I asked my principal, **Paul Clemens**, if I could share an email and discussion that we had today in order to further converse about this topic and share my own thinking. Paul agreed, and I’m so happy that he did!

This story begins last week when I **blogged my true confession that walk throughs terrify me**. I received many comments on this post, including those from **my principal Paul**, **vice principal Kristi**, and **another principal that I highly respect, Carol**. Paul and Carol had a similar solution when suggesting a way that I could overcome my fear: *invite the principal into the classroom, but with an activity in mind. *Basically make the walkthrough on your terms. I liked the idea, and today I decided to give it a try (sort of). 🙂

Very late on Friday night (around 11:30 pm), I **blogged about my reflections for the week**, and as a follow-up Twitter conversation to this blog post, **Colin Harris** and I decided to share a math problem between our classes, but online. Colin, a Grade 6 teacher from York Region, wanted to help me meet my first goal of “making math more meaningful.” He knew that we are working on mean, median, and mode, and his class is doing the same. Colin suggested creating a math problem, having students solve it in groups, and then sharing the solutions in a Math Congress, but through Today’sMeet. I loved the idea, but I was initially hesitant, as I knew that we were finished the unit on Monday and I wanted to start our new unit today. **Angie Harrison**, a Full-Day Kindergarten Teacher from York Region and a friend of both of ours, followed the conversation and convinced me to give “mean, median, and mode” one more day — *as one last attempt to consolidate learning.* I was convinced! 🙂

When Colin sent me the Today’sMeet Room link today, I felt brave, and I decided to email Kristi and Paul inviting them to join in on the conversation. I thought that looking in online first might be a good stepping stone for me before they came back into the classroom. Well it turns out that Kristi was away today, and Paul said that he’d come by the class at noon (*when we started the discussion*). Okay, here it goes! 🙂

It does turn out that inviting the principal in makes things less stressful. *Yes, *I was very aware that Paul was there, and I even made a couple of comments to him, but then I got immersed in the activity and the students, and I kind of forgot that he was still in the room. 🙂 At one point, I looked up and he was gone. So I sent a tweet thanking him for joining us, and at the nutrition break, I sent an email asking him for feedback. *Please note that this is not about Paul evaluating me. Yes, it’s my Teacher Performance Appraisal year, and yes, as such, he can (and will) evaluate me. But I was looking for ways to improve, and I wanted to hear his feedback. That’s why I asked.*

The first response that I noticed was Paul’s tweet:

I replied with my thoughts and with the feedback I received from my students (**please read from the bottom, up**).

That’s when I realized that the questioning approach stresses me out, 🙂 and I really just wanted to hear his feedback, so I went and asked. Paul must have sent me an email in the meantime, so we actually discussed this email together:

**My thoughts:**

**– great to see the kids connecting with other students!**

**– I wonder if any of them found it frustrating or difficult to keep up or follow (one student was taking a long time to enter his comments and the group had already moved on).**

**– I like the idea of having different rooms for different questions**

**– I think it would be better to have a more rich activity to discuss… perhaps to share a response after reading a common article, story or book (again… diff. rooms for diff. topics… allow students to pick topics to discuss).**

**I liked the experiment!**

I appreciate that Paul’s open for differing opinions, and we didn’t completely agree on how things went, but his email and discussion did get me thinking. Here are my thoughts:

- I asked the students for feedback after the Today’sMeet Room discussion, and none of the students mentioned that they were frustrated. I didn’t observe any frustration either.
*Yes,*some students took longer to answer than others, but if you look at**the transcript**, you’ll see that in the end, all of the students caught up with the conversation. The great thing about a typed conversation is that students can read through it at their pace, and respond to comments at anytime that they want, as the comments remain in print and can always lead to new discussions. - That being said, Paul’s comment here made me think about differentiated instruction, and if more choices would have benefitted students. Maybe giving the option of some students to reflect together through Skype while others reflected together on Today’sMeet would have helped. As I went group to group, I noticed that some students felt more comfortable sharing information aloud, while others did better in writing. Students solved this problem by talking about the solution first (
*if need be*), and this worked, but I wonder if this other option would have worked more.**What do you think?**

- I also like the idea of different rooms for different questions, but I agree with Colin’s comment as well.

