Expect The Unexpected

Today was the first day of “Math Is Everywhere” Week. We want students to realize the value in math, and we want them to engage in meaningful discussions about math as well. Today, students were asked to bring in a “book that has to do with any topic in math.”

When I saw the focus for today, I thought that students would bring in books like, Mouse Shapes, where math is embedded as part of the story. With this in mind, I was completely surprised by what I saw. Almost all of the students brought in math workbooks. I hadn’t considered this possibility at all.

This new focus on problem solving though has taught me to “expect the unexpected.” There is not one right answer. Meet students where they’re at and move them forwards. So for our Sharing Time today, students shared the books that they brought in and how these books relate to math:

Then I thought of my overall goal. I want students to see that math does not need to be taught in isolation. I want them to see that they can look and find math in everything that they do.  Here’s my plan then: tomorrow, I’m going to have them pick storybooks and look for “math” in these books. What will they see? Will they be able to apply what we’ve learned in class to what they see in these storybooks? Can they create their own math problems and share their own math stories? I’m interested to see what happens!

What would you do given this same situation? I’d love to hear your ideas as well!

Aviva

When Incredible Happens …

On Tuesday night, I blogged about a math activity that we did in class. Kelly McCrory, our fantastic math facilitator, responded to my blog post with this question:

Her comment got me thinking, and so on Wednesday morning, I created this new math problem that we did in class today:

This math problem addressed Kelly’s question, and I was very interested to see what the children did and if they could figure it out.

Students worked in partners with a bag of shapes (more than what they needed) and the math question. Just like with our previous problem, they could show their thinking on a white board, on the Livescribe Pens, or on various screencasting iPad apps.

When I started walking around talking to the groups of children, I noticed what I would have expected to see. Most of the students looked at the hexagon and the trapezoids, and figured out how to put two trapezoids together to make a hexagon. The majority of groups had more difficulty with the rhombuses. Some groups put the rhombuses down beside the hexagon and tried to move them around to create a hexagon. Other groups tried sticking the rhombuses underneath the hexagon until they made a hexagon shape of their own. Still other groups figured out to put the rhombuses on top of the hexagon.

There was one group that finished quicker than the other ones. I went to talk to this partner group, and I asked them, can you mix the rhombuses and the trapezoids to make a hexagon? How do you know? I walked away, and let them play. A few minutes later it was time to tidy up and discuss our findings, and that’s when this partner group came running up to me so excited: “Look, Miss Dunsiger! Look what we did!”

I was amazed! I created this problem, and I was sure that I knew the solutions, but this group did something that I didn’t expect. This group did something that I’m not even sure I could recreate. Wow! This is when “incredible” happens …

All of a sudden, our “reflect and connect” conversation changed. Now we looked at what this group created, and we discussed if this hexagon could replace the one in our picture and why. Below is a pencast of our conversation:

Now I know that I led the students to come to this conclusion. What could I have done differently, but still ended with the same result? The thinking that the children share is great, and I’m glad that they explain why they changed their mind, but I wish that I didn’t sound so “leading.” I’d love to hear some suggestions about changes that I could make!

While I know that I wasn’t perfect here, seeing a student push my thinking gave me an even better appreciation for the math problem solving process. I was genuinely thrilled when I saw this photograph, and I hope that I’ll continue to have more amazing problem solving moments like I had today. When have students surprised you by their answers? I’d love to hear your stories too!

Aviva

How Focusing On Math Has Made Me A Better Teacher

As many of you know, my goal for my Annual Learning Plan was to improve my math instruction by incorporating more problem-solving into math. For a while now, I’ve been sharing my learning journey as I try, and fail, and try again with this goal of mine. While I continue to notice my own areas of weakness, I also know that my students are becoming much better math problem-solvers. They are really explaining their thinking in math, and not just focusing on the answer, but focusing on how they know the answer. All of my students are showing progress!

What I especially love though are the unexpected surprises: I’m getting better at asking questions in all areas of the curriculum and the students are getting better at answering them. I especially noticed this last week during various science activities. Last week, the Grade 2 students had to make a toy that floated on water. The student in the video below was one of the first ones done, and while his toy floated, it also turned over. The toy still met the project requirements, but instead of just being happy enough with this, I got this student to rethink his design, make changes to the toy, and eventually get it to float upright.

