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Critical Features of Classrooms from "Making Sense" by Hiebert…
Critical Features of Classrooms from "Making Sense" by Hiebert
Role of the Teacher (Ch 3): Teacher is a facilitator of learning
Teacher selects appropriate sequences of problems
Sharing information only when essential (better to let students figure out on their own)
Grow a classroom culture with a focus on methods and collaboration
Teacher DOES NOT tell, demonstrate, then instruct students to practice. Instead, students discover on their own
"Questioning Your Way to the Standards" by Mewborn and Huberty
Question-Listen-Question method: importance of questions and follow up questions that evoke thoughtful responses
Do not rush to correct answer by merely telling
Questions that encourage students to be attentive to other students' thinking
Questions that ask for "different ways"
Students can be teachers too
Balance between student autonomy and structure and control by teacher
Must have sound mathematical knowledge and be familiar with standards
Open to alternative methods
Adapting to a changing society
Flexible thinking
Conceptual understanding as primary goal
Understanding is complex, can be achieved at many different levels
Asking "why" questions
Making connections with past learning
Built through reflection and communication
Students are engaged and motivated intrinsically
Genuine problems that invite students to problem solve on their own
Sound mathematical ideas are the "currency of the classroom"
Mistakes are seen as opportunities
Classroom culture of collaboration and interaction
Use of a variety of mathematical tools
All students are equals and learning is made accessible to everyone