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

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

2. This presentation is
available for download at
http://www.slideshare.net/ffeldon/
cmc3-fall-2012-give-it-all-you-got

3. August 31, 2012, 7:13pm
A “Blue Moon”?

4. Question: “Which is bigger, half of a small
pizza or one-fourth of a large?”

5. r1 r2

6. r1 r2
If ¼ AL > ½ AS
then ¼ π r12 > ½ π r22 → ¼ r12 > ½ r22
→ r12 > 2 r22
and r1 > 2 r2

7. Sizes
Small (10”)
Medium (12”)
Large (14”)
X-Large (16”)

8. Mmm…
Is 14 > 10 2 ?

9. Explain your answer.

10. The Problem…

11. The Problem…
• Content is ubiquitous
• College teaching is no longer about
the lecture

12. PatrickJMT on YouTube

14. MOOC: Massive open
online courses

15. August 28, 2012

16. The Solution…
What can YOU do?
Right NOW ?

17. The Solution…
• Summarize, highlight and motivate; ignite a
shared intellectual endeavor; relate math
in the classroom to the real world

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

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

21. 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 !

22. 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!

23. • Communication
- Students talk more; you talk less. In class:
mini-lectures punctuated by individual, pair or
group work and explain their answers. Online:
Respond every day but make interaction 25%
teacher-to-student and 75% student-to-student

24. Fifty Ways to Leave Your Lectern
“The ABC’s (Bloom’s Affective, Behavioral
and Cognitive goals) should be more equally
balanced.”
-- Dr. Constance Staley, Professor of
Communication, University of Colorado

25. • Communication
- Students talk more; you talk less. In class: mini-
lectures punctuated by individual, pair or group
work and explain their answers. Online: Respond
every day but make interaction 25% teacher-to-
student and 75% student-to-student
• Connectivity
- Research shows a sense of community
increases success and retention. Foster
“productive struggle,” thinking through problems
and sharing viewpoints. More illuminating for
students than hearing you do it.

26. “Productive Failure”: Why Floundering
is Good--Attempting to figure
something out on your own produces
better results than having guidance
from the very beginning.”
-- Annie Murphy Paul, Learning Theorist,
Time.com “Health & Science,” August, 2012

27. • Collaboration
- We’re all in this together. We’re all here
to help each other. The best way to learn
something is to explain it so someone else.
Blooms’ taxonomy. Incorporate peer review and
cloud computing. Advise students to ask
questions: “I or another student will reply right
away!”

30. “Mathematics is not a careful march
down a well-cleared highway, but a
journey into a strange wilderness,
where the explorers often get lost.”
-- W. S. Anglin, author of Mathematics: A
Concise History and Philosophy, 1994

32. Improving Fluid Intelligence with Training on Working Memory, 2008, by
Jaeggi, Buschkuehl, Jonides and Perrig

33. Which of these are Correct Rules and which are
Mal-Rules? Explain your answer. You may give
examples.

34. 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.

35. A solid wood cube, 1 foot on an edge, was
sawed into eight smaller congruent cubes.
The smaller cubes were then reassembled to
form the longest possible rectangular prism.
What is the percent change in surface area?

36. Mathematical Misfit
Which fits best: a square peg in a round hole, or
a round peg in a square hole?
To be more precise, if you take a circle and fit it
just inside a square, or take a square and fit it
just inside a circle, which fills up proportionally
more space?

37. Are -59 and (-5)9 the same,
or are they different? Explain
your answer.

38. Which is better? To get 1/3 Off the
price 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

39. New Book Trailer:
http://www.youtube.com/watch?v=3c6_Hzgqfmg

40. Educational Philosophies
Direct Instruction vs. Constructivist Learning
1. Teacher is active 1. Student is active
2. Learning is “poured” into 2. Autonomous Learning
the student by reading 3. Sources – Teacher, Peers,
or lecturing. Textbook, Library, Internet
3. Textbook Driven 4. Concrete Experience
4. Drill – Rote Memory 5. Trial and Error Learning –
5. Practice – Rote Discuss, Correct Mistakes
6. Student is observing. 6. Teacher Facilitator
Nancy Allen, Ph.D., College of Education, Qatar University, “Active
Learning Strategies and Techniques”

