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Arch Concepts through Positive and Negative Examples

Explore teaching arch concepts by analyzing near-misses, generalization, and specialization. Utilize positive and negative examples to enhance learning and comprehension of arch properties. Experiment with version spaces managing multiple models for effective teaching.

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Arch Concepts through Positive and Negative Examples

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  1. Version Spaces Learning by managing multiple models

  2. Learning by analyzing differences • Student must learn a concept. How do you propose to teach the concept? • Consider the concept of an “Arch”

  3. What make’s an arch an arch • Teacher can provide examples and counter examples: • An arch is made up of • Supports • Top • What are an arch’s properties?

  4. Near-miss improves understanding NOT an ARCH But close Near-miss can add a link System learns “must-support”

  5. Near-miss is a negative example of the concept Negative example can remove (or modify) a link

  6. Positive example can help generalize Arch’s top can be a brick OR a wedge

  7. Negative Examples allow us to • Generalize or Specialize? • Positive Examples allow us to • Generalize of Specialize?

  8. Version Spaces: Learn by managing multiple models

  9. Version spaces • Each time a general model is specialized, that specialization must be a generalization of an existing specific model. • Corollary: Each time a specific model is generalized, that generalization must be a specialization of an existing general model • Each time a general model is specialized that specialization must not be a specialization of ANOTHER general model

  10. John’s allergies

  11. Version Space General [?,?,?,?] Specific [Sam’s,breakfast,friday,cheap]

  12. [Lobdell, lunch, Friday, expensive] • Negative example: • What happens to “Most general model”? • Cannot be lobdell’s must be Sam’s • Cannot be lunch, must be breakfast • Cannot be expensive, must be cheap • Both samples say Friday, so that feature must not matter • What happens to “Most specific model”?

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