effective integration of dynamic representations and …€¦ · introducing… group scribbles...
TRANSCRIPT
Effective Integration of Dynamic Representations and Collaboration to Enhance Mathematics and Science Learning
Jeremy Roschelle, SRI International, California USA
KEYNOTE
Over the past 20 years, mathematics achievement of US 8th graders has been:
A. Improving?B. Declining?C.Staying the Same?
Pop QuizK
EYN
OTE
2
Results from US National Assessment of Educational Progress (NAEP)
Average mathematics scale scores, grades 4 and 8: 1990–2003
At least a grade level of improvement since 1996
-- Judy Sowder
But most students still at the basic level. Unlikely to hit national goal by 2014 of all proficient.
Improving… but not fast enough.
Pop Quiz 2
Which factors predict high 8th grade scores?A. Use of computers
B. Use of graphing calculators
C. Solving problems from the textbook
More results from NAEP
Which factors correlate with high 8th grade scores?A. Use of computers
B. Use of graphing calculators
C. Solving problems from the textbook
Why?
•Computers used for drill & practice at the basic level or poorly integrated
•Graphing calculators used as representational tools for math at the proficient and advanced levels
This Talk: What is Effective Integration?
The Challenge of Effective Integration
Crossing the Chasm
Most educational technologies start with visionary promise but never achieve impact beyond a few exciting demonstration classrooms…
Keynote Overview
1. Graphing Calculatorsa success!
2. A mini-theory of effective integrationefficiency & innovation
3. Handheld Collaborationemerging with promise
Graphing Calculators
Integration?
50% of U.S. high school students have one…
… other countries use it too.
But is it effective?
What does research say?Positive correlations at scale
“Eighth-graders whose teachers reported that calculators were used almost every day scored highest. Weekly use was also associated with higher average scores than less frequent use. In addition, teachers who permitted unrestricted use of calculators and those who permitted calculator use on tests had eighth-graders with higher average scores than did teachers who did not indicate such use of calculators in their classrooms.” NCES, 2001
NAEP Scores with and without a calculator, by SES
0
10
20
30
40
50
60
70
Lower SES Higher SES
Graphing Calculator
NA
EP P
erce
ntile
Sco
re
With Without
What does research say?Strong findings in experiments
• Gains across grade levels• Operations• Conceptual understanding• Problem Solving
40
50
60
70
80
90
100
Elementary Middle HighPerc
entil
e of
Ave
rage
Stu
dent
afte
r Tre
atm
ent
Operational Conceptual
Ellington’s metaanalysis of 54 experiments:
What does research say?Strong findings in experiments
In Algebra specifically…
Why? Socio-Cognitive Theory
• Cognitive load• GC frees resources for problem solving
• Dual coding theory• Graphical + Linguistic coding enhances learning
• Multiple representations• Effectively mediate social construction of meaning
How did graphing calculators cross the chasm?
Simple, inexpensive, robust technology
Built a huge teacher training network
Integration into National Standards
Incorporation in curricula
Required on assessments
Simple, Robust, Inexpensive Technology
•About $100•Batteries last 3 months•Don’t break•Relatively buzzword-free•Functionality is focused on mathematics content
Train the trainers network
• Teacher-led effort to integrate calculators in mathematics improvement
• For trainers, offers continual learning and improvement
• For teachers, offers localized supportBurt Waits & Frank Demana
T3 Operates in over 12 countries including Australia
Healthy Symbiosis BetweenTeachers and Technologists
Waits & Demana,Ohio State
Tom Ferrio,Texas Instruments
Building a Breakthrough Business ConceptMost “innovations” came from teachers; Texas Instruments
nurtured, listened, & evolved their product.
See Eric Von Hippel “Democratizing Innovation”
Integration into National Standards
Calculators and computers are reshaping the mathematical landscape, and school mathematics should reflect those changes. Students can learn more mathematics more deeply with the appropriate and responsible use of technology. They can make and test conjectures. They can work at higher levels of generalization or abstraction.
When Working mathematically, students … use technologies such as geometry software, graphics calculators and spreadsheets.
Incorporation in Curricula & Testing
Incorporated on key tests, such as Advanced Placement Calculus & Statistics
What does effective integration look like?
