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!
Making the Shift: The Power of Student Discourse
A growing body of research shows that we learn complex knowledge and skills best when we engage in discourse and have the opportunity to question, conjecture, and explore (Smith & Stein, 2016). Many math classrooms in the United States use a "I do, we do, you do" lesson structure, where the teacher presents a way to solve a problem, does another one or two problems with class input, and then assigns problems for students to try on their own. In this structure the teacher takes on the cognitive load of sense making and problem solving, instead of the students. Math is presented as a series of procedures to be memorized instead of a rich set of concepts to be explored. Learning math in this way limits student understanding of the subject and has resulted in inequitable student achievement. Students see math as about right answers and speed, instead of as a set of interrelated concepts and tools they can use to explore the world around them.
As we strive to develop critical and creative problem solvers we must shift from the “I do, We do, You do” lesson structure to something more along the lines of “You, Y’all, We” (Green, 2015). In a "you, y'all, we" lesson structure students bear the cognitive load by engaging in the critical thinking skills of sense-making and problem solving individually, then share their different problem solving strategies with each other, and finally students discuss how the different strategies relate to the underlying mathematical concept. The teacher’s primary role is as discussion orchestrator and the students’ primary role is to engage in problem solving and make sense of the mathematics together.
Why not just make the switch then? Why doesn’t everyone just dive into a discussion based lesson structure like “You, Y’all, We” or Launch, Explore, Discuss?
The answer...because it’s complex, difficult work!
The resources on this site have been curated to help you make the leap into collaborative mathematics facilitation! Grab a colleague, pick a strategy, and give it a try together. And remember, when it doesn’t work well the first time do not give up! Our students need us to persist too.
Citations:
Smith, M. S., & Stein, M. K. (2016). 5 practices for orchestrating productive mathematics discussions. The National Council of Teachers of Mathematics.
Green, E. (2014). Building a Better Teacher: How Teaching Works (and How to Teach It to Everyone. W.W. Norton
Former eighth grade teacher Katerina Milvidskaia and her former student, Sarah discuss the rationale for the You, Y'all, We, lesson structure and unpack the student experience.