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Metacognition is a conscious process where individuals are aware of their cognitive and executive processes, such as planning before solving a problem or self-monitoring during reading. For instance, a writer may need help with composing a piece. The situation involves a writer who is working on a piece of writing, but while doing so, they realize that something is missing. They notice that their characters lack depth or details. This realization occurs because the writer is reflecting on their...
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Cognitive learning is based on purposive behavior, incidental learning, and insight learning.
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During Piaget's concrete operational stage, from ages 7 to 11, children exhibit a marked increase in logical thinking skills, specifically in relation to tangible, real-world events. This stage is characterized by the development of several essential cognitive concepts, including conservation, reversibility, and classification, all of which support the child's evolving capacity for structured thought.
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Controlled processes in human consciousness represent high-alert mental states where individuals deliberately focus their attention on achieving specific goals. Controlled processes can be seen in situations like mastering new technology, where a person might become so absorbed that they ignore surrounding distractions. Such processes involve selective attention, requiring one to concentrate on particular elements of experience while disregarding others. These are governed by executive...
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Conceptual Knowledge, Procedural Knowledge, and Metacognition in Routine and Nonroutine Problem Solving.

David W Braithwaite1, Lauren Sprague1

  • 1Department of Psychology, Florida State University.

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Summary
This summary is machine-generated.

Students use conceptual knowledge in math when procedural knowledge is weak, with doubt mediating this relationship. Metacognition plays different roles in routine versus nonroutine problem-solving.

Keywords:
ArithmeticConceptual knowledgeDecimalsFractionsMathematical cognitionMetacognitionProcedural knowledge

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Area of Science:

  • Cognitive Psychology
  • Educational Psychology
  • Mathematics Education

Background:

  • Understanding how students utilize conceptual knowledge in mathematics problem-solving remains a challenge.
  • Existing research often overlooks the interplay between procedural and conceptual knowledge, and metacognitive influences.

Purpose of the Study:

  • To investigate the conditions under which students recruit conceptual knowledge during math problem-solving.
  • To examine the mediating role of metacognitive processes, specifically doubt, in the relationship between procedural and conceptual knowledge.
  • To differentiate the functions of metacognition in routine versus nonroutine mathematical tasks.

Main Methods:

  • Two studies involving university students solving fraction and decimal arithmetic problems.
  • Think-aloud protocols and analysis of written work to code for conceptual knowledge use and doubt.
  • Additional tasks included explaining solutions and solving nonroutine problems.

Main Results:

  • Conceptual knowledge use during routine calculations was associated with doubt, not accuracy.
  • Doubt during routine calculations was negatively associated with accuracy.
  • Conceptual knowledge use in explaining solutions correlated with accuracy, but only when not used during calculation.
  • Doubt in nonroutine problem-solving was positively associated with accuracy.

Conclusions:

  • Students may use conceptual knowledge in routine math problems when procedural fluency is low, with doubt acting as a mediator.
  • Metacognitive processes, like doubt, appear to serve distinct roles in routine versus nonroutine mathematical problem-solving.
  • Findings highlight the complex interactions between procedural knowledge, conceptual knowledge, and metacognition in learning mathematics.