Instructional Shift 10: Make "Why?" "How do you know?" "Can you explain?" classroom mantras.

Chapter 11: Just Ask Them “Why?”

What should we see in an effective mathematics classroom?

-Every student answer is responded to with a request for justification.

Listed below are strategies to support two different ways to examine the information in Chapter 11

Method I
  • Prerequisite Activity: Visit the classroom of three different colleagues prior to the team meeting. It is not necessary that all three colleagues are mathematics teachers. The teachers should not be informed of the purpose of the visit. Ask for volunteers for the sake of collecting data. Participants should remain anonymous. Record student responses to questions and the teacher's follow-up questions and/or feedback.
  • Activity I: Provide teachers with a copy of Standards for Teaching Mathematics. Provide teachers with a copy of the question/response data from the Prerequisite Activity to be used as a Real-World Scenario. Work as a group to analyze this data. Questions to guide the discussion might include:
    • How many times are students providing one-word answers?
    • How did the teacher respond to the one-word answers?
    • How does the teacher respond to incorrect answers?
    • How does this reality compare to the reality we are trying to create by facilitating discourse as described in the Standards?
    • Follow-up this activity by having teachers read Chapter 11. After a discussion of the reading, challenge teachers to think about their individual classrooms and how they might improve student learning by requiring students to explain, "Why?"

      Standards for Teaching Mathematics.doc

      Sample Real.doc

Method II
  • Activity II: Have teachers read Chapter 11. Divide the team into two groups. Each group will receive a copy of student work for solving an equation. Group A - The problem has been worked out correctly by the student at the board. Group B - The problem was not worked out correctly by the student at the board. Each group will develop a list of questions. Group A will develop questions to determine if the student has conceptual understanding or procedural knowledge and to deepen understanding. Group B will develop questions to challenge thinking and guide the student in finding his or her errors. Groups will share out the questions developed. Guide the teachers through a discussion of the text in conjunction with this activity.

    Board Scenario.doc

  • Follow-up Activity: Have teacher partner to agree to visit one another's classrooms. Each pair should commit to visit long enough to record student teacher interactions for the check of one problem of the warm up or homework check. Each pair should discuss how the reading and activity has impacted his or her planning of lessons and/or reflection on student learning.

-Both teachers and students consistently and frequently use “Why?” “Can you explain that?” “How do you know?” or equivalent questions.

  • The teacher should create a climate where students feel comfortable asking questions and taking a risk. Have teachers share the strategies that they use to invite students to challenge answers and ask questions. Work together to develop a list of question stems teachers might use to ask students why and encourage them to explain and justify answers.

-Dismissive responses such as “No,” “Wrong,” “Not quite,” and their equivalents are absent from the classroom.

  • Discuss possible teacher responses to incorrect answers.
  • Lifeline strategy: If a student gives an incorrect answer he or she may call on a fellow student to provide assistance.