Week+4

=Week 4: Geometric Reasoning, Focus on Symmetry=

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

[|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
media type="custom" key="6570087"

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... media type="youtube" key="6gmP4nk0EOE" height="385" width="480"

Task Grids
. 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.
 * || **4-1**

//Ideas to consider: analyze your find from the points of view of multiple representations, problem posing and solving, Bloom's taxonomy and Van Hiele levels.// || . 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.
 * 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 || [] || [] || [] ||
 * Sam Morrison || [] || [] || [] ||
 * GRice || [] ||  || [] ||
 * 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/ ||
 * || **4-4**

You can find some inspiration at: Revisit 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. || [] || I did make up task 4-8 in place of this one || [] || [] || Personal learning network video media type="youtube" key="mghGV37TeK8" height="385" width="480" Attend the live class meeting on Wednesday. Bonus 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.
 * []
 * http://geogebrawiki.wikispaces.com/
 * [] (some basic tutorials)
 * [] (some basic tutorials in the "locally produced handouts" section)
 * [] (video tutorials) || **4-5**
 * 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 || []
 * 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 || [] || Ethan, Peter and I are working together as a team.
 * Sam Morrison || [], still working on the applet thing. || [] ||
 * GRice || [] || I am working with Grace
 * Doug Snyder || [|Geogebra Screencast] and [|Blog Post] || [|Comment on Bobbo's Blog] ||
 * RStock || http://bobbo1.wordpress.com/2010/08/02/geogebra/ || [] ||
 * Al_J_Williams || Done. || Posted an assessment upgrade on Sam's blog. ||
 * || **4-6**

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:**
 * Calculus for 7yo Wednesday 9:30pm
 * #mathchat Thursday 7:30pm
 * Deep Research Questions with Alan Kay Saturday 2pm
 * [|TappedIn K-20 math resources] Tuesday 7pm
 * [|Overview of Mathematica software] Wednesday 10am or 11pm


 * General ed events:**
 * [|Creative Commons and its Impact] Wednesday 6am
 * [|21st Century Learning EdTechTalk] Tuesday 2pm (the moderator did not show up for this one even though the event was posted at the site)
 * [|#Edchat] Tuesday noon and 7pm
 * [|VoiP and Telephony best practices] Wednesday 12:30
 * [|Edublogs serendipity unconference] Friday 7pm
 * [|TappedIn Teaching Teachers Forum] Thursday 9pm
 * [|How to use TappedIn for PD and learning] Saturday 7pm
 * [|Education Nation] Thursday 8pm


 * Sources of events**
 * http://mathfuture.wikispaces.com/events
 * []
 * []
 * []
 * []
 * #mathchat
 * [|Wolfram Education]
 * [|#edchat] || **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. || http://ktgee24.wordpress.com/2010/08/19/missed-class-reflection-wed-84/ || [] || [] || [] || [] || [] Milton Chen (of edutopia) Interview [] || [] || [] || [] || [|Webinar Review] || I missed two live events during Week 3. Here is a review of [|The ABC's of PLN] || .
 * 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
 * aheleniak || Wed class meeting || Calculus for 7yo Wednesday 9:30pm
 * Peterhorn33 || Wed || [] ||  ||
 * EthanL || Wed. class || Overview of Mathematica
 * Paul McDowell || Mon/Wed this week || Calculus for 7yo Wednesday 9:30pm
 * Sam Morrison || Wed. class meeting || Calculus for 7yo Wednesday 9:30pm, [] || [] ||
 * GRice || Attended Mon. & Wed. ||  ||   ||
 * Doug Snyder || Done || Calculus for 7yo Wednesday 9:30pm
 * RStock || Attended Wed. session || [] ||  ||
 * Al_J_Williams || Done || [] || On Saturday at 11:30am, could not register for this site. Would not allow any password i entered. ||

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: media type="custom" key="6570279" .