41. Changes – Course Goals
Direct Instruction vs. Constructivist Learning
Familiarizing students Ensuring that students learn
with key concepts how to use those
concepts

44. Fitzroy Kennedy, University of Alabama, “Critical and
Creative Thinking”

45. Changes – Teacher’s Role
Direct Instruction vs. Constructivist Learning
Dispenses information Designs and manages the
and concepts overall instructional
process

46. Changes – Student’s Role
Direct Instruction vs. Constructivist Learning
Passive 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”

47. Describing Levels and
Components of a Math-Talk
Learning Community
• What does the transformation to reform
mathematics teaching look like?
• What would such a classroom look like?
• How do teachers, along with their
students, get there?
Kimberly Hufferd-Ackles, Karen C. Fuson, and Miriam Gamoran Sherin,
Northwestern University, NCTM Journal for Research in Mathematics
Education, March 2004

48. Describing Levels and
Components of a Math-Talk
Learning Community
Shift over Levels 0-3: The classroom
community grows to support students acting
in central or leading roles and shifts from a
focus on answers to a focus on mathematical
thinking.

49. Describing Levels and
Components of a Math-Talk
Learning Community
• Level 0: Traditional teacher-directed
classroom with brief answer responses from
students
• Level 1: Teacher begins to pursue student
mathematical thinking. Teacher plays central
role in the math-talk community

50. Describing Levels and
Components of a Math-Talk
Learning Community
• Level 2: Teacher models and helps students
build new roles. Some co-teaching and co-
learning begins as student-to-student talk
increases. Teacher physically begins to move
to side or back of the room

51. Describing Levels and
Components of a Math-Talk
Learning Community
• Level 3: Teacher as co-teacher and co-
learner. Teacher monitors all that occurs, still
fully engaged. Teacher is ready to assist, but
now in more peripheral and monitoring role
(coach and assister)

52. Action Trajectories for Teacher
and Student

55. The BIG Problem…

56. The BIG Problem…
Real World Classroom

57. “Mathematical reasoning in *the
real world and] workplace differs
markedly from the algorithms
taught in school.”
-- John P. Smith, Educational Psychologist,
Michigan State University

58. Breaking News:
You do NOT have to
be an expert to solve
this problem!

59. Breaking News:
You do NOT have to
adopt a certain
curriculum or
textbook to solve the
problem!

60. Breaking News:
You do NOT have to
use a particular
method of instruction
or mode of delivery
to solve the problem!

61. My Proposal:
All you have to do is
“leave the lectern” as
often as possible, and
promote the 3C’s!
(Communication, Connectivity
and Collaboration)

62. My Proposal:
That alone will
closely duplicate the
environment of the
workplace!

63. My Proposal:
…will make problem-
solving more like the
real world!

64. My Proposal:
…will engage students
and restore the sense of
enjoyment and
adventure in teaching
for you!

65. My Proposal:
…will reform the
teaching and learning
of mathematics in your
classes!

66. My Proposal:
…will increase
students’ success,
retention and your
popularity!

67. Five Guiding Principles on How
Mathematics Can
and Should be Taught
From the Co-Authors of IMACS
Institute for Mathematics & Computer
Science, 2012
http://www.eimacs.com/blog/2012/08/algebra-is-not-the-problem-part-2/

68. Five Guiding Principles on How
Mathematics Can
and Should be Taught
1. Mathematics is an important intellectual
discipline—not merely a collection of
algorithms for performing calculations.

69. Five Guiding Principles on How
Mathematics Can
and Should be Taught
2. The subject matter of mathematics is
ideas, not notation.

70. Five Guiding Principles on How
Mathematics Can
and Should be Taught
3. Mathematics is an organized body of
knowledge.

71. Five Guiding Principles on How
Mathematics Can
and Should be Taught
4. Mathematics gives us understanding
over the real world.

72. Five Guiding Principles on How
Mathematics Can
and Should be Taught
5. Mathematics is a form of artistic
expression.

73. http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html

74. You–each one of us–
can make a difference!

76. technically,
the glass is always
full.

77. Thank You
ffeldon@coastline.edu
Available for download at
http://www.slideshare.net/ffeldon/
cmc3-fall-2012-give-it-all-you-got