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Learning with understanding

Learning with understanding. Learning with understanding. The story about Benny. Learning with understanding. Learning with understanding. Learning with understanding. Benny's rules and other examples build up to: Criticism of Programmed learning

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Learning with understanding

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  1. Learningwithunderstanding

  2. Learningwithunderstanding The story about Benny

  3. Learningwithunderstanding

  4. Learningwithunderstanding

  5. Learningwithunderstanding • Benny's rules and other examples build up to: • Criticism of Programmed learning • Lack of focus on developing concepts and understanding can make students develop inexpedient and wrong understanding/rules • Students create their own understanding no matter what • Exaggerated focus on rules in math can make the students focus on remembering rules instead of understanding rules as meaningful generalizations

  6. Learningwithunderstanding It is not enough that students learn to master rules and procedures. They must understand in order to know when and how to apply. This has the implication that mathematics must appear as a coherent body of concepts and methods instead of isolated rules to remember.

  7. Learning with understanding 5 characteristics of learning with understanding (Carpenter and Lehrer 1999). The student constructs relations between what is learnt and the new to be learnt develops, expands and utilizes/applies mathematical knowledge deliberately reflects on and inquires new concepts and methods instead of unconscious adaption expresses subject understanding in speech, writing, drawing, diagram and symbols makes the subject matter her/his own. So students consider knowledge as something quite different from something you have just been told.

  8. Learningwithunderstanding Childrenwithoutalgorithms

  9. Learningwithunderstanding Behaviorism (Skinner)Simple model: Stimulus Response Positivistic through it’s intention of basing psychology directly upon observable facts avoiding models for mental phenomena which are not observable The idea of learning as a direct response to stimulus (teaching) implicates that you can test teaching methods like you test medicine, which is of course nonsense Problem: You cannot consider a teaching learning process through such a simple model.

  10. Cognition Piaget got interested in children’s patterns of systematic thinking. Through a comprehensive research program based on semiclinical interviews of many children Piaget and his co-workers found some regularities in children’s thinking including systematic differences between different age groups. This result is well known as his stage theory and central concepts like assimilation and akkomodation. Source: ATHERTON J S (2010) Learning and Teaching; Assimilation and Accommodation [On-line] UK: Available: http://www.learningandteaching.info/learning/assimacc.htm Accessed: 9 January 2011

  11. Learningwithunderstanding Stages of Cognitive Development

  12. Cognition Some of Piaget's Key Ideas

  13. Cognition Svovlsyre Mikkel: 30*10 = 20*20 (skema fra +)

  14. Cognition - Constructivism • Based on Piaget it becomes a common perception that • Knowledge and learning are matters for the individual • Knowledge is in the mind of the individual • Constructivism (von Glasersfeld) phrase it like this: • knowledge is not transmitted and received passively, but actively built by each individual • understanding is not a question of discovering an objectively existing world but reorganizing your experience • http://video.google.com/videoplay?docid=-7841878207694220233#

  15. Cognition - Constructivism Basedon the ideathateachindividualconstructs his/her ownknowledgeonecan ask: Whatdo weknow?

  16. Cognition - Constructivism A model of Vygotsky’stheory of language and conceptdevelopment (Høines) Mind: Conceptcontent Refer to symbolises Externalinfluence Expressions Experiences

  17. Language - Vygotsky Codes which are used freely carrying concept content are called first order language – below there are 2 parallel first order languages Mind: Concept content on 7 Experiences Counting to 7, writing 7, hearing 7 ”seven” Expressions

  18. Language - Vygotsky A new content expression introduced needs some translation via a well known expression – 7 is second order language Mind: Concept content on 7 Experiences Counting to 7, hearing 7 7 ? ”seven” Expressions

  19. Language - Vygotsky Working and training makes 7 a first order language – no need for translation Mind: Concept content on 7 Experiences Counting to 7, hearing 7 7 ”seven” Expressions

  20. Language - Vygotsky According to Vygotsky concept content and language about it develop simultaneously – knowledge cannot be speechless First order language: You express spontaneously using first order language and think and learn by means of first order language. Second order language:

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