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Cognitive Learning01:21

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Cognitive learning is based on purposive behavior, incidental learning, and insight learning.
E. C. Tolman's theory of purposive behavior emphasizes that much behavior is goal-directed. He argued that to understand behavior, we must look at the entire sequence of actions leading to a goal. For instance, high school students study hard, not just due to past reinforcement but also to achieve the goal of getting into a good college.
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Mathematical induction is a structured method of proof used to confirm the truth of statements involving natural numbers. Consider the sum of the first n natural numbers:This formula describes a pattern that appears to hold true as more terms are added. To verify that it is valid for all natural numbers, mathematical induction proceeds in two essential steps. The first is the base case, where the formula is tested for the initial value, typically n = 1. Substituting into both sides confirms the...
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E. C. Tolman emphasized the purposiveness of behavior — the idea that much of our behavior is goal-directed. For instance, employees who aim for a promotion work diligently to meet their targets. Tolman argued that when classical conditioning and operant conditioning occur, the organism acquires certain expectations. In classical conditioning, a child might fear a dog because they expect it to bite. In operant conditioning, a person might consistently work overtime because they expect a...
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Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics BM-PROMA
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Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics BM-PROMA

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Perceptual learning modules in mathematics: enhancing students' pattern recognition, structure extraction, and

Philip J Kellman1, Christine M Massey, Ji Y Son

  • 1Department of Psychology, University of California, Los AngelesInstitute for Research in Cognitive Science, University of Pennsylvania.

Topics in Cognitive Science
|August 29, 2014
PubMed
Summary
This summary is machine-generated.

Perceptual learning (PL) modules significantly enhance mathematics education by improving students' ability to discover and process information. These modules foster rapid, lasting improvements in complex cognitive and symbolic tasks.

Keywords:
AlgebraExpertiseFluencyLearning technologyMathematics instructionMathematics learningPattern recognitionPerceptual learning

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Area of Science:

  • Cognitive Psychology
  • Educational Technology
  • Mathematics Education

Background:

  • Traditional educational approaches focus on declarative and procedural knowledge.
  • Expertise studies highlight perceptual learning (PL) as a key component for information extraction and skill improvement.
  • PL involves common processes of discovery and selection applicable to both sensory and complex cognitive tasks.

Purpose of the Study:

  • To investigate the application of perceptual learning modules (PLMs) in mathematics learning.
  • To assess the effectiveness of PLMs in improving complex mathematical task performance.
  • To determine if PL effects extend to symbolic processing and complex cognitive tasks.

Main Methods:

  • Development and testing of three distinct PLMs targeting different aspects of mathematical performance.
  • Implementation of PLMs in middle and high school mathematics settings.
  • Focus on practice in information extraction, pattern recognition, and structural understanding rather than rote problem-solving.

Main Results:

  • The MultiRep PLM improved students' ability to generate graphs and equations from word problems.
  • The Algebraic Transformations PLM dramatically increased the speed of equation solving by focusing on structural transformations.
  • The Linear Measurement PLM demonstrated successful transfer to novel measurement and fraction problems.

Conclusions:

  • PL techniques can address neglected aspects of learning, such as information discovery and fluent relation processing.
  • Perceptual learning is effective even for complex tasks involving symbolic manipulation.
  • Well-designed PL technology can yield swift and durable learning gains in mathematics.