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Teaching
    a pedagogical framework




                                 Darren Kuropatwa
                              adifference.blogspot.com
i n g
    am
f r
Three Pedagogical Principles
Three Pedagogical Principles
Studentsʼ Errors and Misconceptions
(Principle 1)          Based on Previous Learning
Students come to the classroom with conceptions of numbers grounded in
their whole-number learning that lead them astray in the world of rational
numbers; e.g. multiplying always makes numbers bigger.




                x                      =
          Teachers must engage studentsʼ preconceptions
Understanding requires factual knowledge
                                and conceptual frameworks




                The Knowledge Network:
(Principle 2)   New Concepts and New Applications
3
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Principle 3

Learning is facilitated through the
use of metacognitive strategies ...




     A metacognitive approach
     enables student self-monitoring
eror analysis
Find the error ...
Three Pedagogical Principles


                x    =
community
community
just like we all learned in kindergarden
music from the                                                   thanks
freemusicarchive.org

“Blues for Oliver” (by Benny Golbin)
http://freemusicarchive.org/music/Benny_Golbin/~/Blues_for_Oliver
Photos
     holding hands by flickr user JonathanCohen
     http://www.flickr.com/photos/jonathancohen/4084485753/


     Goldener Bilderrahmen - gold picture frame by flickr user eriwst
     http://www.flickr.com/photos/eriwst/2303608353/


     I’m waiting for my man by flickr user onkel_wart
     http://www.flickr.com/photos/onkel_wart/2038421770/
                                                                                                    sweet potato cake by flickr user awhiskandaspoon
                                                                                          http://www.flickr.com/photos/awhiskandaspoon/3046642768/




     you’ve been framed by flickr user Yersinia                                                1965 Canadian Quarter Reverse by flickr user Astro Guy
     http://www.flickr.com/photos/yersinia/2439823650/                                             http://www.flickr.com/photos/astroguy/4292081808/


     Framed! by flickr user freebird4                                                                          Smarties Graph #3 by flickr user sneeu
     http://www.flickr.com/photos/freebird4/143459063/                                                http://www.flickr.com/photos/sneeu/3204193019/


      How People Learn                                                                                     Find the error by flickr user Daniel Paquet
     http://books.nap.edu/catalog.php?record_id=9853                                            http://www.flickr.com/photos/danielpaquet/847908552/




      How Students Learn                                                                                                             Lost in Thought
     http://books.nap.edu/catalog.php?record_id=10126                                           http://www.flickr.com/photos/johnbolland/1544108261/

     MMMMM, Sourdough Pancakes for Breakfast by flickr user Chiot's Run                                                    Geese by flickr user swan-t
     http://www.flickr.com/photos/chiotsrun/4311640086/                                                 http://www.flickr.com/photos/swan-t/50979299/

      Pewter Letters Numbers                                           We are all under One Sky by flickr user MaureenShaughnessy (aka MontanaRaven)
     http://flickr.com/photos/lwr/sets/72157594512642436/                                         http://www.flickr.com/photos/montanaraven/48290744

      This body is networked                                                                               Geese Flying by flickr user superstrikertwo
     http://flickr.com/photos/funksoup/403990660/                                           http://www.flickr.com/photos/superstrikertwo/3270702845/

     291220082456 by flickr user roland                                                                                   Silhouette of a family of five
     http://www.flickr.com/photos/roland/3148183909/                                        http://www.flickr.com/photos/13010608@N02/3082540785/

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Teaching (a pedagogical framework)

  • 1. Teaching a pedagogical framework Darren Kuropatwa adifference.blogspot.com
  • 2. i n g am f r
  • 3.
  • 4.
  • 5.
  • 8.
  • 9. Studentsʼ Errors and Misconceptions (Principle 1) Based on Previous Learning Students come to the classroom with conceptions of numbers grounded in their whole-number learning that lead them astray in the world of rational numbers; e.g. multiplying always makes numbers bigger. x = Teachers must engage studentsʼ preconceptions
  • 10. Understanding requires factual knowledge and conceptual frameworks The Knowledge Network: (Principle 2) New Concepts and New Applications
  • 11. 3 4
  • 12. 0.75 3/4 3:4 3 4 $0.75 75%
  • 13. 0.75 3/4 3:4 3 4 $0.75 75%
  • 14. 0.75 3/4 3:4 3 4 $0.75 75%
  • 15. 0.75 3/4 3:4 3 4 $0.75 75%
  • 16. 0.75 3/4 3:4 3 4 $0.75 75%
  • 17. Principle 3 Learning is facilitated through the use of metacognitive strategies ... A metacognitive approach enables student self-monitoring
  • 23.
  • 24.
  • 25. just like we all learned in kindergarden
  • 26. music from the thanks freemusicarchive.org “Blues for Oliver” (by Benny Golbin) http://freemusicarchive.org/music/Benny_Golbin/~/Blues_for_Oliver
  • 27. Photos holding hands by flickr user JonathanCohen http://www.flickr.com/photos/jonathancohen/4084485753/ Goldener Bilderrahmen - gold picture frame by flickr user eriwst http://www.flickr.com/photos/eriwst/2303608353/ I’m waiting for my man by flickr user onkel_wart http://www.flickr.com/photos/onkel_wart/2038421770/ sweet potato cake by flickr user awhiskandaspoon http://www.flickr.com/photos/awhiskandaspoon/3046642768/ you’ve been framed by flickr user Yersinia 1965 Canadian Quarter Reverse by flickr user Astro Guy http://www.flickr.com/photos/yersinia/2439823650/ http://www.flickr.com/photos/astroguy/4292081808/ Framed! by flickr user freebird4 Smarties Graph #3 by flickr user sneeu http://www.flickr.com/photos/freebird4/143459063/ http://www.flickr.com/photos/sneeu/3204193019/ How People Learn Find the error by flickr user Daniel Paquet http://books.nap.edu/catalog.php?record_id=9853 http://www.flickr.com/photos/danielpaquet/847908552/ How Students Learn Lost in Thought http://books.nap.edu/catalog.php?record_id=10126 http://www.flickr.com/photos/johnbolland/1544108261/ MMMMM, Sourdough Pancakes for Breakfast by flickr user Chiot's Run Geese by flickr user swan-t http://www.flickr.com/photos/chiotsrun/4311640086/ http://www.flickr.com/photos/swan-t/50979299/ Pewter Letters Numbers We are all under One Sky by flickr user MaureenShaughnessy (aka MontanaRaven) http://flickr.com/photos/lwr/sets/72157594512642436/ http://www.flickr.com/photos/montanaraven/48290744 This body is networked Geese Flying by flickr user superstrikertwo http://flickr.com/photos/funksoup/403990660/ http://www.flickr.com/photos/superstrikertwo/3270702845/ 291220082456 by flickr user roland Silhouette of a family of five http://www.flickr.com/photos/roland/3148183909/ http://www.flickr.com/photos/13010608@N02/3082540785/