As students begin to feel comfortable with the classroom environment and begin to engage in mathematical thinking, the instructor helps focus the students on the most critical mathematical concepts (the “big ideas”). In the textbook, the big ideas are identified at the start of the section as learning objectives. By including problems and activities aligned with these learning objectives as part of the classroom instruction, instructors reinforce the importance of these core concepts. Empowering resources for the instructor include exercises not assigned for homework, activities from the Classroom Activity Guide, worked-out examples from the text, and activities from the interactive lecture materials. The instructor may use these resources for on-board examples or small-group activities.

When students are working in teams on an assigned task, the instructor facilitates the learning and mastering of the big ideas by doing the following:

  • Redirecting student thinking through effective questioning
  • Posing alternative ways of thinking and alternate strategies to be considered
  • Providing a mini-lecture to fill in gaps in student understanding
  • Asking a student to share his/her thinking with the class
  • Requesting that a student paraphrase, clarify, or extend another student’s thinking
  • Requiring a student to demonstrate her understanding of the problem using multiple representations
  • Allowing for the pursuit of a dead-end strategy recognizing that this helps to develop persistent problem-solving

At the conclusion of a group activity, student presentations should be used to motivate mental engagement and reinforce the newly acquired learning. Students are randomly chosen to represent their team’s work. Students can use a hand-held whiteboard or a document camera to display their work. While a student is presenting, others in the class actively listen and ask themselves, “Do I agree?” and “Does this make sense?” Students need to feel comfortable and encouraged to disagree and to challenge what is presented in a constructive and positive way. Some activities may extend over multiple class periods.

Student-centered classrooms are characterized by more thinking than remembering, In these classrooms, students do much of the thinking and help shape the day’s lesson consistent with the learning objectives. By being simultaneously flexible and focused, the instructor allows students to explore yet refocuses them as needed to ensure the big ideas are addressed. The instructor continually remembers that the purpose of the lesson is to make sense of mathematical ideas and use those ideas to set up and solve problems.

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