### I. General Information

**School Name:** Brooklyn Elementary School

**School District:** SD#71 Comox Valley

**Inquiry Team Members:** Naomi Radawiec: naomi.radawiec@sd71.bc.ca

**Inquiry Team Contact Email:** naomi.radawiec@sd71.bc.ca

### II. Inquiry Project Information

**Type of Inquiry:** NOIIE Case Study

**Grade Levels Addressed Through Inquiry:** Intermediate (4-7)

**Curricular Areas Addressed:** Mathematics / Numeracy

**Focus Addressed:** Core competencies (for example, critical thinking, communication, problem solving), Growth mindset

**In one sentence, what was your focus for the year?** Building a thinking classroom in math by keeping students engaged and thinking, prioritizing core competencies of collaboration and perseverance, and communicating the purpose behind math learning that values thinking rather than mimicking and memorization.

### III. Spirals of Inquiry Details

**Scanning:** We interviewed students about math specifically, and asked the three questions: *What are you learning and why is it important*? *How is it going with your learning*? *Where are you going with your learning*? We noticed that students were able to explain what they were learning and give some examples of areas for improvement. Some seemed to know how they were doing with their math learning, but didn’t know how they knew.

In September, during the scanning phase, we began building a thinking classroom and doing stand up math in groups using vertical whiteboards. Instructions for collaborative thinking tasks are given in 3-5 minutes, with students standing during the instruction. Students were put into random groups of three for stand up math. They engaged in the thinking task as a group, then did “Check your understanding Questions” afterwards.

During the scanning, we noticed students were engaged and loving standup math, but when we talked about it at student-led conferences, some parents were concerned that the math wasn’t challenging enough. A few parents who experienced math instruction in different countries said that the math was “too easy in Canada,” and more challenging where they lived previously.

This got us thinking about how students are communicating their math learning to their parents. Are they understanding the purpose behind HOW we do math and why it’s vastly different from math instruction in many other places (and traditional math instruction that us teachers grew up with). What is considered challenging math? If something is fun and they are in the flow, (and it is a just-right or good-fit challenge) does it feel challenging to them?

During the scanning we were already seeing how stand up math, and building a thinking classroom, was positively impacting student learning in a huge way. But we saw the need to focus more on communicating the WHY behind how we do math…so that students could take ownership and explain how it benefits them in their learning. We wanted them to understand how it is very different from direct teacher instruction which tells them what to do and stops their thinking… which values memorization, involves many worksheets, lots of homework and busy work.

We focused on this First People Principle of Learning: *Learning is holistic, reflexive, reflective, experiential, and relational (focused on connectedness, on reciprocal relationships, and a sense of place)*. This principle is foundational and deeply connected to our math learning journey this year.

The OECD Principles of Learning also helped us reflect on traditional models of math teaching (and how they don’t put learners at the center) and prioritize planning learning tasks keeping in mind what we know about the nature of learning.

**Focus:** We were wondering, do our students see the value in how they are learning math? Do students see thinking as learning when they are doing stand up math in a group? Do they view the thinking classroom style of learning as challenging and worthwhile/effective? We wanted to help students understand and communicate the why (purpose) behind how they are learning and what they are learning (stand-up math, random groupings, math concepts, perseverance & collaboration)?

**Hunch:** Thinking is important for learning, and we’ve noticed that traditional math teaching styles and learning tasks often do not get students engaged in deep thinking. Math instruction is given and then students are asked to mimic what the teacher has already shown them. We began asking ourselves, are we asking students to actually think?

After beginning to shift math learning to engage students in deep thinking, collaboration, and problem solving at the vertical whiteboards (stand-up math), we wondered if we were communicating enough with students the purpose behind this way of learning. We noticed a need to be explicit and open with students about the why behind doing math differently than the paper/pencil/worksheet math they were used to in previous years.

Of all the curricular areas, we feel that in Math it is often the easiest to slip into teaching the way we were taught. It is the hardest subject to be innovative because teachers often feel the most push to “cover” the curriculum and get through all the content. Math is often the subject that students dread, and many students have a fixed mindset about their capabilities in math. Through the research (and our observations) we’ve noticed the need to dramatically shift what math learning looks like. Change and innovation in math teaching is something we’ve been working on steadily over the past few years (and many other educators are doing amazing work in this area). This year we really wanted to focus personally on making big changes in the way we teach math, and prioritize noticing when we fall back into old ways of teaching that don’t ask students to think.

**New Professional Learning:** We learned about how to build a thinking classroom in math specifically by reading Peter Liljedahl’s book “Building Thinking Classrooms in Mathematics K-12.” We found his “Building thinking classrooms framework” and descriptions of optimal teaching practices to be incredibly helpful in making big changes to the way we teach math.

We also used Jo Boaler’s “Positive Math Norms” to establish a growth mindset culture with our community of learners.

**Taking Action:** Instead of using the “I do, we do, you do,” model of teaching math, we decided to dramatically shift our teaching style with the goal of keeping students engaged, thinking, collaborating and communicating in small groups.

