Communicating Thinking In Math
Exploring the Impact of Rich Tasks and Number Talks
Collaborative Inquiry at Elmcrest Public School - The SWST Initiative
As part of the Student Work Study Teacher Initiative in Peel, Elmcrest Public School in Mississauga was selected to work as part of the collaborative model. Teachers are invited to connect with the SWST teacher and conduct a Collaborative Inquiry that will allow the SWST and the teachers to co-plan, co-learn and co-debrief in order to better understand student thinking and have a positive impact on student learning.
What is the SWST Initiative? (Student Work Study Teacher)
As part of the Student Work Study Teacher Initiative in Peel Elmcrest Public School in Brampton was selected to work as part of the collaborative model. Teachers are invited to connect with the SWST teacher and conduct a Collaborative Inquiry that will allow the SWST and the teachers to co-plan, co-learn and co-debrief in order to better understand student thinking and have a positive impact on student learning.
Inquiry Details:
·SWST in classroom 2 days/week
·Collect student work
·Triangulate data-observation,conversation and products
·Observe and share findings
Student Selection:
· Collaborative process with host teacher
· "Students of mystery"
· Students working through level 2
· 2-3 students per host teacher
·Engage in collaborative inquiry to learn more about your students thinking
.Build trusting relationships that are open to wonderings
· Receive release time to co-plan, co- analyze, co- debrief and discuss student work
· Gain instructional resources for your school
Welcome to Elmcrest Public School
Introduction
September 2015 was an atypical start to the learning year. In Ontario, teachers were engaged in job action that affected the work and actions of elementary teachers. This job action also had a large impact of the role of the SWST in the Peel District School Board. This September also brought about large changes in staffing with reorganization process that affected many teachers and students across the board.
During this time I began my work at Elmcrest Public School in Mississauga. I was invited into the learning environments of a Kindergarten classroom, a grade 1, a 1/2 and a 4/5 classroom. I worked with small groups of students and supported the teacher in the classroom. I was able to establish relationships with many of the teachers. As the job action settled and word spread I had the opportunity to work in several classrooms. Many of the teachers at Elmcrest had done some work on using Number Talks in their classrooms. Their school success goal includes theory of action with a focus on cultivating a growth mindset towards numeracy, the use of rich tasks and making problem solving strategies visible.
As the job action settled the SWST initiative began to unfold focused in a kindergarten, a grade 1 and a 4/5 classroom. In all three spaces we began with a lines of developing math talk and communication. This inquiry supported the school success goal and was based on student need.
In the grade 1 class I worked mostly with math and supporting students in sharing and developing their mathematical thinking. The grade one classroom had many math routines in place that encouraged math talk. The teacher began to observe that students required additional support when sharing their thinking in writing and practicing their skills.
In the Kindergarten and 4/5 class we began to focus in on collaboration and group work norms as we explored math talk.
Visible Thinking Routines with Teachers Support The Development of Emerging Themes
Visible Thinking Routines With Teachers
Although it is becoming more common place for teachers to use visible thinking routines with students the use of these routines for teacher thinking and collaboration seems to be effective practice.
When meeting with teachers to review our documentation and generate a Theory of Action we used a See-Think-Wonder Routine made our thinking visible and served to frame our conversations around student work. This routine was very valuable as it helped us to generate rich discussions that were focused on observable behaviours in student work and allowed us to challenge some of our bias and assumptions as we explored our "Thinking" and questioned the student evidence that may or may not support theses ideas. Out of these discussions we genereated emergent themes to explore in each classroom space. This routine created a culture of thinking and collaboration as we began our work.
Emerging Themes
We met to reflect on the documentation and reflect on what practices were effective in each learning space and what factors seemed to hold learners back. A common theme emerged throughout the grade levels that students were unable to clearly share their thinking. There seemed to be many factors that were limiting student learning. In each space teachers wanted to hear more evidence of understanding and increase students use of math language. Teachers wanted to see an increase in student engagement and find ways to have all students participate in learning.
