## Collaboration On The Web – Quick Links

More notes will be up here on friday, but for now, here is easy access to the necessary links.

**Presentation (Prezi) Here**

- https://prezi.com/secure/5bd521c065b84d81a8195ced4b703c52782ac592/
- video: http://www.youtube.com/watch?v=NugRZGDbPFU&safety_mode=true&persist_safety_mode=1

**Participate On These Links**

Online MindMapping

- http://www.mindmeister.com/78582444/when-and-why-do-our-students-need-to-collaborate
- http://www.mindmeister.com/
- http://www.mapul.com/
- http://www.creaza.com/

Virtual Stickies

- http://www.wallwisher.com/wall/2011jan27
- http://www.edistorm.com/
- http://www.linoit.com/
- http://www.listhings.com/

Virtual WhiteBoarding

- http://www.twiddla.com/477005
- http://www.creately.com/
- http://www.dablleboard.com/
- http://www.imaginationcubed.com/

Collaborative Documents:

- https://docs.google.com/document/d/1aNVBEg5bIJML7GSNCkFiOQmWMCkRTPXRHdSmrBAvmNI/edit?hl=en&authkey=CIfe47IB
- http://www.live.com/
- http://ietherpad.com/
- http://www.mixedink.com/

## Join an ASCD Group: Technology for Teaching and Learning

The ASCD is a top-notch educators organization that provides books, resources and various PD opportunities to teachers. The ASCD Annual Conference is an amazing experience and should be on a list for any educator to attend.

One are that the ASCD lacks in is support for technology in education. I hope to change this by forming an ASCD Professional Interest Community (PIC) titled: Technology for Teaching and Learning. Please join me in the formation of this ASCD community by signing up here! Both ASCD members and non members can join, the only requirement is that there are a minimum of 15 ASCD members.

## Virtual Learning Coming … Now!

On January 5 2011, Microsoft brought virtual reality to the masses by announcing Avatar Kinect. Avatar Kinect will allow users to engage in virtual environments, through an avatar that will depict real facial expressions and movements. Users will be able to enter virtual environments as their avatar, and engage in conversations and various other activities – even learning activities. This could push virtual reality to the critical mass that would make virtual learning environments feasible for millions of people.

Avatar Kinect will be able to run on the over 50 million XBox 360’s that already sit in living rooms – and these numbers are growing fast. It is possible that the software will eventually become available to all Windows users which is about 1 billion people. In the not too distant future this may be a regular way you connect with your students and colleagues – at which point I can finally stop having to worry about aligning my interactive white board!

## Things You Can Do Today To Enhance Student Learning

With all of the talk about education reform and standardized assessments I’m sure some teachers are feeling a bit overwhelmed or powerless. To re-empower teachers (including myself), I started a list of things that classroom teachers can easily start doing tomorrow in the classroom. I’m just starting the list, please help it grow by sharing your own ideas in the comments section.

- Get rid of rows of desks, get kids sitting in groups. Learning doesn’t happen in isolation.
- Have a class discussion. I don’t mean talk to your kids about something, I mean get all the students talking! (shameless self-plug, but it makes my point)
- Take a break from grades, and give students descriptive and useful feedback.
*Read more about this on**Joe Bowers blog* - Engage students with Post-it notes – students can write comments and questions on them while reading/learning/listening and stick them in their books. Very simple, very effective.
- Let student questions drive the learning – a simple example of how this might look is given by John Scammel on his blog
- Student lead reviews – at the beginning of class, get students to review what they learned last class, and use this as the starting point for the new learning.
- If it’s in their textbook, don’t make them write it. I used to do this too; give notes that students don’t really need. If you really want them to have summary notes of the textbook, teach them to take their own – that is much more powerful learning.
*Read about the Cornell note taking system for an idea of what I mean.*

This is by no means a comprehensive list, so I encourage you to share your ideas by commenting below. Good luck tomorrow

## The Role of 21C Skills in Learning Mathematics

*This post is the written form of a presentation I gave in a class that I am taking. The purpose was to show how I’ve been dealing with the tensions between 21st century skills and the work I’ve been doing in some math classrooms. The prezi (which lacks detail but shows a good over-view) is **available here.*

Twenty first century skills have been a topic of discussion in Alberta since 1987 when Alberta Education published *Essential Concepts, Skills and Attitudes for Grade 12*. Since then various organizations have used the term ‘21st century skills’ to refer to a set of overarching skill sets and competencies to be developed throughout a child’s schooling (ISTE, 2007; Partnership for 21st Century Skills, n.d.; Alberta Education, 2010).

