## Student Creativity in Math

Today, using ClassFlow my class did an interactive math lesson/diagnostic on combining like terms. We started by classifying terms so that I could get an idea how students thought about numbers with integer coefficients and exponents.

Students came up with some super awesome and TOTALLY unexpected ways of classifying these terms. One student put the terms on a number line, but also alphabetically. It was fascinating. One that I will definitely be coming back to for more discussion. Some students put the numbers in order based on absolute value of the coefficient and then some students grouped them based on variable (like terms).

I’ll be honest, my students were so creative, it totally caught me off guard a few times. I’m not sure I consolidated all their ideas very effectively. It opened up a whole new way to start future conversations. From todays student responses we could have consolidated and moved our thinking along in the concepts of ordering integers, patterning and sequences or combining like terms. I forced the conversation to combining like terms. This is what we consolidated today, but I can’t wait to use their responses from today to take us into those other conversations at a later date.

At the end of the lesson today students created an Educreation video using their laptops or iPads and made their own “combining like terms” question in partners and then solved it while recording their steps. This provided an entry point for all students. Students still grappling with the concept created a question such as 1x + 1x = 2x. Students moving along in their thinking created a question such as 2x – 4y + 3x +7 = 5x – 4y + 7 . Within Educreations we can watch each others questions and how they solved them.

## Math Talk and Ownership of Learning

I’m teaching a math class for the first time in about 8 years. I’m loving it. I used to teach mostly math, but its been a long time.

We are wrapping up a mini-unit, or “big idea” on solving linear systems. We started off doing an inquiry activity to figure out what solving linear systems was all about conceptually. We looked at what this meant graphically. This activity ended up bringing up a lot of skill review from grade 9 (equations of a line, slope, graphing linear functions, writing linear functions, algebra). I got to see just how creative my Grade 10’s can be during this inquiry activity.

Next, students divided up into pairs within groups of four. Each pair mastered one other method of solving linear systems (substitution or elimination). Students used materials I provided them online and any other materials they could find. Their task was to become masters of that method and prepare a lesson for the rest of their group.

During the “teach each other” lesson, the discussion in class was fascinating. They were on topic almost the entire class. Students were asking each other excellent questions. They were debating, rewording and finding multiple ways to explain things. After some debate and discussion I would suddenly hear a student say “wait! I want to try that!”. I’m sorry, you WANT to try that? That is something I don’t think I used to hear in my math classes when I was the one doing all the teaching.

One student came up to me and said “I have a gap. I’m struggling with rearranging formulas, solving equations”. After spending the better part of a period talking with each other about the math, and often struggling to grasp the concepts, students were taking ownership of their learning. Thinking about learning. When I’m the one doing the teaching, students often take a passive role. However, when they were learning from each other, they seemed to take a more aggressive approach, advocating loudly for what they needed to learn the concept.

Next week we will be doing an activity to help focus on solving equations for any variable. The best part is, they requested it. I’m not shoving it down their throat. Students will be provided with a variety of ways to brush up on this skill and can choose what works best for them (an interactive online gizmo, reading content, video, etc.).

I am very impressed with the math talk that happened in the classroom while they were teaching each other different strategies to solve linear functions. I hadn’t anticipated that it would encourage them to take so much more ownership of their own learning.

## Student Creativity in Math

Today in class we took cue from Dan Meyers three-act math lessons. Students watched the first part of a video clip of two people racing. Thy needed to pull the math out and determine who was going to win.

When I sent them to work, each group had a tablet or computer that I provided with the video on it and then all the smart phones they were packing and could manage.

Most groups used timer apps on their phones and gathered data points to plot a distance-time graph for each runner. A couple groups played around with the runners speed and the distance and determined the time it would take each runner.

Then, one group really surprised me. They pulled out a MacBook, downloaded the video, threw it into video editing software and got data points from the distance each runner went per frame. It was great. They broke the video down into frames and somewhere in there I lost understanding of what they were doing (technologically). I didn’t need to know. It generated lots of great math talk and conversation in class within their group, between groups as we did a “gallery walk” type thing and lastly as a whole-class during the consolidation.

