Final Project

The Assignment

Think back on all the things you have learned so far this year and create (not copy) four problems that are representative of what you have learned. Provide annotated solutions to the problems; they should be annotated well enough for an interested learner to understand and learn from you. Your problems should demonstrate the upper limit of your understanding of the concepts. (I expect more complex problems from a student with a sophisticated understanding than from a student with just a basic grasp of concepts.) You must also include a brief summary reflection (250 words max) on this process and also a comment on what you have learned so far.

Timeline
You will choose your own due date based on your personal schedule and working habits. The absolute final deadline is May 11, 2007. You shouldn't really choose this date. On the sidebar of the blog is our class Google Calendar. You will choose your deadline and we will add it to the calendar in class. Once the deadline is chosen it is final. You may make it earlier but not later.

Format
Your work must be published as an online presentation. You may do so in any format that you wish using any digital tool(s) that you wish. It may be as simple as an extended scribe post, it may be a video uploaded to YouTube or Google Video, it may be a SlideShare or BubbleShare presentation or even a podcast. The sky is the limit with this. You can find a list of free online tools you can use here (a wiki put together by 2 Canadian teachers specifically for this purpose). Feel free to mix and match the tools to create something original if you like.

Topics:
You will each choose one of the following topics to address:

• Limits
• Differentiation & the meaning of the derivative
• Implicit Differentiation & Related rates
• Extrema, Optimization, Concavity
• Integration, Areas
• The Fundamental Theorem of Calculus
• Differential Equations
• Integration & Volumes

A consideration of analytical, graphical, and numerical approaches, approximation versus calculation, and applications, where possible, would help you to plan a thorough explanation of your topic.

Choice of topics will be given in order of request. The first person to post gets 1st choice. The last person gets whatever is left.

Summary
So, when you are done your presentation should contain:

(a) 4 problems you created. Concepts included should span the content of at least one full unit. The idea is for this to be a mathematical sampler of your expertise in mathematics.

(b) Each problem must include a solution with a detailed annotation. The annotation should be written so that an interested learner can learn from you. This is where you take on the role of teacher.

(c) Your presentation must be published online in any format of your choosing. Experts are recognized not just for what they know but for how they demonstrate their expertise in a public forum.

(d)At the end write a brief reflection that includes comments on:

• Why did you choose the concepts (not the unit) you did to create your problem set?
• How do these problems provide an overview of your best mathematical understanding for your topic?
• How did the publishing requirement effect either your enjoyment of or ability to complete the task?
• Did you learn anything from this assignment? Was it educationally valuable to you? (Be honest with this. If you got nothing out of this assignment then say that, but be specific about what you didn't like and offer a suggestion to improve it in the future.)
  
  
  
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