###### Mathematics

#### How Does That Help Your Learning?

Who would have known the simple phrase, **“How does that help your learning?”**, would drive the way I viewed the teaching of mathematics? Returning to a classroom position after ten years of supporting teachers in their instruction, I knew that I wanted to do things differently. I knew that I could not or would not teach in what we, in education, call a “traditional way.” I had always been an advocate of teaching through problem solving. I had, for years, also advocated for the use of manipulatives and teaching and practising of strategies in mathematics. Students I worked with in my career were always asked to share their strategies and to connect these strategies to ones that their classmates shared.

The summer prior to my return to a classroom position, I realized though that I wanted my students to reflect on their learning and in order for them to do that, I needed to reflect on my own learning and teaching as well. Upon reflection, I was proud of the instruction that I had given students, but I knew that I needed to do more. I needed the students that I was going to work with to be thinkers, deep thinkers, who regularly reflected on their learning. What I didn’t know was how I was going to do it!

So, when I returned to the classroom that Fall, I added in reflection time to our daily schedule. Without a dedicated time to reflect, students would not get to that next level of learning – metacognition. Developing students’ metacognition needed to be a focus of my math instruction. Students showed that they were really good at sharing “what they had done” but found it difficult to reflect on how what they did helped their learning. Now the challenge was how to develop that? What seemed to “pop” out early in that September was the question – “How does that help your learning?” At the time, I had no idea that this question would foster a love of learning.

*The question, “How does that help your learning?” quickly became a standard in the classroom. This water bottle, with the question screened on it, was a gift from a student. *

It seemed so simple, but it wasn’t! Students didn’t know what to say and as a result there was a lot of silence at first. What I decided to do was model my own metacognition for my students. I often shared with them my own learning from what I did during our learning time. We often also brainstormed for each other what we learned from what we did. Students began to develop skills. They learned to reflect. They learned to challenge the thinking of classmates in appropriate ways, they learned to connect their current learning to determine their future steps in learning. It did not all happen at once and there were many days that I could have given up, but I was determined (some would say stubborn!) to make it work. Did it work for all students? Yes, I believe in various ways, it did. What developed were students questioning/collaborating with other students about their learning and whether the reflection on their learning was deep enough or not. What more could a teacher want?

*Reflection periods were held twice daily. These reflection periods became a part of the daily schedule and students used these boards to identify when the reflection(carpet) time would begin, allowing students the opportunity to begin to think of how they were going to share how the activities or tasks they were working on helped deepen their knowledge. This also helped students work on identifying, writing and showing time in an authentic way. *

Students answered the question, “How does that help your learning?” in different ways. Some shared how it challenged what they had always believed. For example, when students were practising subtraction many believed that you always took the smaller number away from the bigger number. But upon further investigation, realized that this might not always be true. Some students shared that they had more questions about a particular area in mathematics, trying to see if they could generalize patterns, or steps to solve problems. Some students shared that they realized that they still did not understand a particular concept in mathematics that they had been studying. This often led to other students offering to support them in their learning. This reflection time led to deeper understanding of concepts, insight into how I, as their teacher, could further support them in their learning, as well as richer mathematical discussion than just sharing of strategies. It was during this reflection time that I also prompted/questioned, scaffolded, or explicitly shared the mathematical language that would enable them to get to a deeper level of thinking. That simple question, “How does that help your learning?” empowered students to go to that deeper level, to own their learning, and to collaborate with each other in building knowledge.

*Learning from prompts/provocations/tasks often were the topic of the reflection time. Using loose parts, wonderings, and open ended questions allowed students to choose learning appropriate for themselves, but also provided a focus to connect this different learning during the reflection period. *

Students learned, through experience, practice and support, to reflect on their learning. This reflection, coined by the question, “How does that help your learning?”, seemed to drive us to deeper metacognition. I’m sure other questions would have worked as well, but it was amazing to see students questioning others, looking for them to self-reflect and share what learning in “math” they had. They essentially were “noticing and naming” their own learning. Students began to use the terms “noticing and naming” during their own reflection and also while questioning classmates. Often, I would hear them say something like, “You told us what you did, or noticed what you did, but can you name the learning that came from what you did?” This collaboration during reflection helped push the thinking of everyone in the room, including myself! It even led a student to ask me, after a Professional Development day, to name the learning that I had. Wow! I was being held accountable too and I couldn’t have been prouder. This application of knowledge in meaningful ways demonstrates true learning. When we, together, supported the development of metacognition, through reflection, we developed our thinking skills to a whole new level.

*A student created flow chart where the student reflected on her learning. Notice the reflecting reference – “clecting your nolig” (collecting your knowledge) and how it also includes an outcome. *

Including reflection in my mathematics learning time proved to be powerful in so many ways. How do you use reflection in the classroom to develop student thinking? What questions do you use to develop and foster student metacognition? What has been the impact? What is the evidence?

**Amy Zorzetto**has worked for the Hamilton-Wentworth District School Board (HWDSB) for almost 20 years. She has held many positions including classroom teacher (primary, junior and intermediate), Math Facilitator, and Elementary Program Consultant. After being in system roles for almost ten years, she decided to return to the classroom to implement her learning using an inquiry based program, with a focus on empowering students to develop thinking skills through reflection. Her passion is in the teaching and learning of mathematics and you can follow her journey on Twitter with the Twitter handle of @mathymom.

## One Comment

## Ramona Meharg

TY for the share. I have a high school developmental ed class, and we’ve been working hard on this. The best reflection has come out of their passion projects I think because they are so invested in it and have the language they need to talk about it. We’ll keep at it!