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Larsen Liljedahl PME 2017 Generative Moments PowerPoint Presentation

Exploring
generative
moments of
interaction between
mathematics
teachers on social
media
Judy Larsen, Simon Fraser University
Peter Liljedahl, Simon Fraser University
PME41 2017
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MTBoS
- Dylan Kane
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What can we learn?
MTBoS
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- Dylan Kane
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Complexity
Self-organized system
Individual agents generate macro-behaviours
Aims to understand ‘collective-knowing’ where learning is expanding the space
of the possible
Conditions for complex emergence
Internal diversity
Redundancy
Neighbour interactions
Decentralized control
Organized Randomness
Specialization
Trans-Level
Learning
Liberating Constraints
Davis & Simmt (2003)
Davis & Sumara (2006)
PME41 2017
Complex Systems
Self-organized systems
Individual agents generate macro-behaviours
Aims to understand ‘collective-knowing’ where learning is expanding the space
of the possible
Conditions for complex emergence
Internal diversity
Redundancy
Neighbour interactions
Decentralized control
Organized Randomness
Specialization
Trans-Level
Learning
Liberating Constraints
Davis & Simmt (2003)
Davis & Sumara (2006)
Zone of Creative
Adaptability (Lewin & Regine,
2000)
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How sources of diversity and redundancy can contribute to complex
emergence, or ‘collective-knowing’, in the MTBoS?
Data
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254 Tweets
87 Users
Over 4 days!!!
52/87 school teachers
+84 singles
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Depth of threads
+84 singles
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Non-continuing
+84 singles
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Continuing
10 threads
155 tweets
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Diversity and
Redundancy
+84 singles
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What I love about this mistake is it leads
to new methods for finding roots!
Yeah it stretched my math brain.
Patterns?
Redundanc
y
Share pedagogical approaches
Familiar with instructional
routine
Share over 500 common
followers
Diversity
Examples
Lots of redundancy
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+84 singles
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I explain to them that right for the
wrong reason is not correct!
There are many answers,
did you check them?
What if this doesn’t work
for the student?
+84 singles
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Redundanc
y
Mathematics teaching
Diversity
Diversity of purpose
Pedagogical approaches
#MTBoS membership
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Lots of diversity
+84 singles
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Equation string
Thinking through the
mathematics
+84 singles
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Discussion about specific
example choices
Redundanc
y
Thinking like a learner
Generating examples
Invoking shared language
Using instructional routines
Teaching without telling
Diversity
Example choices
Mathematical approaches
Mathematical representations
Mix of Redundancy
and Diversity
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Conclusions
Complex
Emergence
Non-
productive
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Conclusions
Expanding the space of possibility occurs when
there is enough redundancy for productive
communication, but with adequate diversity to
spur generativity. Complex
Emergence
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Conclusions
Consensual domain of the MTBoS includes:
Thinking like a learner
Generating examples
Invoking shared language
Using instructional routines
Abiding by pedagogies of ‘teaching without telling’ Complex
Emergence
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Conclusions
Variance in the mathematical approaches and
representations served as productive sources of diversity.
Complex
Emergence
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Thank-you
Judy.Larsen@ufv.ca
JudyLarsen.ca/presentations
@JudyLarsen3
PME41 2017
Liljedahl@sfu.ca
PeterLiljedahl.com/presentation
s
@pgliljedahl
Implications for future research . . .
MTBoS seems to create space for generating an ideational network
of mathematical tasks, pedagogy, and beliefs about mathematical
teaching and learning, which is a rich source of data
Products of the MTBoS and their implications for teaching could be
explored
Roles and personas could be contributing to complex emergence,
which could be further explored
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