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Problem-solving allows students to develop understanding and explain the processes used to arrive at solutions, rather than remembering and applying a set of procedures.
Rather than directing a lesson, the teacher needs to provide time for students to grapple with problems, search for strategies and solutions on their own, and learn to evaluate their own results.
More recently, teachers have come to understand that becoming mathematically literate is also a complex problem-solving activity that increases in power and flexibility when practiced more often.
A problem in mathematics is any situation that must be resolved using mathematical tools but for which there is no immediately obvious strategy.
Teachers who get this right create resilient problem solvers who know that with perseverance they can succeed.
Problems need to be within the students’ “Zone of Proximal Development” (Vygotsky 1968).