I. General Information
School Name: Courtenay Elementary School
School District: SD#71 Comox Valley
Inquiry Team Members: Heidi Jungwirth: Heidi.jungwirth@sd71.bc.ca, Alison Walkley: Alison.walkely@sd71.bc.ca
Inquiry Team Contact Email: heidi.jungwirth@sd71.bc.ca
II. Inquiry Project Information
Type of Inquiry: NOIIE Case Study
Grade Levels Addressed Through Inquiry: Primary (K-3), Intermediate (4-7)
Curricular Areas Addressed: Mathematics / Numeracy
Focus Addressed: Differentiated instruction, First Peoples Principles of Learning, Growth mindset, Indigenous pedagogy, Self-regulation
In one sentence, what was your focus for the year? Our inquiry evolved from focusing on math anxiety in the first year, to focusing on growth mindset in mathematics in the second year.
III. Spirals of Inquiry Details
Scanning: Before you start reading the details of our inquiry, I will explain how we have written it up. Most of the writing comes from my (Heidi, intermediate teacher) perspective. In a few places, Alison (primary teacher) has added her thoughts. Since it might get confusing to know who is talking, I have put either (primary) or (intermediate) in brackets so that you can know whose perspective you are reading.
From our work in the first year, we knew that the children were doing much better. Using the 4 key questions on an ongoing basis develops a climate of retrospection and inquiry in your classroom. This opens up the possibility of non-judgmental conversations about how a child is really doing. When a teacher and a student can sit beside each other and work on a challenge together, it creates a culture of collaboration and shared joy. Interestingly, when we changed our pedagogy to an inquiry-based model, the students took the lead. Differentiation came naturally, as students felt safe in challenging themselves and each other. Students wanted to learn and took joy in (finally) closing the gaps in knowledge that they had struggled with for so long. Our learning journey in mathematics became our story.
Focus: In year 1, this inquiry came about because of my (intermediate teacher) frustration with the lack of math learning going on in my classroom and my inability to do anything about the math anxiety that was prevalent amongst my students. I sought the collaboration of a colleague (primary teacher) who was knowledgeable about math pedagogy. Together we worked on figuring out the reasons that this was happening.
In year 2, we wanted to go deeper and figure out why we had been so successful in the first year, so that we could permanently make changes to our math programs. Sometimes you can be successful and not really know why. It is only by taking the time to reflect and have conversations that you can understand the reasons for the positive changes that have taken place. When we understood why the journey had been so successful, we were able to build on what we had learned in the first year.
Hunch: We had more than a few hunches about why students were flailing in mathematics. A societal norm of believing “I’m just not good at math” was probably the most prevalent. How many people have you encountered that have this belief? Maybe you have it yourself. What we realized in our second year is that the prevalent attitude (perhaps even societal attitude) about mathematics was very fixed. You either were smart at math or not. You either found math easy or you struggled. There was no way to climb out of the pit when you didn’t understand what was going on, so you had better just give up. This alone could explain why so many people just give up.
Until I began this inquiry, I relied a lot on the spiral nature of the mathematics curriculum. If students didn’t understand a concept, then it didn’t really matter because they would review in the next grade. Maybe they would catch on then. In the meantime we needed to move on because there was a lot of material to cover. No wonder there were tears.
My main frustration through all these years of struggling with teaching math was that I knew that students didn’t understand what we were doing, but I didn’t have tools to figure out where their learning deficits lay. I didn’t know what they didn’t know and I didn’t have a way to figure it out.
Having Alison as my inquiry partner was invaluable because she had already figured a bunch of this out. She is an avid reader of research and was familiar with the advances in math pedagogy. She was able to guide me through my frustration and shared ways that she had created an attitude of curiosity towards learning math in her class.
