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Garofalo, Joe; Trinter, Christine P.; Swartz, Barbara A. – Mathematics Teacher, 2015

One method of proof is to provide a logical argument that demonstrates the existence of a mathematical object (e.g., a number) that can be used to prove or disprove a conjecture or statement. Some such proofs result in the actual identification of such an object, whereas others just demonstrate that such an object exists. These types of proofs are…

Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Secondary School Mathematics

Bu, Lingguo – Mathematics Teacher, 2013

Many preservice teachers come into teacher education programs with a rule-based view of mathematics, a view that is to a large extent indicative of their previous school experiences. In teaching preservice elementary school teachers, this author has used his instrumental understanding as the starting point for rich discussions about the…

Descriptors: Preservice Teachers, Student Teacher Attitudes, Mathematics Instruction, Elementary School Mathematics