WMPS 2013
ENVIRONMENTS TO OCCASION PROBLEM
SOLVING
- Peter Liljedahl
WMPS 2013
CREATIVITY
INVENTION
DISCOVERY
AHA!
2000
SOME BACKGROUND
WMPS 2013
CREATIVITY
INVENTION
DISCOVERY
AHA!
PROBLEM
SOLVING
SOME BACKGROUND
2000
WMPS 2013
AHA!
POSITIVE
AFFECT
2003
DESCRIPTIVE RESULT
WMPS 2013
PROBLEM
SOLVING
POSITIVE
AFFECT
2003
PRESCRIPTIVE INTERVENTION
WMPS 2013
If 6 cats can kill 6 rats in 6 minutes,
how many cats are required to kill 100
rats in 50 minutes?
- Lewis Carroll
2004
PRESCRIPTIVE INTERVENTION
WMPS 2013
If 6 cats can kill 6 rats in 6 minutes,
how many cats are required to kill 100
rats in 50 minutes?
-Lewis Carroll
2004
PRESCRIPTIVE INTERVENTION
WMPS 2013
thinking
classrooms
occasion problem
solving
conducive to problem
solving
2003
2013
QUEST
WMPS 2013
problem
solving
problem
solving
BOTH A MEANS AND AN END
TASKS
WMPS 2013
just do it
teaching
problem
solving
teaching
with
problem
solving
EARLY EFFORTS
2005
2006
TASKS
assessing
problem
solving
teaching
with
problem
solving
EARLY EFFORTS
some were able to do it
they needed a lot of help
they loved it
they don’t know how to
work together
• they got it quickly and
didn't want to do any
more
• they gave up early
FILTERED THROUGH
EXISTING NORMS!
WMPS 2013
just do it
•
•
•
•
2005
2006
WMPS 2013
thinking
occasion problem
classrooms
solving
conducive to problem
solving
2003
2013
QUEST + BYPASS NORMS
MY OWN
TEACHING
 learning teams
 workshops
 master's students
 undergraduate courses
 guest teaching
 teachers' questions and
comments
 observation
 proxies for engagement
 proxies for engagement
METHODOLOGY: CASTING ABOUT
WMPS 2013
INSERVICE
TEACHERS
tasks
hints and extensions
level
how we give the problem
how we answer questions
room organization
how groups are formed
student work space
assessment
…
DESIGNED-BASED RESEARCH
WMPS 2013
•
•
•
•
•
•
•
•
•
•
POSITIVE EFFECT
tasks
good tasks (???)
hints and extensions
managing flow
level
level to the bottom
how we give the problem
orally
room organization
defront the room
how we answer questions
3 types
how groups are formed
visibly random groups
student work space
vertical non-permanent surfaces
assessment
4 purposes
…
FINDINGS
WMPS 2013
VARIABLE
POSITIVE EFFECT
tasks
good tasks (???)
hints and extensions
managing flow
level
level to the bottom
how we give the problem
orally
room organization
defront the room
how we answer questions
3 types
how groups are formed
visibly random groups
student work space
vertical non-permanent surfaces
assessment
4 purposes
…
FINDINGS
WMPS 2013
VARIABLE
• answering
questions
• oral instructions
• defronting the
room
• assessment
• flow
• good tasks
• vertical nonpermanent
surfaces
• visibly random
groups
FINDINGS – BIGGEST IMPACT
WMPS 2013
• levelling
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VERTICAL NON-PERMANENT
SURFACES
TYPE II: quantitative(ish)
• five different treatments per class
• 5 classes
• time measurements
• criterion measurements (0, 1, 2, 3)
METHODOLOGY
WMPS 2013
TYPE I: qualitative
• written reports
• interviews
• field notes
QUALITATIVE
WMPS 2013
• This was so great [..] it was so good I felt like I
shouldn't be doing it.
• I will never go back to just having students work in
their desks.
• How do I get more whiteboards?
• The principal came into my class … now I'm doing
a session for the whole staff on Monday.
• My grade-partner is even starting to do it.
• The kids love it. Especially the windows.
• I had one girl come up and ask when it will be her
turn on the windows.
Percent
100
90
80
70
60
50
40
30
20
10
0
100
intends
to try
QUALITATIVE
95
98
98
tries it
after 6
weeks
intends to
continue
WMPS 2013
UPTAKE (n=300)
VERTICAL NON-PERMANENT
SURFACES
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PROXIES FOR ENGAGEMENT
• time to task
• time on task
• time to first mathematical notation
• amount of discussion
• eagerness to start
• participation
• persistence
• knowledge mobility
• non-linearity of work
horizontal
non-perm
vertical
permanent
horizontal
permanent
notebook
N (groups)
10
10
9
9
8
time to task
12.8 sec
13.2 sec
12.1 sec
14.1 sec
13.0 sec
time on task
7.1 min
4.6 min
3.0 min
3.1 min
3.4 min
first notation
20.3 sec
23.5 sec
2.4 min
2.1 min
18.2 sec
discussion
2.8
2.2
1.5
1.1
0.6
eagerness
3.0
2.3
1.2
1.0
0.9
participation
2.8
2.3
1.8
1.6
0.9
persistence
2.6
2.6
1.8
1.9
1.9
mobility
2.5
1.2
2.0
1.3
1.2
non-linearity
2.7
2.9
1.0
1.1
0.8
QUANTITATIVE(ish)
WMPS 2013
vertical
non-perm
WMPS 2013
VISIBLY RANDOM GROUPS
•
•
•
•
•
•
students become agreeable to work in any
group they are placed in
there is an elimination of social barriers within
the classroom
mobility of knowledge between students
increases
reliance on the teacher for answers decreases
reliance on co-constructed intra- and intergroup answers increases
engagement in classroom tasks increase
students become more enthusiastic about
mathematics class
Liljedahl, P. (in press). The affordances of using visually random
groups in a mathematics classroom. In Y. Li, E. Silver, & S. Li (eds.)
Transforming Mathematics Instruction: Multiple Approaches and
Practices. New York, NY: Springer.
VISIBLY RANDOM GROUPS
WMPS 2013
•
Percent
100
90
80
70
60
50
40
30
20
10
0
93
91
88
intends
to try
tries it
after 6
weeks
QUALITATIVE
93
intends to
continue
WMPS 2013
UPTAKE (n=200)
random groups
vertical surfaces
tasks
WMPS 2013
THREE PILARS
• how do I keep this up AND work on the
curriculum?
• how do I assess this?
• where do I get more problems?
• I don't know how to give hints?
TOGETHER
WMPS 2013
• I've never seen my students work like that
• they worked the whole class
• they want more
Percent
100
90
80
70
60
50
40
30
20
10
0
94
intends
to try
QUALITATIVE
90
90
92
tries it
after 6
weeks
intends to
continue
WMPS 2013
UPTAKE (n=124)
WMPS 2013
WHY IT WORKS - THEORIES
WHY IT WORKS - THEORIES
WMPS 2013
1st PERSON VICARIOUS EXPERIENCE
WMPS 2013
QUESTIONS
& ABUSE
Q&A
WMPS 2013
THANK YOU!
liljedahl@sfu.ca
www.peterliljedahl.com/presentations
WMPS 2013
• participant observer (Eisenhart, 1988)
• field notes from observations, interactions, and
conversations
• interviews with 12 students and teacher
• analytic induction (Patton, 2002)
METHODOLOGY
WMPS 2013
• 3 lessons prior to implementation
• 3 weeks after implementation
• once every 2 weeks for 2 months