Microsoft Research Faculty Summit 2002

1
Microsoft Research Faculty Summit 2002

• John Peterson
• Languages for Math and Science
• Education
• Yale University

2
Overview

• Computers and K-12 education languages for the
  classroom
• A language for mathematical visualization
• Implementation details .NET to the rescue
• Bringing computer technology to educators
• Classroom experiences
• Conclusions and future research

3
Computers in the Classroom

• Our Goal
• Use computers to improve the education of all
  students in core areas of the high school
  curriculum.
• Exploit state of the art ideas developed in the
  programming languages community.
• Build languages that allow students to describe
  and experience objects in a learning domain.

4
Computer Languages in School
Should we use general purpose programming
languages to teach core high school subjects?
Oh Boy! Virtual methods!
l

Tell me about threads!
Can I use dynamic loading?
5
No!

• We need languages that are appropriate to
  specific learning domains
• Languages must be accessible to everyone - not
  just those interested in programming
• But
• Languages should be expressive capable of
  capturing large learning (for example, all of
  high school mathematics)

6
Languages and Learning

• What can languages do for students?
• Visualize abstract concepts in new ways
• Support creative exploration as well as problem
  solving
• Interact with the student for rapid exploration
  of a learning space
• Support new instructional styles that are based
  on artistic principals as well as science
• Provide a conceptual model of a domain

7
Educational Domains

• Mathematics visualization of abstract objects
  and concepts (functions, geometry)
• Physics and science interactive experiments
  (robotics), simulations
• Arts graphics and music
• We are not interested in teaching computing
  itself (Dr. Scheme addresses this)

8
A Language for Mathematical Visualization

• We have used Pan, a language of functional
  images, as the basis for an educational language
• Pan was developed by Conal Elliott at MSR
• Other influences
• Mathematica
• Geometers Sketchpad
• Dr Scheme

9
The Super Duper Graphing Calculator

• The most widely accepted computational tool in
  high school math is the graphing calculator
• Simple everyone can use and understand it
• General can be used throughout the curriculum
• Integrated used widely in texts activities
  using graphing calculators are common in the
  classroom
• Our goal is to build on this foundation
• Visualizations beyond line on paper
• Easier to program

10
Functional Programming

• Our work uses functional programming as a
  semantic basis
• Programs consist of definitions and expressions.
  Definitions are unordered.
• Definitions may be parameterized
• k 4
• f(x,y) xsine(y)-k

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Advanced Features

• Type inference to ensure correctness of the
  program. Students do not see the type system -
  it is implicit
• Higher order functions allow functions to be
  passed as parameters
• Patterns provide a natural syntax for
  destructuring values such as points
• Interaction is supported by a special bind
  operator, lt-, and simple widgets
• A module system allows students and instructors
  to build libraries

12
FPs and Math

• Why FPs? The building blocks are in place early
  in the math curriculum (as per one particular
  curriculum )
• Variables and expressions elementary school
• Functions and parameters grade 7
• Function composition grade 8
• Abstraction using functions grade 8

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Semantic Simplicity
Students can understand the operation of the
system using only basic mathematics plus a few
extra concepts such as colors or name scoping.
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Writing a Program

• Instructor writes a viewing function

image lt- imageSelect(Choose an image) scale
lt- slider(Scale, 0.1, 10, 1) rotation lt-
slider(Rotation, 0, 360, 0) xOffset lt-
slider(X center, -200, 200, 0) yOffset lt-
slider(Y center, -200, 200, 0) warp(i)
scaleImage(scale, translateImage((xOff
set, yOffset), rotateImage(i))) lens(
f) f(warp(image))
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Writing a Program

