Integrating Mathematics and Animation: Catching Content Instruction Up with Urban Sixth Graders Inte

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Integrating Mathematics and Animation Catching
Content Instruction Up with Urban Sixth Graders
Interests and Expertise
gismo
at Washington University in St. Louis
American Education Research Association Annual
Meeting 2007, Chicago IL April 10, 2007
Project support from NSF Grant 0531120
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Project Staff and Contributors

• Jere Confrey, Project Director and P. I.
• Alan Maloney, Senior Research Scientist
• Kenny Nguyen, Ph. D. Student
• J. Lewis Ford
• Virtual Ed, Inc. Greg Hammond, Bruce
  Butterfield, Eric Hammond
• Austin Programming Solutions Pedro Larios

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Outline

• Overview of GISMO 2006 Summer Workshop
• Research Design
• GISMO Graphs n Glyphs Design and Demonstration
• Breakout Groups
• Evolving student conceptions of animation
• Mathematical understanding in context of
  animation
• Conclusions and Future Work

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Context

• Urban St. Louis students lack fluency with basic
  math skills (adding and subtracting integers and
  measurement)
• 3-week workshop, 5 days/wk, 3 hr/day
• 8 rising 6th graders
• Recruited via schools in high-poverty district

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GISMO Summer Workshop

• Topics and Activities
• Vices and Virtues
• Extracurricular
• Student Projects
• Student and Parent reactions

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Topics and Activities
GISMO Summer Workshop

• Directed drawing
• (with and without feedback)
• Model building--elbows, (adapted from Penner et
  al., 1997)

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Topics and Activities
GISMO Summer Workshop

• Elevator animations

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Topics and Activities
GISMO Summer Workshop

• Battleship game
• Transformations translations and reflections
• Matching, in Graphs n Glyphs
• Similarity and Scaling

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Topics and Activities
GISMO Summer Workshop

• Solving Mazes
• Building animations

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Vices and Virtues of Mathematics!

• Not believing that you can understand
• Not insisting that you can understand
• Not working systematically/step by step
• Laziness
• Rushing or Racing
• Not checking your work
• Not listening
• Not finishing

• Confidence
• Persistence
• Discipline and Practice
• Consistency
• Patience
• Care
• Listening
• Finishing

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Extracurricular Activities--Games
GISMO Summer Workshop

• Traffic Jam
• Set
• Logix
• River Crossing
• Tangrams

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Student Reactions

• 100 retention
• Kids arriving early, staying late
• Kids took laptops home to work on animations, to
  use the internet, and to troubleshoot the
  software
• Kids took logic games home to play with siblings
  and parents.
• Daily discussions with parents about workshop

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Student Reactions

• Ohso thats why you had us work on coordinate
  graphing for 2 days before we started the
  software!

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Parent Reactions
GISMO Summer Workshop

• From As mom
• Your program increased As awareness of the
  different things she can do with Math and
  science. It has given her an outlook and
  motivation that she needed to encourage her to
  pursue higher goals in these areas.

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Parent Reactions
GISMO Summer Workshop

• From As mom
• one of my friends who is an engineer at Boeing
  encouraged her to keep the strong interest
  because our future especially needs females to
  advance. She is arranging to take A to her job
  to show her how some of the planes are built.

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Parent Reactions
GISMO Summer Workshop

• From Ts mom
• My son is ADHD. In 3 weeks he got more out of
  the program than he did all year in some classes.
  I think this program is great for kids with
  learning disability...my son stayed focused and
  on task.

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Student Reactions

• From S, in a school what I did last summer
  exercise I don't like summer camps so
  naturally I thought a camp about math and other
  subjects unknown to me seemed dumb especially
  seeing as I did not have a choice.  But boy, was
  I wrong.  It was such a tremendous experience and
  in the end I was glad I went."
• From D, in email 6 months later my dad was
  asking me questions about stuff I should have
  learned by now in school and a lot I of them I
  hadn't been taught in school but I knew them from
  GISMO. An example of one of those things would be
  how to reflect, rotate, and translate objects.

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Student Reactions

• told me that she shouldve paid even more
  attention to what they were doing in summer,
  because it would have been useful in her classes.

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Student Animation Projects
GISMO Summer Workshop

• Dancing Fish
• Jets
• Wheelies
• My Dog

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• We cant have fun and work in school but we do
  here.