New Professional Learning: The inquiry built on the learning that we had done in the previous year. We continued to use the”First Steps in Mathematics” assessments and learning activities. We continued using the SNAP Assessments (from SD 33). We explored the use of Pedagogical Documentation in Math, which turned our mathematics learning into a story. We explored First People’s Principles of Learning and sought out ways to apply this to mathematics. We partnered with our Indigenous Education department and had a number of “Indigenous Explorations” as part of our math curriculum. We read some professional books and ordered many more! The two books we have found the most helpful so far are: “Mathematical Mindsets” by Jo Boaler and “Teaching Student Centered Mathematics” by John Van de Walle et al.
Less expected and most exciting was the professional learning that we embarked on together to create materials that we couldn’t find. Based on the professional reading we were doing and the assessments we were using, Alison and I created a number of curricular and hands-on materials for the students to use. We used these with our students and revised them as needed.
Taking Action: The most significant action I took (intermediate) this year was putting aside the expected pace and depth of math learning (work quickly through a large number of concepts which only gives time to learn algorithms and develop tricks to get the right answers) and focusing instead on correcting the learning deficits that my students had. I realized that I could use tools (SNAP Assessment, First Steps) to pinpoint what they didn’t know and provide remediation. Time needed to be taken, so that the students could deeply learn.
I think I can confidently say that if a student (early intermediate) is struggling with mathematics, they need remediation in their understanding of number (number sense). It’s a lot like expecting students to read and understand text when they don’t know their phonics. They might struggle along and figure out some things, but there is no deep understanding and no ability to take learning to a higher level. I think that this just might be the cause of math anxiety.
In this inquiry, we were able to find assessments and activities through SNAP and First Steps, but things really took off when we had the confidence to develop our own materials. Alison (primary) had been doing this for years and she used this expertise to expand her materials into the intermediate curriculum. She created a series of booklets based on the SNAP assessment to give students daily practice in working with numbers. I (intermediate) used these for the second half of the school year and the progress that the children made was incredible.
Once again following Alison’s lead, I learned how to create “Class Books” about my class’ math learning. Alison’s class book was so popular, she had to make a second copy so that the children didn’t have to wait so long before they could have another turn. In both classes, the class books were read every day during read-to-self time. This not only turned their math learning into a story, it also (unknowingly to them) provided reinforcement of their math learning.
Alison and I worked together to create a math journal that was used as the main “math book” for the year. We used the math journals for both standard curricular work and for math explorations. Students looked forward to challenging themselves with their math learning, and it was inspiring to see their confidence grow as they worked in their journals.
Once we figured out what the students didn’t know, we were able to create hands-on learning materials for students to use to support their learning. We also created remediation activities that were done with an educational assistant.
This is what Alison (primary) wrote:
Early in the year I used First Steps to assess my students’ understanding of counting principles and subitizing. I used these assessments to inform my teaching around these concepts and to provide individualized support to students who needed it. These assessments allowed me to identify the specific skills or concepts my students needed help with. By addressing these needs early in the year, we were able to come together as a group and make fantastic progress as a class. In the spring my students did the SNAP assessment. They were excited to show what they could do…every student felt confident!
Photo descriptions: (top) student work on fractions in their math journal, (middle) student work doing remediation about number sense, (bottom) a group of students doing work in their math journal about multiplication.
Checking: Before I share this story with you, I think that it is important for you to know that Alison had been teaching math this way for years. Her role in this inquiry (in many ways) was to be a mentor and provocateur. Math learning in her class (primary) has been refined through this inquiry; math learning in my class (intermediate) has undergone a seismic shift.
I can best illustrate the change in my (intermediate) students by giving some examples of what I am seeing. Keep in mind how things used to be in math class. Students would cry. Students would sneak out of class. There was all sorts of negative behaviour. I described teaching math as a nightmare.
This year, students skip down the hallway, spontaneously singing “I love math”. Students beg to stay in at recess and work in their math journals. We have discussions about complex math topics. The math books I purchased for our class library are always being read. Students play math games during free choice time. Math is consistently chosen as a favourite subject (and this is by students who I would consider as struggling).
