Week+3

=Week 3: Algebraic Reasoning and Calculus Thinking, Focus on Linearity=

toc The focus of this week is linearity, the idea central to algebra and playing a key role in calculus. We will use linearity as an example of a linchpin concept in curricula.

Escher used non-linear transformations in many of his works.


 * The objectives** of Week 3 are:
 * First introduction to Bloom's taxonomy: to define the six levels of thinking
 * To apply knowledge of multiple representations and problem solving to algebra and calculus
 * To define the idea of linearity, to use it in algebra or calculus task design, and to critique lessons about linearity

The main technology tools this week are Wolfram|Alpha, forums, Diigo, screencasts, blogs, email groups, live webinars, online videos and wikis.

Audio Introduction
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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 Wimba virtual room]. You can also use the room for class collaboration outside of these hours.


 * Monday 7-8pm** community study and Q&A hour
 * Wednesday 8-9pm** weekly class discussion
 * Friday 8-9am** community study and Q&A hour

There are eight required tasks, two bonus tasks and a make-up task this week.

Visual Interlude
If you get dizzy during transitions, relax or close your eyes before clicking the "Next" button. Prezi is a free tool for making non-linear presentations. There is no sound in this presentation - play your own music!

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Task Grids
. Find one source supporting the use of Bloom's Taxonomy in education and one source against it. What is your opinion about its usefulness for algebra and calculus tasks? Link your sources and briefly describe what they say in your blog or in a screencast, and give the address here. Add sources to your Diigo bookmarks.
 * || **3-1**

//Bonus idea: in addition to sources you used before, consider iTunes U free lectures. [|Here is the search that finds a few about Bloom's Taxonomy]. You need to have iTunes installed to use it.// || **3-2** Design a student task or a mini-unit centered on understanding of linearity, either for algebra or calculus. You don't have to write up a detailed lesson plan; write just enough for another teacher to be able to build on your general idea. Make sure you include a description of an appropriate assessment. Keep in mind the overall vision provided by the five most important math ed principles you named in Week 1, and align your task with some of the principles you consider important. || **3-3** Online, find a task or a lesson plan that involves linearity. Write your "math ed connoisseur" critique of the task in your blog, linking the source, or make a screencast about it.

//Ideas to consider: analyze your find from the points of view of multiple representations, problem posing and solving, and Bloom's taxonomy.// || . Join one of the following groups and find a discussion you find highly relevant. Respond to it.
 * GraceA || http://gk1as.wordpress.com/2010/07/29/pros-and-cons-…looms-taxonomy/ || [] || http://gk1as.wordpress.com/2010/07/31/math-ed-connoisseur/ ||
 * MariaD ||  ||   ||   ||
 * KateG || http://ktgee24.wordpress.com/2010/07/27/blooms-taxonomy/ || http://ktgee24.wordpress.com/2010/07/29/55/ || http://ktgee24.wordpress.com/2010/07/27/graphing-linear-equations-lesson-plan/ ||
 * aheleniak || http://teachy79.wordpress.com/2010/07/30/blooms-taxonomy/ || http://teachy79.wordpress.com/2010/07/31/student-task-on-linearity/ || http://teachy79.wordpress.com/2010/07/30/linear-algebra-problems/ ||
 * Peterhorn33 || http://wp.me/pZvA3-I || http://wp.me/pZvA3-z || http://wp.me/pZvA3-E ||
 * EthanL || http://esivel.wordpress.com/2010/07/27/research-on-blooms-taxonomy/ || http://wp.me/pZtr1-Q || http://wp.me/pZtr1-L ||  ||
 * Paul McDowell || [] || [] || [] ||
 * Sam Morrison || http://semhouston1.wordpress.com/wp-admin/post.php?post=30&action=edit || [] || [] ||
 * GRice || [] || [] || [] ||
 * Doug Snyder || [|Doug's Blog on Bloom's] || [|Linearity - Substitution Method in Algebra] || [|Linear Systems Lesson Plan Critique] ||
 * RStock || http://bobbo1.wordpress.com/2010/07/26/pros-and-cons-of-blooms/ || http://bobbo1.wordpress.com/2010/07/26/linearity/ || http://bobbo1.wordpress.com/2010/07/26/more-on-linearity/ ||
 * Al_J_Williams || http://ajw0812.wordpress.com/2010/07/26/blooms-taxonomy-the-good-and-the-bad/ || http://ajw0812.wordpress.com/2010/07/27/9th-grade-algebra-1-lesson-plan-on-linearity/ || http://ajw0812.wordpress.com/2010/07/27/critiquing-a-linearity-lesson-plan/ ||
 * || **3-4**


 * [|http://mathforum.org/kb/forum.jspa?forumID=63 (moderated, approval required)]
 * [|http://mathforum.org/kb/forum.jspa?forumID=206 (moderated, registration required)]
 * [|http://community.tes.co.uk/forums/25.aspx (registration required)]

If you participate in a more recent discussion, people are more likely to reply to you. || **3-5** Use Wolfram|Alpha to solve a system of linear equations. How does access to this tool change learning tasks? Reflect on your blog, providing a link to your solved system (which you can copy from the url line in your browser after using W|A to solve it), or make a screencast. || **3-6** Revisit task: make a blogroll for your blog. Consider including other class blogs, which you can find in Week 1, Task 1-4. Add any ed blogs you would like to read regularly, or recommend to readers of your blog.

[|WordPress how-to] [|Google Blogspot how-to]

Follow links to class blogs from your new blogroll, check out what people write, and leave them constructive comments (three or more this week, for starters).

