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# CMC3 Fall 2012 Give It All You Got V3

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Reform the teaching of collegiate mathematics in your classroom immediately with these hot tips, guidlines and resources!

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### CMC3 Fall 2012 Give It All You Got V3

1. 1. Give It All You Got! Break Away from the 3R’s To the 3C’s Fred Feldon, Coastline CC CMC3 South Fall Conference Los Angeles Mission College October 6, 2012
3. 3. August 31, 2012, 7:13pmA “Blue Moon”?
4. 4. Question: “Which is bigger, half of a smallpizza or one-fourth of a large?”
5. 5. r1 r2
6. 6. r1 r2 If ¼ AL > ½ ASthen ¼ π r12 > ½ π r22 → ¼ r12 > ½ r22 → r12 > 2 r22 and r1 > 2 r2
7. 7. SizesSmall (10”)Medium (12”)Large (14”)X-Large (16”)
8. 8. Mmm…Is 14 > 10 2 ?
10. 10. The Problem…
11. 11. The Problem…• Content is ubiquitous• College teaching is no longer about the lecture
13. 13. MOOC: Massive open online courses
14. 14. August 28, 2012
15. 15. The Solution…What can YOU do? Right NOW ?
16. 16. The Solution…• Summarize, highlight and motivate; ignite a shared intellectual endeavor; relate math in the classroom to the real world
17. 17. The Solution…• Summarize, highlight and motivate; ignite a shared intellectual endeavor; relate math in the classroom to the real world• Guide and direct students; community trumps content
18. 18. The Solution…• Summarize, highlight and motivate; ignite a shared intellectual endeavor; relate math in the classroom to the real world• Guide and direct students; community trumps content• Monitor progress; follow 80-20 Rule
19. 19. The Solution…• Summarize, highlight and motivate; ignite a shared intellectual endeavor; relate math in the classroom to the real world• Guide and direct students; community trumps content• Monitor progress; follow 80-20 Rule• The 3 C’s !
20. 20. The Solution…• Summarize, highlight and motivate; ignite a shared intellectual endeavor; relate math in the classroom to the real world• Guide and direct students; community trumps content• Monitor progress; follow 80-20 Rule• Emphasize Communication, Connectivity and Collaboration!
21. 21. • Communication - Students talk more; you talk less. In class:mini-lectures punctuated by individual, pair orgroup work and explain their answers. Online:Respond every day but make interaction 25%teacher-to-student and 75% student-to-student
22. 22. Fifty Ways to Leave Your Lectern “The ABC’s (Bloom’s Affective, Behavioraland Cognitive goals) should be more equally balanced.” -- Dr. Constance Staley, Professor of Communication, University of Colorado
23. 23. • Communication - Students talk more; you talk less. In class: mini-lectures punctuated by individual, pair or groupwork and explain their answers. Online: Respondevery day but make interaction 25% teacher-to-student and 75% student-to-student• Connectivity - Research shows a sense of communityincreases success and retention. Foster“productive struggle,” thinking through problemsand sharing viewpoints. More illuminating forstudents than hearing you do it.
24. 24. “Productive Failure”: Why Flounderingis Good--Attempting to figuresomething out on your own producesbetter results than having guidancefrom the very beginning.” -- Annie Murphy Paul, Learning Theorist, Time.com “Health & Science,” August, 2012
25. 25. • Collaboration - We’re all in this together. We’re all hereto help each other. The best way to learnsomething is to explain it so someone else.Blooms’ taxonomy. Incorporate peer review andcloud computing. Advise students to askquestions: “I or another student will reply rightaway!”
26. 26. “Mathematics is not a careful marchdown a well-cleared highway, but ajourney into a strange wilderness,where the explorers often get lost.”-- W. S. Anglin, author of Mathematics: A Concise History and Philosophy, 1994
27. 27. Improving Fluid Intelligence with Training on Working Memory, 2008, by Jaeggi, Buschkuehl, Jonides and Perrig
28. 28. Which of these are Correct Rules and which areMal-Rules? Explain your answer. You may give examples.
29. 29. In the picture below, which is the graph of the function and which is the graph of its derivative? Explain how you got your answer.
30. 30. A solid wood cube, 1 foot on an edge, was sawed into eight smaller congruent cubes.The smaller cubes were then reassembled toform the longest possible rectangular prism.What is the percent change in surface area?
31. 31. Mathematical MisfitWhich fits best: a square peg in a round hole, ora round peg in a square hole?To be more precise, if you take a circle and fit itjust inside a square, or take a square and fit itjust inside a circle, which fills up proportionallymore space?
32. 32. Are -59 and (-5)9 the same,or are they different? Explainyour answer.
33. 33. Which is better? To get 1/3 Off theprice of an item? Or 1/3 More for the same price? -- Michael Tsiros, Marketing Professor, University of Miami School of Business, 9/1/2012 Full article at http://www.twincities.com/ci_21446847/bad- math-skills-cause-customers-miss-bargains-study