We wondered if increasing students ability to share their thinking would result in them having a deeper level of conceptual understanding.
All teachers at Elmcrest had some experience starting to implement Number Talks as a strategy to improve numeracy. We decided that focus on the regular use of Number Talks was one strategy to investigate. We also wanted to find ways to implement rich open tasks that would encourage problem solving and critical thinking in order to encourage conversations between students and their peers as well as students and their teachers. Creating an environment where these rich open conversations could take place was the first step.
In all spaces for different reasons there was a need to focus on the climate for learning. We decided to focus on co-constructing criteria and classroom norms. We began to explore and learning about The use of talk moves and enrich student learning.
Brainstorming Success Criteria For Group Work
Co-Constructed Success Criteria for Group Work
Learning Goals and Success Criteria in Content Areas
Intentional Talk by Elham Kazemi and Allison Hintz
This text provided a framework for sharing mathematical thinking through rich discussions. The text suggests methods for creating an effective environment for Open Strategy Sharing. The resource and how to use Talk Moves to support classroom discussions and a culture of thinking and problem solving.
Math Expressions by Dr. Cathy Marks Krpan
"Developing Student Thinking and Problem Solving Through Communication"
This text explores developing a culture of Mathematical Expression and Collaboration and Inquiry through the lens of effective communication.
Mindset By Carol S. Dweck, Ph.D.
In Kindergarten We Focused on Cooperative Games To Enhance Climate For Learning
Collaboration - Working Together
In order to support the development of group work skills and scaffold the transition from parallel play to interactive play, students engaged in collaborative games. Students worked in small groups, sometimes teachers, DECE's or the SWST joined the groups to model conversations and sharing. We monitored changes in conversations and interactive play and strategically planned math games and cooperative play activities to encourage taking of turns, speaking and listening to each other and problem solving.
A Focus on Friendship - Valuing our Classmates
Equity and Inclusion
Student Voice - Math Talk in Kindergarten
Primary Classes Focused on Climate For Learning and Fostering Positive Mathematical Mindsets
Positive Math Mindset- Math Games and Thinking Tasks
We wanted math to involve thinking, to be hands on and fun, a series of rich open tasks that promote thinking and allow student the opportunity to practice important skills and make deep connections.
When using Open Tasks, "there are many ways to approach the task, and there is no single correct solution. All students can provide a solution relevant to their personal mathematics knowledge and experience and fully participate in a classroom discussion."(Capacity Building Series:Differentiating Mathematics Instruction, Sept, 2008)
Teachers co-planned rich learning games to encourage student conversations and learning. We intentionally focused on games and activities that would encourage turn taking and math conversation. Some tasks were designed to have, and multiple solutions or representation in multiple forms. (Positive Norms to encourage in Math Class by: Jo Boaler)
By "seeing the value of peer interaction and providing opportunities for students to work together in various types of groupings so they can explore a common interest, share perspectives and build on each other's learning" (Capacity Building Series: Student Voice: Transforming Relationships,2013)
Using Drama and Literature to Connect to Math
When reflecting on student need the teacher identified writing as an area of need in both language and mathematics. WE wondered what would happen if we really focused on linking writing, math, drama and literature for students.
"Teachers who include writing experiences in their classrooms set the stage for active problem solving, invention and discovery, increased reading and improved content learning." (Dempsey, Kuhn, and Martindill , 2009)
Connecting reading writing and drama to mathematics became part of our learning goals.
In grade one we co-planned activities to engage students in dramatic experiences to increase student engagement and make meaningful connections to mathematical concepts. Evidence suggests that using Drama is an effective way to engage students in mathematical learning. Gerofsky explores Heathcote's suggestion that, "using whole group improvisation drama in mathematics education engages students through immersive emotional and contextual modes of understanding."
