Week 4: Geometric Reasoning, Focus on Symmetry


The topic of this week is geometric reasoning, with focus on symmetry, a key idea at all levels of geometry.

The_Tyger.gif
Print by Hugh MacLeod of gapingvoid.com

The objectives of Week 4 are:
  • To define levels of geometric reasoning within the Van Hiele model
  • To discuss whether levels apply to groups, persons, or particular activities of a person
  • To design activities connecting algebraic and geometric reasoning

The main technology tools this week are GeoGebra, 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 are welcome to invite colleagues and friends to this open room, if they are interested in participating, through this Guest Access link. 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 seven required tasks, two bonus tasks and one make-up task this week.

Musical Interlude

Check out linearity as a key metaphor...


Task Grids

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4-1
Find an article, a video, a blog post or any other media piece on the topic of the Van Hiele Model. Critique the media piece and the model in the context of your teaching. In addition, address the question: do the levels of the model apply to groups of students, individual students, or particular tasks students perform? Can the same person be at different levels at the same time in his or her life? Use your blog with text and/or screencast. Put the link to the media piece you find in Diigo.
4-2
Design a student task or a mini-unit centered on the concept of symmetry. Your goal is to use both geometric and algebraic reasoning within the unit. 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.
4-3
Online, find a secondary level task or a lesson plan that involves symmetry. Write your "math ed connoisseur" critique of the task in your blog, linking the source, or make a screencast.

Bonus_task.jpgIdeas to consider: analyze your find from the points of view of multiple representations, problem posing and solving, Bloom's taxonomy and Van Hiele levels.
GraceA
http://gk1as.wordpress.com/2010/08/04/critique-of-van-hiele-model/
http://gk1as.wordpress.com/2010/08/05/symmetry-lesson
http://gk1as.wordpress.com/2010/08/05/symmetry-critique/
MariaD



KateG
http://ktgee24.wordpress.com/2010/07/30/van-hiele-model-article-critique/
http://ktgee24.wordpress.com/2010/07/29/symmetry-lesson/
http://ktgee24.wordpress.com/2010/07/29/symmetry-lesson-critique/
aheleniak
http://teachy79.wordpress.com/2010/08/03/van-hiele-model/
http://teachy79.wordpress.com/2010/08/04/student-task-on-symmetry/
http://teachy79.wordpress.com/2010/08/04/symmetry-lessonunit/
Peterhorn33
http://wp.me/pZvA3-X
http://wp.me/pZvA3-T
http://wp.me/pZvA3-14
EthanL
http://wp.me/pZtr1-1q
http://wp.me/pZtr1-1M
http://wp.me/pZtr1-1t
Paul McDowell
http://prmarcadia.wordpress.com/week-4/week-4-task-1/
http://prmarcadia.wordpress.com/week-4/week-4-task-2/
http://prmarcadia.wordpress.com/week-4/week-4-task-3/
Sam Morrison
http://semhouston1.wordpress.com/2010/08/03/the-van-hiele-model/
http://semhouston1.wordpress.com/2010/08/05/symmetry-student-task/
http://semhouston1.wordpress.com/2010/08/05/symmetry-in-kaleidoscope-designs/
GRice
http://gailly123.wordpress.com/2010/08/09/van-hiele-model/

http://gailly123.wordpress.com/2010/08/09/symmetry-lesson-critique/
Doug Snyder
van Hiele Levels' Critique
Symmetry in the Real World
Symmetry Lesson Plan Critique
RStock
http://bobbo1.wordpress.com/2010/07/30/the-van-hiele-model/
http://bobbo1.wordpress.com/2010/07/30/symmetry-2/
http://bobbo1.wordpress.com/2010/08/01/symmetry-critique/
Al_J_Williams
http://ajw0812.wordpress.com/2010/08/03/task-4-1-van-hiele-model/
http://ajw0812.wordpress.com/2010/08/03/symmetry-mini-unit/
http://ajw0812.wordpress.com/2010/08/04/symmetry-lesson-plan/
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4-4
Download GeoGebra, a free teaching and learning software. Build a GeoGebra applet you would use with students to make a point, demonstrate a property, show something beautiful, etc. You can focus on any subject you teach, not necessarily geometry. Embed the applet in your blog post explaining how you will use it with students. You can make a screencast if you prefer explaining in voice. Also embed the applet into this wiki, at the Applet Collection page.