Starts with:1. A simple, inexpensive technology built on important
socio-cognitive principles2. Symbiotic relationship between teachers and
technologists allowing for “democratic innovation”Results in:
• Systemic support for “crossing the chasm”including teacher professional development, standards, curriculum & assessment integration
• Research results demonstrating effectiveness
Part Two: The cognitive revolution and technological revolutionaries
Douglas Englebart
Legendary Inspiration at
SRI
Herbert Simon
Nobel prize-winning leader of the cognitive
revolution
Englebart
In 1968, demonstrated• The mouse• Hypertext• Collaborative screen sharing• Graphical interface
http://sloan.stanford.edu/mousesite/1968Demo.html
Believed in Augmenting Human Intelligence:
Collaborative use of dynamic representations
Technology as a revolutionary cultural tool
Simon
Won the Nobel Prize for economic theory:
• Limited Rationality• People make good, not optimal decisions
A leader in the cognitive revolution
Representations matter to cognition
Domain specific knowledge
(in reaction to his work) social cognition
Englebart & Simon Together
Limited rationality + revolutionary tools…Simple Tools for Pedagogical Revolutionaries
Domain-specific + mediating collaboration…Domain-specific collaborative representations for learning
What Education Needs:Simple Tools for Revolutionaries
What Education Needs:Simple Tools for Revolutionaries
ImpracticalTheorist
RoutineExpert
What Education Needs:Simple Tools for Revolutionaries
AdaptiveExpert
(Hatano)
What Education Needs:Simple Tools for Revolutionaries
DigitizingLectures
VirtualRealities
What are the simple tools that teachers can grow with?
Keynote Overview
Graphing Calculatorsa success!
A mini-theory of effective integrationefficiency & innovation
Handheld Collaborationemerging with promise
Handheld Collaboration
Teachers already adopting handheld response systems. There is much more we can do!
Response Systems
Teacher presents questionStudents respond individually
Instant histogram results
How It Works
We identified consistent benefits in 26 studies
Benefits• Greater student engagement (16)• Increased understanding of complex subject matter (11)
• Increased interest and enjoyment of class (7)• Promotes discussion/interactivity (6) • Helps students gauge their own level of understanding (5)
• Teachers have better awareness of student difficulties (4)
Impressive results in physics
Why Start Here?
It’s Happening!• Teachers swarming conference booths.• Tremendous amount of re-invention and action research by practitioners ($15 million)
• Teacher support resources published; teacher support networks forming.
• Technology advancing rapidly (IR -> RF -> 802.11 -> Zigbee); graphing- or PDA-based.
Why Start Here?
It Fits•Fits what teachers do every day – work with full classrooms of children
•Affordable (around $1000 per classroom)•Addresses teachers’ “pain” – are my students engaged and paying attention?
Why Start Here?
Capabilities Advancing(series of examples)
1. Extends to Images
2. Extends to Text
3. Extends to mathematics
From simple contributionsof each student
(make a fn that goes throughthe point 6,4)
To full class discussionof a more complex concept
(characteristics of a familyof functions)
4. Extends to participatory simulations
Make your y value twice your x value…
Participation in Shared Artifact + Discussion & Reflection
Introducing… Group Scribbles
Hypercard : 1984 Mac ::Group Scribbles : Wireless Classroom
Post-It Note Metaphor
Leverages SmartBoard, Stylus-Based, Wireless Classroom
Allows classroom brainstorming
Where…?
Collaborative activities
Everyone participates…
Concluding Remarks
Simple, inexpensive, robust cognitive technology
Symbiotic innovation by teachers and technologists
Integration into National Standards
Incorporation in curricula
Required on assessments
How did Graphing Calculators cross the chasm?
Concluding Remarks
What are the simple tools that teachers can grow with?
Simple Tools for Pedagogical Revolutionaries
Concluding Remarks
HyperCard for the Wireless Classroom
Group Scribbles
With inspiration and help from:• Corey Brady, Louis Abrahamson, Bill Penuel, Larry
Gallagher, Charlie Patton, Lisa Brady-Gill, Krista Davis, Chris DiGiano, Patti Schank, Zaz Harris, Deborah Tatar, Raj Chaudshury and many more…
Thank you!