Clip 1/18: Planning Quadratic Functions

Phil Tucher, the math coach, first asks the teacher, Barbara Shreve about the lesson. Barbara describes a unit about quadratic equations that the class has been currently engaged in. The lesson involves students using expressions, equations, factoring, the quadratic equation, intercepts and other attributes of quadratics. Students often learn procedures using these math tools, in order to find the roots or zeros of an equation, or to graph a function or to transform an expression or equation into a different form. Students often mix up the procedures with the purposes. Barbara designed a lesson to confront these misconceptions. Phil often uses a strong coaching technique of restating what he heard for clarification and emphasis. Another strategy Phil uses to clarify and probe the mathematics is to ask the teacher to provide an example of a problem the students will be tackling. Barbara talks about a very powerful design in her lesson. She uses examples of student work for student to analyze for correctness and to compare solutions. She also uses a matching task to help students identify the different mathematical attributes of quadratics (equations, intercepts, expression, roots, etc.) and learn how it is used them to solve problems. Besides the mathematics of the lesson Phil also inquires about pedagogical strategies Barbara has planned in the lesson. This includes question about language and vocabulary. Many of the students are not strong in their use of academic language. Many are also English learners. Barbara describes how she plans to address issues around vocabulary. Another issue around instructional practice that Phil raises is about student working together particularly in small groups. Phil articulates the dilemma that teachers face in helping students work together independently, but still providing enough support so students have access to the problem and don’t shut down. Barbara runs with the idea and further explains the tensions teachers must deal with and decisions they make to support learning while helping students be independent thinkers. Phil then specifically inquires about the students in the class and he asks Barbara to identifying students or particular groups she is especially attentive to at this time. Barbara discusses a few groups, an English learners group and a group with a new learning agenda. She asks Phil to focus on specific questions that she is trying to answer for herself: What evidence is there that students are starting to make generalizations?