Responsive Math @DixiePSchool
Opening Up Possibilities to Make Meaning in Math
Part 3
A Collaborative Inquiry by Educators at Dixie Public School, Peel District School Board
The Student Work Study Initiative provides an opportunity for documentation of the Collaborative Inquiry to take place.
Theory of Action
If we use a balance of purposeful, focused activities in response to student need then students’ conceptual knowledge of number sense will be deepened, student engagement and communication of their thinking will be enhanced.
Working theories of action continually evolve to respond to the strengths and needs of the students.
What Can We Learn From Number Talks?
We continued our work with Number Talks within a grade three classroom. Other grade levels from Kindergarten to grade 5 began to also use Number Talks within their classrooms. The documentation below, taken from a grade three classroom, can be interpreted as students actively making meaning of mathematics.
Students Responding to Each Other
Students Changing Their Thinking
Students Demonstrating Reasoning
Students Discussing Efficiency
We explored having students think about the efficiency of the strategies that they were looking at on the white board. Once students held a variety of strategies and had begun to pay attention and think critically about each other's thinking, we built in the concept of efficiency. In the transcript, two students were talking to each other in a sidebar conversation and comparing the two solutions which prompted a whole group discussion on efficiency. Students shared what they thought the word efficient meant.
What Can We Learn When We Experiment with Number Talks?
We decided to have two small group work periods. Students could be in like groups for number talks (where they worked on similar skills) and in mixed groups where students could draw on each other's strengths for small group word problem work. We were fortunate to have the SWST, CT and In School Support Teacher to facilitate groups. Our administrator also participated in our co- learning journey and led a group. Initially we began our word problem groups with a teacher present and then we gradually had the students work in small groups on their own.
During the small group structure, the SWST observed that students were participating with each other. Students were talking to each other to ask for help and to ask why or how a student had arrived at a certain point.
When students had the opportunity to work with each other in small groups, they used each other as resources in order to make meaning of the math at hand. In the last photo pictured above these two students are puzzling over each other's solutions. They then returned to look at their own work. It can be interpreted that they are looking at each other and really trying to figure out what was happening with their math work.
Using small groups in two different ways was an experiment with the structures we used to teach math in the classroom. We were exploring the answer to the question, "What happens when...?" in response to student learning.
What Can We Learn When The Entire School Talks About the Same Thing?
This organizational structure of division meetings and whole school meeting enabled educators to access multiple perspectives and dialogue about student learning. When teachers who were starting with number talks wondered about differentiation, the grade 3 teacher was able to share her small group format. In turn the grade 3 teacher was intrigued by the grade 1 teacher who had just started with student led number talks. Kindergarten teachers shared how they had incorporated Number Talks into their loose parts inquiry centres. Modifications were suggested for the students in the JGLD classroom who require memory aids. Colleagues were able to share how they were collecting and using assessment from the Number Talks to forward plan instruction.
Educators were able to observe and discuss differing strategies for annotating number talks. Our thinking was pushed when we debated whether students should annotate their own explanations. Having the opportunity for professional dialogue that was grounded in our own student learning felt relevant and motivating.
What Can We Learn When Students Use Personalized Math Tool Kits?
Additionally students were given time to independently choose and create mathematical activities with their tool kits. This structure of individualized tool kits was then also used in the grade two classrooms. Students were able to use their math tool kits with their math partners. Classroom teachers reported that having their own tool kits encouraged the students to use and be fluent with using the mathematical thinking tools. Students were managing their own learning and would choose to work on a particular skill such as skip counting repeatedly. We wondered whether this was a step in mastery learning. The tool kit has also been incorporated into small group work where students can work on a math task of their choice.
The use of the individual math tool kit has been another structure that allows us to answer the question "What happens when..? and observe that students when given the opportunity are capable of thinking about and working through their own ways of making meaning of mathematical concepts and ideas.
What Can We Learn When We Focus on Deepening Conceptual Understanding?
We had learned about the power of the number line in part 2 of our inquiry and the use of the number line spread in the school. In the grade two classroom, classroom teachers introduced the use of the number line and connected it to the calendar routine. Classroom teachers cut apart the calendar in a number line and used a number sense routine to have students determine elapsed time between dates. Students in the grade three used a vertical number line during the number routine, Count Around the Circle. Students used the Number Line as a thinking tool to help them work through problems. They began to say they were using the number line in their head.
Classroom teachers used the Contexts for Learning Mathematics Kits. In the Grade 1/2 classroom students used the Rekenrek from their tool kits with their math partners to consolidate their understanding of the relationship between addition and subtraction while playing a math game from Fosnot's Double Decker Bus lesson. In the Grade 3 classroom, students actively constructed the meaning of the symbol for multiplication as they measured the height of buildings in Grocery Stamps and Measuring Strips.
Learning Goals and success criteria were linked to Mathematical ideas. This enabled students to push their own mathematical thinking. In the grade three classroom, students would self-assess their own work by looking at the success criteria.
Key Learnings & Continued Wonderings
Within the grade three classroom, students surveyed each other on their favourite subject and Math was the favourite for many students even over Physical Education. Students would request Number Talks during the day. On the EQAO questionnaire, almost all the students checked that they liked math most of the time in the attitudinal survey. This qualitative evidence can be interpreted to demonstrate the importance of creating a climate that is safe for sharing and risk taking in mathematics. When students are creating and sharing their own ideas within the classroom, they feel part of a knowledge building community.
Likewise a school wide focus on Number Talks led to a knowledge building community for the educators at the school. Educators were able to use and implement a common language for students in terms of numeracy. The conversation included the content of mathematical knowledge.
Pedagogical documentation enables us to see if our intentions match the outcome and continuously respond to student learning.
Collaborative inquiry is based in the belief that teacher efficacy and student efficacy are related and are a critical element when thinking about mathematical instruction.
Classroom teachers strongly believed that they could impact student learning. As culturally responsive educators, we reaffirmed our beliefs that we view "the social identities of students as assets rather than as deficits or limitations".
Visual models and representations are powerful tools for student thinking and learning.
We are wondering if the use of guided math or math workshop will be a beneficial structure for student learning.
Research & Resources
A Student Work Study Collaborative Inquiry 2016
Karen Wright Grade 1 Teacher
Leah Vu Grade 1/2 Teacher
Amy McCaughan, Grade 1/2 Teacher
Suja Zachariah, Grade 3 Teacher
Gillian Read Instructional Coach
Meg Echlin, Principal
Janet D'Silva, Student Work Study Teacher
Twitter: @janetdsilva