Maria H. Andersen
Muskegon Community College
teachingcollegemath.com
Problem:   
Inquiry-based learning is great, 
in theory, 
but time-consuming in reality.
http://xkcd.com/657
what if LOTR 
was a textbook? 
How DO 
children
learn?
they
give 
it a 
try
they push at boundaries
"The brain is made to fill in blanks."
- Raph Koster, A Theory of Fun
We tend to LIKE something if we are able to "see" the patterns in it 
When this happens, we begin to "groove" in the patterns ... to seek them out and to expect them. 
the brain functions on three levels of thinking
conscious thought
mathematical
assigning values
making lists
recalling facts
sorting and packaging
integrative
associative
intuitive
"common sense"
autopilot
reflexes
running "scripts"
a simulation or a formal system where choices and rules are important
allows you to practice patterns and permutations of patterns
games are exercises 
for the brain
as we learn the patterns,
we seek novelty and difficulty
"Fun from games arises out of mastery. It arises out of comprehension. It is the act of solving puzzles that makes games fun. In other words, with games, learning is the drug."
- Raph Koster, A Theory of Fun
"Boredom is the brain casting about for new information. It is the feeling you get when there are no new patterns to absorb."
Line Gem
Flower Power
Catch the Fly
Factortris
NLVM Circle Game
http://nlvm.usu.edu/en
http://bit.ly/9uhSJF
http://hotmath.com
http://funbasedlearning.com
http://www.funbrain.com/
Math Baseball
Multiplication "Game"
http://www.softschools.com
http://www.mangahigh.com
"How do I get somebody to learn something that is long and difficult and takes a lot of commitment, but get them to learn it well?"
Question that game designers ask themselves ...
- Dr. James Gee 
"the best instruction hovers at the boundary of a student's competence"
- Andy diSessa, Cognitive Scientist
[Video games] tend to encourage players to achieve total mastery of one level, only to challenge and undo that mastery in the next, forcing kids to adapt and evolve.
- Dr. James Gee, University of Wisconsin
Wired Magazine, 2003
-Rath Koster, A Theory of Fun
Tombstone City
Munchman
http://www.flickr.com/photos/dinah/239650274/
Babylonian
 "Cheat Codes"
2
5
12
28
35
75
[ !?*!? ]
60
61
59
Think like a Babylonian
http://gwydir.demon.co.uk/jo/numbers/babylon/index.htm
Revelation #1:
Technology is making "content" irrelevant. It's what you're able to do with the content that's important.
Revelation #4:
I can still play the video games I played when I was a child.
Revelation #3:
My students, some of whom can't seem to learn algebra, CAN seem to learn complex video games that require logic, memorization, and teamwork, and strategy. 
We've been trying all sorts of untested strategies to improve algebra outcomes for decades, with little or no forward progress.
Revelation #2:
http://www.flickr.com/photos/bobfoldsfive/2596985632/
Sorry bobfoldsfive, I am using this image without permission because I can't seem to log in to Yahoo to ask for permission. Please don't be mad!
http://www.flickr.com/photos/twid/410697715/
http://www.flickr.com/photos/mrjoro/89187454
http://www.flickr.com/photos/kkseema/2042946052
http://www.flickr.com/photos/seandreilinger/959010447
they
try
over
and
over
and
over
http://www.flickr.com/photos/wwworks/3039389897
they seek patterns
http://www.flickr.com/photos/table4five/2055458712
GAME
Learning is not Linear. 
 Math Textbooks Are.
Problem:   
- Raph Koster, A Theory of Fun
On linear learning paths, 
students often get stuck
because of one concept.
Problem:   
the act of mastering a problem mentally
FUN
Problem:   
We give away the
"cheat codes" for the game (algebra) up front.
boring
some games just make games lame
some games are more like puzzles
and some games get it just right
Designing and using activities where students learn new concepts by actively doing and reflecting on what they have done. The guiding principle is that instructors try not to talk in depth about a concept until students have had an opportunity to think about it first (Hastings, 2006).
Inquiry-based Learning
addition & subtraction of integers
simplifying like terms
3x+4+2x-7
multiplication and division of integers
solving 
one-step equations
x+3=6
finding  points that 
fit x+y=5
absolute value
e.g. |-8|
graph an inequality on a number line
where do we want our students brains' to be?
why did 
you go in to teaching?
AHA! 
is the brain having fun
1
2
3
4
5
6
See if you can figure out Babylonian without the "cheat codes"
a game is a delicate balance between
boredom 
and frustration
Waker
http://gambit.mit.edu/loadgame/waker.php