There seems to be consensus among the educational organizations regarding what 21st century skills are, each noting the following skills: critical thinking, problem solving, communication, collaboration, information fluency, citizenship and technology literacy. As a 21st Century Literacy consultant my job is to foster 21st century skill development of students in my work with teachers and in classrooms. It has been particularly difficult to do this in mathematics classrooms which has led me to wonder: do 21st century skills have any place in the mathematics classroom? I analyzed the Alberta Mathematics Program of Studies 10 – 12, as well as research in the field of mathematics education, looking for a relevance of 21st century skill development in the schooling of mathematics.

There seems to be a clear connection between 21st century skill sets and the tenants of the Mathematics Program of Studies in Alberta. The philosophy of the program states “Meaningful student discussions also provide essential links among concrete, pictorial, and symbolic representations of mathematics” and “The learning environment should value, respect and address all students’ experiences and ways of thinking, so that students are comfortable taking intellectual risks, asking questions and posing conjectures”. These statements directly identify the necessity of disciplinary discourse in the learning of mathematics.

The program further identifies 7 processes that are “critical aspects of learning (Mathematics Grade 10-12, pp 4). These processes include: communication, connections, mental mathematics and estimation, problem solving, reasoning, technology and visualization. Even though the program explicitly states a need for discourse, communication and reasoning, these processes aren’t built into the outcomes as they are in other Alberta Education Program of Studies (Social Studies, Science and English/Language Arts). Another point of interest are the 21st century skills that aren’t mentioned: collaboration, innovation, information fluency and digital literacy.

Research in mathematics education does suggest that at least some of the 21st century skills are important to the learning of mathematics. Lampert (2005/1990) distinguished there was a difference between traditional school mathematics and the discipline of mathematics. Traditionally, school mathematics has involved students being told mathematical principles and then using those principles to solve problems. In the discipline, ‘knowers’ of mathematics make conjecture, identify assumptions, and challenge one another and themselves to develop new understandings that are shared by those involved in the discourse of the discipline. Lampert suggested in order for our students to become ‘knowers‘ of mathematics “[A student] needs to be able to stand back from his or her own knowledge, evaluate its antecedent assumptions, argue about the foundations of its legitimacy, and be willing to have others do the same” (Lampert, 2005/1990 pp 154). This type of conjecturing, reasoning and arguing is how students develop an understanding of the mathematics as a discipline and it occurs through authentic discourse between students.

The National Council for Teachers of Mathematics also identifies the importance of collaboration and verbal exchange. They state “Interacting with others offers opportunities for exchanging and reflecting on ideas… Students should work effectively with others” (NCTM, 2000 pp 349). Mathematics and mathematical understanding doesn’t develop in isolation – it develops through frequent and meaningful interactions with others in a community.

Twenty first century skill sets are well-defined and agreed upon by various organizations. These skills are very directly stated in the Alberta Mathematics Program of Studies showing their importance in the program, despite not being as well-developed as in other content areas. They are also showing up in research and important literature, suggesting that 21st Century skills were important far before the 21st century – simply put, these skills lead to the learning of mathematics. The question that will further drive much of my thinking is *how can teachers develop 21st century skills, specifically discourse and collaboration, in the secondary mathematics classroom?*

References

International Society for Technology in Education. (2007) *National Educational **Technology Standards for Students* (2nd ed.)

Alberta Education. (2010). *Inspiring Action on Education: A Discussion Paper* [Data file]. Retrieved from http://engage.education.alberta.ca/uploads/1006/20100621inspiringact86934.pdf

Alberta Education. (1987). *Essential Concepts, Skills and Attitudes for Grade 12* (2nd draft). Edmonton, AB.

Partnership For 21s Century Skills. (n.d*.). Framework for 21st Century Learning*. Retrieved October, 28 2010, from http://www.p21.org/index.php?option=com_content&task=view&id=254&Itemid=120.

National Council of Teachers of Mathematics. (2000). *Principles and Standards for **School Mathematics.* Reston, VA.

Lampert, M. (2004) When the Problem Is Not the Question and the Solution Is Not the Answer: Mathematical Knowing and Teaching. In Carpenter, T. P., Dossey, J. A., & Koehler, J. L. (Ed.) Classics in Mathematics Education Research (pp. 153-169). Reston, VA: The National Council of Teachers of Mathematics. (Reprinted from *American Educational Research Journal*, Spring 1990, 27, 29-63)* *

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