Luckily for me, most groups did graph data points, enabling us to have the conversation I was aiming for on solving linear systems graphically. I was also given some great insight into my students minds when I realized how upset/frustrated some were that we were using a linear model. They pointed out that as a runner starts they are not going full speed yet and that it takes a while. This opened up a whole-new conversation that I hadn’t intended on having (yet clearly should have predicted) about comparing linear and non-linear functions.

Overall, I was very impressed with their creativity, willingness to take risk in solving problems, their math talk or communication and general engagement. We are definitely ready to look at algebraic ways to solve these linear systems now.

This is a very large class of very noisy, bouncy, bubbly grade 10’s. I do think we are well-suited for each other. ðŸ™‚ A fun group.

## Learning Math Together

Last summer the LNS came in to see a few teachers in our board in action. I’ve talked a lot (including at ECOO) about these great teachers and the projects they completed last year. A quick overview of their project is now available on edugains here:

Other information about the project (including resources) can be found at learningmathtogehter.wikispaces.com

## Jac Rocks

Hows that for an egotistical blog post title?

I’ve struggled for a long time to make this blog post. A few weeks ago I got a SMART Notebook file from a grade 6 teacher I worked closely with this year. We worked together on a project called Learning Math Together (LMT). We found ways to connect this grade 6 class to a grade 4/5 class on the other side of the board to do math collaboratively. They used polycom video conference equipment, adobe connect, TIGed, Aviary Education and a few other technologies.

This SMART Notebook file from the teacher was an image they left written comments on with each letter of “Jac Rocks” linked to an audio file of a song. The audio files were all songs created by students to thank me. Normally I would listen to the songs (tear up) and share with a few close friends and family members. I would not post this online to share. BUT… after thinking pretty long about it. I need to share it.

I need to share it because these songs are not a reflection of my work. They are a reflection of their teachers work. I believe their gratitude has been transferred to me, but is truly for their teacher. The world needs to hear more stories of what happened in this grade 6 math class this year (a few posts I’ve written about this class include Plan B’s, day of SMART Boards, music math) .

I was in their class between 6-10 times this year. I helped co-teach lessons with their teacher when she was using a million different tools to connect students. The students loved me because their teacher and I had an excellent collaborative relationship. We got along wonderfully, laughed tons and took lots of risk trying new things. Students pick up on this.

I just played the audio file for my parents. They asked “how did the students know those were the things you were trying to do? That those were your goals?”. They verbalize all the things we hoped they would get out of the math program. The things the students mention in their songs that really make me happy are:

• increased confidence
• math is fun
• many different ways to do things
• taking risk to solve problems and learn is necessary
• have to work hard to solve problems
• try different tools
• they feel smart

All of these things are reflective of the learning environment the teacher set up in her class (not my participation). I got all the thanks from the students because every time I showed up we did something insane, chaotic and fun (hence I was there to help). Realistically, it was the teacher who set up the environment, relationships and learning activities that helped develop these values in her students.

I’ve converted the file to an audio file and roughly removed all the student names. I’ve also taken out the image where the students write me comments. There is fourteen minutes of audio, but listening to even a few minutes is a great way to hear how these students have put value on collaboration, fun, doing things many different ways, taking risk and creativity.

I love when students verbalize the result of reflective practice and ongoing teacher learning. Who better to help us gauge what works and what needs improvement?

Marci (@marciduncan), thank you for a wonderful year and letting me into your class to experience all the great things going on. Congrats on playing a large role in the development and success of 27 amazing children all with different learning needs. You have empowered them to continue their learning in ways that works for them.

I now have to plan my response in song to these amazing students. Any ideas?

## Music in Math, Patterning

Last week I had the honor of working with a few teachers (Marci Duncan @marcedun and Michele McGuires @3kidzmum) on a math lesson. These two teachers work on opposite sides of the district and co-planned their lesson by adobe connect and skype and then co-taught their lesson using Polycom video conferencing equipment and an assortment of other tools.