I’m not sure how to facilitate this many different rooms. I wonder if a staggered start time would work. Then only those students answering that question would be online at that time, and students would rotate. Other students could be involved in meaningful math activities within the classroom. Something to consider. **What solutions do you have for this problem?**

- It’s Paul’s last comment that really got me thinking. As I mentioned to him today, I’m not sure that I agree with him on this. I think that this activity was a rich one (
**mean and median collaborative problem**).*Yes*, students were told what to calculate, and they were given specific numbers to use, but there wasn’t just one right answer. As you can see from**the transcript**of the conversation, students did not always agree. They tried to push each other’s thinking though. They asked “why” questions, and used the prompt a lot of “tell me more.” They presented creative solutions, and at times, even made me consider different options (*I kind of liked the idea of taking the mean and median and averaging them. I wonder if this would work.*) - In our conversation today though, Paul had me questioning if this was more of a “closed question.” I wonder if we could make it more open-ended.
**Could we have let students choose numbers to use? Could we have encouraged students to create their own mean, median, and mode meaningful problems to share to prove that they really understand these concepts? Could we have gotten students to create a situation where mean would be better than median, and vice versa? Could we have extended the application component (be it through chatroom discussion or video conferencing)? How could we make this work, and should we make this change?** - I will say this:
*I’ve used Today’sMeet for many different activities in the past (usually Language ones such as the ones that Paul suggested), and I really like the idea of using it in Math.*This activity got students thinking and communicating about math. They did so with an authentic audience, and by far, this is what my students appreciated the most about this activity. They love collaborating with another class and sharing their learning, but in such an engaging way! So I think that I will use this tool again for math, but maybe with an even more open-ended problem.**What do you think?**

Now comes my biggest personal reflection from today: *I’m glad that this was an engaging activity, but I want to be more than “engaging.” *There are many ways to engage students: *often if you make learning fun, students will be engaged*. I want it ALL though: *I want the engagement, and possibly even more so, I want the learning. ***What are your thoughts on today’s activity? How can we make it better? **Here’s to trying again!

Aviva

Here’s a conversation that I had on Twitter about this post. I really like this new option. What do others think?

Hi Aviva

As I have been observing my teacher candidates I have seen several lessons dealing with median, mean and mode and what I think is missing is real world uses for the concepts. They understand better when they need to use the concepts to deal with a problem they can relate to. One student asked “why do I need to know this?” If you can challenge students with meanful problems there is more engagement. One teacher candidate had students collect their own data after they had listed possible data sources & then use it to find the median , mode & mean. Next each group will present their findings. It was great to watch the process in action.

Thanks for the comment, Carol! I agree with you about this, and in fact, did a lot of reflecting on this last week based on feedback from a colleague. I thought that today’s question showed the real-world connection. Doesn’t it? I was actually impressed with the number of students that started asking about & sharing other real-world uses for mean, median, & mode in the Today’sMeet Room. In this type of collaborative problem solving environment, how could we have emphasized these real world connections more? Thanks Carol!

Aviva

Congratulations on taking a risk and joining your classes together. The question was posed after you had done some work on mean, median and mode. I feel the question was a good consolidation question that provided students an opportunity to consolidate their thinking and justify their opinion. The question wasn’t about crunching numbers. It was about justifying the purpose of using mode, median or mean. It was open ended in a sense that it welcomed all ideas but provided a context for students to give their reasoning behind their thinking. Today’s meet provides a transcript of their thinking and their opinions. What a great piece of assessment to use. As an adult it actually put purpose behind the math terms mean, median and mode for me.

Celebrate your successes and plan out next steps. This was a huge step forward in collaboration between boards. Bravo on taking a risk. Your students need to see you taking risks too.

Angie

Thanks for the comment, Angie! It was actually interesting that you mentioned the assessment data, as I realized just how much this provided last night as I put the transcript into a GoogleDoc. I saw who understood the concepts, who still had some misunderstandings, and who can calculate the mean and median, but don’t understand the purpose of each. Even though we’re officially done the unit now, I can still go back and work 1:1 or in small groups with students that are still confused.

I was also able to question the students on their thinking as their posts appeared. This helped me see why students did what they did and if they understood their reasons. Working with Colin was great, as if I missed an interesting post, he got it, and I could benefit from his questions too (and vice versa). This speaks to the power of having two teachers in the room.

Now all of that being said, reflecting and looking at ways to improve for the next time is a good thing, and I really appreciate my principal for jump starting that reflection process for me. Colin and I have already discussed other options, and I hope we can do this again! Thanks Angie for pushing me into taking this risk: it was a great experience!

Aviva