“Equitable teaching and learning of mathematics can only proceed in an environment where students engage deeply with significant mathematical ideas,” have opportunities to express their math thinking and interact with the thinking of others, take responsibility for their learning, and work together in productive ways. (Russell, et. al., 2022, p. 3) Discussions, Math Workshop, and partner work are Investigations 3 structures that offer critical opportunities to develop and support an equitable math learning community. This 3-part blog series offers guidance about how these structures can promote equity in the mathematics classroom and support the identity and agency of all students, especially those who have been historically marginalized in mathematics.
How Partner Work Supports Equity
As defined in A Framework for Reflecting About Equity in the Investigations Mathematics Classroom, “a strong collaborative mathematics community gives students the opportunity to work together to solve problems, to learn from each other, to take risks, to support and encourage others, and to be supported and encouraged by others in their growth as math learners.” (Russell, et. al., 2022, p. 5) Throughout Investigations students work in partnerships as they engage in activities, play games, and discuss their work and ideas. Understanding what it means to “be a good partner,” and how to make space for each person’s ideas, are important aspects of an equitable learning community.
The following factors, in bold, are important to consider when creating and supporting partnerships that develop students’ mathematical identity and sense of agency. In blue, you’ll find questions to reflect on with students, about how partnerships are working and how they can be improved to support the goal of equitable participation.
Planning for Partner Work
Creating equitable partnerships requires thinking ahead about a variety of factors. Partnerships will likely vary depending on the activity, or on students’ math, social, or language needs. Sometimes it might make sense to assign partners randomly or to allow students to select their own partners. Regardless of how partnerships are determined, working cooperatively is a goal. Together, generate a list of things good partners do (e.g. take turns, share materials, listen to each other’s ideas). Periodically, discuss some aspect of partner work together.
- What is fun about working with a partner? What can be challenging? Do you have ideas that help you work better together?
- What are some things partners need to do to work together productively? What’s an example of how you and your partner worked cooperatively? What helped you do that?
- How did you manage your time so you and your partner could complete the math work you needed to do?
Being a Good Partner: Games
Games are one of the most common partner activities. Playing games provides the opportunity for students to share their thinking, to consider and try on others’ ideas, and to develop strategic and efficient strategies over time. Engage students in conversations about what it means to be a good partner and a good sport.
- How will/did you and your partner decide who goes/went first? who will deal/dealt the cards?
- When one partner is taking their turn, what should the other person be doing?
- If your partner is stuck and asks for help, how can you give a suggestion that helps them keep thinking about the math?
- When you are finished playing a game what should partners do? (i.e. congratulate each other, clean up together)
Being a Good Partner: Activities
Students often work cooperatively on an activity or task. Like game-playing, this is an opportunity for students to express their ideas, to listen to and learn from others, and to compare and contrast different strategies and representations. Talk with students about how to share the work equitably.
- How can partners work together so that each person is contributing their ideas equally?
- If the activity requires you to record your thinking or solution, how can partners make sure they represent the work of both people?
- What’s an example of a hint or clue your partner gave you, that helped you without telling you the answer or what to do?
Sharing Ideas
Whether students are playing a game or working cooperatively on a task or activity, listening and responding to each other are important skills. Talking with a partner also provides students with a more private, less risky way to share their ideas compared to whole class discussions. Gather students’ ideas about how they can exchange ideas in ways that are inclusive and respectful.
- How can partners make sure that each person has a chance to share their ideas?
- How will your partner know you are really listening to them?
- What if you don’t understand or disagree with your partner’s idea/answer? What are some things you could say or ask?
- If you notice that your partner is being quiet, how can you invite them to share their idea?
- If you feel like your partner is taking over the activity or doing all the talking, what can you say to let them know you would like to contribute too?
“Turn and Talk”-ing
Turn and Talks are quick pair conversations that happen in the midst of a whole class discussion. They ask partners to check in about a specific question or idea. Both students have time to share and sometimes are asked to share their partner’s idea when back in the whole group. Ask students to reflect on what a productive turn and talk looks and sounds like.
- How did you and your partner decide who would speak first? How did you make sure both people had a chance to share their thinking and one person didn’t take up all the time?
- Did you and your partner have the same idea or a different idea? If your ideas were different, what did you talk about?
- Did you understand your partner’s idea? What could you do if you weren’t sure? What question could you ask?
While the beginning of the school year is a natural place to lay the foundation for productive partnerships, it is important to continually revisit and reflect with students on how they are working together. For support thinking about how to take up this work from the start of the year, see Developing an Equitable Math Learning Community in Unit 1.
This is the third in a series of three blogs about structures in Investigations 3 that offer students opportunities to see themselves and each other as active and contributing members of their math community. Part 1 explored Discussions and Part 2 looked at Math Workshop.
References
Russell, S.J. et al. (2022, September). A Framework for Reflecting about Equity in the Elementary Mathematics Classroom. Investigations Center for Curriculum and Professional Development.
