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Dickman, Benjamin – Mathematics Teacher, 2018

What do nonroutine algebra problems look like for a second-year algebra course, and where can such problems be found? Starting from the belief that even challenging, nonroutine problems should be solvable with the resources that students possess, Benjamin Dickman proceeded to formulate a small collection of tasks to push students into integrating…

Descriptors: Mathematics Instruction, Algebra, Problem Solving, Mathematical Logic

Dickman, Benjamin – Mathematics Teacher, 2016

Guessing, for Pólya, is an important way of getting an initial handle on a mathematical problem. An argument can be made to place guessing in any one of the first three steps of the four-step approach to problem solving as described in "How to Solve It" (Pólya 1945). It could be a part of understanding the problem, devising a plan, or…

Descriptors: Problem Solving, Mathematics Instruction, Calculus, Fractions