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Metacognition is an important factor of mathematical problem solving. Metacognition is the ability to monitor and control our own thoughts, how we approach the problem, how we choose the strategies to find a solution, or ask ourselves about the problem, in the other word, it can be defined as think about thinking.
The five strands of Mathematical Proficiency are conceptual knowledge, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. Honestly, as a student, I was really good at memorizing and following procedures.
Strategies for solving the problem Draw a model or diagram. Students may find it useful to draw a model, picture, diagram, or other visual aid to help with the problem solving process. Act it out. Work backwards. Write a number sentence. Use a formula.
The five mathematical proficiencies Conceptual understanding, Communication using symbols, Fluency, Logical reasoning and Strategic competence can be applied and connected by using a range of real-life contexts to introduce and explore mathematical concepts, as well as to consolidate them.
Problem Solving. Reasoning and Proof. Communication. Connections. Representation.
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They were based on five key areas 1) Representation, 2) Reasoning and Proof, 3) Communication, 4) Problem Solving, and 5) Connections. If these look familiar, it is because they are the five process standards from the National Council of Teachers of Mathematics (NCTM, 2000).

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