Visible Thinking in Math @ BWF
Students Using Purposeful Math Talk at Brian W Fleming P.S.
A collaborative inquiry by the grade three team to explore the use of strategy sharing during math talk at Brian W. Fleming P. S.. Moving students beyond show and tell of math strategies towards a deeper understanding during mathematical discussions was explored.
Theory of Action
If students share, discuss and reflect on math strategies as part of the process when solving word problems then students will be better able to communicate their thinking and more likely to consolidate their learning of mathematical concepts.
Open Vs Closed Questions Explored
Open routed questions were used to enable students to demonstrate their representation in a variety of ways.
Criteria for Math Talk and Math Writing
Dr. Cathy Marks Krpan's indicators for math talk and math writing were use for problem solving.
Co-Constructing Criteria for Solving Word Problems
The students worked together to talk and think about steps to take when working on solving word problems. A list of criteria was constructed.
Direct Instruction
Explicit instruction focused upon the fact that problem solving involves several steps. The process of arriving at the answer was emphasized over determining the correct answer.
Collaboration
Reflection and conversation about observations of students, conversations with students and student work took place amongst teachers. After reading the Hintz article, strategy sharing by students during math talk was explored.
A Focus on Math Strategies
During collaborative reflective time, our focus on math strategies widened. We were able to share teaching strategies in response to student need. For example we discussed the use of the number line as method of representation of student thinking.
Strategy Sharing
Students were encouraged to use their own method of arriving at a solution. They then shared their strategy. All methods were accepted.
Thought Provoking Student Conversation
Students debated whether a cylinder had an edge. Students were justifying their thinking orally. Each student defended their viewpoint allowing students to see that math is not just a right or wrong answer but can be discussed and investigated.
Making Connections
Learning goals of discussions ranged from making connections across mathematical concepts to consolidating math concepts. Here the relationship between time and fractions was examined.
The Solution was Provided
In order to emphasize the process rather than the correct answer, the solution was provided.
Reflecting on Strategies
When students reflect on their own method of arriving at a solution, self-assessment is taking place. Students are in the driver's seat for their learning.
A Variety of Strategies #1
Students wrote blog posts about their strategies enabling them to consolidate their learning .
A Variety of Strategies #2
A Variety of Strategies #3
A Variety of Strategies #4
Student Voice
Listen to student J as he describes the use of strategy sharing in math class and how it impacts his learning in mathematics.
Listen as student A describes why strategy sharing is helpful and math talks are important in primary math class.
The Pedagogy of Listening
"A pedagogy of listening often includes documenting evidence in the various forms that make student thinking visible and provide a record for discussion, reflection and analysis. This process is ongoing and is used to support growth and improvement (Capacity Building Series – Pedagogical Documentation, 2012)." from Student Voice Transforming Relationships Capacity Building Series
Characteristics of Math Talk -Dr. Cathy Bruce
According to Dr. Cathy Bruce, math talk enables students to negotiate meaning and increase depth of understanding. It is characterized by genuine talk, more student talk than teacher talk and a star pattern of student interaction. Click on the links below to view 3 clips well worth watching!
Establishing Norms for Math Talk
"The first presentation is the starting point for a much richer discussion that involves building on, disagreeing, agreeing rather than presentations of discrete information"~Dr. Cathy Bruce
Creating Opportunities for Rich Math Talk is Essential
Opportunities for students to present their thinking in different ways is important. It is also important to emphasize how these different representations are interacting. This is a powerful way to build communication in the math classroom. ~Dr.Cathy Bruce
Key Learnings & Next Steps
- Inquiry is ongoing and iterative. As this inquiry continues to unfold, new learnings emerge and reflection and response to student needs takes place. The inquiry of students mirrors the inquiry of teachers. As students reflect on their learning, teachers also reflect on their learning.
- "If students are given the opportunity to grapple with complex tasks, to observe good models of thinking, reasoning, and to justify their solutions they will develop a view of math as meaningful and as something that they personally can engage with and understand." (Smith, Stein, 2011)
- A mathematical climate that supports focusing on the process of arriving at the solution instead of determining the right answer leads to risk taking on the part of the students.
- When students are sharing their solutions, they are comparing and contrasting.Comparing and contrasting is a way for students to make connections in their learning.
- Connecting the Learning goal to a mathematical concept/idea can help to push the thinking forward and prevent strategy sharing into a show and tell type situation.(Smith, Stein, 2011) chapter 2
- When teachers have conversations about concepts of mathematics in the classroom, students observe the teachers as learners and thinkers. Students are exposed to the value of collaboration and learning in mathematics. The level of discourse in the classroom is equivalent to the level of mathematics discussion.
Research & Resources Used to Support our Inquiry
Contexts for Learning Mathematics Kits -Catherine Twomey Fosnot
Teaching Student Centred Mathematics -John Van de Walle
Big Ideas from Dr. Small; Eyes on Math; Good Questions, Great Ways to Differentiate Mathematics-Marian Small
Student Work Study Initiative at Brian W. Fleming 2014
A collaborative inquiry with two grade three teachers, Candice McManus and Murray Wilson and a Student Work Study teacher, Janet D'Silva.
@PDSBSWSTs
@janetdsilva