Last November, I wrote a short blog post titled, Screencasts of Student Math Thinking. In this post, I also included a link to a glog I created containing four screencasts that were created by grade 6 students explaining their group’s multiplication strategies after an initial multiplication lesson. Since that post, there has been a lot of attention around the world on Kahn Academy where students learn from concepts and strategies from videos (screencasts).

I love the idea of screencasting and I think what Kahn Academy is attempting to do is pretty cool. However, I love screencasts even more when they are created by students. When students create math screencasts it enhances their metacognition. It forces them to think about their math thinking not once but multiple times since they can play back their video, watch and listen to themselves explain their strategy or solution. They can edit and record multiple times until they feel that their screencast is appropriate for their classmates to view. The rest of the class can also benefit from screencasts because they can be exposed to different solutions and strategies to the same problem. In addition, the screencasts are more engaging by virtue of them being created by students and using student language. Also, with websites like Screencast.com screencasts are not limited to the hard drive of a single classroom computer but can be accessed via web link from any computer with an internet connection. This would allow students and their parents/guardians to view them from home.

I truly believe in the benefits of screencasting for students in the math classroom. For the past year, I have been religiously promoting it in my school board as a great tool to enhance student metacognition and math communication. Many teachers seem to like the idea of it but I haven’t really seen it fully implemented in classroom. I’ve mainly seen teachers create their own screencasts similar to Kahn Academy and no disrespect to Khan Academy or to teachers but I don’t find teacher/adult generated screencasts very interesting or engaging. I would argue that students prefer to create the screencasts themselves and watch other student created screencasts. So I ask the question Why? Why isn’t screencasting being implemented in the math classroom? Is it too difficult? Too time-consuming?

I would love to know your thoughts on screencasting and how you would implement it in your classroom.

I was introduced to concept of “Whiteboarding” when I read Frank Noschese’s fantastic blog post titled, “The $2 Interactive Whiteboard” As a former math teacher and math facilitator I was drawn to whiteboarding and socratic dialogues. The whiteboard is such a simple, low tech tool but promotes collaboration, problem solving, communication, basically all of the 7 mathematical processes that I blogged about a few months ago. If you have a few minutes to spare, read the following 5 pg. article on whiteboarding.

There are so many benefits to whiteboarding in the classrooms. I won’t go into details since you can read them on Frank Nochese’s blog mentioned above. However, one question I brought up to Frank on his post was what the difference was between using a whiteboard and just plain chart paper (which up to this point I used very frequently). Other than the obvious benefit of saving paper and trees, he refered to a researcher Colleen Megowan who studied different types of whiteboarding and the affect on student dynamics. Althought it didn’t actually make it into the research paper, she did look at the differences between chart paper and whiteboards and her observations make perfect sense.

When students collaborate using a chart paper most of the thinking and reasoning usually happens before the marker actually touches the paper. This may be due to the fact that students don’t want to make mistakes. Therefore, when students do start writing on the chart paper, it is a summarization of the conversation and the thinking and reasoning that took place before. In addition, Colleen spoke of the “power of the marker” and the fact that usually it is the same student that ends up with the responsibility with writing on the chart paper. Maybe these students are leaders of the group, have the neatest handwriting, or just get to the marker before everyone else but what these students write is their interpretation of the group’s conversation and may not necessarily represent the group’s collaborative thinking.

When students use whiteboards, the writing usually happens as the students converse, reason, and think collaboratively. The ideas written on the whiteboard evolve as the conversation unfolds and is a better representation of the group’s thinking than if written on chart paper. Because the markings can be easily erased, students are immediately inclined to write without hesitation. Whiteboards are also less intimidating for students and encourage multiple students to contribute and write. In addition, Megowan spoke about the “power of the eraser” and the fact that writing can be erased changes the group dynamics and allows a new role (the eraser) to emerge within the group.

After reading more literature on whiteboarding and socratic dialogues, I was hooked and immediately saw the benefits not only for math but in all subject areas and needed to have a set of six whiteboards for myself to try out. I wanted whiteboards with similar dimensions to standard chart paper (24″ x 32″). I looked into getting whiteboards from Staples but the cheapest whiteboards with the dimensions I was looking for cost about $28 each (with tax, close to $200 for six). I needed a cheaper alternative and Frank mentioned on his blog that educators were going to homedepot, Lowes, or Rona and purchasing 4′ x 8′ tileboard and cutting them into six smaller sections (24″ x 32″). However, my online searches on these stores’ websites for tileboard came up with nothing. I phoned multiple home depots and Rona’s in my surrounding area and several phone calls later, I finally found a Rona that had one panel of 4′ x 8′ tileboard in stock. With my school board discount, I was able to purchase the panel for $37 and didn’t have to pay for the cutting since Rona gives you the first 3 cuts for free. So all in all, each whiteboard came to approx. $6.17. Not quite $2 whiteboards but I am very happy with my whiteboards and I’m very excited to implement and share the whiteboarding strategy with the teachers in my school board.

I’m not advocating that we abolish chart paper from the classroom. Chart paper still has it’s place for ideas that need to have a permanent fixture in the classroom. (anchor charts, learning goals, success criteria) However, there are situations in the classroom where using whiteboards would be more effective for collaboration, thinking, and reasoning than chart paper. The benefits of whiteboarding shouldn’t be ignored and should have a place in the classroom as well. I would love to hear your comments on how you use the whiteboarding strategy in your classroom.

In my next blog post, I will be looking at various websites that offer online whiteboards that allow students and teachers to collaborate online and see if the whiteboarding concept can be implemented in a digital environment. Perhaps the digital environment would have an effect on group dynamics not seen in typical face to face whiteboarding interactions or perhaps new roles would emerge from collaborating online.

Last year, I co-taught in a grade 6 classroom and gave the students the following problem as a part of an initial lesson to begin a unit on division,

“165 parents will be attending a family math night in your school gym. They will sit at tables in groups of 6. How many tables need to be set up?”

We asked the students to work collaboratively to solve the problem in more than one way and to show their math thinking. Below are two solutions from two different groups.

Which group has a better understanding of division? I showed these two solutions to many teachers and at first glance, many chose the group that solved the problem using long division. Why? The main reasons were efficiency and a percieved higher level of thinking. Many teachers viewed long division as a faster strategy and the latter, a time consuming low level strategy. However, is efficiency the ultimate goal in mathematics and does it mean that students that use very efficient standard algorithms to solve problems have a good comprehension of the mathematics?

The standard algorithm for division was invented long before the calculator and was viewed as the most efficient way to divide. However, I don’t think it was viewed as the most efficient way to teach division. Yet, the standard algorithm is frequently the first (and sometimes the only) strategy that is introduced to students when teaching operational sense. The standard algorithm, like many other division strategies can be a great strategy but only if it is understood. For many students, the standard algorithm for division is difficult to understand which forces them to rely on the memorization of the steps without any conceptual understanding of division. If given the opportunity, students are capable of coming up with their own invented strategies for division. More importantly, these are invented strategies that make sense to them which would lead to a better conceptual understanding. Below are the same solutions to the division problem mentioned above but I have included the students’ final statements that answer the question.

The group of students that used a longer and “less efficient” strategy had a better understanding of division than the group that solved using long division. It is crucial that students be given an opportunity to solve problems and on their own in as many ways as they can and allow them to share and dicuss their strategies with their classmates. By doing so, they may be more likely to make connections between their own strategy with others and move towards a conceptual understanding of a more efficient strategy. When you take a step back as a teacher and let the students loose with math and allow them struggle with guidance, you could be pleasantly surprised with their results and the discussion of their results is where you will find that the most teaching and learning occurs.