What Makes A Good Math Problem?

Good math problems value the process of using critical thinking skills by having students participate in open-ended experiences that have a clear goal but a variety of solution paths, it does not value the result or simply the right answer to a math question.  Good problems should connect the mathematics students learn at school with its application in their everyday lives, making it more meaningful and relevant to the learner.   By developing strategies that can be applied to new situations, good problems encourage students to reason their way to a solution among many solutions.  A rich problem allows for representation of mathematical ideas and model situations, using concrete materials, pictures, diagrams, graphs, tables, numbers, words, and symbols.  It also promotes the collaborative sharing of ideas and strategies by having students talk about mathematics. Since good math problems are appropriate, rich, challenging, and engaging, it should help students find enjoyment in mathematics and extend the student’s thinking by still having it relate to a key concept or big idea.