Communication in Mathematics
Supposition
Students that participate in gallery walks and receive descriptive feedback from the teacher are more apt to explain their thinking with justification.
My inquiry evolved as I collaborated with teachers to assist students in being able to communicate their thinking in mathematics. I began to wonder "how can students communicate their thinking in a variety of ways and how does this communication assist students to fully understand the concepts being taught?"
Mathematical Processes
Edugains
Methods
 I worked in four schools in total, two from October to January and two from February to June
 School visits were twice a week
 Worked with students in grades 1, 2, 3, and 6
 Used the colearning model at some locations
 Evidence was collected and shared through the triangulation of data (field notes, interviews and video recordings)
Problem Solving Checklist Many classroom teachers used a problem solving checklist to assist students in deconstructing math problems  Modified Checklist Students working through levels one and two required the checklist to be broken down into more manageable steps.
 Math Talk Open ended questions allow students to talk in greater detail and minimizes simple responses. Some "talk move" strategies include:
For more information on open ended questions please visit LNS Capacity Building Series Asking Effective Questions. www.edu.gov.on.ca/eng/literacynumeracy/inspire 
Problem Solving Checklist
Modified Checklist
 Think and Plan
 Problem Solving and Communication
Math Talk
Some "talk move" strategies include:
 Revoicing
 Repeating
 Adding On
 Wait time and
 Reasoning
For more information on open ended questions please visit LNS Capacity Building Series Asking Effective Questions. www.edu.gov.on.ca/eng/literacynumeracy/inspire
Literature Review
Text Resources
 Math Expressions Dr Cathy Marks Krpan's book focuses on:
 Literacy and Numeracy Secretariat

Text Resources
 Making Math Meaningful to Canadian Students K8 by Marian Small
 Growing Success: Assessment, Evaluation, and Reporting in Ontario SchoolsMinistry of Education
Math Expressions
 A Culture of Mathematical Expression
 A Culture of Collaboration and Inquiry
 Mathematical Discourse
 Reading in Mathematics and
 Writing in Mathematics
Evidence
Problem Solving Culminating Tasks that were administered to all students in the grade, allowed teachers to moderate student work. Some students need to discuss their solutions orally with the teacher even after a task has been completed. This ensures assigning the appropriate grade.  Partner Problem Solving Students need many opportunities to work with a partner to explain their thinking  Gallery WalksAfter several months of students engaged in gallery walks, I decided to ask students about their participation in them as I wanted to further understand the role of communication in the mathematics. SWST What is it like in your math class when you do a Gallery Walk? Richard When I do a gallery walk I start getting what we’re suppose to do. Charlie You get to learn from other people and can see the answer. Elisha You learn from the people. 
Problem Solving
Partner Problem Solving
Gallery Walks
After several months of students engaged in gallery walks, I decided to ask students about their participation in them as I wanted to further understand the role of communication in the mathematics.
SWST What is it like in your math class when you do a Gallery Walk?
Richard When I do a gallery walk I start getting what we’re suppose to do.
Charlie You get to learn from other people and can see the answer.
Elisha You learn from the people.
Descriptive feedback Students benefit from oral and written feedback from the teacher. This feedback provides students with immediate information on what the are doing well in and what areas need further improvement.  Quiz Several "pop" quizzes are given to students as check in points. Again, this allows students to determine what specific steps they need to take to improve (problem solving or communication) and it allows the teacher to determine the next steps in instruction.  Gallery WalksSWST Do you like the gallery walks? Elisha Yes, you get to talk about how people organized their communication. Rebecca It’s different. I learn how to get good communication doing the gallery walk. SWST How Rebecca? Rebecca By reading and choosing which one I like and can get information from. SWST What do you do during a gallery walk? SWST How? Sam Sometimes you make mistakes and you’re not perfect. You have to tell them how to improve like underline the important information, correct spelling. Sam It tells the important parts of what it is about. 
Descriptive feedback
Quiz
Gallery Walks
SWST Do you like the gallery walks?
Elisha Yes, you get to talk about how people organized their communication.
Rebecca It’s different. I learn how to get good communication doing the gallery walk.
SWST How Rebecca?
Rebecca By reading and choosing which one I like and can get information from.
SWST What do you do during a gallery walk?
Sam You have to tell the stuff they need to work on and what’s good about their work.
SWST How?
Sam Sometimes you make mistakes and you’re not perfect. You have to tell them how to improve like underline the important information, correct spelling.
SWST Why underline?
Sam It tells the important parts of what it is about.
Student Voice
SWST When you do math, do you prefer talking about it or just working on your own?
Malika and Aryan both say at the same time Talking about it.
SWST Why?
Malika If we need help we can talk about it.
Aryan We can share our ideas and plans.
SWST Do you learn from one another?
Aryan Yes, we learn from one anothers’ habits and ideas.
Malika How we can improve.
Aryan How we think and can correct our mistakes.
SWST Do you ever find that you can learn from others and that you can teach something too?
Malika and Aryan Yes!
SWST Do you ever teach someone else the strategies you’re using?
Malika Yes, we discuss them and then we tell them our strategies.
Aryan They tell us their strategies too.
SWST Does that help you?
Aryan and Malika Yes.
SWST How?
Malika It helps us understand their way of thinking.
Aryan Yes, so we understand what’s going on in their mind and our mind and we combine our thoughts and answers.
Key Learnings
 Oral Communication (speaking and listening)
 Written Communication (reading and writing)
 Symbolic, graphical, or pictorial communication
 Physical communication through active involvement with manipulatives.
Historically, we as educators have given more credit to written communication than any other form.
I have also learned that students need time to discuss their ideas, strategies and solutions when problemsolving in mathematics. This allows them to justify their thinking and reflect on what they've learned. Through these discussions teachers can identify what students are thinking and determine what instruction students need to move their thinking further.
Conclusion
If students communicate their thinking in a variety of ways orally, visually and in written form when problemsolving in mathematics then students will have a better understanding of the concepts. My inquiry has lead me to believe that when students participate in gallery walks they are more apt to communicate their solutions to their peers clearly. Students listen to one another’s mathematical thinking. Oral communication allows students to use mathematical vocabulary and explain why something is correct or incorrect. Written and pictorial communication provides students with the opportunity to show their thinking. Students stated that gallery walks allow them to “see the answer”.
The purpose of academic discourse in the mathematics classroom is to determine what students are thinking. Asking open ended questions, using “talk move” strategies and providing students with descriptive feedback all contribute to allowing students to communicate their thinking clearly. It is through effective questioning that allows the teacher to determine how students arrive at a conclusion. Once teachers understand student thinking then they provide the necessary feedback to expand their thinking and what is causing the confusion in their thought processes. ( Small, 2009, pg.70)
When students work in learning environments where purposeful talk is present and the teacher facilitates discussions and asks further questions then students will communicate their thinking clearly and with justification.