You can find some inspiration at:
4-5
revisit.pngRevisit task: Find a partner in the class. Your goal is to help one another build on designs of last week's student tasks. You can work together and discuss "what can you do with it" - add resources, pose interesting problems, make introductions more intriguing, ask students deep questions, and so on. Post improvement suggestions as comments to your partner's blog post from last week, and reply to comments in your own blog post, until you feel a substantial progress is made on both. You can also discuss your designs on the phone or in the Wimba room, and post summaries in blog comments.
GraceA
http://gk1as.wordpress.com/2010/08/27/geogebra/
I will be working with Gail in completing this task.http://gailly123.wordpress.com/2010/08/04/linearity-lesson-solving-a-system-of-equations/
MariaD


KateG

did make-up task 4-8
aheleniak
http://www.screencast.com/t/MDI3YTE1M
http://www.screencast.com/t/NTY3YzU3Y
I did make up task 4-8 in place of this one
Peterhorn33
http://wp.me/pZvA3-11 Applet
http://esivel.wordpress.com/2010/07/28/linearity-research-project/#comments
EthanL
http://wp.me/pZtr1-1P
http://prmarcadia.wordpress.com/week-3/week-3-task-2/#comments
Paul McDowell
http://prmarcadia.wordpress.com/week-4/week-4-task-4/
Ethan, Peter and I are working together as a team.
http://peterhorn33.wordpress.com/2010/08/03/4-3-online-lesson-plan/#comments
Sam Morrison
http://semhouston1.wordpress.com/2010/08/04/geogebra/, still working on the applet thing.
http://ajw0812.wordpress.com/2010/07/27/9th-grade-algebra-1-lesson-plan-on-linearity/#comment-24
GRice
http://gailly123.wordpress.com/2010/08/08/transformations-applet/
I am working with Grace
http://gk1as.wordpress.com/2010/08/05/linearity-lesson-plan/#comment-4
Doug Snyder
Geogebra Screencast and Blog Post
Comment on Bobbo's Blog
RStock
http://bobbo1.wordpress.com/2010/08/02/geogebra/
http://snyderdoug.blogspot.com/2010/08/linearity-in-algebra-lesson-plan.html?showComment=1281196641028#c8718403196965060814
Al_J_Williams
Done.
Posted an assessment upgrade on Sam's blog.
Personal learning network video


4-6
Attend the live class meeting on Wednesday.
Bonus_task.jpgBonus task: attend community study hours on Monday and/or Friday
4-7
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 - many of them are only announced a few days ahead of time.

Math ed events:

General ed events:

Sources of events
4-8 Make-up task (optional)

This will count as a task, to replace any one you miss during the course for grade counting. Join The Educator PLN Ning: http://edupln.ning.com
Look around the site, especially the videos on the front page. Reflect on the idea of PLN and its possibilities for your personal path in your blog.
GraceA
Mon & Wed
http://mathfuture.wikispaces.com/Calculus+by+and+for+Young+People
http://gk1as.wordpress.com/2010/08/05/pln-4-8/
MariaD



KateG
away; attended wk 2 and 3 Friday sessions as extras, will blog in response to Wed. mtg archive upon return
http://ktgee24.wordpress.com/2010/08/19/missed-class-reflection-wed-84/
http://ktgee24.wordpress.com/2010/08/14/classroom-2-0-sat-814/
http://ktgee24.wordpress.com/2010/07/29/pln/
aheleniak
Wed class meeting
Calculus for 7yo Wednesday 9:30pm
http://teachy79.wordpress.com/2010/08/05/calculus-for-7-year-olds-math-2-0/
http://teachy79.wordpress.com/2010/08/03/pln-the-personal-learning-network-for-educators/
Peterhorn33
Wed
http://wp.me/pZvA3-19

EthanL
Wed. class
Overview of Mathematica
http://wp.me/pZtr1-1H
Milton Chen (of edutopia) Interview
http://wp.me/pZtr1-1X
http://wp.me/pZtr1-1m
Paul McDowell
Mon/Wed this week
Calculus for 7yo Wednesday 9:30pm
http://prmarcadia.wordpress.com/week-4/week-4-task-7/
http://prmarcadia.wordpress.com/week-4/week-4-task-8/
Sam Morrison
Wed. class meeting
Calculus for 7yo Wednesday 9:30pm, http://semhouston1.wordpress.com/2010/08/05/don-cohen/
http://semhouston1.wordpress.com/2010/08/03/educator-pln-ning/
GRice
Attended Mon. & Wed.


Doug Snyder
Done
Calculus for 7yo Wednesday 9:30pm
Webinar Review
I missed two live events during Week 3. Here is a review of The ABC's of PLN
RStock
Attended Wed. session
http://bobbo1.wordpress.com/2010/08/05/calculus-for-second-graders/

Al_J_Williams
Done
http://ajw0812.wordpress.com/2010/08/03/edtechtalk-not-so-live-event/
On Saturday at 11:30am, could not register for this site. Would not allow any password i entered.
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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-4.jpg

Voice explanation about tasks:

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