Creating class culture and growth mindset:

We showed videos and established our math norms that promote a growth mindset and encourage students to persevere, make mistakes and prioritize deep understanding vs. speed. In the beginning of the year we set up the class culture by offering a variety of highly engaging non-curricular math tasks to solve at the whiteboards.

Random groups of three:

Instead of choosing groups, for the entire year we used either cards or popsicle sticks to randomly select the groups (usually 3 students per group). It took a while for students to get used to these random groupings. We talked about the WHY behind random groups and after a few days students were happy with it and no longer asked to change the groups. As a teacher, I loved using the cards or popsicle sticks to make random groups, and I will never go back to making groups myself again!

Defronting the room:

We kept the desks in pods instead of in rows facing the front of the room. This affected students as they were able to collaborate more and it encouraged us teachers to talk less.

Instruction and how tasks are given:

Instructions for collaborative thinking tasks were given in 3-5 minutes, with students standing during the instruction. Because we had the desks in pods, students were able to stand in the “rainbow zone” in a “u” shape facing the smart board (spaced out, not in one line, students chose where to stand).

Vertical whiteboards – Standup math:

Once students were in random groups at the vertical whiteboards they began working on the thinking task. Non-permanent boards promoted more risk-taking and standing up helped them stay engaged and focused.

Thinking tasks:

We focused on giving tasks that would get students thinking, and keep them engaged for longer periods of time. After setting up the class culture by doing only highly engaging non-curricular tasks, we then started to focus more on infusing curricular content into the tasks.

Answering and asking Keep Thinking questions:

Instead of giving students “stop thinking” questions/answers, our goal was to be intentional about what we were saying to the groups while they were persevering through a challenging task. Were our questions/answers helpful for stretching their thinking? Or, did they stop their thinking by giving them answers? This was not easy to do!

Hints and Extensions – Maintaining Flow:

We tried to keep students in the flow by providing hints if they needed support, and extensions if they needed more of a challenge.

Note taking:

We learned about how traditional styles of note taking (copying things that the teacher has written) are not effective for students actually learning what we intend for them to learn. Many students do not look back on their notes, and the note taking process doesn’t engage them in thinking! So we stopped requiring students to copy any notes, and focused on quick instruction (standing) before stand-up math and learning through thinking tasks, then “check-your understanding” questions. Having students take their own notes (deciding what they will need) is a next step for us and we did not get to that point with our learners this year.

Check-your understanding questions and Assessment of learning:

After solving problems collaboratively at the stand-up whiteboards, students sometimes did “Check your understanding” questions at their desks. We communicated that the purpose of doing this work was to check their understanding of the concepts. By doing this, we could assess who was struggling with certain concepts and needed more direct support while others completed the questions independently. We also assessed where students were at frequently by asking them to place their name magnets on the learning board (learning continuum), showing 1, 2, or 3 with their fingers, doing exit slips, and completing more cumulative “show what you know” assessments.

Self Assessment of Core competencies – Collaboration and Perseverance:

We focused on talking explicitly about and co-creating criteria for two very important competencies in math: collaboration and perseverance. After creating rubrics for each (focusing on one at a time), students were asked to self-assess how they were doing with those competencies. This boosted their ability to collaborate and persevere! Risk-taking is another important math competency (based on the research done by Liljedahl) and our next step is to try to focus on that one more next year.

**Checking:** We asked the four key questions to students at the end of the year. They also reflected on their math learning and on stand-up math. We noticed that they had a good understanding of what they were learning and most knew how they were doing (similar to the scanning phase).

Where we noticed the most change was in students’ perspective on how we learn math. During the scanning phase, students and parents were not aware of the purpose behind stand up math and why it is more effective than traditional approaches. Below are some quotes from students, and you can see from their rich reflections that this style of math learning impacted them positively, and they saw the value in it.

Student Reflections during Checking stage (June):

“I’m doing way better in math. I think it is important because at my old school my teachers had very traditional ways of teaching. They would stand at the front of the class and talk while the students memorized. Here, we have very interactive ways of teaching math, and that has helped a lot.”

“Standup math is more effective because if you just sit there and try to memorize a sheet that the teacher gave you well…it’s boring for most of the people. Why? Because we’re not using our super creative minds and discovering ways to solve our math task or sheet (whatever you want to call it). What I like about standup math is that you get turns and you can see how other people think and how they solve it differently than you.”

“Stand up math has helped me so much this year. It is more effective than memorizing because you are actually interacting with people and thinking for yourself. Stand up math helps develop all four competencies, especially thinking and collaboration. What I like about standup math is that you get to work with other people and solve problems.”

“I think that standup math helps students by keeping them engaged in their math. It helps us get less distracted. It keeps us free thinking and being more open-minded. Standup math helps us think more clearly. I like stand up because it helps my back!”

“I think stand up math helps with learning because we are more focused and engaged when we are standing. It is better than memorizing a bunch of facts and the teachers just telling you the answer. It is good for yourself to figure it out.”

“Stand up math helps by focusing more on what to do and having people to help you. It helps with collaboration.”

