Here are some key points about the pedagogical principle of understanding requiring both factual knowledge and conceptual frameworks:- Students need to learn basic facts and procedures, but these are not sufficient for understanding without conceptual frameworks to organize and use this knowledge. - Conceptual frameworks allow students to see how different facts and ideas relate to each other. They provide mental structures for comprehending new information.- Well-developed conceptual frameworks enable students to apply what they know to new situations and problems. Factual knowledge without frameworks tends to remain disconnected and hard to use productively. - Teaching should aim to develop both factual knowledge and conceptual frameworks in parallel. New facts are best learned when linked to existing frameworks, and frameworks evolve
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The document provides guidance for students on how to succeed in mathematics class by arriving prepared with materials, doing homework, asking questions, getting extra help, forming study groups, and participating regularly online. Key practices emphasized include reviewing notes daily, setting aside regular time for homework, and asking lots of questions about anything not understood.
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Semelhante a Here are some key points about the pedagogical principle of understanding requiring both factual knowledge and conceptual frameworks:- Students need to learn basic facts and procedures, but these are not sufficient for understanding without conceptual frameworks to organize and use this knowledge. - Conceptual frameworks allow students to see how different facts and ideas relate to each other. They provide mental structures for comprehending new information.- Well-developed conceptual frameworks enable students to apply what they know to new situations and problems. Factual knowledge without frameworks tends to remain disconnected and hard to use productively. - Teaching should aim to develop both factual knowledge and conceptual frameworks in parallel. New facts are best learned when linked to existing frameworks, and frameworks evolve
Semelhante a Here are some key points about the pedagogical principle of understanding requiring both factual knowledge and conceptual frameworks:- Students need to learn basic facts and procedures, but these are not sufficient for understanding without conceptual frameworks to organize and use this knowledge. - Conceptual frameworks allow students to see how different facts and ideas relate to each other. They provide mental structures for comprehending new information.- Well-developed conceptual frameworks enable students to apply what they know to new situations and problems. Factual knowledge without frameworks tends to remain disconnected and hard to use productively. - Teaching should aim to develop both factual knowledge and conceptual frameworks in parallel. New facts are best learned when linked to existing frameworks, and frameworks evolve (20)
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Here are some key points about the pedagogical principle of understanding requiring both factual knowledge and conceptual frameworks:- Students need to learn basic facts and procedures, but these are not sufficient for understanding without conceptual frameworks to organize and use this knowledge. - Conceptual frameworks allow students to see how different facts and ideas relate to each other. They provide mental structures for comprehending new information.- Well-developed conceptual frameworks enable students to apply what they know to new situations and problems. Factual knowledge without frameworks tends to remain disconnected and hard to use productively. - Teaching should aim to develop both factual knowledge and conceptual frameworks in parallel. New facts are best learned when linked to existing frameworks, and frameworks evolve
- 1. De Ma sig still tte n rs! ropatwa Da rren Ku ropatwa 2.0 u B C-SA .me/dkeira / CCEY-Nge about ndnSglvThe d Fernci er 2012 i Enmtb raa o ob 19 Oct Su se / g the , innipeg Watchin W Watching the Sunset / Fernando Silveira / CC BY-NC-SA 2.0
- 2. <begin>
- 3. <design>
- 4. Design: first, let’s get visual ...
- 5. Robie House
- 6. gton D C metro station Washin
- 7. peace optimism fun trustworthy ecology enlightenment flamboyant dependable illness happiness warmth committed Government-issued energy stimulant, balance of youthful Colour exciting red simulation fun energy exciting Messages and blue calm lighthearted draws attention and Meanings timeless authoritative practical stability, purity solid reliability cleanliness approachability neutrality powerful
- 9. "Grand Design" Spiral Galaxy M81
- 11. e si gn D Robie House
- 12. e si gn D funct ional Robie House
- 13. e si gn D funct ional intentional Robie House
- 14. e si gn D funct ional intentional beautifu l Robie House
- 15. Why should kids care about learning?
- 16. Why should kids care about mathematics?
