem? Will your students be able to understand the real world issues that you address?

Are there any demonstrations or experiments that might illustrate the ideas you want to teach? (it’s ok if there are not)
Can you use mathematics in this problem that is at their level?
How will you help the students create a record of what they have learned?

You should videotape this lesson and view the video afterwards. Prepare a videotape of each time you work with your students on this project. If possible ask someone to do the videotaping rather than do it yourself or use a tripod. Hopefully you can produce a tape in which you can clearly see and hear what is happening in the lesson. Not only should you be able to hear the teacher you should also be able to hear the students interacting with the teacher and with each other.

Your Learning and Teaching report should include the following components (not necessarily in this order).

The topic you chose
A description of how you adapted this topic to your students’ level
A detailed description of the lesson that you planned
A statement as to how you connected this lesson to real life
An explanation of how you expected your students to solve or approach this problem
How did your students react to this lesson? Do you think they learned what you hoped they would? Did they gain any appreciation for the uses of mathematics?
What did you notice while you were watching the video that you didn’t notice while you were teaching?
How could you improve the learning experience if you did it again? Consider the task and your preparation as well as your role and the students’ roles during the lesson.
Submit all of the videos you made.