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Pre/Post-Test (Math) Results

• 25-point test, NAEP 2005 items, measuring
• Spatial reasoning
• Cardinal directions
• Measurement
• Ratio
• Coordinate graphing
• Similarity and scaling
• Angles
• Rotation
• Integer addition/subtraction
• Comparing decimals

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Pre/Post(Math) Results
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Pre/Post(Math) Results
t-test results Pre-test mean 7.9, s.d.
4.8 Post-test mean 11.5, s.d. 4.6 t-3.6 plt.008
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Project Research Design

• Design Study
• Small group of students, rising 6th graders,
  urban school district
• Mathematics curriculum integrated with new
  animation software, Graphs n Glyphs

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Project Goals

• To engage students in modeling how to represent
  3-dimensional objects and their movement on
  2-dimensional screen/plane
• Strengthen Core Number Knowledge and Reasoning
  through Visualization and Representation
• To link to learning trajectories via
  supplementary and embedded activities and tasks
• To make explicit the underlying mathematics (and,
  eventually, science) behind graphics, motion,
  and, subsequently, optics and acoustics
• To develop transitional software to introduce
  students to animation and 3-D graphics as a
  potential career trajectory and component of
  technology education

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Features of Successful Educational Programs for
At-Risk Students
Adapted from Jolly et al., 2004

• Deep Engagement
• Relevance (immediate and long-term)
• Creativity
• Continuing Support
• Opportunities, Resources and Guidance
• Genuine Content Knowledge
• Increasingly Rigorous Content

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Research Questions

• Can mathematical ideas underlying animation
  software be made visible and accessible to
  under-performing sixth graders?
• What are young students conceptions of animation
  and modeling, and how do they change as students
  begin to understand the need for a formal
  representational system for control of animations
  on computers?
• To what extent can we remediate mathematical
  content weaknesses and introduce new ideas such
  as distance, measurement, adding and subtracting
  integers, graphing, similarity, ratio and
  proportion, scaling, and geometric
  transformations?
• What kinds of animations will students produce?

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Approach

• Draws on concept of a micro-world
• learning environments for the appropriation of
  knowledge and, as a consequence of this change in
  focus, the transitional object takes on a central
  role (Hoyles, 1993, p. 2)

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Graphs n Glyphs Software

• Overview of Design
• Demonstration of Software

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Modeling of animation
Coherence
System One
System Two
(Connection)
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Essential Characteristics of Modeling
Confrey, Maloney, Ford and Nguyen, June 06

• Purpose indeterminate (situation, circumstance,
  or set of conditions) to more determinate
  (situation, circumstance or set of conditions).
  
• Two systems and a mapping between them. Meaning
  flows in both directions.
• Both systems structure composed of objects and
  relations. The mapping may include resemblance of
  form or function.
• Alternative models are always possible.
• There are always limits of applicability for any
  model.

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Essential Characteristics of Modeling
Confrey, Maloney, Ford and Nguyen, June 06

• Modeling is an iterative, cyclical, evolutionary
  process, using inscriptions and creating
  indicators.
• Modeling also involves products which supply
  explanations, likelihoods, and predictions.
• Modeling must address the degree of accuracy
  obtainable via criteria of consistency and
  coherence.
• Evaluation of model accuracy, effectiveness,
  flexibility, useability, simplicity,
  extensibility, generalizability.
• Modeling ranges from metaphoric to strictly
  mathematical.

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Graphs n Glyphs(Model of animation)
Coherence
Space and motion Objects in space
Combination of tools 1. create objects
(sequences of points ) 2.animate them (based on
transformations)
Connection
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Graphs N Glyphs

• Level 1 demonstration

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Concept of Transitional Software

• Incorporate professional-level software
  operational paradigms and design features (via
  consultation with professional animators)
• File-structures, menus, timelines and controls
  are all standard, and employed on real projects,
  to build fluency in IT skills
• Prepare students to transition readily to
  professional software (i.e. 3DSMax, Flash)
• In the service of robust content conceptual
  development (mathematics)

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Design and Implementation of Transitional
Software requires a team of

• Mathematics Educators / Software Designers
• Professional Digital Animators
• Software Engineer

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Professional Context Animation
Transitional Software
Learner-Centered Design
Subject Matter Content Mathematics
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Professional Context Animation

• Modeling the 3-D world on a 2-D space
• Creating/replicating objects on 2-D plane
• Motion on 2-D plane
• Sequencing motion via a timeline
• Visual feedback and interactivity
• Telling a story, using visual and audio
  representations

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Learner-Centered Design

• Dynamic software environment
• Multiple simultaneous representations
• Movement between two representations can be
  configured either bidirectionally or
  unidirectionally
• Adaptations of professional software features to
  serve content conceptual development (pivot
  point, scaling, point representations)

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Subject Matter Context Mathematics

• To represent 3-D objects in motion in 2-D screen
  space, by building objects via sequences of
  connected points, and moving them via
  transformations. Math topics include
• Measurement
• Positive and Negative Integers addition and
  subtraction,
• Coordinate graphing
• Transformations translation, rotation, scaling,
  stretching, reflection
• Ratio, similarity, and scaling

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The Design Collaboration Space the GISMO Blog

• Graphs n Glyphs design blog

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GISMO Directions and Future Work
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Graphs n Glyphs Levels

• Two-dimensional objects, transformations, simple
  animations
• Three-dimensional objects, optics, and light, and
  the basics of triangle trigonometry
• Sound and acoustics, and principles of periodic
  functions
• (Animation sequencing at each level)

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Breakout Groups
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Breakout Discussions

• Animation to facilitate mathematics (Alan)
• Matching activities, mazes, and building
  animations
• Mathematics to facilitate animation (Kenny)
• Introducing measurement and distance, integers,
  graphing

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Breakout Group 1 Evolving Concepts of Animation

• Concepts of Animation
• Directed Drawing Task
• Elevatorssimulating animation
• Transformations translation, rotation,
  reflection
• Completing a Match
• Negotiating Mazes
• Designing and implementing animations
• Ratio and scaling (not formally taught time
  constraints).