• Definition of the user interface (sliders)

image lt- imageSelect(Choose an image) scale
lt- slider(Scale, 0.1, 10, 1) rotation lt-
slider(Rotation, 0, 360, 0) xOffset lt-
slider(X center, -200, 200, 0) yOffset lt-
slider(Y center, -200, 200, 0) warp(i)
scaleImage(scale, translateImage((xOff
set, yOffset), rotateImage(i))) lens(
f) f(warp(image))
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Writing a Program
image lt- imageSelect(File) scale lt-
slider(Scale, 0.1, 10, 1) rotation lt-
slider(Rotation, 0, 360, 0) xOffset lt-
slider(X center, -200, 200, 0) yOffset lt-
slider(Y center, -200, 200, 0) warp(i)
scaleImage(scale, translateImage((xOff
set, yOffset), rotateImage(i))) lens(
f) f(warp(image))
Image manipulation functions
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Using the Lens

• Student defines an object (here, an equation
  mapping 2D points to 2D points)
• Student creates a visualization

k lt- slider(k, 0, 10, 1) f(r _at_ theta) (r _at_
theta kr)
lens(f)
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The result
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Implementation Issues

• How does this work?

C Program
Interactive Viewer
Student Program
Pan-based compiler
C JIT
Student interface
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.NET Aspects

• Use the JIT to get high performance
• Dynamic loading of compiled objects brings new
  viewers into the environment
• Portability is essential
• .NET libraries for user interface
• C used to write the IDE
• Software will be freely available to anyone with
  .NET

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Educational Issues

• Building a better language wont get educators to
  use it. There is much more to do beyond writing
  software
• Supporting materials
• Teacher training
• Formal assessment
• Learning strategies

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Partnerships

• This work is a collaboration with many other
  groups
• Educators curriculum development and integration
• Psychologists formal assessment
• Students the ultimate source of feedback

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Educational Agenda

• Study educational methodology how to make the
  best use of this system
• Provide supporting material (activities, lessons,
  texts) and teacher training
• Ensure that the system interacts effectively with
  users, handling errors in a student appropriate
  manner
• Seek compatibility with existing educational
  material

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Experiences

• We have tested this in the classroom with a
  simple lesson that includes
• Colors
• Images as functions
• Image lensing
• Coordinate Systems
• Patterns

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The Lensing Viewer

• Using the lens viewer, we can explore
• domain and range
• slopes
• continuity
• symmetry
• patterns

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Slide used in an 8th grade algebra presentation
A transformation f (x,y) (xx, yy) This
means when you look at (x,y) you see (xx,
yy) If you look at (2,2) youll see (4,4)
y
x
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Classroom Use

• The class received a 1 hour lecture with many
  examples.
• Students were asked to create new lens effects as
  a homework assignment
• Working individually with students, these effects
  were turned into a gallery

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Hey Mom! Look What I Made in Math!
I See You by Aparna f(dist _at_ angle) (dist _at_
ramps(k,angle))
Mr. Ridgeway by Heidi f(dist _at_ angle)
(distk1 _at_ anglek2dist)
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Hey Mom! Look What I Made in Math!
Open Wide by Melodie f(dist _at_ angle)
(distdist/40 k1sine(dist/k2)_at_ angle)
Mr. Sids New Hair by his class f(dist _at_ angle)
(distk1 _at_ anglek2dist)
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Status

• Initial math visualization language should be
  ready Fall 2002
• Current work is focused on usability handling
  errors in an appropriate manner
• Curriculum development and formal assessment will
  start as the language becomes usable
• Explore different learning styles
• Starting work on a music language

31
Conclusions

• This research can make a significant impact on
  the educational system
• Computers can provide new learning experiences
  that exploit creativity
• Expose students to basic principals of
  computation without the complexity of a full
  programming language
• We need to prove to educators that computer
  languages are useful in teaching core curriculum
  areas such as math and science

32
Thanks to .

• Team members David Eisenstat, Emmanual Imbeah,
  Jian Yuan, Paul Hudak
• Microsoft Research
• Conal Elliott
• Pace Center
• Dr. Scheme
• Educators and students who have suffered through
  initial trials