It is also important to show growth through the use of assessments. At the end of the year, I re-assessed my students using both a SNAP assessment and a First Steps assessment. In my class (intermediate) there was improvement in every student. The most improvement came from the students who struggled the most. In one case, a student went from not being able to name a number (1 234 is one two three four) to being able to name numbers in the ten thousands (12 345 is twelve thousand three hundred forty-five).
In Alison’s (primary) class, students are doing math work way beyond what would be expected at their grade level. There has been a discussion about the differences/similarities between infinity and negative infinity.
Here is what Alison (primary) wrote:
One student who did not yet have one to one correspondence and could only count to 10 at the beginning of the year went on to work with numbers to one hundred. Perhaps more importantly, she moved from needing help to contributing ideas in our class math talks. She often told me how much she loved math and would generate a whole page of math in her journal in the morning.
In the second half of the year, students started the day working in their math journals. They used this time to record their own math ideas, often making patterns in their work. We also spent time sharing these ideas as a class and students were inspired by one another’s work. One student remarked, “I love patterns!” There was a chorus of me too from the nearby students. I love the beauty of numbers, especially the patterns. I’m glad my students got to feel this too.
Our class math books grew to two volumes this year. Documenting our learning in our class math books literally made our learning visible. Students were able to see the connections between the hands on materials and the mathematical numbers and symbols we use to communicate math ideas. They learned to read math and to see how math can be represented in materials, pictures, words, and numbers. Students poured over these books during free time and at read to self. They also enjoyed taking them home to share with their families. These books made a significant impact on student learning.
Reflections/Advice: Alison and I have been working on this inquiry for two years now, and for a lot of the time I (intermediate) was struggling. I described it as swimming around in the mud. Changing the way I taught math was really hard. I made changes before I really understood what I was doing. I trusted Alison and was grateful for her mentorship and expertise, but a lot of the time I really didn’t know what I was doing.
It was part way through the second year that things began to get clear. I had established routines. The materials that we had developed were successful. The students were loving math class.
It was late in the year, when Alison and I were discussing our inquiry that I had one of those moments when everything becomes clear. I realized that this whole inquiry was about changing mindset.
I wrote earlier about changing my mindset as a teacher. Through this inquiry, I realized that math anxiety was caused by the students having a fixed mindset about learning math. It makes sense. If a student doesn’t have a working understanding and confidence about number, then it must seem like math is impossible to learn.
By using math assessments to pinpoint where the deficits lay in the students’ math learning, we were able to use tools and remediation to change those misunderstandings. The students can now see that numbers make sense. I believe that this has been the reason for the dramatic shift in the students’ attitude and accomplishment in math learning.
Here is what Alison (primary) wrote:
This year I felt more confident using hands on materials, math journals, math talks, and our class books. I can see how these elements weave together to support students in developing competencies in math … and how they can support students in coming together in a community where all students feel confident as mathematicians.
Advice:
The second part of this section is called advice, so here it goes: If you are struggling with teaching math (or anything, really) it takes courage to seek out the answers to why things are not going well. It took me years to get to the point where I was willing to tackle the challenge of math anxiety, and I still can’t believe the change I have seen in my students, or how quickly it has come about. I had to lean into the discomfort of changing the way I was doing things.
I sought out the help and mentorship of someone who was doing things well. I spent more than a year “swimming around in the mud” before things became clear. In the end, I had to trust my inquiry partner, Alison, and I had to trust in the process of inquiry.
Interestingly, both Alison and I have seen the benefit of working with an inquiry partner that teaches at a different grade level. For Alison, (primary) it was beneficial to see where the children were headed with her learning, and it helped her to see the reasons for what she was doing. For me (intermediate) it was beneficial to learn about the pedagogy of early learning.
Most importantly, perhaps, there was safety in learning with a teacher who wasn’t working at the same grade level. There is sometimes the temptation to compare how your class is doing against the other class when you are working with a same grade teacher. Working with a teacher from a different grade level removes this challenge.