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Environments to Occasion Problem Solving . - Peter Liljedahl. CREATIVITY INVENTION DISCOVERY AHA!. 2000. SOME BACKGROUND. CREATIVITY INVENTION DISCOVERY AHA!. PROBLEM SOLVING. 2000. SOME BACKGROUND. AHA!. POSITIVE AFFECT. 2003. DESCRIPTIVE RESULT. PROBLEM SOLVING. POSITIVE - PowerPoint PPT Presentation
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WM
PS
2013
ENVIRONMENTS TO OCCASION PROBLEM SOLVING
- Peter Liljedahl
WM
PS
2013
SOME BACKGROUND
CREATIVITYINVENTIONDISCOVERY
AHA!
2000
WM
PS
2013
SOME BACKGROUND
CREATIVITYINVENTIONDISCOVERY
AHA!
2000
PROBLEM SOLVING
WM
PS
2013
DESCRIPTIVE RESULT2003
AHA!
POSITIVEAFFECT
WM
PS
2013
2003
PROBLEMSOLVING
POSITIVEAFFECT
PRESCRIPTIVE INTERVENTION
WM
PS
2013
PRESCRIPTIVE INTERVENTION
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
WM
PS
2013
PRESCRIPTIVE INTERVENTION
If 6 cats can kill 6 rats in 6 minutes, how many cats are required to kill 100 rats in 50 minutes?
-Lewis Carroll
NOTHING
2004
WM
PS
2013
conducive to problem solving
occasion problem solving
thinking classrooms
QUEST
20032013
WM
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2013
BOTH A MEANS AND AN END
problem solving problem solving
WM
PS
2013
EARLY EFFORTS
just do it
teaching problem solving
teaching with
problem solvingTASKS
20052006
WM
PS
2013
EARLY EFFORTS
just do it
teaching with
problem solvingTASKS
20052006
• 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!
assessing problem solving
WM
PS
2013
conducive to problem solving
occasion problem solving
thinking classrooms
QUEST + BYPASS NORMS20132003
WM
PS
2013
METHODOLOGY: CASTING ABOUT
INSERVICE TEACHERS
learning teams workshops
master's students
teachers' questions and comments
observation proxies for engagement
MY OWN TEACHING
undergraduate courses
guest teaching
proxies for engagement
WM
PS
2013
DESIGNED-BASED RESEARCH
• tasks• hints and extensions • level • how we give the problem• how we answer questions • room organization• how groups are formed• student work space• assessment• …
WM
PS
2013
FINDINGS
VARIABLE POSITIVE EFFECTtasks good tasks (???)
hints and extensions managing flowlevel 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
…
WM
PS
2013
FINDINGS
VARIABLE POSITIVE EFFECTtasks good tasks (???) hints and extensions managing flowlevel 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 groupsstudent work space vertical non-permanent surfacesassessment 4 purposes
…
WM
PS
2013
FINDINGS – BIGGEST IMPACT
• good tasks• vertical non-
permanent surfaces
• visibly random groups
• answering questions• oral
instructions• defronting the
room
• levelling•
assessment• flow
WM
PS
2013
VERTICAL NON-PERMANENT SURFACES
WM
PS
2013
METHODOLOGY
TYPE I: qualitative• written reports• interviews• field notes
TYPE II: quantitative(ish)• five different treatments per class• 5 classes• time measurements• criterion measurements (0, 1, 2, 3)
WM
PS
2013
QUALITATIVE
• 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.
WM
PS
2013
QUALITATIVE
intends to try
tries it after 6 weeks
intends to continue
0102030405060708090
100100
95 98 98
UPTAKE (n=300)Pe
rcen
t
WM
PS
2013
VERTICAL NON-PERMANENT SURFACES
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
WM
PS
2013
QUANTITATIVE(ish)
vertical non-perm
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
WM
PS
2013
VISIBLY RANDOM GROUPS
WM
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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 inter-
group 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.
WM
PS
2013
QUALITATIVE
intends to try
tries it after 6 weeks
intends to continue
0102030405060708090
100
93 91 8893
UPTAKE (n=200)Pe
rcen
t
WM
PS
2013
THREE PILARS
task
s
vert
ical
sur
face
s
rand
om g
roup
s
WM
PS
2013
TOGETHER
• I've never seen my students work like that• they worked the whole class• they want more
• 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?
WM
PS
2013
QUALITATIVE
intends to try
tries it after 6 weeks
intends to continue
0102030405060708090
10094 90 90 92
UPTAKE (n=124)Pe
rcen
t
WM
PS
2013
WHY IT WORKS - THEORIES
WM
PS
2013
WHY IT WORKS - THEORIES
1st PERSON VICARIOUS EXPERIENCE
WM
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2013
Q & A
QUESTIONS & ABUSE
WM
PS
2013
WM
PS
2013
METHODOLOGY
• 3 lessons prior to implementation• 3 weeks after implementation• once every 2 weeks for 2 months
• participant observer (Eisenhart, 1988)• field notes from observations, interactions, and
conversations• interviews with 12 students and teacher• analytic induction (Patton, 2002)