The sixth graders are gathered in pairs and trios around a half dozen vertical white boards, thinking about n. Math teacher Selina Hedigan wrote the equation 8n + 6 = 2(4n + 3) = 14n on the class white board and asked the students to determine if the algebraic statement was true or false.
Some groups talk for a moment, pick up their markers and start writing. Other groups seem stuck.
Hedigan opens a toolkit of tips that support the sixth graders in understanding and applying the foundations of algebra.
She brings students back to the class white board and models methods of distribution and substitution to solve the equations, affirming them with the knowledge that they are using math skills they developed in elementary school to do this work.
Hedigan reminds the students: If you don’t know how to proceed, go and look at what another group is doing and come back to your group to share ideas.
She also coaches students on what to ask each other. “Instead of ‘what did you get,’ ask, ‘can you show me how you got that?’”
She knows that mathematical thinking becomes more clear and precise when students talk through problems.
As Hedigan moves from group to group, she prompts the students to show their work. “When you show your work, you can double check it—and share your solution pathway with others.”
Beyond making their work public, using vertical white boards keeps students alert and on their feet. The small groups also differ each day. As students entered the class, they picked cards which put them in random groups, giving them exposure to many types of learners.
At the end of class, everyone gathers around one group’s white board to follow their solution pathway. “Show me if you are beginning to understand using substitution and the distributive property to solve algebraic equations—fist to five,” asks Hedigan. Around the room, five fingers go up.