“I think standup math has helped me learn better this year. With more than one person in a group, it helps for the others to learn. In the past years, I have just gotten instruction and then we would get a sheet and work on our own.”

“Because you are standing up and your friends are helping you do the math together. Standing helps you listen more because you are doing something instead of sitting down.”

“It’s better to stand up and think than just the teacher giving you the answers. It makes you free think. It’s almost like Minecraft, you have to figure out what to do, you have to think.”

“Stand-up math is good because students are collaborating with one another and using their thinking skills. I like that you work with some of your classmates during stand-up math.”

“…you have to think rather than memorize stuff. Thinking is better. I like stand up math…you get to work in groups. You develop thinking competencies.”

“Standup math is a good way to learn stuff without the teacher saying it. Standup math is good with perseverance. It is active and it can help you in math. Standing is better than sitting at a desk. It’s better than a piece of paper.”

“Stand up math has made math fun and more exciting when you finally solve a problem with your classmates and it’s helped me with being more collaborative and part of a team this year. I think it helps with developing collaboration.”

“Standup math helps me. It is easier to think while you do standup math and it is a good way to do math. It makes you focus more with my math and it makes it a lot easier to do your thinking.”

“Standup math is good because we can learn from each other. It helps improve social skills. It helped me with my collaboration in math.”

“Standing helps you focus more because when you’re sitting you may feel you can just stay there until it’s over.”

“Standup math is better than sitting in a desk and memorizing everything. This way you actually need to think and solve problems, not just have the teacher tell you everything.”

“It will get you thinking and understanding the math better. It is good to learn collaboration.”

Collaboration in math is important because…

“If you don’t collaborate with other people, you won’t develop good social skills and it makes math more fun for the kids.”

“It makes you learn better because you can get help.”

“When we are doing standup math it is important to collaborate with the other classmates.”

“It helps with social skills and their peers may teach them as well.”

“It brings us closer.”

“You can do stuff with other people.”

“It helps you critical think and it helps you do math.”

“If you learn to collaborate in math, you can help others and work out problems in a group.”

“It can help you in the future.”

“It helps you develop team working skills and makes it more fun.”

“It is good to work in partners so you both think and you both learn.”

“It teaches you how to communicate or how to work with other people to build your communicating strength.”

“We can learn from each other.”

“Math in real life is going to be with a lot of people.”

“If there’s something you can’t do in math you can learn from others.”

“You need to work together because if you help someone with math, they will help you back.”

“If you don’t know something that others do you can talk to them to understand.”

“You have to work with others.”

“It is important so you know how to work well with others.”

“If you don’t know how to collaborate it will be hard.”

Perseverance is important in math because…

“You really won’t learn anything without working really hard and keep going even when it is different.”

“You should always try your best, and ask for help when you need it. Persevere. It’s important because you learn more when you do.”

“It is important to persevere no matter how hard the math question is.”

“If you don’t persevere then you might not learn as much.”

“You don’t give up and you keep working when it’s hard.”

“If you give up you stop trying and you won’t know it because you stopped doing it.”

“You don’t give up. You could talk to your group and think in different ways. You work hard and don’t give up.”

“Learn and actually work on math instead of giving up immediately.”

“Is good for math and not giving up.”

“You can get more accomplished that way.”

“It is important because you need to persevere when you are confused. I use it.”

“It is good not to give up on yourself and to try all the time.”

“Because giving up is not good for your mind and you have to keep learning to get better.”

“If we did not persevere we would not learn anything.”

“You need to persevere in math or else you can’t do it!”

“Even when it gets tough you need to keep going and not give up.”

“You can’t give up in math because if you do you won’t get it done.”

“If something is hard, you can not give up.”

“You have to persevere through the hard stuff.”

“So you don’t give up.”

“If you give up you won’t learn at all.”

**Reflections/Advice:** After reading student reflections on their math learning this year, it is evident that they understand the purpose behind stand-up math! Thinking and collaboration were core themes that emerged from the data. Students seemed very aware of how standup math has helped them learn math this year.

Stand-up math connects in many ways to the OECD principles of learning. Learners are at the center, engaging thinking tasks focus on their cognition and growth, and they are actively engaged in their learning. Students “construct their learning through engagement and active exploration.” Stand-up math is collaborative and connects to OECD principle number two about the social nature of learning and co-operative group work specifically. Stand-up math helps push learners of all abilities because they are learning from and with each other. They are engaged and having fun during stand-up math so they experience more positive emotions. Individual differences are recognized as students with a variety of skills/background knowledge and strengths are put in random groups so that they can learn together. Stand-up math stretches learners as the teacher checks in with groups, providing “keep thinking questions” rather than giving feedback that stops student thinking.

Through this inquiry we learned about the importance of prioritizing building a thinking classroom, and noticing when we might slip into older styles of teaching that we may have grown up with. It is easy to get lost in focusing on the wrong thing in math (covering curricular content) rather than focusing on getting students thinking and engaged. Making changes to the way we do math with our students has not only made the math learning more deep and meaningful for students, but also made it more fun for us as teachers!