As a read through the first few chapters of Visible Learning For Teachers by John Hattie, I was immediately drawn to his statements about student learning and impact. According to Hattie, almost any intervention/influence in education and has a positive effect on achievement when the bar is set low. When the bar is set at zero everything works. Through his 900+ meta-analyses involving 60 167 studies and 88 652 074 people, Hattie was able to determine a benchmark that he used to compare the effects of a total of 138 interventions. He then used this benchmark to set a bar in order to identify the effectiveness of an influence such as homework. Using the effect sizes of influences and his benchmark, Hattie was able to rank 138 influences from most effective to least effective.

Hattie’s benchmark to identify whether an influence is effective or not, really made me reflect about the interventions I perceive to be the most effective and how I make these determinations. Do I take the time to reflect on how much of an impact my influences will have on student learning? Will some influences have a greater impact on student learning than others? I believe these are essential questions that need to be asked and discussed amongst school leaders, teachers, and students in order to ensure that the strategies and interventions are high in impact. In the opening chapter of his book, Hattie asks, “What is the nature of the learning that you wish to impact?” He encourages educators to be evaluators of their impact and to constantly recognize not only how student learning is being impacted but also how much. Moreover, he stressed the importance of this evaluation of impact occurring as a school community that involves teachers, school leaders, and students. When key stakeholders can be transparent and make their thinking and learning visible, then the evidence of student learning and the effect of impact can be discussed, understood and acted upon.

References

Hattie, J. (2012). Visible learning for teachers: Maximizing impact on learning. (pp. 1-269). New York: Routledge.

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 created another interactive comic using Bitstrips that would allow students to investigate arrays and multiplication. In this activity, students help Mr. Ro arrange desks into rows and columns for the first day of school (I know, I know, very teacher-directed seating arrangement) by clicking and dragging desks and into their desired position. The comic problem is open-ended to allow students to create arrays with 12 desks all the way up to 24 desks and to create a variety of arrays for the same number of desks. I have shared this activity in http://bitstripsforschools.com and I would love to get feedback on how this activity goes if you try it with your class.

Recently, I have been working with staff on integrating Bitstrips For Schools into their classrooms. Most of the ideas that were discussed involved using Bitstrips for literacy, social studies, history, health, and even science. However, math never really entered the discussion. So I searched the shared math activities that were posted by other teachers on the Bitstrips For Schools website and only found a total of eight activities. All of these activities consisted of instructions for students to create their own comics. Here is an example of a shared activity that was posted:

Grades: 6-8, Subjects: Mathematics

Create a 3 panel strip to explain how to calculate the area of a triangle and/or parallelogram.

This particular application of Bitstrips is more of an assignment which focuses on students creating a product based on a set task. However, I thought that this program could also be used to create comics based on math word problems. In addition, these comics could be interactive as well due to a feature in Bitstrips that allows students to take an existing comic, ‘re-mix’ it, and save it as a separate comic.

The following is a primary algebra word problem:

Mr. Ro gave a handful of jelly beans to Jonah and to Sam. When they counted them Jonah had 3 red and 2 green and Sam had 5 red and 4 green. They realized one of them had more than the other. What could they do to make sure each had the same number of jelly beans? Justify your answer.

I took this word problem and turned it into the comic below:

In bitstripsforschools.com, I could share this comic as an activity and assign it to my class so that when they log in it would show up in their ‘Activities’ section. The students would then ‘re-mix’ the comic and rearrange the jelly beans, type their justifications in the caption boxes, and save it as their own comic. Teachers and students could also provide feedback on each others comics via the commenting feature. I could see students creating their own interactive math comic problems as well and sharing with the rest of the class to solve.

I would love to hear your thoughts on this idea. I have shared this activity in the Bitstrips For School shared activity section for teachers. Please try it out and let me know how it works out for you.

All educators have great ideas, lessons, and success stories that occur in their classrooms everyday and I believe that these ideas, lessons, and success stories need to be shared. As teachers, we constantly try to find ways to make student thinking visible but I think this applies to us as well. We need to find ways to de-privatize classroom teaching and make teacher thinking visible. By increasing the transparency of teaching practice between classrooms, schools, boards, even countries we could learn so much from each other. If you taught a great math lesson that really engaged your students, why not pass that lesson on to others to use? If you had a teachable moment or a break through with a particular student why not share that inspiring story so that other teachers can learn from it as well?

Conditions are being created in schools that promote transparent teaching such as PLCs, co-teaching, teacher moderation, release for team planning, demonstration classrooms, networking between schools. However, I find that none of these things can really allow teachers to truly share their ideas and narratives of their teaching experiences without being interrupted in someway. I also find that with many of the strategies mentioned above, reflective practice often gets overlooked. Reflective practice is essential for my own professional growth which is where blogging comes into the picture. Blogging provides an outlet for my thoughts on education and it allows me to tell my narrative without interruptions. However, the reason why I love blogging so much is that it makes my thinking visible to others. It makes my teaching practice transparent so that other educators can hopefully benefit or gain some insight from it. I learn so much from reading the reflections and narratives of other educators through their blogs and I know that the teachers and students that I work with can only benefit from this transparency of teaching practice.

