Monthly Archives: October 2015

In-Class Group Project Activity 10/29/15 ‚Äď Refine Your Group Conjecture

Assignment.  Your goal for today is to refine the conjecture you decided on during your last class meeting.  Some things to consider:

  • Specificity: The conjecture should be stated clearly. ¬†It should include all information necessary to be understood by someone who is familiar with graph theory terms (vertex, edges, paths) and familiar with the assignment (walking tours). ¬†A reader should be able to tell from the statement¬†whether a conjecture applies to a given drawing or not.
  • Generality: Your conjecture should apply to more than just a single specific graph (it can apply to a collection of similar graphs, for example, as long as you describe exactly what types of graphs you are considering).
  • Drawing:¬†You can create a drawing to accompany your conjecture, but your conjecture should be understandable without the picture.
  • You can revise your conjecture as a group if you wish – but try to come up with something similar.
  • You can add additional clarification to your conjecture.
  • You can extend your conjecture to include more types of graphs.

OpenLab #8: Hold your breath and dive into math – Vi Hart

Vi Hart describes herself as a “recreational mathemusician” – she has a unique approach to mathematics and its connections to the world. ¬†In this assignment you’ll be exploring some of her videos (she has a YouTube channel here), and using them as a basis for creating a new blog post.

Assignment (Due November 5, 2015).  Create a new blog post responding to the instructions below. Creating a new blog post allows you more flexibility than simply leaving a comment. You have the ability to edit your work after you submit it, and to include photos, videos and other media. It also allows you to contribute to the public content of our course website.

You can get started by clicking the plus sign at the very top of our site¬†(if you don’t see it, make sure you are logged in to the OpenLab). Detailed instructions on creating a new blog post can be found here¬†(see “Writing a Post” in the middle of the page). You should create a new post including the following:

  • The title should include the word “Videos” and also your name.
  • Your post should include responses to all three parts of the assignment described¬†below.
  • Under “Category,” select “OpenLab Assignments” (you will see this on the right side of the screen)
  • Under tags, enter “OpenLab 8”, “Vi Hart”, and any¬†other tags you think¬†describe the videos you watched (for example, you might choose “pi” if it’s a video about pi). ¬†Don’t forget to click “Add” after entering your tags in the box.
  • When you’re done, click “Publish” (the blue button towards the top right on the screen).

Instructions:

Watch at least three different videos by Vi Hart from  https://www.youtube.com/user/Vihart/ .  You should:

  • choose videos at least 2 minutes in length
  • choose¬†videos that are related to¬†math in some way
  • choose three videos, at least two of which should not appear on her front page (older or less popular videos). ¬†For a full list of her videos, click the “Videos” button near the top of her page – or click here. ¬†Scroll to the bottom and click “Load more” to see older videos.

In your post, include a response to each of the following three Parts:

Part 1. Include a link to each video you watched (3 minimum), the title, and a one or two sentence description of what the video was about.

Now choose one video to focus on.  You MUST watch it 3 times. Use it as the basis for parts 2 and 3.

Part 2.  Write one paragraph discussing the contents of the video:

  • How did you feel watching it? Did you like it, or not? Were you confused? Inspired? Bored? Excited? Bewildered? ¬†Why?
  • What is one thing you learned¬†from the video?
  • What is one question you¬†have after watching it?

Part 3. ¬†Write a one-paragraph reflection discussing what the video could mean to your own math teaching. ¬†Is it math? Is it teaching? Is it relevant to the work you will be doing in the classroom?¬†Is there¬†any connection to the earlier¬†reading assignment Lockhart’s Lament? ¬†Any other thoughts?

Extra Credit. ¬†You can earn extra credit by responding to one of your classmates’ posts. ¬†As always, be kind, be respectful, be honest.

OpenLab #7: Proof Journal

Your assignment for the next week is to try to prove the conjecture that your group created in class on Tuesday, 10/22/15.  You must spend at least 90 minutes working on this.  Trying to prove something can consist of many different activities, such as the following (you do NOT have to do all of these things Рyou can choose how to spend your time Рthey are provided for inspiration only).

  • coming up with ideas, and testing them out (for example, by creating puzzles and trying to solve them)
  • trying to understand what the conjecture says
  • trying to solve puzzles that other people created
  • trying to create puzzles (and solve them yourself)
  • communicating¬†with other members of your group (talking, emailing, etc.)
  • trying to write down a proof
  • other stuff…

As you work, keep track of what you are doing, thinking, and feeling (this is metacognition Рan idea that discussed way back in OpenLab #2).  What did you do during the time you spent?  Did you create any puzzles?  Did you solve puzzles?  Did you change your mind about whether the conjecture is true or false?   Did you have any new ideas about how to prove the conjecture?  Did you have any ideas that you gave up on?  How did you feel as you worked Рwere you frustrated/confused/happy/depressed? Why? Did your mood change along the way?

Assignment (Due Thursday, 10/29/15):  Submit a journal of your efforts in the comments below.  Your response should be at least 300 words.  Describe what you did during the 90 minutes you worked, and express in some way what you were thinking and feeling during the process.  Your response can include puzzles or other work you did along the way.