As my oldest daughter entered Junior Kindergarten last week and my youngest entered her child care centre, I officially became immersed in the world of early learning programs. My first real eye opener was the fact that almost all assessment in child care programs and kindergarten is done through observation and based on children’s oral language. For educators, this means A LOT of documenting.

I noticed in my youngest daughter’s childcare program, they document by taking many pictures and writing down anecdotal notes for each pictures with the style of learning (ie. visual, auditory, kinesthetic). They told me about the large amounts of time that goes in to this kind of documentation. My immediate thought was how technology could be used to effectively enhance this process of assessment. There must be an app out there somewhere that could help with this kind of documentation.

Well, the other day, I discovered that such an app exists! It’s called Mental Note and according to the website, it combines pictures, voice recordings, sketches, and text all on the same page.

So if a student is demonstrating some style of learning, I could take a picture, audio record what I am observing, annotate the picture using the pen feature, and add a few words of text to briefly describe what the student was doing. All of the notes taken can be stored on the iphone/ipad/ipod touch but the notes can also be e-mailed as a PDF with the audio as a separate attachment or backed up in the cloud to your Dropbox account.

I installed the Mental Note Lite app for free (but only comes with a maximum of 2 notes) to my iphone and tested it out and I was very impressed. The full version costs $2.99 and comes with unlimited notes. Here is a sample of a note that I quickly took of my daughter playing (without the 11 second audio clip).

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.

John Van deWalle, Cathy Fosnot, Marian Small, and Marilyn burns are all key researchers when it comes to mathematics in education. According to these researchers, an ideal math lesson consists of three parts. The HWDSB math facilitation team refers to the three parts as: 1) Getting Started 2) Working On It 3) Reflect and Connect.

Let’s just say we are going to teach a grade 5/6 initial three part problem based lesson on multiplication and the goal of this lesson is simply to see what multiplication strategies students are bringing to the table. The “Getting Started” part of the lesson would involve some sort of activation of students’ prior knowledge related to multiplication (simple problem). During the “Working On It” part of the lesson, the following problem could be presented to the class.

29 students are going on a field trip to a museum. The field trip will cost $20 per student. How much will it cost for 29 students to go on the field trip?

This is an example of an open routed question. There is only one answer but there are multiple strategies to get the answer. Therefore, we ask the students to solve the problem in groups and in more than one way. The first strategy will come naturally for some students however, the second strategy may be more difficult to come up with. Again, the goal of the lesson is to see all the multiplication strategies that the students will use solve the problem. As the students “work on it” we would circulate around the classroom asking questions about students’ strategies, guiding students through the process, and allowing mistakes to occur (these will be addressed during the “reflect and connect”). It is also important to note that not every group needs to be finished before moving on to the “reflect and connect”. Sometimes incomplete solutions provide good starting points for classroom discussion.

The third part of the math lesson is the most important part of the lesson but often the part that gets left out by teachers. It is also considered by many teachers as the most difficult part of the math lesson to facilitate. The “reflect and connect” is when the learning of the math concepts really occurs because the learning comes from the student work. This is the part of the lesson where students are given an opportunity to explain their strategies and solutions and where teachers are given an opportunity to focus on key strategies and concepts by guiding a math discussion through strategic questioning. This math discussion is very important because the conversation is less teacher centred and more student centred. Students ask each other questions about their solutions, make connections between their solutions, and defend their math solutions. The goal of the “reflect and connect” is to create the culture of a math community that allows students to take risks and where mistakes are considered to be opportunities for new learning. Ideally, this is what the “reflect and connect” should and could be like however, it takes time to get there. Students need time to learn how to ask appropriate questions, give constructive feedback, and receive constructive feedback. Teachers need time to learn how to ask probing and guiding questions and look for connections between student work.

There are a few ways to conduct a “reflect and connect”. The following article titled, Communication in the Mathematics Classroom explains three different approaches of math communication that can be implemented during a “reflect and connect”: 1) Gallery Walk, 2) Math Congress, and 3) Bansho.

My next post will focus on the gallery walk and a possible way to enhance math communication via Lino it using the following student solutions:

Math plays an important role in developing 21st century learners. The Ontario Math Curriculum states, “An information- and technology-based society requires individuals, who are able to think critically about complex issues, analyse and adapt to new situations, solve problems of various kinds, and communicate their thinking effectively. The study of mathematics equips students with knowledge, skills, and habits of mind that are essential for successful and rewarding participation in such a society”. I believe the habits of mind that the curriculum refers to are the seven mathematical processes: problem solving, reasoning and proving, selecting tools and strategies, reflecting, making connections, representing, and communicating. These processes are not only essential to the acquisition of math but are also significant in preparing students to be successful in a 21st century society. They promote collaboration, sharing of ideas, risk taking, discovery and allow opportunities to argue and defend solutions and strategies. Teaching through the mathematical processes would not only deepen students’ knowledge and understanding of math but also develop a community of critical thinkers, problem solvers, risk takers, and collaborators.

Below are some links to resources for teaching through the math processes:

Last year, I came across a very interesting blog that helped changed my perception of the web in education. Stretch Your Digital Dollar by Katy Scott offers useful ideas for integrating technology into all classrooms. After reading her blog about screencasts, I became fascinated by the possible positive implications this could have in the math classroom. This year, I am looking to delve deeper into screencasting and investigate its positive impact on student learning. I’m interested to hear/see how other educators incorporate this great use of technology in their own classrooms.

I have posted a Glog containing student screencasts of the multiplication strategies that they used to solve a word problem.