Communication Developing Persistence Quote 1 Tony I like the PAR Its like we get to come to class and be wrong and thats okay Then later we get to revise our work and be right ID: 651975
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Slide1
Preliminary Research
Persistence
CommunicationSlide2
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
ReinholzSlide3
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
ReinholzSlide4
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
ReinholzSlide5
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.Slide6
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.Slide7
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.Slide8
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.Slide9
Introductory Courses
Student expectations
PersistenceSlide10
Adapting Traditional Textbook ProblemsSlide11
Modifying traditional HW
Great problem but…
You can calculate without getting much insight
(Griffiths et al., 1999)Slide12
Modifying traditional HW
Slide Courtesy of Stephanie
Chasteen
, University of Colorado BoulderSlide13
Modifying traditional HWSlide14
Modifying traditional HWSlide15
Adapting Traditional Problems
Take the idea furtherSlide16
Courtesy of Colleen Lewis, Harvey
Mudd
UniversitySlide17
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?
2 minutes
20 minutes2 hours2 days2
yearsSlide18
Which of the following could you imagine adding on to a more traditional homework problem in your discipline to support good problem solving practices?
Sketch something
List your assumptions
Check your answer for consistency Explain your findingsOther None of the above