35. 35. Educational PhilosophiesDirect Instruction vs. Constructivist Learning1. Teacher is active 1. Student is active2. Learning is “poured” into 2. Autonomous Learning the student by reading 3. Sources – Teacher, Peers, or lecturing. Textbook, Library, Internet3. Textbook Driven 4. Concrete Experience4. Drill – Rote Memory 5. Trial and Error Learning –5. Practice – Rote Discuss, Correct Mistakes6. Student is observing. 6. Teacher Facilitator Nancy Allen, Ph.D., College of Education, Qatar University, “Active Learning Strategies and Techniques”
36. 36. Changes – Course GoalsDirect Instruction vs. Constructivist LearningFamiliarizing students Ensuring that students learn with key concepts how to use those concepts
37. 37. Fitzroy Kennedy, University of Alabama, “Critical andCreative Thinking”
38. 38. Changes – Teacher’s RoleDirect Instruction vs. Constructivist LearningDispenses information Designs and manages the and concepts overall instructional process
39. 39. Changes – Student’s RoleDirect Instruction vs. Constructivist LearningPassive recipients of Responsible for the information and acquisition of content content and for working collaboratively with other students to learn how to use it Larry Michaelsen, University of Oklahoma, “Getting Started With Team-Based Learning”
40. 40. Describing Levels and Components of a Math-Talk Learning Community• What does the transformation to reformmathematics teaching look like?• What would such a classroom look like?• How do teachers, along with theirstudents, get there? Kimberly Hufferd-Ackles, Karen C. Fuson, and Miriam Gamoran Sherin, Northwestern University, NCTM Journal for Research in Mathematics Education, March 2004
41. 41. Describing Levels and Components of a Math-Talk Learning CommunityShift over Levels 0-3: The classroomcommunity grows to support students actingin central or leading roles and shifts from afocus on answers to a focus on mathematicalthinking.
42. 42. Describing Levels and Components of a Math-Talk Learning Community• Level 0: Traditional teacher-directedclassroom with brief answer responses fromstudents• Level 1: Teacher begins to pursue studentmathematical thinking. Teacher plays centralrole in the math-talk community
43. 43. Describing Levels and Components of a Math-Talk Learning Community• Level 2: Teacher models and helps studentsbuild new roles. Some co-teaching and co-learning begins as student-to-student talkincreases. Teacher physically begins to moveto side or back of the room
44. 44. Describing Levels and Components of a Math-Talk Learning Community• Level 3: Teacher as co-teacher and co-learner. Teacher monitors all that occurs, stillfully engaged. Teacher is ready to assist, butnow in more peripheral and monitoring role(coach and assister)
45. 45. Action Trajectories for Teacher and Student
46. 46. The BIG Problem…
47. 47. The BIG Problem…Real World Classroom
48. 48. “Mathematical reasoning in *thereal world and] workplace differsmarkedly from the algorithmstaught in school.” -- John P. Smith, Educational Psychologist, Michigan State University
49. 49. Breaking News: You do NOT have tobe an expert to solve this problem!
50. 50. Breaking News: You do NOT have to adopt a certain curriculum ortextbook to solve the problem!
51. 51. Breaking News: You do NOT have to use a particularmethod of instruction or mode of deliveryto solve the problem!
52. 52. My Proposal: All you have to do is“leave the lectern” asoften as possible, and promote the 3C’s! (Communication, Connectivity and Collaboration)
53. 53. My Proposal: That alone willclosely duplicate the environment of the workplace!
54. 54. My Proposal:…will make problem-solving more like the real world!
55. 55. My Proposal: …will engage studentsand restore the sense of enjoyment and adventure in teaching for you!
56. 56. My Proposal: …will reform the teaching and learningof mathematics in your classes!
57. 57. My Proposal: …will increasestudents’ success,retention and your popularity!
58. 58. Five Guiding Principles on How Mathematics Can and Should be Taught From the Co-Authors of IMACSInstitute for Mathematics & Computer Science, 2012 http://www.eimacs.com/blog/2012/08/algebra-is-not-the-problem-part-2/
59. 59. Five Guiding Principles on How Mathematics Can and Should be Taught1. Mathematics is an important intellectual discipline—not merely a collection of algorithms for performing calculations.
60. 60. Five Guiding Principles on How Mathematics Can and Should be Taught2. The subject matter of mathematics is ideas, not notation.
61. 61. Five Guiding Principles on How Mathematics Can and Should be Taught3. Mathematics is an organized body of knowledge.
62. 62. Five Guiding Principles on How Mathematics Can and Should be Taught4. Mathematics gives us understanding over the real world.
63. 63. Five Guiding Principles on How Mathematics Can and Should be Taught5. Mathematics is a form of artistic expression.
64. 64. http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html
65. 65. You–each one of us–can make a difference!
66. 66. technically,the glass is always full.