Using interaction to reinforce conepts and metacognition in college mathematics classes

1. “…And Equal
Participation for All”
Using Interaction to Reinforce
Concepts and Metacognition in
Mathematics Classes
Fred Feldon
Coastline CC

2. “The best thing to learn first is
how to learn.”

3. Keep students engaged

4. Increase Metacognition

5. “There must be far less telling
on the part of the teacher,
and far more doing on the
part of the student.”
Jean Piaget

6. So, how do I do it?
• How much class time will I lose?
• How do I cover all the content?
• How do I quit being the “sage on stage”?
• How do I keep them from taking shortcuts?
• How do I teach them the “best way” or the
“right way” to get an answer?
• How do I make sure they don’t Facebook,
text or e-mail during class time?
• How can students possibly learn everything
on their own that I normally cover in my
lectures????

7. So, how do I do it?
• YOU are still the Professor
• YOU provide a course outline, syllabus,
schedule, learning resources, supplemental
material, student support, tutorial
resources, academic rigor and standards of
behavior
• YOU create a safe, non-threatening
classroom environment
• YOU make sure students are engaged and
participate equally

8. So, how do I do it?
• YOU change student attitudes from a “Fixed” to
a “Growth” mindset
• YOU cheer students on and let them know when
they are on the right track
• YOU highlight important points made during
discussion
• YOU question students and ask them to explain
their thinking and justify their answers
• YOU correct misconceptions/misunderstandings
• YOU may provide direct instruction on topics
students appear to be struggling with

9. So, how do I do it?
• YOU will discover the joy of doing what is
uniquely human and more interactive, rather
than simply delivering lectures.
• YOU will have more time to interact personally
with students, to mentor, advise, review
individual work, and answer questions
• YOU will learn more
than ever about your
subject matter and the
way students learn!

10. So, how do I do it?
• Avoid omniscient, overbearing or evaluative
comments that inhibit future participation
• Sustain the interaction and create a rich
environment for critical thinking to flourish

11. So, how do I do it?
• “Students like to be spoon fed. It’s easier for
them. But they need to learn how to feed
themselves. That means putting a plate of food
in front of them and giving them a spoon. Those
of us who have kids know what happens next
and it isn’t pretty. But is there a better way
to learn how to eat?”
-- Maryellen Weimer, PhD
Professor Emeritus of Teaching and
Learning, Penn State University

12. So, how do I do it?
• Flash cards, go down the rows, up and down
your roster, use sticks in a cup, random number
generator or get an app, to call on students
at random

13. The Big Question:
How do I replicate this
interaction online?

14. Obstacles:
• 85% of Coastline’s math enrollment is online
• Each section has 40-80 students
• Interaction & communication is
asynchronous
• Communicating mathematically is difficult
with a keyboard
• Students may have limited equipment and
varying comfort levels with technology

15. Some Possibilities:

16. Some Possibilities:
• The Magic of Mistakes
• Angelo-Cross CAT
 Muddiest Point
 Documented Problem Solutions
 Audio and Videotaped Protocols
 Student Generated Test Questions
• Mal-Rules vs Correct Rules
• Math Was/Math Is

17. Some Possibilities:
r1
r2
Which is bigger, one-half of a small pizza,
or one-fourth of a large? Explain your
answer.

18. Some Possibilities:
Which is better? To get 1/3 Off the
price of an item? Or 1/3 More for
the same price? Explain your
answer.
-- Michael Tsiros, Marketing Professor, University of Miami
School of Business, 9/1/2012
Full article at http://www.twincities.com/ci_21446847/badmath-skills-cause-customers-miss-bargains-study

19. Which of these are Correct Rules and which are MalRules? Explain your answer. You may give examples.
• More at www.slideshare.net/ffeldon/
cmc-fall-2012-give-it-all-you-got-v3

20. Thank You
ffeldon@coastline.edu
This presentation is available to download at
http://www.slideshare.net/ffeldon