At Great Hockham's school in Norfork, UK, drama is having a positive impact on learning in mathematics. At Elmcrest students acted out their number stories when creating addition sentences and developing word problems. When learning about money student both and sold items from one another. The use of drama as a tool for creating a positive climate for learning and fostering rich learning should be further investigated.
It seemed that connecting mathematics to literature and drama increased student engagement and student's conceptual understanding of mathematical concepts. We focused on literature that connected to mathematical concepts and used drama to encourage students to interact with their math ideas in a meaningful way.
Math All Around Us - A Focus On Inclusion
In the fall our focus was to create an inclusive learning environment connects learners to the task and increases student engagement. We wanted all learners to see themselves as mathematicians. The teacher used a photograph to lead a math discussion with the prompt, "What math do you see?" Students shared their thinking about mathematical ideas, broadened their ideas of what math is, and saw math in the world around them. Students were able to connect to math in their environment. By using photographs from their own environment every student was able to find an entry point and engage in the math talk. Following principals of Intentional Talk (Kazemi & Hintz) and helping students orient themselves to mathematical ideas and see that all ideas are valued set the stage for deepening math talk and prepared students to engage in open strategy sharing throughout the school year.
Pedological Documentation To Support Student Learning When Students Participate In Documenting Their Own Learning
“We document the learning journey through student eyes,” reports another educator participating in an Ontario collaborative inquiry. When students are active participants in the documentation, they come to learn more about their own thinking"(Capacity Building Series: Pedalogical Documentation Revisited,2015)
Students who engaged in documentation of their own learning showed strong student engagement and an ability to explain their thinking and articulate information about their work.
Student Pedalogical Documentation In Math
Student Pedological Documentation In Language
Students Using Technology to Capture and Share Thinking and Research Information
Junior Climate for Learning
Talk Moves - Creating a Positive and Respectful Learning Envirnment
An Early Math Conversation During Group Work
Emerging Use Of Talk Moves and Thinking Strategies
Students Supporting Each Others Thinking
Co-Teaching - We Are All Learners
We are all teachers and we are all learners. Co-learning was at the heart of every lesson. Teachers and students all share the role of teacher and learner. We all co-constructed knowledge. Each person in the room had valuable ideas to contribute to the learning. Students shared ideas and strategies and even named them after each other. On a test one student wrote, I used "Alex's strategy"; the students owned the math.
Number Talks - Everyones Ideas Are Valuable
Number Talks had a large impact on student engagement, creativity and problem solving. Students stated that seeing each others strategies helped them learn. As a SWST I knew we had something important happening when the teacher was emailing me at 11 at night to share pictures and conversations from the days Number Talk and when I arrived in school students would great me with excited chatter asking if I could come and watch them engage in a Number Talk. There was exciting learning taking place.
When Students Take The Lead
There was a pivotal shift in the classroom experience in our grade 4/5 class. Students who were vocal about not wanting to be in the class, not wanting to participate in math began to raise their hands. They contributed ideas and strategies to the learning and saw their ideas valued. Then, they started asking questions!
It seemed that when the teacher turned the tables and used their questions and their learning needs to guide her teaching, student learning was enhanced. The SWS and the teacher began intentionally listening for the students questions and wonderings.
The questions we heard BECAME the classroom learning.
We posed provocations such as "What happens when you add and even and an even number?" Then students started asking, "What happens if we add an odd and an odd number?" We tracked these questions and monitored group learning. The students were engaged in the work as it was their work. Our EA in the room often commented on the richness of our back and forth of the co-learning environment. One day her words ended up being the provocation of student learning. Students were curious and confident to help her understand her question.
There was a positive impact to the asset based approach. There was a strong elements of equity and inclusion in the classroom as all students could see themselves in the work they were engaged in. All questions were valued and explored, the work was rich and deep. Grade four and five students were engaged in critical thinking and problem solving, they grappled with ideas around equivalency of decimals and fractions, and their relationship to whole numbers. A passion for mathematical learning had been fostered. Learning math had become a passion, a challenge, understanding became the goal, something students engaged in and were not fearful of.
