“Attending to student voice … serves to enhance our understanding of the ongoing relationship between the teacher and student as co-constructors of knowledge and practice within the classroom.”
(page 2) The Learner’s Perspective Study: Attending to student voice in Student voice in mathematics classrooms around the world.
This blog is a mathematical mirror of Annette’s resource Investing in our students- student voice. Annette provided some excellent suggestions about how to create an environment in your classroom to support and enable students to have a voice both in their responses to others and as a part of their learning process within the context of the subject of English. Student voice in mathematics, and the teacher’s ability to create opportunities for mathematical discourse focused on students’ ways of thinking and working, is at the heart of quality teaching.
Similar to Annette’s ideas, I have grouped these loosely under the headings
- classroom communication,
- the classroom and
- strategies for teaching in mathematics.
Classroom communication
“The teacher’s skilful questioning plays a vital role in … helping students to identify thinking processes, to see the connections between ideas and to build new understanding as they work their way to a solution that makes sense to them.”
Asking effective questions, Ontario Ministry of Education
When we invite young children to notice & wonder, what does it sound like to discuss what "notice" "wonder" mean? You can say I notice__ when you want to share something you see or observe. You can say I wonder__ when there is something you're curious about. @MFAnnie @maxrayriek
— Allison Hintz (@allisonhintz124) 25 October 2018
Good teachers are good questioners. Asking the right types of questions to promote student thinking and to elicit solutions is an art form. An easy way to start is by asking Noticing and Wondering questions. Allison Hintz (co-author of Intentional Talk) recently tweeted about really digging down into what these words mean and what are we looking for from our students as responses. Asking What do you notice is an open door for students to look for things they already know, or to see similarities or differences, or to look through mathematical eyes to see a pattern. Then asking What do you wonder encourages students to think about what might be, or to wonder if this happens somewhere else, or if it’s something that always happens. To notice and wonder is to create a bridge between the known and the unknown.
In Tracy Zager’s book, Becoming the maths teacher you wish you’d had, she has a chapter titled ‘Mathematicians ask question’ this chapter is solely focused on improving as a teacher through asking good questions, allowing students a voice in asking good questions, and learning how to listen. Tracy talks about noticing and wondering, posing problems and the flow to new problems and further questions that answers often bring. Tracy also suggests using a great website www.101qs.com which I’m keen to try out.
“In maths classes, students mostly answer someone else’s questions… they rarely get to ask their own questions, pose their own problems, generate their own ideas.”
Tracy Zager Becoming the math teacher you wish you’d had
Great task to promote rich mathematical discussion. I wonder what would happen if you challenge them to try arranging again it a different way...#mathschat #engagingmaths @MathsNSW @learnPSNSW https://t.co/1CXPd2eJXd
— Dr Catherine Attard (@attard_c) 25 October 2018
Classroom communication in mathematics needs to be structured and planned for. Good questions don’t always come easy! I take the time to map out the questions I plan to ask during my mathematics lessons (I also often rehearse or try out the task myself first!). Planning what you intend to ask means that your questions have purpose and link to your lesson’s concept or intention. The questions also assist the lesson’s flow and are often set up to target and deal with any misconceptions students may have.
For assistance with how to go about some of this planning, the book I mentioned earlier, Intentional Talk: How to Structure and Lead Productive Mathematical Discussions by Elham Kazemi and Allison Hintz is essential reading. They share a number of excellent strategies and discussion types for the mathematics classroom including; Open Strategy sharing and Targeted Discussion – these help to make the most out of students sharing their work beyond the teacher simply choosing a student who wants to share.
The classroom
“[Students] are communicating mathematically when they describe, represent and explain mathematical situations, concepts, methods and solutions to problems.”
NESA, Mathematics K-10 Syllabus
Your classroom walls should speak the language of mathematics. Most classrooms have evidence and samples of students’ writing and artwork adorning the walls, but what about their mathematics work? How are your students’ mathematical voices being represented visually? Are students able to draft their mathematics work and solutions? Are they given opportunities to re-draft? Are their solutions shared up on the walls?
Using walls that teach and numbertalks during multiplication problem solving. @KotaraSthPublic #nswdoe #mbb4n pic.twitter.com/n83ocGbOgj
— katherin cartwright (@kath_cartwright) 25 May 2017
I have seen some wonderful classrooms where there are mathematical investigation walls and problems left there for students to solve when they want to take on the challenge. These are walls that teach. As teachers, we like posters and images up on our walls and most classroom have these for mathematics topics too. However, students often do not actually use them to assist them when they are struggling. Having students’ work on the walls and their own hand-made posters, signs and investigations is a way to encourage students refer to these visuals. Try not to clutter your space but only have things useful for the next week or two’s lesson up for students to view. Stop classroom clutter and Decrease classroom clutter to increase creativity provide some good advice for teachers.
Strategies for teaching in mathematics
“Within our classrooms, students must learn to engage in classroom discourse and practices that serve both social and cognitive functions.”
(page 4) The Learner’s Perspective Study: Attending to student voice in Student voice in mathematics classrooms around the world.
