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


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.jpg
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




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!



Task Grids

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3-1
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.

Bonus_task.jpgBonus 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.

Bonus_task.jpgIdeas to consider: analyze your find from the points of view of multiple representations, problem posing and solving, and Bloom's taxonomy.
GraceA
http://gk1as.wordpress.com/2010/07/29/pros-and-cons-…looms-taxonomy/
http://gk1as.wordpress.com/2010/08/05/linearity-lesson-plan/
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
http://prmarcadia.wordpress.com/week-3/week-3-task-1/
http://prmarcadia.wordpress.com/week-3/week-3-task-2/
http://prmarcadia.wordpress.com/week-3/week-3-task-3/
Sam Morrison
http://semhouston1.wordpress.com/wp-admin/post.php?post=30&action=edit
http://semhouston1.wordpress.com/2010/07/31/student-task-focused-on-linearity/
http://semhouston1.wordpress.com/2010/07/31/sample-lesson-plan-solving-system-of-linear-equations/
GRice
http://gailly123.wordpress.com/2010/08/03/blooms-taxonomy/
http://gailly123.wordpress.com/2010/08/04/linearity-lesson-solving-a-system-of-equations/
http://gailly123.wordpress.com/2010/08/02/lesson-plan-review-slope/
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/
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3-4
Join one of the following groups and find a discussion you find highly relevant. Respond to it.


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.pngRevisit 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://mathforum.org/kb/thread.jspa?threadID=2093820&tstart=0
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://mathforum.org/kb/message.jspa?messageID=7138345&tstart=0
http://wp.me/pZtr1-18
Done
Paul McDowell
http://mathforum.org/kb/message.jspa?messageID=7097142&tstart=15

Teacher Accountability & Social Promotion
http://www.screencast.com/users/prm_arcadia/folders/Jing/media/bb48411c-bc04-475b-91f3-038cb0abe0e8
http://prmarcadia.wordpress.com/
Sam Morrison
Waiting for approval
http://semhouston1.wordpress.com/2010/07/31/wowlfram-alpha/
Done
GRice

http://gailly123.wordpress.com/2010/08/02/solving-equations-using-wolfram-alpha/
Done
Doug Snyder
ActivInspire Question
Doug's Wolfram Alpha Webcast
Doug's Blog
RStock
http://mathforum.org/kb/thread.jspa?threadID=2096119&tstart=45
http://bobbo1.wordpress.com/2010/07/27/wolfram-alpha-task/
http://bobbo1.wordpress.com/
Al_J_Williams
http://community.tes.co.uk/forums/p/426683/5796254.aspx#5796254
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/

Musical Interlude




3-8
Attend the live class meeting on Wednesday.
Bonus_task.jpgBonus 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.

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:

General ed events:

Sources of events
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): http://www.ncssm.edu/courses/math/Talks/PDFS/icme_8.pdf

In your review, consider several "pro" and "con" arguments in regard to this approach.
GraceA
Wed and Fri
Project Euclid scholarly libraryWednesday, July 28, 9:30pm
Collaborative online project training for teachers Wednesday, July 28, 7pm
Instructional design liveFriday, July 30, noon

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-9/
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.
Attended on Wed.
http://gailly123.wordpress.com/2010/08/02/response-to-live-event-72910-fractions/

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/

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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-3.jpg
Voice explanation about tasks: