Effective Math Communication
Strategies for Making Student Thinking Visible
Overview of the SWST initiative in Peel
SWST's work together with classroom teachers through the process of collaborative inquiry to study student experiences to better understand what contributes to student achievement.
We observe student thinking, document student learning, analyze evidence of student learning, and reference research that supports our learning.
A digital monograph and supposition paper is written by each SWST and shared with the Superintendents, School Effectiveness Leads, School Administrators and the Ministry. The digital reports are currently in the process of being housed at J.A. Turner professional library.
Further information about the impact of the SWS Initiative is detailed in the "Evaluation of Student Work Study Teachers Initiative Report" which was conducted by the Research, Accountability, School Success Planning Department.
SWS research has been used to inform ministry monographs, the Primary Reading Discussion Paper and various LNS Webcasts. SWS research informs and impacts our system through the sharing of our learning at staff meetings, Educator Resource Teacher and Regional Ministry Meetings.
Communciation in Mathematics
If students communicate their thinking in a variety of ways orally, visually and in written form when problem-solving in mathematics, then students will have a better understanding of the concepts and be able to explain their thinking.
Students that participate in gallery walks and receive descriptive feedback from the teacher are more apt to explain their thinking with justification.
Descriptive Feedback
When oral and written descriptive feedback is given to students by the teacher and their peers, students are provided with immediate information to determine what areas they were successful in and what areas need further improvement.
Gallery Walks
Students that are engaged in purposeful dialogue with their peers, communicate their thinking and justify their reasoning. Students reported the following about communication in mathematics:
Student: When I do a gallery walk I start getting what we are supposed to do"
Student: "You get to learn from other people and can see the answer"
Student: "You get to talk about how people organize their communication"
Student: " It's different. I learn how to get good communication doing the gallery walk"
Student Thinking
Student thinking and reasoning is justified when they explain their solutions orally, visually and in written form.
Documentation of Mathematical Thinking
If documentation of mathematical thinking and strategic questioning using technology is provided then students are able to self-reflect on their learning. This study explores the notion that documentation of mathematical discourse using technology provides a venue for metacognition of student learning. Thus allowing educators and students to inform their learning and practice, analyze their thinking patterns, and substantiate assessment `as` learning to promote higher metacogntive abilities.
Student Explanation and Self Reflection
Student: Well I was only thinking about squares and diamonds and I didn’t think about other shapes.
SWST: How does knowing this help you to answer the question?
Student: It helps me to think about more solutions and that I didn’t try other shapes
Documentation
Through documentation of mathematical thinking it was evident that the students understood perimeter and area. The product alone could not capture all of the students self reflection, or make their thinking visible.
Technology was used to document student thinking in the following ways:
- explaining their thinking
- having conversations with each other to solve the problems
- answering effective questions by Teacher and SWST
This was essential for students to review problem solving steps and deepen their understanding, make connections and check reasonableness.
Assessment 'as' Learning
After the student reviewed his video:
Student: I realized that I didn’t really know what an isosceles triangle was, I kept going back and forth and guessing.
Student: I understood what to do and I explained it, like that an obtuse angle is bigger than 90 degrees and an acute angle is smaller than 90 degrees.
Student: I understand what triangles are called and why you call them that.
The student corrected any misconceptions of the mathematical problem immediately, affirmed what was known confidently and stated if the learning goal was reached.
The Mathematical Climate in the Classroom
Interview
Strategy Sharing
Next Steps
The Mathematical Processes
"Learning mathematics results in more than a mastery of basic skills. It equips students with a concise and powerful means of communication. Mathematical structures, operations, processes, and language provide students with a framework and tools for reasoning, justifying conclusions, and expressing ideas clearly. Through mathematical activities that are practical and relevant to their lives, students develop mathematical understanding, problem solving skills, and related technological skills that they can apply in their daily lives and eventually in the workplace." The Ontario Curriculum Grade 1-8 Mathematics, 2005 (pg.3)
Key Learning in Mathematics
- Inquiry begins at the students desk
- Mathematical processes are evident when students communicate and document their thinking through problem solving activities
- Problem solving plans, risk taking environments, purposeful math talk and descriptive feedback are important elements in fostering student thinking
- Embracing 21 Century Learning leads to student engagement
- Pedagogical documentation allows students' metacognitive abilities to become visible and allows students to self-assess effectively
- Students learning is enhanced when they have procedural and conceptual knowledge combined
- All elements of a comprehensive numeracy program (modelled, shared, guided and independent) need to be present
Digital Monographs of 2012-2013
Learning From and With Others