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Yopp, David – Teaching Children Mathematics, 2010
Understanding logical necessity is an important component of proof and reasoning for teachers of grades K-8. The ability to determine exactly where young students' arguments are faulty offers teachers the chance to give youngsters feedback as they progress toward writing mathematically valid deductive proofs. As defined, logical necessity is the…
Descriptors: Feedback (Response), Logical Thinking, Elementary School Teachers, Mathematical Logic
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Groth, Randall E.; Burgess, Claudia R. – Teaching Children Mathematics, 2009
Online conversations help teachers engage in constructive criticism and attend more carefully to aligning lesson plans with problem solving. This article describes a strategy for using an online discussion board to help teachers evaluate one another's lesson plans. The online peer-review activity suggests that fostering critical pedagogical…
Descriptors: Group Discussion, Lesson Plans, Criticism, Peer Evaluation
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Cramer, Kathleen A.; Monson, Debra S.; Wyberg, Terry; Leavitt, Seth; Whitney, Stephanie B. – Teaching Children Mathematics, 2009
Appropriate concrete and pictorial models allow students to construct meaning for rational numbers and operations with the numbers. To develop deep understanding of rational number, sixth through eighth graders must experience a variety of models (NCTM 2000). Since 1979, personnel from the Rational Number Project (RNP), a cooperative research and…
Descriptors: Number Concepts, Grade 8, Arithmetic, Mathematics Instruction