**Collaborative Mathematics Spaces for Secondary School, College, and University**

For the past 8 years I have been experimenting with online mathematical collaboration with the Math-Towers website for students in Grades 6 to 10. More recently I have been exploring the possibilities of combining GeoGebra with a wiki tool to provide mathematics collaboration spaces for students in secondary school and university.

GeoGebra is an open-source Java-based dynamic mathematics tool. It links numeric, algebraic, and geometric representations and provides basic computer algebra (CAS) functions. Since it is written in Java the integration with other web-based tools such as wikis is relatively easy. Using skills that many students already possess, small groups could work together in an asynchronous manner; building on each other’s ideas by picking up a GeoGebra problem solution effort where another student had left it, doing some more work, and then posting their ideas on a new wiki page.

These ideas are more fully developed in the paper *GeoGebra as a Component of Online Collaborative Mathematics Investigations: Present Work Toward Realizing a Dream* given at the First North American GeoGebra Conference, July 27-28, 2010, Ithaca College, New York.

The link below takes you to a series of pages that model a possible collaboration on a high school problem.

An example of simple online collaboration on a high school modelling problem.

I am presently exploring the possibility of doing something similar by combining GeoGebra and MediaWiki. Since both MediaWiki and GeoGebra are open-source, adjustments in operation are possible and we may be able to automate some of the saving and uploading steps that students would presently need to do with PBworks wiki.

**Adding Video for Communication and Sharing:**

Increasingly sharing across the web is taking place via video. At the end of 2010 Canadian high school and college/university age Internet users were on average spending close to 20 h per month while viewing in excess of 200 online videos (comScore, 2011). Thus students might find it more “natural” to present their thinking and GeoGebra manipulations in video format rather than text on a wiki page. Jing (TechSmith, 2010) and the related website, www.screencast.com makes this easy to accomplish and at no cost.

A model of simple online collaboration with video. This is the collaboration linked to above, but with the teacher and students making explaining their GeoGebra action via video rather than text.

**Blended Mathematical Collaboration using a Wiki, GeoGebra and Jing:**

During the first semester of the 2011-12 school year Jill Lazarus and I collaborated on a project to use a PBworks wiki, GeoGebra, and Jing to support mathematics communication, sharing and collaborative problem solving with her Ontario, Grade 10, Academic Mathematics class. On January 21, 2012 we used the poster below to outline and present the results of our project (click on the image to get the full PDF version).

To view a recording discussing the project outlined in the poster above go to the **Supporting Collaborative Mathematics Explorations using a Wiki, GeoGebra, and Jing **page in the wiki of the **Math 2.0 Interest Group**.

For detailed instructions concerning the tools and procedures required for the collaboration described above see the instructions within the Math 2.0 wiki on the **Collaborative Online Investigation** page .

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