In the past they’ve done really neat lessons including one where students studied the devastation in Haiti, then created 2-D plans for rebuilding 8 buildings for a new village in Haiti. The students did this in groups with students from the other class using Adobe Connect. After planning their buildings (sketches) collaboratively the grade 6 class created diagrams on isometric dot paper of the buildings and then created the layout (birds eye view) of the village. These drawings were shared with partners in the other class using Taking IT Global Education (TIGed.org). Team members in the grade 4/5 class then created the nets for the buildings and had to actually build the village based on the to scale drawings made by the grade 6s. At the end the groups shared their final products using the Polycom video conferencing equipment. Pretty fascinating!

Back to last week, the teachers decided to do a lesson involving math and music looking at patterns. After an introduction via Polycom the classes split off into Adobe Connect rooms where two students from the grade 4/5 class were working with two students from the grade 6 class. In their Adobe Connect rooms they determined the characteristics that their pattern music would have (number of beats per measure, tempo, if it was a growing, shrinking or repeating pattern). Then the groups went to create music using aviaryeducation.com on their own. So, one pair in each class was going to create music that would be different but have the same basic characteristics. After creating their music, students went to their partners music (shared via aviaryeducation.com), listened to it and looked at it then made a comment describing the pattern using math talk. An extension activity included a discussion forum where students compare their pattern to their partners and describe the similarities and differences.The classes were brought back together via Polycom at the end of the period to share some of the patterns and comments created and consolidate the math.

There were a whole host of adults in the room for this lesson and video cameras going, so we were all a bit nervous about potential things that could go wrong. In the end, the lesson went very smoothly. Below are some examples of the music students can create using aviaryeducation.com. There are also images of what the music creator looks like and how they created the patterns.

The one tiny glitch that happened was that as we were doing the activity, the beta version program was changing! All of a sudden new buttons were showing up, new layouts, new links, etc. Students would save their work one way, but then had the figure out how to save it again the next minute because it had changed. As this started happening we cringed and hoped that no one would notice. And guess what? No adults watching did…. (until we told them). This is because these particular students who have been participating in lessons like this all year have learned that sometimes technology works and sometimes you need to problem solve (a lot) when it doesn’t. During one lesson the Polycom wasn’t working and then the sound card on a laptop wouldn’t work to use Adobe Connect and so we ended up sharing a screen on Adobe Connect with no visual of each class and did the audio part of the lesson across two iPhones plugged into speakers and on a skype call. Students have watched and participated in enough problem solving over the year that they just rolled with the beta software changes (even with the stress of video cameras and strange adults in the room). The skills developed to respond this way when things don’t go as planned are almost as critical as the actual math (perhaps even more so???).

## Day of a Hundred SMART Boards

A few weeks ago I was invited into one of my favourite Grade 6 classes. They were struggling with multiplication, so the teacher set up an activity where her 6’s taught a variety of multiplication strategies to the 4’s. The students worked in groups and each chose a different strategy to show the Grade 4 students. They chose which tools were needed to run their stations and created all files or manipulatives they needed.

As I walked around and chatted with my friends I was amazed at some of the things I saw. Each group had chosen to create a SMART notebook file with demonstrations, practice and games. One group used whiteboards. One group used the document camera. The Grade 6’s completely took ownership of making sure the 4’s understood their strategy. They wanted them to like their station best and so did everything they could to make it fun and enjoyable. The Grade 6’s wanted the 4’s to use their strategy the most in the future and took it as a personal challenge. They also wanted positive feedback for their station on the reflection pieces the Grade 4’s were completing at the end. The 4’s were excited to try the fun things the 6s had created (and maybe a little afraid to say “no” when asked to participate?).

