Status & Mindset Interventions
In her book Strength in Numbers: Collaborative Learning in Secondary Mathematics, Ilana Horn writes: “Judgements about who is smart based on prior achievement or social categories violate a fundamental principle of equity and are consequential: learning is not the same as achievement” (2012, p.20). The resources below were curated to help you redefine "smarts" in math, disrupt status divisions, develop growth mindsets, and foster a collaborative math community.
Anticipatory Planning
How often does your planning for math involve searching for the "best" problem and then thinking about how you want to teach the problem? It's safe to say this is how most of us approach(ed) lesson planning. The problem with this approach, however, is that it is teacher focused and neglects to consider how students might perceive and respond to the problem. Conversely, anticipatory planning focuses planning efforts on imagining how students might respond to a problem and using that information to plan questions that will push and clarify student thinking and build understanding by sequencing and connecting approaches students are already using.
If you've ever tried to facilitate constructivist math learning in your classroom and it fell short of your expectations, it's likely because the key factor, anticipatory planning, was missing! The template below can help you prepare to facilitate constructivist math learning in your classroom. Grab a planning buddy and give it a try!
Anticipatory Planning
How often does your planning for math involve searching for the "best" problem and then thinking about how you want to teach the problem? It's safe to say this is how most of us approach(ed) lesson planning. The problem with this approach, however, is that it is teacher focused and neglects to consider how students might perceive and respond to the problem. Conversely, anticipatory planning focuses planning efforts on imagining how students might respond to a problem and using that information to plan questions that will push and clarify student thinking and build understanding by sequencing and connecting approaches students are already using.
If you've ever tried to facilitate constructivist math learning in your classroom and it fell short of your expectations, it's likely because the key factor, anticipatory planning, was missing! The template below can help you prepare to facilitate constructivist math learning in your classroom. Grab a planning buddy and give it a try!
Equitable Group Work
Designing group work that provides all students the opportunity to access the mathematics can be challenging, but is critical to the growth of each and every student. Research shows that students who do the most talking also do the most learning. The resources and videos below outline group work strategies that increase equitable interactions in heterogeneous classrooms (Cohen & Lotan, 2014; Horn, 2012).
Building Students' Group Work Skills
Teaching Group Work
There are significant benefits to establishing a positive group work culture in the classroom. When groups work well together, group members push each other's thinking, hold each other accountable for learning, and build on each other's ideas. However, it takes time and consistent classroom structures and messaging for student to learn and develop robust group work skills.
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Strategies such as codeveloping group work norms with students, infusing group roles into your classroom routines, using participation quizzes to reinforce good group work, and accountability quizzes to hold groups accountable for each other's learning will all support students in using each other as resources and build a learning community.
Codevelop Group Norms
Codevelop Group Norms
Codeveloping group norms with students supports collective ownership of using positive group work behavior. In the lesson outlined in this change idea, students analyze examples of groups working together and decide on norms they want to use for their own group work. Two norms that repeatedly come up are: everyone has the right to ask questions and everyone must be able to explain the groups thinking (leave no-one behind!).
Students in Katerina's 8th grade classroom discuss their experience with group work.
Group Roles as Status Equalizers
Group roles provide a useful structure for ensuring equitable participation in group work. They provide each student with responsibilities and 'sound bites' to support them in engaging productively in learning from one another. Students often feel awkward using them at first, however, once they are integrated students report that they significantly deepen the level of mathematical discussion during group work.
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The roles have been designed so that they are intellectually equal and keep everyone 'in the game'. The roles include:
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Team Captain
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Coach
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Accountability Manager
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Skeptic
Roll out Group Roles & Group Roles Participation Quiz
Roll out Group Roles & Group Roles Participation Quiz
Students in Katerina's 8th grade classroom prepare to present their thinking to the whole class and use their group roles to guide their discussion. Group roles are most effective when they are used consistently and thoroughly integrated into the class routines.
Students in Katerina's 8th grade classroom discuss their experience using group roles.
Group roles were the most challenging change idea for MAIC participants to use. However, they are highly effective when integrated into the classroom routines. Katerina models how to be a skeptic, by 'skepticizing' the skeptic as a group prepares to present to launch a whole class discussion.
Embracing ALL of the Ways to Be Mathematical
In oder for students to work productively in groups they need to view mathematics as more than a set of procedures to be memorized and how quickly they can get to the right answer. Two key practices to build a more three dimensional view of mathematics include providing problems worthy of discussion and noticing and reinforcing all the different ways that students are being mathematical – asking questions, looking for and attending to structure and patterns, critiquing the reasoning of others, and creating models of their ideas.
Group worthy tasks include problems where multiple solution strategies are possible, such as pattern problems or other 'low floor, high ceiling' tasks, and tasks that elicit debate and provide opportunity for students (and teachers!) to be skeptics and engage in mathematical discussion.
Modifying Tasks
Shifting Values & Status Interventions
Reinforcing Group Work Norms & Roles
One of the ways to demonstrate to students that you value positive and productive group work is to use participation quizzes to reinforce group work norms & roles. The purpose of a participation quiz is to focus and assess students' group work behaviors while they work on a rich math task. It is important during a participation quiz to only assess the group work behaviors and not to assess the mathematics.
Participation Quiz
Participation Quiz
Participation Quiz
Katerina uses a participation quiz with her 8th grade class.
Holding Students Accountable for Each Other's Thinking
In order for students to learn effectively in groups, they need to listen and understand the thinking of their group mates. Accountability quizzes are a useful way to determine whether all students in a group can explain the groups thinking.
During an accountability quiz the teacher stops by a group during the explore phase and asks a random (or not so random) student to share the groups thinking so far, or to answer a 'why' question. Some MAIC teachers spin a pencil to determine who will answer their question, others use the group roles to select a student.
Accountability Quiz
Katerina uses an accountability quiz to assess a groups understanding of a problem while they prepare for the whole class discussion.