- 17. Why should kids care about mathematics? job skills, needs of science and technology One Of These Buttons Will Get Me Out Of Here / Bart / CC BY-NC 2.0
- 18. Why should kids care about mathematics? job skills, needs of science and technology essential understanding to be a responsible citizen Girly Giggles / Trent McBride / CC BY-NC 2.0 Note: only 48 stars! / David Zeuthen / CC BY-NC-SA 2.0
- 19. Why should kids care about mathematics? job skills, needs of science and technology essential understanding to be a responsible citizen Girly Giggles / Trent McBride / CC BY-NC 2.0 Note: only 48 stars! / David Zeuthen / CC BY-NC-SA 2.0
- 20. Why should kids care about mathematics? job skills, needs of science and technology essential understanding to be a responsible citizen Girly Giggles / Trent McBride / CC BY-NC 2.0 Note: only 48 stars! / David Zeuthen / CC BY-NC-SA 2.0
- 21. Why should kids care about mathematics? job skills, needs of science and technology curiosity beauty essential understanding to play be a responsible citizen and transcendence
- 22. Why should kids care about mathematics? curiosity beauty essential understanding to play be a responsible citizen and transcendence
- 23. Why kids should care about learning. Bubbles / Andrey Zhukov / CC BY-NC 2.0
- 24. Design: first, let’s get visual ... ... now let me tell you about stories
- 26. What’s your personal narrative ...
- 27. What’s your personal narrative ... in 4 slides?
- 33. Can “fun” change behaviour for the better?
- 35. noun Design
- 36. Design verb
- 37. The Coyote as a designer Road Runner: Willy Coyote contro Beep-Beep
- 38. Road Runner: Willy Coyote contro Beep-Beep
- 39. Tim Hartford on trial and error
- 41. I think reckless curiosity would be what the world needs now. Andrew Bird Andrew Bird / Guus Krol / CC BY-NC-ND 2.0
- 42. le ss cur iosity? ning for reck e desi gn lear can w Play & Learn learn by flickr user Mark Brannan http://www.flickr.com/photos/heycoach/1197947341/ Play! by flickr user Matteo Angelino http://www.flickr.com/photos/angelinux/2775107421/
- 43. </design>
- 44. <presentations>
- 45. Hypnotizing Chickens a pre-modern presentation
- 46. Hypnotizing Chickens a modern presentation
- 47. Hypnotizing Chickens a post-modern presentation Little chicken by flickr user Lovro67 http://www.flickr.com/photos/30978323@N02/3755800512/
- 51. “Why would you use Why? words on the screen when they do just fine in your mouth” Seth Godin
- 53. 0 w p m 1 5 Judy Mouth Open by flicker user Jason Nelms http://www.flickr.com/photos/thejs/35407165/
- 54. 0 w p m 2 5 wick rat Lozo u er S ick r us by fl /365 / | 24 393580 ife 303 rn L ode owick/4 to M z lied /suratlo pp os gy A t holo om/pho yc r.c g Ps k adin ww.flic Re //w : http
- 55. .adobe.com
- 56. Keeping An Eye On Time by flickr user badboy69 http://www.flickr.com/photos/badboy69/2333409688/
- 58. cc licensed ( BY NC SA ) flickr photo by misterbisson: http://flickr.com/photos/maisonbisson/201844037/
- 59. If you can’t explain it simply, you don’t understand it well enough.
- 60. Times New Roman 96 pt Times New Roman 48 pt Times New Roman 30 pt Times New Roman 14 pt
- 61. Can you read this? Can you read this?
