Week 2: Posing and Solving Problems


The topic of this week is: Problems. In particular, we will discuss the difference between problems and other entities - exercises, explorations, definitions, conjectures and so on.

The objectives of Week 2 are to define main entities constituting mathematics, to plan for student problem-posing, to understand the differences between problems and other entities, to list criteria of problem solving, evaluate given material's potential to promote problem solving, and to find problem-solving resources by topic.
The main technology tools this week are Diigo, screencasts, forums, blogs, email groups, live webinars, online videos and wikis.

Audio Introduction




The class live meetings happen three times a week, one of them required, the other two recommended for doing weekly tasks together. During these times, we will meet in
the virtual room (Wimba)
. You are welcome to invite colleagues and friends to this open room, if they are interested in participating. You can also use the room for class collaboration outside of these hours.

Monday July 19th 7-8pm community study and Q&A hour
Wednesday July 21st 8-9pm weekly class discussion
Friday July 23rd 8-9am community study and Q&A hour

There are ten required tasks, one of them revisiting last week's content, and two bonus tasks.

Musical Interlude



Task Grids


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2-1
Install Jing. Use it to record a short opinion piece on Dan Meyer's video on "being less helpful" with math problems, which you can find on TED site. Link your screencast in this grid.

You may need to create an account on http://screencast.com/ first.

"Jing - the missing manual" how-to.

If you have another screencasting tool you like, you can use that. The goal is to make screencasts.
2-4
Reply to any thread tagged WCYDWT on Dan Meyer's (whom you met in task 2.1) blog or a WCYDWT discussion anywhere else. You can reply to the post itself, or to any of the comments.

The blog is a meeting place of many math teachers - a good place for us to be! Link to the thread where you reply and let us know the comment's number. When replying to a comment, start with @commentername
Bonus_task.jpgBonus task: reply to a comment by one of class members.
2-5
On your blog, write a review of an article or a book chapter on mathematical problem solving you read this week. You can select articles using Google Scholar. Some articles will be online and others on paper. The goal of the review is for other teachers to get the gist of the article for use in their work, as well as your evaluation of the contents. Consider Polya's "How to Solve it" as a possibility.
GraceA
http://www.screencast.com/t/MmU2YWM5OTkt
http://blog.mrmeyer.com/?p=6850&cpage=2#comment-262923
comment #74
http://gk1as.wordpress.com/2010/07/22/arts-connected…erdisciplinary/
MariaD
done
http://blog.mrmeyer.com/?p=6850 comment #17

KateG
http://screencast.com/t/MjhkMmI4OTE
http://blog.mrmeyer.com/?p=6870&cpage=1#comment-262930 comment #24
http://ktgee24.wordpress.com/2010/07/24/mathematical-problem-solving/
aheleniak
http://www.screencast.com/t/MjhiOWJjZWUt
http://blog.mrmeyer.com/?p=6850&cpage=2#comment-262858 comment #65
http://teachy79.wordpress.com/2010/07/22/mathematical-problem-solving-article-review/
Peterhorn33
http://screencast.com/t/Y2I5NTliZj
http://blog.mrmeyer.com/?p=6339#comment-263034

EthanL
www.screencast.com
/t/N2QyZTY0YTIt
http://blog.mrmeyer.com/?p=6850&cpage=2#comment-262674 comments #58,60
http://esivel.wordpress.com/2010/07/19/a-review-of-how-to-solve-it-by-g-polya/
Paul McDowell
http://www.screencast.com/t/NTkzMzBkNjQt
http://blog.mrmeyer.com/?p=7436&cpage=1#comment-262925
http://prmarcadia.wordpress.com/week-2/week-2-task-5/
Sam Morrison
http://screencast.com/users/semhouston1/folders/Default/media/4d20205a-489b-4124-b597-fd9327214f73
https://my.arcadia.edu/webapps/portal/frameset.jsp?tab_id=_2_1&url=%2fwebapps%2fblackboard%2fexecute%2flauncher%3ftype%3dCourse%26id%3d_47961_1%26url%3d

