Environments to Occasion Problem Solving

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ENVIRONMENTS TO OCCASION PROBLEM SOLVING

- Peter Liljedahl

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SOME BACKGROUND

CREATIVITYINVENTIONDISCOVERY

AHA!

2000

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SOME BACKGROUND

CREATIVITYINVENTIONDISCOVERY

AHA!

2000

PROBLEM SOLVING

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DESCRIPTIVE RESULT2003

AHA!

POSITIVEAFFECT

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2003

PROBLEMSOLVING

POSITIVEAFFECT

PRESCRIPTIVE INTERVENTION

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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

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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

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conducive to problem solving

occasion problem solving

thinking classrooms

QUEST

20032013

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BOTH A MEANS AND AN END

problem solving problem solving

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EARLY EFFORTS

just do it

teaching problem solving

teaching with

problem solvingTASKS

20052006

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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

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conducive to problem solving

occasion problem solving

thinking classrooms

QUEST + BYPASS NORMS20132003

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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

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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• …

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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

…

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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

…

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FINDINGS – BIGGEST IMPACT

• good tasks• vertical non-

permanent surfaces

• visibly random groups

• answering questions• oral

instructions• defronting the

room

• levelling•

assessment• flow

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VERTICAL NON-PERMANENT SURFACES

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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)

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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.

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QUALITATIVE

intends to try

tries it after 6 weeks

intends to continue

0102030405060708090

100100

95 98 98

UPTAKE (n=300)Pe

rcen

t

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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

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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

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VISIBLY RANDOM GROUPS

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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.

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QUALITATIVE

intends to try

tries it after 6 weeks

intends to continue

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100

93 91 8893

UPTAKE (n=200)Pe

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THREE PILARS

task

s

vert

ical

sur

face

s

rand

om g

roup

s

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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?

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QUALITATIVE

intends to try

tries it after 6 weeks

intends to continue

0102030405060708090

10094 90 90 92

UPTAKE (n=124)Pe

rcen

t

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WHY IT WORKS - THEORIES

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WHY IT WORKS - THEORIES

1st PERSON VICARIOUS EXPERIENCE

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Q & A

QUESTIONS & ABUSE

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THANK YOU!

liljedahl@sfu.cawww.peterliljedahl.com/presentations

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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)