18. 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
19. The Knowledge Network:
(Principle 2)
New Concepts and New Applications
UNDERSTANDING REQUIRES FACTUAL
KNOWLEDGE AND CONCEPTUAL FRAMEWORKS
20. (Principle 3)
Metacognition
A METACOGNITIVE APPROACH
ENABLES STUDENT SELF-MONITORING
66. Credits John Allen Paulos
http://en.wikipedia.org/wiki/File:John_Allen_Paulos.JPG
220 the thinker
http://www.flickr.com/photos/jeope/249159137/ http://www.flickr.com/photos/mattwright/526492646/
How Students Learn reflection
http://books.nap.edu/catalog.php?record_id=10126 http://flickr.com/photos/barnett/206994953/
Pewter Letters Numbers thoughtful
http://flickr.com/photos/lwr/sets/72157594512642436/ http://flickr.com/photos/ronlayters/440835731/
This body is networked Transparency
http://flickr.com/photos/funksoup/403990660/ http://flickr.com/photos/lightmash/2393645062/
The Thinker Sharing
http://flickr.com/photos/renny1967/1509761982/ http://flickr.com/photos/furiousgeorge81/177926979/
DNA Girl Talk
http://www.flickr.com/photos/ghutchis/124782978/ http://flickr.com/photos/e06158/2272739708/
Question mark Big Screen Reflection
http://www.flickr.com/photos/marcobellucci/3534516458/ http://www.flickr.com/photos/benward/181425257/
Mira reading the Griffiths Quantum Text start of the mobile content era
http://flickr.com/photos/ailric/390832774/ http://www.flickr.com/photos/lynetter/329280898
workstation all other images (cc) dkuropatwa
http://www.flickr.com/photos/striatic/241843728/ http://www.flickr.com/photos/dkuropatwa/tags/adayinthelife/
My Class Blogs 2008-2009
AP Calculus AB (2008-2009) Applied Math 20S (Fall 2008)
http://apcalc2008.blogspot.com http://am20sf08.blogspot.com
Applied Math 40S (Winter 2009) Pre-Cal 20S (Fall 2008)
http://am40sw09.blogspot.com http://pc20sf08.blogspot.com
Pre-Cal 40S (Winter 2009) Pre-Cal 30S (Fall 2008)
http://pc40sw09.blogspot.com http://pc30sf08.blogspot.com
67. thanks
Darren Kuropatwa
http://adifference.blogspot.com