Communication as classroom culture. For students to feel comfortable communicating mathematically, they need to first feel comfortable communicating at all. Your classroom needs to be a safe place for students to share their thoughts and strategies about how they solve tasks. Sharing involves risk, and for any students with maths anxiety, being open to others may be very scary. Annette in her resource talked about growth mindset and Carol Dweck’s work, as did I briefly in a previous blog. A focus on students seeing themselves as ongoing learners who may not know something yet, but can always improve, is needed in all subject areas of schooling. Creating group norms is one way to set up a positive school culture where both teachers and students understand: “this is just the way we do things here”. Group norms work best when they are co-designed with students in setting up your classroom (and mathematics) culture. Youcubed’s group norms are a great place to start.
Talk moves are another teaching strategy to structure the way you talk with your students and how they learn to discuss their mathematical thinking in a positive way with each other.
Talk Moves:
- Wait time
- Turn and talk
- Revoicing
- Reasoning
- Adding on
- Repeating
- Revise your thinking
A5
— Mark Chubb (@MarkChubb3) 26 October 2018
If we ask simple right/wrong Qs, and only hear from 1 kid who already had their hand up to answer us, we might have a false sense of student readiness.
To fix this we should:
-ask questions that involve more thought
-use talk moves (below) to include more Ss
#elemmathchat pic.twitter.com/5z1WPDy9Qk
Kazemi and Hintz also use talk moves in their book and there are now many versions of posters and lists that describe what talk moves are. A paper The Literacy of Mathematics written by Jenni Way and Jannette Bobis for PETAA (Primary English Teaching Association Australia) also discusses the benefits of using Talk Moves in the mathematics classroom. The NSW Department of Education have since made their own version of the Talk Moves poster for teachers that you can access via their Literacy and Numeracy newsletter.
Number talks also promote mathematical discourse in the classroom and provide students with a voice to share their learning.
“During number talks, students are asked to communicate their thinking when presenting and justifying solutions to problems they solve mentally. These exchanges lead to the development of more accurate, efficient, and flexible strategies.”
Sherry Parrish, Number Talks Build Numerical Reasoning
After trying #numbertalks my students are begging me for more!! Look at all these way to solve this problem📚✏️ pic.twitter.com/IPXfdBS3ee
— Miss Elliott (@edwmisselliott) 25 October 2018
Number Talks are used as a lesson starter, ignition activity, launch or warm up (whichever term you use) at the beginning of a lesson. It is a time to build mental computation skills, foster number sense and to develop communication skills. You can use the talk moves in conjunction with a Number Talk to guide the way students respond to you and share their ideas with each other. I find that using the turn and talk strategy works well within a number talk and also the adding on strategy as it encourages students to listen to each other’s solutions, so they can build on to what their peers have shared. For more information regarding number talks see the links below.
Resources
Plan for the math by doing the math https://thelearningexchange.ca/projects/honouring-student-voice-in-mathematics/
Use Productive Talk Moves to enhance class discussions
Talk moves in science Talk Science Primer
Number talks to grow mathematical minds
https://www.mansw.nsw.edu.au/events/category/number-talks-in-the-k-6-classroom
https://tedd.org/activities/number-talks/
https://www.teachingchannel.org/video/student-participation-strategy
https://www.youcubed.org/forums/topic/5-talk-moves-of-a-very-effective-teacher/
https://www.teachingchannel.org/blog/2017/10/26/tch-tips-number-talks
https://www.kqed.org/mindshift/47820/how-kids-benefit-from-learning-to-explain-math-thinking
References
Chapin, S., O’Connor, C., & Anderson, N. (2009). Classroom Discussions: Using Math Talk to Help Students Learn, Grades K-6 (second edition). Sausalito, CA: Math Solutions Publications.
Kaur, B., Anthony, G., Ohtani, M., & Clarke, D. (Eds.). (2013). Student voice in mathematics classrooms around the world. SensePublishers.
Kazemi, E., & Hintz, A. (2014). Intentional talk: How to structure and lead productive mathematical discussions. Portland, Maine: Stenhouse Publishers.
Humphreys, C., & Parker, R. (2015). Making number talks matter: Developing mathematical practices and deepening understanding, grades 4-10. Stenhouse Publishers.
O’Connell, S., & O’Connor, K., (2007). Introduction to Communication, Grades 3–5. Heinemann.
NSW Education Standards Authority (NESA). (2012). Mathematics K-6 syllabus. Sydney, NSW.: Author.
Parrish, S. (2010). Number talks: Helping children build mental math and computation strategies, grades K-5. Math Solutions.
Parrish, S. D. (2011). Number talks build numerical reasoning. Teaching Children’s Mathematics, 18(3), 198-206.
Ray-Riek, M. (2013). Powerful problem solving: Activities for sense making with the mathematical practices. Portsmouth, NH: Heinemann.
Way, J. & Bobis, J. (2017). The literacy of mathematics. PETAA Paper, 208. Primary English Teaching Association Australia (PETAA), Sydney.
Zager, T. (2017). Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Stenhouse Publishers.