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Timeline
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Task Build a model of an elbow
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What characteristics of a good model did students
identify from elbow model activity?

• What makes a good model?
• Having exact movement
• Having it look like an elbow
• Dont go with your original plan and it comes out
  better (Revise it in light of things that youve
  done)
• What are models for?
• Teach people something that you might not be able
  to try otherwise
• Teach people how the original thing might work
• What models have you built?
• Solar system, Volcano, Ocean floor.
• (something you cant see, so you build a model of
  it.)
• How do you know when a models right?

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Task Compare clips of animations, observe how
animators make animations feel alive or
realistic

• They make it feel like the real world.
• Faces / bodies look realistic (same features as a
  regular person)
• Drawings and scan on the computer
• sensors on a persons body motion capture
• Realistic things in scenes.
• Real-looking rivers and water (and things
  floating), trees
• Motion and the sound, and shadows, and a lot of
  detail
• Characters that breathe
• Good animation the words really match the
  mouth.
• Action and drama

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What students said about how animators make the
world feel alive Shrek
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What students said about how animators make the
world feel alive Shrek

• things that real animals and people actually do
• motion
• texture on rocks, etc.
• breathing, sighs
• the way donkey stretched
• sound
• mouths more realistic, with tongues and teeth
• shadows

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What students said about how animators make the
world feel alive Spirited Away
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What students said about how animators make the
world feel alive Spirited Away

• Waters motion, waves and foam, bubbles
• The moon, stars, and clouds looked realistic
  (puffiness, 3-dimensional, and colors).
• But--mouth motion doesnt match speech as well
  (but overdubbed in English from Japanese).

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What students said about how animators make the
world feel alive Peppa Pig
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What students said about how animators make the
world feel alive Peppa Pig

• Not realistic! Just drawing, not as much like
  animation.
• Animals cant talk. but ogres, donkeys,
  dragons?
• Mouths didnt match perfectly, just open and
  close like circles, straight lines, no teeth or
  tongues.

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Directing drawing tasks

• From a picture, one person describes, the other
  records the description of the picture. Recorder
  cant see the picture. Goal the recorder draws
  as accurate a copy of the picture as possible.
• Trial 1 Recorder and Describer talk freely to
  each other, describer can see what the recorder
  is doing, and answer questions.
• Trial 2 Describer cannot see the Recorders
  work, but they can talk freely. Recorder can ask
  questions.
• Trial 3 Only the Describer can speak, cannot
  watch the Recorders work. Recorder may not ask
  questions.

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What strengths / weaknesses seen in directing
drawing communications?

• What strategies, techniques worked to get a good
  drawing
• Location, size, direction to draw, shapes
  overlapping, naming shapes.
• Comparisons to familiar objects.
• Challenges
• Not knowing names for geometric shapeshad to
  describe (hexagon, for instance). But later
  picked these up quickly.
• Describing where to place shapes and how to
  orient a shape.
• Did not try to use measurements of any kind.
• Knowing when to ask questions of describer to
  check accuracy (trials 1 and 2)
• Concept of feedback introduced computers dont
  automatically give feedback (we must learn to be
  precise in the way we tell them what to do).

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Task simulate animations with elevators
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When students simulated animations with
elevators, what were the characteristics of their
projects?

• BET Awards Show, car races, MJ DUNK (try try
  again)
• Story-driven, elaborate scripts and staging
• Part of task for another group to use the
  script to re-enact?
• Students recognized that the scripts lacked
  enough explicit animation directions
• Only one used scaling (MJ DUNK)

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Task matching exercises
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When students undertook matching exercises, what
issues arose?

• For translation the nature of the
  correspondence Matching the location of two
  objects by choosing corresponding points on the
  objects.
• Reflections Location of the pivot point, and
  how to move it if it were not on desired line of
  reflection
• Rotations Students were barely comfortable with
  90o and 180o rotations. Inexperienced with angle
  measure.
• Checking Predictions
• relied heavily on visual feedback,
• Diminishing difficulty with accurate prediction x
  (horizontal) and y (vertical) directions.
• Continuing difficulty with reflections, rotations.

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In building animations, what issues arose for
students?

• Making an animation

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In building animations, what issues arose for
students?

• Story elements sound, background pictures,
  pictures of themselves
• Mathematics elements
• Complexity number of points of objects, number
  of objects, coordinating multiple objects,
  synchronizing events.
• Bugs in application

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End