Preliminary Research
• Persistence
• Communication
Developing Persistence
Quote 1
Tony*: “I like the PAR. It's like we get to
come to class and be wrong, and that's
okay. Then later we get to revise our
work and be right.”
*Pseudonym
Courtesy of Dan Reinholz
Developing Persistence
Quote 2
Mike*: “PAR is good. I like how we can
put our initial solution down, and even
if it's wrong it doesn't really matter,
because we can just talk about it with
a group member the next day, and
figure it out together. And generally
you don't get stuck on a wrong
solution, you figure it out.”
*Pseudonym
Courtesy of Dan Reinholz
Quote 3
Andy*: “It would be almost impossible
if I had to do it myself. It’s when I get to
talk to other people, and when I get to
bounce ideas off them and hear their
ideas that I can see why it’s right or
wrong, and how to justify that.”
*Pseudonym
Courtesy of Dan Reinholz
Schoenfeld Study
• 230 students (112 female, 118 male) enrolled
in high school mathematics courses in NY
State
• “The students were enrolled in three highly
regarded high schools with good graduation
and college-placement rates. All the students
were in the academic, college-bound track.”
Schoenfeld, A. H. (1989). Explorations of students' mathematical
beliefs and behavior. Journal of Research in Mathematics
Education, 20(4), 338-355.
How long should it take to solve a
typical homework problem?
• Average < 2 minutes
• 0 responses over 5 minutes
Schoenfeld, A. H. (1989). Explorations of students' mathematical
beliefs and behavior. Journal of Research in Mathematics
Education, 20(4), 338-355.
What is a reasonable amount of time
to work on a problem before you know
it's impossible?
• Average: about 12 minutes
• Longest response: 20 minutes
Schoenfeld, A. H. (1989). Explorations of students' mathematical
beliefs and behavior. Journal of Research in Mathematics
Education, 20(4), 338-355.
Representative Student Quotes
• "Up to 2 or 3 minutes. I would work on a
problem for about 10 minutes before deciding
it's impossible."
• "It would probably take from 30 seconds to 2
minutes. I usually give up after 3 or 4 minutes
if I can't do it."
Schoenfeld, A. H. (1989). Explorations of students' mathematical
beliefs and behavior. Journal of Research in Mathematics
Education, 20(4), 338-355.
Introductory Courses
• Student expectations
• Persistence
Adapting Traditional Textbook
Problems
Modifying traditional HW
• Great problem but…
• You can calculate without getting much insight
(Griffiths et al., 1999)
Modifying traditional HW
Slide Courtesy of Stephanie Chasteen,
University of Colorado Boulder
Modifying traditional HW
Modifying traditional HW
Adapting Traditional Problems
• Take the idea further
Courtesy of Colleen Lewis, Harvey Mudd University
Predict:
High school students were asked “How
long would you work on a math problem
before you know it is impossible?” What
do you think the longest response time
was?
A)
B)
C)
D)
E)
2 minutes
20 minutes
2 hours
2 days
2 years
Which of the following could you
imagine adding on to a more
traditional homework problem in your
discipline to support good problem
solving practices?
A)
B)
C)
D)
E)
F)
Sketch something
List your assumptions
Check your answer for consistency
Explain your findings
Other
None of the above