Productive Failure
The notion of productive failure (PF) directly relates to the problem-solving approach. Generally, students will not be able to deduce the right conclusion or answers about math concepts the first time they attempt it; however, by persisting and thinking on their own, they develop higher cognitive functions which lead to a deep conceptual understanding and greater retention of mathematic principles. This is productive failure. Even though students may not be getting the answer or the main idea on the first try, the inquiry process feeds their conceptual understanding which is much more productive than learning procedurally or through rote.
The Productive Failure in Learning Math study (2013), completed by Cognitive Science, discusses the most effective design for the productive failure (problem-solving method) process.
Key Design Features for Productive Failure (p. 12):
The Productive Failure in Learning Math study (2013), completed by Cognitive Science, discusses the most effective design for the productive failure (problem-solving method) process.
Key Design Features for Productive Failure (p. 12):
- a) the problem must admit multiple solutions, strategies, and representations, that is, afford sufficient problem and solution spaces for exploration
- b) the problem should activate learners' prior knowledge—formal as well as intuitive—to solve the problem. Whether or the extent to which the learner is able to correctly solve the problem will depend, in part, upon the amount and nature of guidance provided
- c) students must themselves generate and explore solutions and not simply be presented with peers’ solutions
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