- 62. Helvetica 96 pt Times New Roman 96 pt
- 65. Bonnie Bassler teaches biology
- 67. Bonnie Bassler @ TED #slides 5
- 68. Bonnie Bassler @ TED #slides 5 uses a “black slide” (so really 6 slides)
- 69. Bonnie Bassler @ TED #slides 5 uses a “black slide” (so really 6 slides) time taken 1min 37 sec
- 70. Bonnie Bassler @ TED Simplifies complex ideas
- 71. Bonnie Bassler @ TED Simplifies complex ideas Unexpected bacteria vrs human
- 72. Bonnie Bassler @ TED Simplifies complex ideas Unexpected bacteria vrs human Credible (Dr. Bassler)
- 73. Bonnie Bassler @ TED Simplifies complex ideas Unexpected bacteria vrs human Credible (Dr. Bassler) Concrete (bacteria)
- 74. Bonnie Bassler @ TED Simplifies complex ideas Unexpected bacteria vrs human Credible (Dr. Bassler) Concrete (bacteria) Emotional (passion & laughter)
- 75. Bonnie Bassler @ TED Simplifies complex ideas Unexpected bacteria vrs human Credible (Dr. Bassler) Concrete (bacteria) Emotional (passion & laughter) Story (wanna know what she says next?)
- 77. If you can’t explain it simply, you don’t understand it well enough.
- 78. Eric Berlow: How Complexity Leads to Simplicity
- 80. </presentations>
- 81. <teaching>
- 82. A Pedagogical Framework x =
- 83. Three (practices and) principles
- 84. Three (practices and) principles
- 86. Students’ 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 students’ preconceptions
- 87. Understanding requires factual knowledge and conceptual frameworks The Knowledge Network: (Principle 2) New Concepts and New Applications
- 88. 3 4
- 89. 0.75 3/4 3:4 3 4 $0.75 75%
- 90. 0.75 3/4 3:4 3 4 $0.75 75%
- 91. 0.75 3/4 3:4 3 4 $0.75 75%
- 92. 0.75 3/4 3:4 3 4 $0.75 75%
- 93. 0.75 3/4 3:4 3 4 $0.75 75%
- 94. kn owl edge isn’t s in our head een us ’s b etw it David Weinberger Everything is Miscellaneous
- 95. Principle 3 Learning is facilitated through the use of metacognitive strategies ... A metacognitive approach enables student self-monitoring
- 96. eror analysis
- 97. Find the error ...
- 98. community
- 99. community
- 102. A Pedagogical Framework x =
- 104. the flickr® assignment 89
- 106. What is descriptive language, and why is it important to your writing? (Brooksie's Symbolic)
- 107. WHAT I'M READING NOW / Chris / CC BY-NC-SA 2.0
- 108. Analogy is the motor of the car of thought. untitled / null0 / CC BY 2.0
- 109. analogy:thinking :: motor:car untitled / null0 / CC BY 2.0
- 110. What does Pi sound like?
- 113. ever ything T tea ching is NO he project. d Lea rning they start t Proje c t Base now b efore need to k they Horse and cart / Christian Guthier / CC BY-NC-SA
- 114. the developing expert voices project 98
- 115. DEVious
- 116. Watch and Learn: DEVious
- 117. Teasers ...
- 120. THE STORY OF H.
- 137. <design challenge 1>
- 138. What’s your personal narrative ...
- 139. What’s your personal narrative ... in 4 slides?
- 146. <design challenge 2>
- 147. my first class "All learning pivots on who we think we are, and who we see ourselves as capable of becoming." Frank Smith
- 148. Hi
- 149. The Escalator ... escalator What does this have to do with school?
- 150. The Escalator ... escalator What does this have to do with school?
- 151. Learn to do what mathematicians do. Magic is true! by flickr user photographer padawan
- 152. "All learning pivots on who we think we are, and who we see ourselves as capable of becoming." Frank Smith
- 153. Critical Path to Success!! A student who wants to succeed in this course will: •!Always be on time for class. time
- 160. MY CREDIT I know I have lost by flickr user Monkey Magic
- 161. Critical Path to Success!! A student who wants to succeed in this course will: • Alway arrive to class prepared to work with all materials needed. graphing calculator
- 162. Critical Path to Success!! A student who wants to succeed in this course will: • Alway arrive to class prepared to work with all materials needed. 3-ring binder loose leaf paper notebook or duotang graphing calculator
- 163. Critical Path to Success!! A student who wants to succeed in this course will: • Alway arrive to class prepared to work with all materials needed. 3-ring binder loose leaf paper notebook or duotang 12 pencils graphing calculator
- 164. Critical Path to Success!! A student who wants to succeed in this course will: • Alway arrive to class prepared to work with all materials needed. 3-ring binder loose leaf paper notebook or duotang 12 pencils graphing calculator
- 165. Critical Path to Success!! A student who wants to succeed in this course will: • Alway arrive to class prepared to work with all materials needed. 3-ring binder loose leaf paper notebook or duotang 12 pencils geometry set graphing calculator
- 166. Critical Path to Success!! A student who wants to succeed in this course will: • Always attempt ALL their homework assignments.