The challenges of running the activity included finding enough portable SMART boards to bring down so 5 stations could be created. I had assumed it would be an organizational nightmare, but was completely wrong. Grade 6’s really stepped up to organize the Grade 4s. A few times I walked by a station (during the first centre especially) and saw a Grade 6 struggling to explain a concept. Each time I almost jumped in to help, but luckily held off long enough to see another Grade 6 hop in and respectfully redirect the conversation in a way that made sense to everyone. The Grade 6’s really had to know their stuff! Anything they were shaky on, was quickly consolidated.Â A couple things that stood out included a student who rarely participates, jumped right in and demonstrated excellent leadership for the full block. Another student acted as a journalist and went around making notes of students doing positive things. At the end he announced a list of students who had done something positive and shared this with both classes. To be honest, it was wonderful to see SMART boards being used by groups of students to collaborate.Â

I had a blast visiting the class and was talking today with one of the Netherlands teacher-trainers visiting this week. He asked if it was something I would consider writing about and sharing on my blog. You know the way a teacher can ask you a question that makes you think that it was something you thought of and want to do? ðŸ™‚ So, thanks Henke for the push! My adventure on the “day of a hundred SMART boards” definitely should be shared. ðŸ™‚

## The Day of Plan B’s

You know those days when nothing works out as planned? I mean…. NOTHING? We had one of those days this week. My colleague Jim Carleton aptly named it The Day of Plan B’s (and plan C’s and plan D’s). We had two classes on either side of the school board (about 90 km apart) who were co-teaching a math lesson together. The plan was to use the Polycom video conferencing equipment for the introduction which included discussing the situation in Haiti after the earthquake, showing photos of the destruction and then sharing the video Waving Flag. After the introduction including a discussion of 3-D shapes and some of the characteristics, the classes were to break into groups. Two students from each classroom were on a computer in Adobe Connect and were going to work with a pair from the other class. Their task was to design 9 buildings using 3-D shapes and then the birds eye view of their rebuilt village for Haiti. They had to choose the buildings that were most important to Haitians (not our students, so for example, most included a church). This was day one. Over the next week the Grade 6 class was going to use Geometers Sketchpad for some further activities with their 3-D buildings and the map of the village. The Grade 4/5 class was going to build the buildings using nets. They would then reconnect with their partners to consolidate the activity.

So, day one, myself and Jim are on either end of the video conference with the teachers. I get a text message “we have no v/c lets use Adobe Connect for the introduction”. The polycom wasn’t working. Ok, so we connect to an adobe room and get going. The microphone on one of the computers isn’t working. And, my computer on the guest wireless won’t connect to adobe connect at all. Ok, so there goes plan b. We ended up doing a teleconference with two iPhones. On each end we plugged the phones into speakers, skype called each other and then shared the lesson via adobe connect shared screen on the computer without a microphone. And it actually worked. Kinda.

When the time comes for breakout groups the students all go into three adobe connect rooms. We frantically tried to get them all into the correct breakout rooms and the grade 6’s sharing the SMART notebook file with their grade 4/5 partners. With all the time we had lost problem solving the video conference we ran out of time and never got the students into the right break out rooms. They ended up just introducing themselves in the chat and connecting with each other. In the end, it was the biggest lesson fail ever, yet we were all still smiling and laughing. The teachers we are working with are awesome!

The next day we tried take 2 and made a few changes. First of all we remembered to bring the replacement camera for the polycom unit we were supposed to bring in the first place ðŸ™‚ Then, we decided break out rooms weren’t our best choice for this project and created 12 separate adobe connect rooms and then assigned them to the partners. We also decided that we didn’t need the SMART notebook file, the students could simply share right on the whiteboards within adobe connect. These were saved and we could go back to them when needed.

I couldn’t make take 2, I was elsewhere, but I got a text message around lunchtime from one of the teachers saying “it worked awesome!”. Looking into the adobe connect rooms after the students had left I can see the chat and whiteboards displaying their work. They did some really neat things and came up with great ways to decide which student was doing which job. The way I figure it, we are always taking with students about persistence and perseverance. Well, this sure was a great example. ðŸ™‚ The day of plan B’s continued on way beyond this failed lesson and into the afternoon, but of course… a little creative problem solving got us where we needed to go.