"I am not afraid of subtraction anymore." (Grade 5 student)
Open Number Line Became the Tool
When collaborating and reflecting on the documentation of student learning we still noted a few students were less involved in the discussions or were "looking around" rather than fully engaged during parts of the number talk. Students who were strong orally and verbally seemed to be improving in their comprehension and their communication of mathematical ideas. Not all students showed this improvement. When thinking about Differentiated Instruction and ways we could teach to student Multiple Intelligences (Gardner) we decided to try engaging students in additional ways.
Students had been involved in co-learning with the teachers ways to use an open number line to number talks. We decided to use white boards to have students work on their number line as we were discussing. Students used these open number lines in Number Talks at first as we learned how to represent our thinking on an open number line and an array. The transfer of this tool was far beyond our expectations. Students loved them and really felt they were able to use them as a tool for problem solving.
Learning Together Using Open Number Lines
Students Using Open Number Lines as A Learning Tool
Early Learning With "Number Lines"
Positive Impact on Teaching and Learning
The teacher had several unanticipated and positive results! Although our intention to increase student engagement was met, we found:
1) Increased confidence in students ability to communicate their thinking and engage in math discussions
We also found that:
2) Students began to use talk moves often in group work and classroom discussions. We even heard these "moves" sometimes in other subjects or non-academic conversations such as problem solving a playground issue.
3) The teachers experienced increased assessment for learning, they had visual access to student understanding and student misconceptions. This detailed look into student learning was regular and accessible. One teacher specifically stated that when using open number lines she had increased access to understanding of student thinking and gaps in their understanding that improved her ability to teach to their needs
4) Increased levels of participation and understanding from some students with special learning needs, increased access for all students
5) We observed an increased use of open number lines in Number Talks, we also noticed a transfer of this tool into group work and independent work when problem solving. Students were using the open number line as a tool to solve problems not just a tool for showing thinking.
One Grade 5 student strongly expressed his fear of subtraction and math in general in class regularly. One day during a math talk he put his hand up and said, "I am not afraid of subtraction anymore...I had to solve it and I decided to use a friendly number...it helped me to solve it on a number line" (Grade 5 Student, Elmcrest)
When it came to learning around fractions, decimals and equivalency the teacher could easily see on student number line the depth of student understanding and teach to student misconceptions around fractions. She was able to group students easily and flexibly based on their learning needs and teach to their gaps. All students demonstrated an increased understanding about fractions as well as a stronger sense of numbers and their connection by working with decimals and fractions together on the open number line.
Meeting Students Learning Needs
In the grade 4/5 Classroom we have several students with learning needs. One student is specifically on an IEP and does not often verbally interact during Number Talks. The second day that we pulled out he white boards in our math discussion and we asked students to make an open number line. We were about to engage in a task where students placed fractions on a number line, as well as decimals. (A wonderful way to see their understanding of proportional reasoning and equivalency)
On this day Student A joined us on the carpet. He sat next to a friend and started to draw on his board. When he turned and smiled and held his board proudly. He was able to engage in the task at his own level, he was able to draw the line an place numbers on the line, he was using the same tools and the same type of activity as the rest of the class. He placed the numbers 1-10 while most students placed fractions and decimals. He was smiling, participating and able to enter the activity. The teacher was able to meet the needs of all learners in a open lesson on white bards by changing the numbers students were using. She was able to then challenge some students who had already grasped the concepts by adding additional numbers for them to work with. Simple yet highly effective Differentiation of Instruction supported a variety of learners needs in one lesson.
