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

For the past 12 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 other online tools to provide mathematics collaboration spaces for students in secondary school and university.

GeoGebra is an open-source dynamic mathematics tool existing in two versions; Java and HTML5. It links numeric, algebraic, and geometric representations and provides basic computer algebra (CAS) functions. Since it is written in Java and HTML5 the integration with other web-based tools such as wikis is relatively easy. Using skills that many students already possess, small groups can work together in an asynchronous manner; building on each others' 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 above, but with the teacher and students 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**.

A journal article by Jill Lazarus and Geoff Roulet describing the project appeared in the June 2013 issue of the *Ontario Mathematics Gazette*. This article can be accessed by clicking on the link below.

**Lazarus, J., & Roulet, G. (2013). Communication in a blended math-talk community: Extending the boundaries of classroom collaboration. ***Ontario Mathematics Gazette*, *51*(4), 34-40.

**Using Padlet as a Platform for Collaboration**

Although the mathematics collaboration in which our pupils have engaged is not "social" in the sense of "social media" there are aspects of the interaction that reflect students' regular personal online experience. We have found that the images and expectations of online interaction that our students have developed within their social media universe carry over into their online mathematics activity. We do not believe that it is appropriate or even possible to have online academic interactions completely mirror social media. On the other hand, we do wish to increase student engagement in online mathematical collaboration and ease the development of the required digital skills. Thus there is value in having interactions parallel those found within social media.

We have found that students have come to expect that a single click of an icon will initiate online operations such as: posting text, images, or videos, or uploading and linking files. Thus there is a need to automate some of the operations involved in the mathematics collaboration described above and in the linked resources. In particular, the tasks of creating, editing, and linking new wiki pages appear to be distractions. To address this we have been experimenting with using Padlet walls as places for collaboration. A full mathematics course still requires the structure provided by a wiki or LMS, but for individual collaborative problem solving activities the class or small groups could be sent off to Padlet walls linked to the larger course home site. An example of this; paralleling the examples of collaboration linked above, can be observed by following the link to the **Modelling Light** Padlet wall.

**How****: The Technical Details:**

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 for work within a **Wikispaces** wiki or click here for **instructions** for work within a PBworks wiki.

**Try It: Contribute to an Online Exploration:**

Using the tools described in the How: Technical Details pages of this wiki you could set up an environment in either a PBworks or Wikispaces wiki and post and initial page introducing a new sollaborative investigation or problem solving activity. If you wish to join an collaboration already in progress two are available:

and

In both cases you will need to establish an account with the wiki service, PBworks or Wikispaces, and then request to join the wiki to be permitted to edit pages.

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