While we all like to get comments saying, "Good point!" or "Thank you for your link!" - after a while such content-free comments become tiresome. It is considered good blogging etiquette to have some content in every comment, in addition to praise or blame, if any. ||
 * GraceA || [] || http://gk1as.wordpress.com/2010/07/31/wolframalpha-solver/ || Done ||
 * MariaD ||  ||   ||   ||
 * KateG || http://ktgee24.wordpress.com/2010/07/27/math-forum/ || http://ktgee24.wordpress.com/2010/07/28/wolframalpha/ || http://ktgee24.wordpress.com/ ||
 * aheleniak || http://mathforum.org/kb/thread.jspa?messageID=7140211&#7140211 || http://teachy79.wordpress.com/2010/08/01/wolfram-alpha/ || http://teachy79.wordpress.com/ ||
 * Peterhorn33 || http://peterhorn33.wordpress.com/2010/07/29/assignment-3-4/ || http://peterhorn33.wordpress.com/2010/07/29/3-5-wolfram-alpha-post/ || http://peterhorn33.wordpress.com/ ||
 * EthanL || [] || http://wp.me/pZtr1-18 || Done ||
 * Paul McDowell || []

Teacher Accountability & Social Promotion || [] || [] || I'm #27. Tried to bring multiple representations into the forum! || http://ajw0812.wordpress.com/2010/07/27/wolframalpha-solving-system-of-equations/ || http://ajw0812.wordpress.com/ ||
 * Sam Morrison || Waiting for approval || [] || Done ||
 * GRice ||  || [] || Done ||
 * Doug Snyder || [|ActivInspire Question] || [|Doug's Wolfram Alpha Webcast] || [|Doug's Blog] ||
 * RStock || [] || http://bobbo1.wordpress.com/2010/07/27/wolfram-alpha-task/ || [] ||
 * Al_J_Williams || http://community.tes.co.uk/forums/p/426683/5796254.aspx#5796254

Musical Interlude
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Attend the live class meeting on Wednesday. //Bonus task: attend community study hours on Monday and/or Friday// || **3-9** 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.
 * || **3-8**

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 25th - many of them are only announced a few days ahead of time.

[|40-second guide to Twitter chats]


 * Math ed events:**
 * [|Supporting statistical thinking through a capstone project.] Tuesday, July 27, 2:30pm Registration on the page required.
 * #mathchat New topic Thursday, July 29th 7:30pm and What tools and methods can we use to make math real? Monday, July 26, 3:30pm


 * General ed events:**
 * Project Euclid scholarly library. Wednesday, July 28, 9:30pm
 * [|Flat Classrooms and Global Collaboration] Tuesday, July 27, 6am (morning! - organizers are in Melbourne)
 * [|It takes a village.] Thursday, July 29th, 7:30pm
 * [|Educational networking alternatives (beyond Ning)] Monday, July 26, 8pm
 * [|Web 2.0 tools]. Tuesday, July 27, 1:45AM
 * [|Collaborative online project training for teachers Wednesday], July 28, 7pm
 * [|YouTube in the Classroom] Thursday July 29th 7pm
 * [|Instructional design live] Friday, July 30, noon
 * [|What's new in Diigo], for teachers Saturday, July 31, noon
 * [|K-3 Resources from ISTE] Tuesday, July 27, 8pm
 * [|**http://reformsymposium.com/**] **Friday-Sunday, multiple events**


 * Sources of events**
 * http://mathfuture.wikispaces.com/events
 * []
 * []
 * []
 * []
 * #mathchat || **3-7 Make-up task (optional)**

This will count as a task, to replace any one you miss during the course for grade counting.

If the task you missed still makes sense to do (i.e. editing our Wikipedia article, which can be done indefinitely), you can go back to the task and do it.

If the task expired (such as a live event), you can do the following: Review "A Local Linearity Approach to Calculus" by Dan Teague (who you may have met at the MathForum, by now): []

In your review, consider several "pro" and "con" arguments in regard to this approach. || [|Collaborative online project training for teachers]Wednesday, July 28, 7pm [|Instructional design live]Friday, July 30, noon ||  || Attended on Wed. || []/ ||  || .
 * GraceA || Wed and Fri || Project Euclid scholarly libraryWednesday, July 28, 9:30pm
 * MariaD ||  ||   ||   ||
 * KateG || Wed. and Fri. || http://ktgee24.wordpress.com/2010/08/19/expert-ways-of-seeing/ || http://ktgee24.wordpress.com/2010/07/29/a-local-linearity-approach-to-calculus-by-dan-teague/ ||
 * aheleniak || Wed class meeting || http://teachy79.wordpress.com/2010/07/31/archive-of-mathchat-fractions/ ||  ||
 * Peterhorn33 || Wed. || http://wp.me/pZvA3-L ||   ||
 * EthanL || Wed. || http://wp.me/pZtr1-O || http://wp.me/pZtr1-1h ||
 * Paul McDowell || Schedule conflict || [] || http://prmarcadia.wordpress.com/week-3/week-3-task-7/ ||
 * Sam Morrison || Attended Wed. || @http://semhouston1.wordpress.com/2010/08/01/nick-provenzanos-everything-i-learned-about-tech-integration-i-learned-from-movies/ ||  ||
 * GRice || Waited for others Mon.
 * Doug Snyder ||  ||   || [|Calculators: What are they Good For??] ||
 * RStock || Attended Wed. || http://bobbo1.wordpress.com/2010/07/29/euclid-project/ ||  ||
 * Al_J_Williams || Attended Wed. || http://ajw0812.wordpress.com/2010/07/27/what-jess-does-with-web-2-0-tools/ ||  ||

Task Dependency Map
This map is made with [|Bubbl.us] It shows dependencies of tasks from the above grids. LIVE tasks have particular times.

Voice explanation about tasks:

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