In the past, my focus was always on the final product: did the students accomplish what was expected or did they not? This new math focus though has made me realize the value of the process over the product. I’ve taken the time to stop, to question students, to encourage them to think, create, try, and fail, and then, instead of becoming frustrated, to try again. My Grade 1 and 2 students are doing more than I ever thought possible, and the language that they’re using as they show their thinking, continues to amaze me.

I’m by no means perfect. I still need to give more wait time. I still need to sometimes question less, and let students figure out more on their own. But I realize this now, and I’m more cognizant of what I say and how I say it. A special thank you to our incredible math facilitator, Kelly McCrory, that continues to push my thinking every day with her questions, comments, and suggestions. Thanks to you, I’m not just becoming a better math teacher, but a better teacher!

How has focusing on math in your classroom made you a better teacher? I’d love to hear your stories too!

Aviva

Encouraging Thinking

The more that I focus on math problem solving in class, the more that I realize that it’s not just about improving math skills, but it’s also about improving thinking skills. Today was a great example of this! In class today, I posed the following question to the students:

Students worked in partners to solve this problem. Some students used the Livescribe Pen and various iPad apps to record their thinking, some students used whiteboards to write down their thoughts, and some students used a combination of the two.

(The photo quality here is not as clear, but it talks about the fact that the rectangle is the best choice because it has four sides and so does the square. It also said that the diamond is not the best choice because it would leave little spaces.)

This activity was really not about the answer. It was about the rationale for the answer. Just listening to the students discussing their answers were incredible. They were using math language, and in a really meaningful context too. Not only were they justifying their decisions, but they were also explaining why the other choices were not good ones. Students were being critical thinkers, and as teachers, isn’t this what we want most out of our students?

During the reflect and connect portion of the problem-solving process, students shared their great ideas too. Here’s a Livescribe pencast of their thinking:

While most students shared that a rectangle would be the best choice, one student (Dana) said that she would pick a diamond. This is where I got stuck. This student had some great thinking, but I wanted her to see the importance of all shapes going in the same direction, as well as the value of not having gaps in between the shapes. I was trying to come up with the right questions to ask, but I felt like I was too leading.

What questions would you have asked? I’d love your thoughts here. If I’m encouraging my students to think then I want to be thinking too. As for this math problem, my students would love to hear what your students think the three Grade 1 teachers should do. What would they recommend and why? Hopefully we can all learn some math together!

Aviva

A 21st Century Fluencies Activity That Does Not Involve Technology

The Hamilton-Wentworth District School Board does a fantastic job of addressing the 21st Century Fluencies without making these fluencies all about technology. While I’m fortunate enough to have access to technology in the classroom, there’s also a lot of value in embedding these five fluencies (solution fluency, information fluency, creative fluency, media fluency, and collaboration fluency) into the classroom program without the use of technology. Watching my students at work today reminded me of this.

For Science today, the Grade 1 students were challenged to make a toy that moves using an energy source of their choice, and the Grade 2 students were challenged to make a toy that floats on water. For the past couple of weeks, students have been bringing in recyclable materials to use to create their toy. On Tuesday, they planned what they were going to do, reflecting on why they thought that their plan would work.

Today was building day! Throughout the process, students were encouraged to think, reflect, and even change their plan, but they also needed to make note of why they chose to do so.

Wow! For this activity, students didn’t touch a computer, an iPad, an iPod Touch, or a Livescribe Pen, but what they learned and shared here was incredible. (Check out the student blogs later for videos of the different “toy tests” from today.) With just the use of recyclable materials, scissors, tape, and glue, we addressed all five fluencies through this single activity.

1) Students had to solve the problem of making a toy that would work, and then adjust their plans when the toy didn’t work (solution fluency).

2) Students had to apply the information that they learned about energy (Grade 1) and liquids and solids (Grade 2), and then decide how to use this information to meet today’s challenge (information fluency).

3) Students created three-dimensional works of art in the toys that they made today (creative fluency).

4) Students recorded what they learned throughout the process and then shared their recordings with a larger audience through their blogs (media fluency).

5) Students collaborated with each other to design their toys and solve problems throughout the process (collaboration fluency).

The best part was listening to the student reflections at the end of the activity. All of the children did a great job of explaining why they did what they did. Listening to their explanations also tell me how much they understand about energy, liquids, and solids. (I particularly love the discussion that begins at 7 minutes and 2 seconds when my students talk about the value of collaboration. Priceless!)

Have you ever done an activity before that involved the use of 21st century fluencies without the use of technology? What were the results? I’d love to hear what you have to share!

Aviva