Making the Case

Expand/Collapse Making the Case


Making the Case is a collection of classroom video examples and background materials to help high school teachers understand and implement the Argumentation and Critique standard from the Common Core Standards for Mathematical Practice.

  • Making the Case: Overview

    This video from Making the Case introduces Common Core Standard #3 for Mathematical Practice: “Construct viable arguments and critique the reasoning of others,” and provides context about implementing the standard in your classroom practice. Reflections from teachers and from math education experts are also included.

    Grades: 9-13+
  • Encouraging Debate

    In this video from Making the Case, teacher Chris Luzniak uses debate structures in his 12th grade pre-calculus class to engage students in argumentation and critique.

    Grades: 9-13+
  • Creating a Culture of Questioning

    In this video from Making the Case, classroom teachers and math education experts focus on the role of questions and discussion in their classroom. In specific, they describe how questions can encourage argumentation and critique, rather than just eliciting correct or incorrect answers in an evaluative way. Classroom examples also illuminate this Common Core Standard for Mathematical Practice in action.

    Grades: 9-13+
  • Planning

    In this video from Making the Case, teachers and math education experts illuminate how to plan classroom experiences that will promote argumentation and critique. Both planning collaboratively with other teachers, and being intentional about the argumentation and critique goals for class, are key to implementing this Common Core Standard in Mathematical Practice effectively.  

    Grades: 9-13+
  • Language Support

    This video from Making the Case shows teachers from different math classrooms at Everett Alvarez Jr. High School in Salinas California, which serves a highly diverse student body including many English Language Learners. The teachers explain and demonstrate strategies they use to support the Common Core Standard for Mathematical Practice on argumentation and critique.

    Grades: 9-13+
  • Differentiating Instruction

     

    This video from Making the Case shows how you might differentiate instruction while encouraging argumentation and critique, supporting the Common Core Standard for Mathematical Practice. It highlights teacher Melanie Smith’s 9th grade geometry class at the Urban Assembly School for Law and Justice in Brooklyn, NY, where students have varied math backgrounds and ambitions.

     

    Grades: 9-13+
  • Argumentation and Review

    This video from Making the Case shows how teacher Nina Vasquez structures test review in her 12th grade AP Statistics Class at Everett Alvarez Jr. High School in Salinas CA. As her students work in groups and do peer grading, they both review and solidify their content knowledge, and refine their skill in making and critiquing arguments, supporting the Common Core Standards for Mathematical Practice.

    Grades: 9-13+
  • Ideas in Action: Build Student Vocabulary

     

    In this video, pre-calculus teacher Chris Luzniak from the Urban Assembly School for Law and Justice in Brooklyn, NY explains his focus on asking students to use precise mathematical vocabulary in their arguments. He provides vocabulary for the math tasks to his students, makes it visible in the classroom on word walls, and insists that students use this language in argumentation, supporting the Common Core Standards for Mathematical Process.

     

    Grades: 9-13+
  • Ideas in Action: Visit Other Classrooms

     

    In this video from Making the Case, math teachers Leticia Lopez and Eddie Torres plan lessons together, and later will observe each other’s classrooms. Visiting other classes provides a chance for teachers to listen for student arguments, to how they form conjectures, present reasoning and critique one another. Observing this in another teacher’s classroom can improve a teacher’s ability to implement the argumentation and critique standard in the Common Core Standards in Mathematical Practice.

     

    Grades: 9-13+
  • Ideas in Action: Give Students Ownership

    In this video from Making the Case, math teacher Chris Luzniak explains how he invites students to post their conjectures on boards in the classroom and sign them. If these get proven as rules or theorems, they are named after the student who first came up with them (paralleling how theorems are named in the mathematical literature). This supports students’ sense of ownership and engagement with mathematics, and can make their connection to mathematical arguments more personal. Having relevant conjectures and rules visible in the classroom also makes these available to students for use in argumentation and critique, supporting that aspect of the Common Core Standards for Mathematical Practice.  

     

    Grades: 9-13+
  • Ideas in Action: Hand it Over to the Students

     

    In this video from Making the Case, math teacher Melanie Smith describes and demonstrates how she structures her lessons so that she can leave the front of the classroom as soon as possible. This approach allows maximum time for students to work together in pairs and groups, increasing the opportunity for argumentation and critique, the goal of Standard 3 of the Common Core Standards for Mathematical Practice.

     

    Grades: 9-13+
  • Ideas in Action: Group Strategically

     

    In this video from Making the Case, Phil Daro, a developer of the Common Core Standard for Mathematics, explains how group work can help students learn math content and provides opportunities for argumentation and critique. It is important to structure groups so that they are productive, students are working to understand each other, and the right level of support and challenge are present among members of the group. 

     

    Grades: 9-13+
  • Ideas in Action: Get a Second Sentence

    This video from Making the Case explains and illustrates the value of expecting students to give second sentences, such as justifications and explanations of their reasoning. This builds their ability to make arguments and critique the arguments of others, the goal of Standard 3 of the Common Core Standards for Mathematical Practice.  

    Grades: 9-13+

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