What About The Curriculum
One concern of the 4/5 teacher as we moved through the process was her ability to cover the curriculum. Teaching that is directly linked to the students needs and generated out of students own questions and examples is fluid and flexible. The teacher cannot set as a firm plan ahead of time. The learning comes from the students. The teacher knew her curriculum yet allowed the classroom learning to be student driven rather than curriculum driven. I assured her that we would continue to use the curriculum as our guide to ensure we were teaching the correct topics and expectations however it no longer became the center of the daily lesson plan. The center of the daily plan was the student work. The assessment for learning, what had they shown the day before? what gaps did we see in their understanding? What questions were they asking? What could they demonstrate well? Could they transfer that skill to another problem? What were they wondering? What did they want to know next?
When the teacher and I sat down and went through the curriculum and "checked' off what we had already covered she was thrilled to see that we had covered all of the expectations we had planned, we noted however the order in which the learning had emerged was different. We had connected things in a meaningful way based on the students. The learning was messy, not linear, yet is was more efficient over the long run because there was a deep student understanding of the relationships between concepts, we noted an emerging number sense in students where items were connected rather than isolated.
The Kindergarten teacher reflected on our conversation and said that in Kindergarten that is the way they plan. Student generated, hands on learning. That they learning experiences are rich and connected to the students.
Jerome Bruner, "introduced the ideas of "readiness for learning" and spiral curriculum. Bruner believed that any subject could be taught at any stage of development in a way that fit the child's cognitive abilities. Spiral curriculum refers to the idea of revisiting basic ideas over and over, building upon them and elaborating to the level of full understanding and mastery.
Our documenatation supports these notions of teaching the curriculum in a spiral so that students interact with curriculum concepts with a spacing effect is far more effective than teaching in a linear way.
Time is always an issue when teachers are planning, although teaching rich problem based lessons that are student based are more time consuming at the beginning, the learning is deep, meaningful and connected so that over a period of months the curriculum actually gets covered in a more efficient yet meaningful way. Rather than simply teaching units in an isolated and unconnected way. Students develop a sense of themselves as mathematicians, problems solvers, they became able to work with math concepts rather than afraid of math.
Keep Calm and SWS On - The Impact of Our Work
SWS is a stance on teaching and learning. It is being a reflective practitioner. It is a lens on the way we view the student and the role they have in the learning process. SWS is to look at student work and let the needs of the unit drive your instruction. As SWST we say teaching and learning needs to, "start at the student desk."
We started at Emlcrest with an open stance to learning and will continue to use this lens to enhance student and teacher learning as we move forward from this initiative.
This open to learning stance will continue to promote student driven instruction in their classrooms and pedagogical documentation to enhance their instruction.
Whether it is infiltrating drama and writing into mathematics to support communication in math; Creating an interesting and engaging provocation to help students explore addition and subtraction, or using Talk Moves during Number Talks and Open Number lines in to develop Number Sense and an open growth mindset in mathematics is key to student achievement. We wondered what would happen in a school where these key concepts are introduced at the kindergarten level and carried through to Junior level schooling and beyond.
Teachers involved in the initiative are sorry to see the initiative come to an end. They see great value in having time to co-plan and co-teach to enrich their classroom experiences for both themselves and their students. They will strive to keep the focus of their work student driven and play based, embedded in rich and meaningful activities that allow students to construct their own learning and use this learning to problems solve and communicate effectively. They benefited from the collective culture of our work and seeing the impact of a strategy across the grades supported and influenced their collective teaching. As our SWS work concludes we will strive to continue to work in a state of inquiry that will drive student achievement.
Deborah Cote, B.A., B.Ed - SWST Teacher, 2016
If you are interested in the SWS work conducted by Deborah Cote at Northwood Public School on Communicating Thinking in Math in the fall of 2015 please feel free to explore the Smore that can be found at the following link.
http://learnteachlead.ca/projects/student-work-study-initiative/?pcat=999&sess=2
For further information on either of these pieces of work please feel free to contact me at Deborah.Cote@peelsb.com.