Give It All You Got!

Break Away from the 3R’s

To the 3C’s

Fred Feldon, Coastline CCCMC3 South Fall ConferenceLos Angeles Mission College

October 6, 2012

This presentation is

available for download at

http://www.slideshare.net/ffeldon/cmc3-fall-2012-give-it-all-you-got

August 31, 2012, 7:13pm

A “Blue Moon”?

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

r1 r2

r1 r2

If ¼ AL > ½ AS

then ¼ π r12 > ½ π r2

2 → ¼ r12 > ½ r2

2

→ r12 > 2 r2

2

and r1 > r2

2

SizesSmall (10”)Medium (12”)Large (14”)X-Large (16”)

Mmm…

Is 14 > 10 ?2

Explain your answer.

The Problem…

The Problem…

• Content is ubiquitous

• College teaching is no longer about the lecture

PatrickJMT on YouTube

MOOC: Massive open online courses

August 28, 2012

The Solution…

What can YOU do?

Right NOW ?

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

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

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 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 !

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!

The Solution…

• 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

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

• 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.

“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

• 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!”

“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

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

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

examples.

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.

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?

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?

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

-- Michael Tsiros, Marketing Professor, University of Miami School of Business, 9/1/2012Full article at http://www.twincities.com/ci_21446847/bad- math-skills-cause-customers-miss-bargains-study

Which is better? To get 1/3 Off the price of an item? Or 1/3 More for

the same price?

http://www.youtube.com/watch?v=3c6_Hzgqfmg

New Book Trailer:

Educational Philosophies

Direct Instruction vs.

1. Teacher is active2. Learning is “poured” into

the student by reading or lecturing.

3. Textbook Driven4. Drill – Rote Memory5. Practice – Rote6. Student is observing.

Constructivist Learning

1. Student is active2. Autonomous Learning3. Sources – Teacher, Peers,

Textbook, Library, Internet4. Concrete Experience5. Trial and Error Learning –

Discuss, Correct Mistakes6. Teacher Facilitator

Nancy Allen, Ph.D., College of Education, Qatar University, “Active Learning Strategies and Techniques”

Changes – Course Goals

Direct Instruction vs.

Familiarizing students with key concepts

Constructivist Learning

Ensuring that students learn how to use those concepts

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

Changes – Teacher’s Role

Direct Instruction vs.

Dispenses information and concepts

Constructivist Learning

Designs and manages the overall instructional process

Changes – Student’s Role

Direct Instruction vs.

Passive recipients of information and content

Constructivist Learning

Responsible for the acquisition of 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”

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

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.

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

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

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)

Action Trajectories for Teacher and Student

The BIG Problem…

Real World Classroom

The BIG Problem…

“Mathematical reasoning in [the real world and] workplace differs markedly from the algorithms taught in school.”

-- John P. Smith, Educational Psychologist, Michigan State University

Breaking News:

You do NOT have to be an expert to solve

this problem!

Breaking News:

You do NOT have to adopt a certain curriculum or

textbook to solve the problem!

Breaking News:

You do NOT have to use a particular

method of instruction or mode of delivery

to solve the problem!

My Proposal:

All you have to do is “leave the lectern”

as often as possible, and promote the

3C’s!(Communication, Connectivity

and Collaboration)

My Proposal:

That alone will closely duplicate the environment of the

workplace!

My Proposal:

…will make problem-solving more like the

real world!

My Proposal:

…will engage students and restore the sense

of enjoyment and adventure in teaching

for you!

My Proposal:

…will reform the teaching and learning

of mathematics in your classes!

My Proposal:

…will increase students’ success, retention and your

popularity!

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/

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.

Five Guiding Principles on How Mathematics Can

and Should be Taught

2. The subject matter of mathematics is ideas, not notation.

Five Guiding Principles on How Mathematics Can

and Should be Taught

3. Mathematics is an organized body of knowledge.

Five Guiding Principles on How Mathematics Can

and Should be Taught

4. Mathematics gives us understanding over the real world.

Five Guiding Principles on How Mathematics Can

and Should be Taught

5. Mathematics is a form of artistic expression.

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

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

technically,the glass is always

full.

Thank You

ffeldon@coastline.edu

Available for download at

http://www.slideshare.net/ffeldon/

cmc3-fall-2012-give-it-all-you-got