Collaboration On The Web – Quick Links

January 27, 2011 Leave a comment

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

Presentation (Prezi) Here

Participate On These Links

Online MindMapping

Virtual Stickies

Virtual WhiteBoarding

Collaborative Documents:

Categories: Uncategorized

Join an ASCD Group: Technology for Teaching and Learning

January 15, 2011 Leave a comment

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.

Categories: Uncategorized

Virtual Learning Coming … Now!

January 5, 2011 Leave a comment

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!

7 Reasons, 6 Tips and 3 Uses: Wikis In The Classroom

November 30, 2010 Leave a comment

It’s been a while since I’ve used wikis in a class (last May I believe), so I thought I needed to remind myself why I liked using them and how I made it work by writing a blog post. If you find this useful, please share  and comment below!
Reasons For Using Wikis
  1. Honor Each Student Using social media such as wikis helps you honor the ideas of each student. Engage your students and let them know that their ideas are valued – give them a platform to share their understandings, and they will.
  2. Make Understanding Transparent When using a wiki that is accessible with any web browser all students can access the knowledge of their classmates even if they are too shy to talk in class or those who miss a day or even weeks.
  3. Teach Your Students To Reference Ideas Wikis are a very easy way for students to begin referencing other work because they can easily put in links to other web based sources
  4. Learn Digital Citizenship Getting your students working on social media gives you an opportunity to teach digital citizen, and allow students to learn how to become effective ‘knowers’ in the 21st century
  5. Use Multimedia Students can add multimedia to their notes/work; links, video, pictures, interactive web applets, cartoons, etc.
  6. Engage Students similar to #1, but specifically focus on the fact that students will be doing work instead of teacher.
  7. Track Student Work Wikis are one of the few tools that allows you to see exactly which user has done what. Use the history function to track student work and edits to know who has been engaged.
Tips For Making Wikis Work In The Classroom
  1. Set Clear Expectations√ The best way to deal with problem behavior is to avoid it with clear expectations. Talk to your students about being good citizens online, and have clear expectations. Students respond well to candid discussions on this topic.
  2. Provide Descriptive Feedback 🙂 Take a few minutes early in the use of wikis to show students the type of ‘posts’ that are productive and effective, and tell them why. Point out ‘posts’ that are less effective, and tell them why.
  3. Structures Help! Using wikis will be very different, so think carefully about how you structure such a lesson in advance. Usually only one user can edit at once. I brought 25 people online to work on 13 wikis (representing 13 concepts). The first time I did this I made 13 bright yellow sheets of paper with the title of each wiki page on one yellow sheet. In pairs, users were told to only edit a wiki if they had the corresponding sheet. Every 5 minutes we switched sheets, until each group had the chance to add to each wiki/idea.
  4. Scaffold Skills If you want students to do research to find media or information, you need to show them how. You may also need to show them how to reference information, use a wiki, take turns, collaborate, share, respond to classmates, etc. If you don’t teach it, don’t expect them to know how!
  5. Provide Frameworks consider providing structures such as questions for them to answer (please don’t turn a wiki into a worksheet!), graphic organizers for sorting research findings, etc. – anything to help students organize their thoughts and get them started.
  6. Be Present The most important thing you can do for your students is be present while they are working. Circle around the classroom frequently, ask students to show you what they have so far. Question them, and have them question you. If you’re not a part of the learning process than why are you getting paid?
Suggested Uses of Wikis During Learning
  1. As a KWL Chart (what I Know, what I Want to know, and what I Learned) The first time I used wikis in class, small groups shared a wiki throughout a two-week unit of study. I posted over-arching questions on the wiki, and the individuals in the group added and updated it. At the end they had a nice document with pictures, text, links, videos and interactive applets that helped them understand the content.
  2. As A Unit Review I’ve seen a few teachers using wikis at the end of a unit to put together interactive multi-media based notes and questions. In these cases the community knowledge had been less of a focus but the simplicity of a wiki expedited student work.
  3. As The Knowledge of the Classroom It is important to honor the ideas and understandings of every student in your classroom. By using wikis you can give each student an opportunity to share their understanding on a topic; a picture, graph, video, experience, applet or other website/resource that helps them represent their understanding. I seen a math teacher once have students use wikis to explain a data set – at the end there were various types of graphs, links images and explanations which became a valuable way for students to gain the perspective of their peers.

I hope I’ve given you some fresh ideas for using wikis in school. These ideas have developed out of work I have done with my district and with my colleague, Susana Gerndt. I would be interested in hearing your feedback in the comments below! 🙂

This post is the third in a series of posts I call “Reasons and Tips”

Things You Can Do Today To Enhance Student Learning

November 28, 2010 Leave a comment

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.

  1. Get rid of rows of desks, get kids sitting in groups. Learning doesn’t happen in isolation.
  2. 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)
  3. Take a break from grades, and give students descriptive and useful feedback. Read more about this on Joe Bowers blog
  4. 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.
  5. Let student questions drive the learning – a simple example of how this might look is given by John Scammel on his blog
  6. 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.
  7. 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

November 26, 2010 Leave a comment

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?


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

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

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)

Getting High School Kids To Talk “Math”

November 24, 2010 3 comments


Today I had the pleasure of working with a dedicated and gifted first year teacher. Tim is doing an impressive job teaching pre-calculus grade 11 and 12 math; he has well prepared lessons and examples, clear explanations and solid answers to student questions. Tim invited me into his classroom to work with him and his students to develop some mathematical discourse with the kids.

The unit of study for todays grade 11’s was circle geometry; students had to learn, prove and apply both the Tangent Radius Theorem and Equal Tangents Theorem

Equal Tangents Theorem: PA = PB

Tangent Radius Theorem: Angle OPQ = 90 degrees

The lesson played out as shown below. Keep in mind the focus is on student talk.

Part 1 – Modelling Teachers (Tim and I) stated the Equal tangents theorem for the students, and walked them through the logic of the proof

Part 2 – We Do Together Teachers stated the Tangent Radius Theorem and elicited ideas from the whole class regarding their understanding of the theorem, the diagram, assumptions, and conjectures. Students were encouraged to use relevant math terms and were probed with open ended questions to guide their thinking.

Part 3 – You Do Together (whole class) a) Students solved a problem that most students could easily prove. b) Then, as a class (this is the “do together” part) students brainstormed relevant terminology and theorems used to do the example proof.

Part 4 – You Do Together (Pairs) Students had 60 seconds to use a diagram and the terms from part 3 to explain/prove the problem to a partner – after 60 seconds they switched roles from listened to speaker.

During part one of the lesson no students used the language of mathematics verbally. During part two, students struggled to use the language (either they weren’t comfortable doing so or they didn’t know how). By part four of the lesson students were very talkative and on topic. The sentences formed by students seemed to be perfectly logical and mathematically correct. It was quite exciting for both Tim and I to see how quickly students became engaged in mathematical discourse when given clear structures and expectations. Tomorrow we will be trying out a write-around (recently called paper-blogging in the blogosphere) and I am quite excited to see the results. My personal agenda is to get students using social media to engage in discourse by the third lesson (approximately 160 minutes of lead up instruction time).

If you’ve been wanting to get students to talk more in your math classes – just give it a try. A couple of simple structures and a few minutes of planning seems to go a long way!

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