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Problem-based learning (PBL) is a teaching method in which students learn about a subject through the experience of solving an open-ended problem found in trigger material. The PBL process does not focus on problem solving with a defined solution, but it allows for the development of other desirable skills and attributes.
Students then plan the strategies, methods, and concrete materials they will use to solve the problem. The teacher will circulate and make observations about the ways students are interacting, and will note the mathematical language they are using as well as the mathematical models they are employing to solve the problem.
Cognitively Guided Instruction is "a professional development program based on an integrated program of research on (a) the development of students' mathematical thinking; (b) instruction that influences that development; (c) teachers' knowledge and beliefs that influence their instructional practice; and (d) the way that teachers' knowledge, beliefs, and practices are influenced by their ...
Provide step-by-step instructions (i.e. illustrate steps to solving a mathematical problem) Encourage students to interact with a new problem or task (i.e. hands-on task that allows students to interact with materials and develop a "need to know") [44] Worked examples: A worked example is a step-by-step demonstration of a complex problem or ...
The teachers’ role in discovery learning is therefore critical to the success of learning outcomes. Students must build foundational knowledge through examples, practice and feedback. This can provide a foundation for students to integrate additional information and build upon problem solving and critical thinking skills. [citation needed]
Problem-based learning is a similar pedagogic approach; however, problem-based approaches structure students' activities more by asking them to solve specific (open-ended) problems rather than relying on students to come up with their own problems in the course of completing a project. Another seemingly similar approach is quest-based learning ...
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