Students want help; they feel they can't learn themselves or they don't want to. Teachers want to help. But helping too much removes the cognitive demand.

1. End the Didactic Contract
By Fred Feldon
Coastline Community College
KYMATYC IGNITE EVENT
February 23, 2018

4. If You Can Learn This:
…You Can Learn Algebra!
“Success in math is much more a function of your study
habits than your brain size. Good study habits are not
rocket science. And don’t say it doesn’t make a
difference unless you’ve tried them. See if short, regular
study times, finding a study buddy or join a study group,
attending every class, and keeping up with homework
make a difference. Bottom line: Most students are way
smarter than they think they are!”
Maryellen Weimer, PhD, Professor Emerita at Penn
State Berks, Faculty Focus, January 17, 2018

5. The Didactic Contract (simplified): Students want help;
they feel they can’t do it themselves or they don’t see a
need to do it. Teachers want to help. But helping too
much removes the cognitive demand.
Guy Brousseau, French professor
emeritus of mathematics education

6. “A didactical practice consists of
putting knowledge into a
communicable, decontextualized,
depersonalized, detemporalized
form.”

7. One Week of a Student’s Electrodermal Activity (EDA)
Poh, Swenson & Picard, 2010
http://affect.media.mit.edu/
pdfs/10.Poh-etal-TBME-EDA-
tests.pdf
Hi-level activity
• Lab
• Study
• Exams
• Homework
• Sleep
Lo-level activity
• Class

9. • Teaching is no longer about
the lecture
• Content is
everywhere!

10. PatrickJMT

11. Instead of giving the answer…
ask a question!

12. BORING:
A local theater is showing an animated movie.
They charge $5 per ticket for a child and $12
per ticket for an adult. They sell a total of 342
tickets and make a total of $2550. We want to
try to find out how many of each type of ticket
they sold. Let c represent the number of
children’s tickets sold and a represent the
number of adult tickets sold.
(a) Write an equation that represents the fact
that 342 tickets were sold.
(b) Write an equation representing the fact that
they made a total of $2550.
(c) Solve the system of equations. How many of
each type of ticket did they sell?
MAKEOVER:
The theater you run charges $4 per ticket for
child tickets and $12 for adult tickets.
(a) What’s a large amount of money you could
make?
(b) What’s a small amount of money you could
make?
(c) Okay, your no-good kid brother is working
the cash register. He told you he made:
• $2,550 on Friday
• $2,126 on Saturday
• $1,968 on Sunday
He’s lying about at least one of those. Which
ones? How do you know?
Dan Meyer, Math’s Storytelling Makeover, April 10, 2017
But Not Just Any Question…

14. Ok, So, What Are Some Good
Questions?? Where Do You Get Them?
Questions that stretch your conceptual knowledge…

15. So, What Are Some Good Questions??
Where Do You Get Them?
Questions with no one, right answer…

16. So, What Are Some Good Questions??
Where Do You Get Them?
Questions with no one, right answer…
Jell-O is the state snack of Utah. If the
Great Salt Lake was filled with Jell-O, how
many calories would there be? Explain
your answer.

17. So, What Are Some Good Questions??
Where Do You Get Them?
Questions with no one, right answer…
f(x) = ax2 + bx + c
Do a brain dump of everything you know
about quadratic functions. Each student must
list something different. Good luck!

18. So, What Are Some Good Questions??
Where Do You Get Them?
Questions that stretch your conceptual knowledge…
If 2 percent milk has 37 percent less
fat than regular milk, what is the
percentage of fat in regular milk?

19. Sources for Non-Routine Problems That Stimulate Discussion
Books
Math Contests Grades 4-6, 7-8 and Algebra, by Conrad & Flegler, Math League Press
Math Contests High School, by Conrad & Flegler, Math League Press
Can You Solve My Problems? By Alex Bellos Math Puzzles Vol. 1, 2 and 3 by Presh Talwalkar
Principles to Actions: Ensuring Mathematical Success for All, NCTM
The Scientific American Book of Mathematical Puzzles and Diversions, by Martin Gardner
What Students Abroad Are Expected To Know About Mathematics: Exams from France, Germany and Japan
Empowering Students by Promoting Active Learning in Mathematics, NCTM
Challenging Math Problems, by Terry Stickels
Websites
http://mathforum.org/problems_puzzles_landing.html http://blog.mrmeyer.com
http://cemc.uwaterloo.ca/resources/potw.php http://donsteward.blogspot.co.uk
http://www.mathleague.com https://ed.ted.com
https://www.mathcounts.org/resources/problem-of-the-week
https://www.math.purdue.edu/pow https://mindyourdecisions.com
http://orion.math.iastate.edu/ehjohnst/PoW/PoW.html
http://www.numberphile.com http://www.openmiddle.com
http://www.sixtysymbols.com http://www.estimation180.com
http://mathmistakes.org https://twitter.com/ExploreMTBoS (Math Twitter Blogosphere)
http://www.sciencealert.com https://twitter.com/MathVault
http://www.iflscience.com http://wodb.ca (Which One Doesn’t Belong)
http://www.ted.com http://www.visualpatterns.org
http://www.smartereveryday.com http://mathquest.carroll.edu/
https://www.youtube.com/channel/UC1_uAIS3r8Vu6JjXWvastJg (Mathologer)
Journals
Journal for Research in Mathematics Education, NCTM
Mathematics Teacher, Monthly Calendar Problems, NCTM
Mathematics Teaching in the Middle School, Monthly Palette of Problems, NCTM

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