BUILDING THINKING CLASSROOMS
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PCMI 2016 BUILDING THINKING CLASSROOMS - Peter Liljedahl @pgliljedahl
Transcript of BUILDING THINKING CLASSROOMS
PC
MI 2016
BUILDING THINKING CLASSROOMS
- Peter Liljedahl @pgliljedahl
PC
MI 2016
CONTEXT OF RESEARCH
NOW YOU TRY ONE
HOMEWORK
TAKING NOTES
REVIEW
LECTURE
GROUP WORK
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NOW YOU TRY ONE
Slacking(n=3)
Checking Understanding
(n=6)Stalling
(n=4)
Mimicking(n=17)
catching up on notes (n=0)
n=32
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TAKING NOTES (n=30)
keep upn=11
TAKE NOTES
don’tn=3
don’t use notesn=27
yesn=3
don’t keep upn=16
USE NOTES TO STUDY
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TAKING NOTES (n=30)
keep upn=11
TAKE NOTES
don’tn=3
don’t use notesn=27
yesn=3
don’t keep upn=16
USE NOTES TO STUDY
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INSTITUTIONAL NORMS
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CASTING ABOUT (n = 400+)
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FINDINGS
VARIABLEproblemshow we give the problem how we answer questionsroom organizationhow groups are formedstudent work spacehow we give noteshints and extensionshow we levelassessment…
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FINDINGS
VARIABLE POSITIVE EFFECTproblems good problems how we give the problem oral vs. writtenhow we answer questions 3 types of questionsroom organization defronting the roomhow groups are formed visibly random groupsstudent work space vertical non-permanent surfaceshow we give notes don'thints and extensions managing flowhow we level level to the bottomassessment 4 purposes…
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FINDINGS
• good problems• 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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PROXIES FOR ENGAGEMENT• time to task • time to first mathematical notation • amount of discussion• eagerness to start• participation • persistence• knowledge mobility• non-linearity of work
EFFECT ON STUDENTS
0 - 3
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verticalnon-perm
horizontalnon-perm
vertical permanent
horizontal permanent notebook
N (groups) 10 10 9 9 8time to task 12.8 sec 13.2 sec 12.1 sec 14.1 sec 13.0 secfirst notation 20.3 sec 23.5 sec 2.4 min 2.1 min 18.2 secdiscussion 2.8 2.2 1.5 1.1 0.6eagerness 3.0 2.3 1.2 1.0 0.9participation 2.8 2.3 1.8 1.6 0.9persistence 2.6 2.6 1.8 1.9 1.9mobility 2.5 1.2 2.0 1.3 1.2non-linearity 2.7 2.9 1.0 1.1 0.8
EFFECT ON STUDENTS Liljedahl, P. (in press). Building thinking classrooms: Conditions for problem solving. In P. Felmer, J. Kilpatrick, & E. Pekhonen (eds.) Posing and Solving Mathematical Problems: Advances and New Perspectives. New York, NY: Springer.
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verticalnon-perm
horizontalnon-perm
vertical permanent
horizontal permanent notebook
N (groups) 10 10 9 9 8time to task 12.8 sec 13.2 sec 12.1 sec 14.1 sec 13.0 secfirst notation 20.3 sec 23.5 sec 2.4 min 2.1 min 18.2 secdiscussion 2.8 2.2 1.5 1.1 0.6eagerness 3.0 2.3 1.2 1.0 0.9participation 2.8 2.3 1.8 1.6 0.9persistence 2.6 2.6 1.8 1.9 1.9mobility 2.5 1.2 2.0 1.3 1.2non-linearity 2.7 2.9 1.0 1.1 0.8
EFFECT ON STUDENTS Liljedahl, P. (2016). Building thinking classrooms: Conditions for problem solving. In P. Felmer, J. Kilpatrick, & E. Pekhonen (eds.) Posing and Solving Mathematical Problems: Advances and New Perspectives. New York, NY: Springer.
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VISIBLY RANDOM GROUPS
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they are placed in• there is an elimination of social barriers within the
classroom• mobility of knowledge between students increases• reliance on co-constructed intra- and inter-group
answers increases• reliance on the teacher for answers decreases• engagement in classroom tasks increase• students become more enthusiastic about
mathematics class
Liljedahl, P. (2014). 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.
EFFECT ON STUDENTS
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TOGETHER
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WHAT ELSE?
• good problems• vertical non-
permanent surfaces
• visibly random groups
• answering questions
• oral instructions• defronting the
room
• levelling• assessment
• flow
