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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

Trinter, Christine P.; Garofalo, Joe – Mathematics Teacher, 2011

Nonroutine function tasks are more challenging than most typical high school mathematics tasks. Nonroutine tasks encourage students to expand their thinking about functions and their approaches to problem solving. As a result, they gain greater appreciation for the power of multiple representations and a richer understanding of functions. This…

Descriptors: Problem Solving, Mathematics, Problem Sets, Mathematical Applications