As a math teacher, I often became frustrated when I gave a math problem to my students only to have a small percentage of the whole class be able to answer the question correctly. Naturally, many of my students became frustrated too. Consider the following problem:

The word problem above is a very specific problem that only has one answer. The fact that there is only one answer is not a serious issue for me or for the students that need to solve it. The issue with a problem like this is the fact that there is only one way to answer it.

This is a very specific problem that requires a very specific solution. If I gave this problem at the beginning of a grade 6 transformational geometry unit or TLCP cycle (Teaching Learning Critical Pathway) there is a good chance that only a handful of students would be able to solve it correctly. This is the kind of problem that I would give at the end of the unit or TLCP cycle since it is a really good assessment OF learning type of problem. Then it should come as no surprise that this problem was taken from the 2008 EQAO math assessment.

But what if I wanted to use this problem to begin my transformational geometry unit? Well, maybe not in its current form but what if I could “open up” the problem so that it wasn’t so narrow and specific and that a lot more students could solve it. Consider the same problem but with some modifications:

This is an example of opening up a very specific math problem. This open problem has more entry points for students than the previous problem since students have a choice in how they can move and manipulate the mat. Open questions are questions that have more than one answer and are great for differentiating instruction in the math classroom. Open questions allow students to solve problems based on where they are at in their math development.

I actually used the “open” gym mat question last year when I helped a grade 6 teacher introduce her transformational geometry unit. At first, the teacher was hesitant. This approach was drastically different from how she usually introduced the unit. In years past, she would introduce each transformation in isolation. First, a note on translations. Second, examples and demonstrations of translations. Third, practice problems involving translations. The three-step process would be repeated for rotations and reflections (This is also how I used to teach math). Therefore, the notion of giving an open problem to her students that allowed them the opportunity to investigate and use any transformation without defining, modeling or practicing them was pretty daunting. However, the results were very eye-opening and informed the teacher’s next steps for the next few lessons. Here are a couple of the student solutions:

All of the students in the class participated and solved the problem in small groups. As you can see from the gallery, there was a range of solutions from the class that brought up some really good discussion during the reflect and connect portion of the lesson where groups were able to explain their solutions to the class and answer any questions about their transformations. Some topics/questions that were discussed were:

efficiency in transformations.

What is the most efficient/fastest way to get the mat to the desired position?

What’s the purpose of the dotted line AB?

points of rotation.

Can an object/shape have more than one point of rotation?

This rich discussion was able to occur because of the openness of the question and the fact that students had the freedom to investigate and use their own math thinking to come up with a solution. It was also very powerful for the students to see that none of the groups came up with the same solution to the problem. The range of students’ solutions also allowed the me and teacher to determine appropriate action for the next couple of lessons.

For more information on differentiating math content using open and parallel questions please read the following article. (A very good read!)

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.

In one of my previous posts about the 3 part problem based lesson, I referred to the third part (reflect and connect) as the most important part of the math lesson since the learning comes from the student work. Students are given the opportunity to explain their math thinking, pose questions, defend their ideas, and make connections with other solutions. The teacher is the facilitator of the discussion as well as a participant. The learning comes from the math community.

The following article describes three approaches to the Reflect and Connect: 1)Math Congress, 2) Bansho, and 3) Gallery Walk.

In this post, I wanted to focus on the gallery walk because to be honest, this is an approach that I don’t use very often when consolidating a math lesson. This is an approach that requires a lot of movement of students in the classroom and could possibly take some time and good management skills to facilitate. In most gallery walks, student solutions are posted around the classroom, and students circulate with sticky notes writing down questions and comments and placing it on the solutions. The idea is for students to read the comments and questions on the stickies about their own group’s solutions and use that feedback to help them prepare the explanations of their work to the class. Problems can arise if students aren’t given enough “wait” time to think of questions or comments to write down on their sticky notes. This can result in comments like, “You spelled multiply wrong.” or “I like how you used the colour red to write your solution.” The goal is to promote higher order thinking and questioning but if students aren’t familiar with a gallery walk or need more time to reflect on the student solutions then perhaps an online gallery walk could be a worthwhile alternative.

Lino it is a great web application that provides you with an online canvas and allows you to post online stickies, pictures, videos, and attachments. You can also share your online canvas with others by sharing its URL. Sharing the URL would allow others to post stickies as well. You can probably see how Lino it could be used to conduct an online gallery walk. To give you an idea of what it could look like, I inserted an screenshot of an online canvas with pictures of four multiplication solutions and stickies with questions and comments posted around them.

The comments/questions were generated by a team of math facilitators when I shared the link with them, which should also give you a good idea of how Lino it could be used for teacher moderation of student work.

By using an online gallery walk, students could post their comments/questions in class or at home and have time to reflect on student work and pose thoughtful questions and comments. Groups could review the feedback the next day and prepare the presentation of their solution to the class.

I would love to hear your thoughts about this alternative approach to communicating in the classroom.