- 167. Critical Path to Success!! A student who wants to succeed in this course will: • Review their class notes every night before going to bed.
- 168. The Curve of Forgetting ... ... describes how we retain or get rid of information that we take in. It's based on a one-hour lecture. more about Learning and Remembering
- 169. The Curve of Forgetting ... ... describes how we retain or get rid of information that we take in. It's based on a one-hour lecture. more about Learning and Remembering
- 170. The Curve of Forgetting ... ... describes how we retain or get rid of information that we take in. It's based on a one-hour lecture. more about Learning and Remembering
- 171. The Curve of Forgetting ... ... describes how we retain or get rid of information that we take in. It's based on a one-hour lecture. more about Learning and Remembering
- 172. Critical Path to Success!! A student who wants to succeed in this course will: • Always ask LOTS of questions about anything they don't understand.
- 173. Critical Path to Success!! A student who wants to succeed in this course will: • Always gets extra help from the teacher when they feel they are falling behind.
- 174. Critical Path to Success!! A student who wants to succeed in this course will: • Find one or two people to be their study partners and form a study group.
- 175. Critical Path to Success!! A student who wants to succeed in this course will: Consistently set a regular time of day to do homework assignments.
- 176. Critical Path to Success!! A student who wants to succeed in this course will: • Participate regulary on the course blog. http://pc40sw09.blogspot.com
- 177. How to Create a Google Account http://tinyurl.com/6f7aae
- 178. How to Sign Up For Blogger http://tinyurl.com/6x83hs
- 179. "All learning pivots on who we think we are, and who we see ourselves as capable of becoming." Frank Smith
- 180. Homework email Mr. Kuropatwa: dkuropatwa@gmail.com get a account sign up at .com
- 181. Homework Riddle me this ... Why are there 360° in a circle? The Riddler Fans Art
- 182. Have a nice day!
- 183. ... and don't forget your homework.
- 184. Photo Credits Graphing http://flickr.com/photos/mewzii/149555960/ 3-ring binders http://farm2.static.flickr.com/1311/1292315430_285d142fbe_m.jpg Sharpener http://flickr.com/photos/big-e-mr-g/192174638/ Studying http://flickr.com/photos/jamilsoni/90538195/ Aqua wins by a point http://flickr.com/photos/jahdakinebrah/92200688/ Studying. As you should probably be doing right now. http://flickr.com/photos/weshph/462633863/ Ross Homework http://flickr.com/photos/laffy4k/418602591/ workstation http://flickr.com/photos/striatic/241843728/ genius http://flickr.com/photos/thearchigeek/223751752/ Smiley Face http://flickr.com/photos/greyarea/1473/ Reviewing Notes http://flickr.com/photos/knott/66465528/ email logo http://flickr.com/photos/surfstyle/354581855/ Questions http://flickr.com/photos/oberazzi/318947873/ Telephone Keypad http://flickr.com/photos/cgc/5259321/ envelope http://flickr.com/photos/bip/420177741/
- 186. <design challenge 3>
- 188. i r f a e o ad m e is most of a trees’ mass is tre from the carbon it breathes A cc licensed ( BY NC SD ) flickr photo by dkuropatwa: http://flickr.com/photos/dkuropatwa/2923120259/
- 190. noun Design
- 191. Design verb
- 192. Now go design something.
- 193. C O N TA C T Darren Kuropatwa twitter: @dkuropatwa about.me/dkuropatwa <end> 2.0 C-SA C BY-N ei ra / C o Silv r nand t / Fe Sunse hing the Watc Watching the Sunset / Fernando Silveira / CC BY-NC-SA 2.0