GRice
http://www.screencast.com/t/YzkzMWQ2NmM
Gail's Comment Comment #30

Doug Snyder
Doug's Screencast
Doug's Comment Comment #33
Doug's Reply Comment #62
Problem Solving Article Review
RStock
http://screencast.com/t/MDEwM2I2Mz
http://blog.mrmeyer.com/?p=6850&cpage=2#comment-262798 comment #61
http://bobbo1.wordpress.com/2010/07/20/problem-solving/
Al_J_Williams
http://www.screencast-o-matic.com/watch/c6iY2pjhp
Original post: http://webmaths.wordpress.com/2010/05/27/wcydwt-bento-box/
My comment posted at my personal blog.
Done
http://ajw0812.wordpress.com/2010/07/20/problem-solving-article-task-2-5/
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2-2
Pick a secondary math topic you like. Make a blog posts with examples of the following content about the topic - the mathematical entities that can be created for it:
  • A definition
  • A conjecture with a proof
  • A piece of software. Include a link or a name, and a screenshot. You can use Jing to make the screenshot. Online math software libraries can be found at:
  • A related art or music piece - use your judgment on what is related to your topic
  • A project or an exploration
  • An exercise
  • A problem
You can find examples online (give links and briefly describe them and quote) or make up your own.
2-3
Reply to the email thread, which MariaD has posted to the email group, about the differences between exercises and problems. You can reply to anyone participating, and post as many comments as you feel needed to carry on the discussion.

Link to the thread: http://groups.google.com/group/ed526b/browse_thread/thread/416b1c121ccaab8
GraceA
http://gk1as.wordpress.com/2010/08/17/quadratic-equations/
done
MariaD


KateG
http://ktgee24.wordpress.com/2010/07/25/explore-a-secondary-math-topic-congruent-angles/
done
aheleniak
http://teachy79.wordpress.com/2010/07/26/secondary-math-problem-fractions/
done
Peterhorn33
http://peterhorn33.wordpress.com/2010/07/25/2-2-slope-intercept-form/
done
EthanL
http://esivel.wordpress.com/2010/07/17/graphs-and-symmetric-functions/
Done
Paul McDowell
http://prmarcadia.wordpress.com/week-2/week-2-task-2/
done - sent via email, having problems getting on mail group
Sam Morrison
http://semhouston1.wordpress.com/wp-admin/post.php?post=20&action=edit
Done
GRice
http://gailly123.wordpress.com/2010/07/26/secondary-math-isosceles-triangles/
Done
Doug Snyder
Linear Systems Explored
Done
RStock
http://bobbo1.wordpress.com/2010/07/19/exploring-the-…gorean-theorem/
Done
Al_J_Williams
http://ajw0812.wordpress.com/2010/07/21/task-2-2-exploring-high-school-math-topic/
Done
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post #3

2-6
The Art of Problem Solving high school forum is helping people solve problems. Look at a few threads and consider how people are using the forum in their problem-posing and problem-solving. Briefly describe your findings, with links to forum threads as examples, on your blog and provide the link to the post here.

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Bonus_task.jpgBonus task: Find someone asking for problem-solving help and help them by leaving a comment; or pose a problem; or offer another representation (graph, table, interactive) for an already-solved problem. You will need to register. Link the thread and what name or alias you used in it.
2-7
Join the group Math Links on Diigo.com http://groups.diigo.com/group/math-links The blue "Join this group" button is on the right. If you do not have a Diigo account, you will be prompted to register (or join using Open ID).
Add five links you found useful in this class, so far, to your bookmarks. You may want to watch the introductory video on the front page of the site. Use the tag ED526b for your links, and other tags you find appropriate.
Add the link to your profile on Diigo to this task grid
2-10
revisit.pngRevisit task: Improve the Wikipedia article on Multiple Representations, made from the content you created last week: http://en.wikipedia.org/wiki/Multiple_representations_%28mathematics_education%29

You can edit for grammar and style, turn words into links to Wikipedia articles, add references to more outside sources, add pictures and otherwise make the article better. Register at Wikipedia and log in before editing to track your contributions.
You may want to read the Wikipedia page on editing pages.

I track sources of ideas back to your blogs and comments in the article draft. You can use it to find "your" parts of the article to start editing. Multiple Representations.

Write a blog post about your Wikipedia experience. You can later edit the post, including updates, if you return to the article to edit it more.
GraceA
http://gk1as.wordpress.com/2010/07/24/percentages/
http://www.diigo.com/profile/gass22
http://gk1as.wordpress.com/2010/07/24/wikipedia-multiple-representation/
MariaD

http://www.diigo.com/profile/mariadroujkova

KateG
http://ktgee24.wordpress.com/2010/07/23/the-art-of-problem-solving/
http://www.diigo.com/profile/kate_gillin
http://ktgee24.wordpress.com/2010/07/24/editing-wikipedia/
aheleniak
http://teachy79.wordpress.com/2010/07/24/the-art-of-problem-solving/
http://www.diigo.com/user/teachy79
http://teachy79.wordpress.com/2010/07/25/wikipedia-experience/
Peterhorn33
http://peterhorn33.wordpress.com/2010/07/25/assignment-2-6-the-art-of-problem-solving/
http://www.diigo.com/profile/peterhorn33
http://peterhorn33.wordpress.com/2010/07/26/2-10-making-the-wiki-a-better-place/
EthanL
Post #3http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=357730http://esivel.wordpress.com/2010/07/21/a-first-impression-of-the-art-of-problem-solving-website/
http://www.diigo.com/profile/esivel
http://esivel.wordpress.com/2010/07/23/editing-wikipedia/
Paul McDowell
http://www.artofproblemsolving.com/Forum/viewtopic.php?f=149&t=358255&p=1958533#p1958533
http://www.diigo.com/user/prm_arcadia

Sam Morrison
http://semhouston1.wordpress.com/wp-admin/post.php?post=23&action=edit&message=6


GRice
http://gailly123.wordpress.com/wp-admin/post.php?post=49&action=edit&message=6
http://www.diigo.com/user/gailly123

Doug Snyder
Area of a Circle
http://www.diigo.com/profile/doug_snyder
http://snyderdoug.blogspot.com/2010/07/wiki-world.html
RStock
Blog Post;
http://bobbo1.wordpress.com/2010/07/22/the-art-of-problem-solving/
Art of Problem Solving link;http://www.artofproblemsolving.com/Forum/viewtopic.php?f=300&t=357511
http://www.diigo.com/profile/rpstock

Al_J_Williams
Have not yet found one that I can answer or one that hasn't already been answered.
http://www.diigo.com/profile/ajw0812
http://ajw0812.wordpress.com/




2-8
Attend the live class meeting on Wednesday.
Bonus_task.jpgBonus task: attend community study hours on Monday and/or Friday
2-9
Attend one or more of the following live events happening online this week. Follow links for instructions on how to use platforms.
You can add other events to this list. They must be free, open to everybody, and recorded.

Say what alias you used to participate, if it's not your name. Contribute something during the meeting - a question, comments in chat, references.

Briefly reflect on the event in your blog. Constructive criticism is especially helpful for event organizers. The blog post needs to link to the event's page.

MariaD will add events on Sunday, July 18th - many of them are only announced a few days ahead of time.

Math ed events:

General ed events:

Sources of events
GraceA
attend monday, wednesday and friday class meetings
Math 2.0 weekly webinar: Egyptian Math in-depth Wednesday July 21st 9:30pm * ArtConnected interdisciplinary tool Tapped In chat Wednesday July 21st 7pm
MariaD


KateG
Wed and Fri class meetings
did make-up task 3-7
aheleniak
Wed class meeting
"It takes a village" - learning cultures and spaces 7:30pm Thursday July 22nd (the time on the site is Melbourne) Response - http://teachy79.wordpress.com/2010/07/23/it-takes-a-village-learning-cultures-and-spaces/
Peterhorn33
Wed class and fri office hours
Twiducate webinar -http://peterhorn33.wordpress.com/2010/07/26/2-9-reflection-on-twiducate-webinar/
EthanL
Wed. class
Math 2.0 weekly webinar: Egyptian Math Wednesday July 21st 9:30pm
http://esivel.wordpress.com/2010/07/22/presentation-on-ancient-egyptian-math/
Paul McDowell
attended wed night wimba class
attend prior event: https://sas.elluminate.com/site/external/jwsdetect/playback.jnlp?psid=2010-06-05.1044.M.B41FC4AB0A3565F8BCAE1B600D6595.vcr&sid=2008350
Sam Morrison


GRice
Attended Monday and Wednesday sessions
http://gailly123.wordpress.com/2010/07/25/what-tools-do-we-use-to-make-maths-real/
Doug Snyder
Attended Wed class Meeting
Attempted to attend several events unsuccessfully. Read through mathchat Twitter transcript and then commented on Al Williams' blog: http://ajw0812.wordpress.com/2010/07/20/week-2-task-9-tweeter-event/
RStock
attended Monday & Wednesday sessions.
Attempted to attend several events but settled for reviewing the transcript of a mathchat Twitter event;http://bobbo1.wordpress.com/2010/07/23/to-tweet-or-not-to-tweet/
Al_J_Williams
done.
"Attended" Tuesday twitter event with comments at my blog.
http://ajw0812.wordpress.com/2010/07/20/week-2-task-9-tweeter-event/
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Task Dependency Map


This map is made with Bubbl.us It shows dependencies of tasks from the above grids.
LIVE tasks have particular times.

Task-dependency-map-Week-2.jpg
Voice explanation about tasks: