educating tomorrow’s algorithmic problem-solvers pierre bierre, algorithmic geometry course...
TRANSCRIPT
Educating Tomorrow’s Algorithmic Problem-Solvers
Pierre Bierre, Algorithmic Geometry course developer AlgoGeom.org, founder
Robb Cutler, co-founder, Computer Science Teachers Association (CSTA) Tutor Crossing, founder
February 10, 2009SUSE ED291 Symposium
Today’s outline
What is CSTA’s plan impart it broadly via a K-12 model curriculum?
What is meant by “computer-science fluency”?
What might be the impact on your educational topic of interest?
25:00 Robb - CSTA’s vision for computer science education
25:00 Pierre - reshaping geometry for algorithmic thinkers (grade 11-12)
20:00 Q/A, roundtable discussion
Today’s outline
What is CSTA’s plan impart it broadly via a K-12 model curriculum?
What is meant by “computer-science fluency”?
What will be the impact on your subjects of interest?
25:00 Robb - CSTA’s vision for computer science education
25:00 Pierre - reshaping geometry for algorithmic thinkers (grade 11-12)
20:00 Q/A, roundtable discussion
Robb Cutler presentation
Algorithmic Geometry
The most powerful medium for solving spatial problems is a blend ofpaper & pencil + software programming
Why algorithmic geometry?
Geometry theory is bending as a result of working in the new medium
High school students deserve up-to-date, relevant math-CS education
Pierre Bierre: degrees in physics, CS, Stanford Neuropsychology 4 years,biotech data analysis & robotics 15 years, inventor recognized by Modern Marvels 2007
Hart-Rudman Commission said to compete globally via math education
Algorithmic Geometry
What is it?
Spatial problem-solving done as a human-machine partnership
computerhuman
creativity stamina
handle
exceptions
error-free
arithmetic
understand
meaning
computationalspeed
++
+
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+
+
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Want geometry concepts that make it easy to delegate work to computer
Examples of conceptual shifts
Pre-computational Algorithmic
∞ n / 0 = error!
use angle to represent 2D direction use direction vector [ x y ]
use angles [ to represent 3D direction
use direction vector [ x y z ]
trigonometry don’t use anymore
slope = dy / dx use direction vector [ x y ]
handle pedagogic cases handle all cases
closed-form solution number-crunching algorithm
pages of complex equations layering of small, bite-sized algos
[ x y ]
“=“ sign used ambiguously a == b (comparison) b a (info copying)
Degree-of-difficulty of algorithmic geometry problems
2D robot arm motor coordination
QuickTime™ and aTIFF (LZW) decompressorare needed to see this picture.r2
r1
sh
el
h
Given:shoulder location shupper-arm length r1forearm length r2 desired reach-point h,
solve for motor angles [shel ]
QuickTime™ and aTIFF (LZW) decompressorare needed to see this picture.
“home” position of motors sh==el == 0
Degree-of-difficulty of algorithmic geometry problems
3D sphere-circle intersection
Problem: solve intersection of sphere and circle3D
SPH
CIR
i1
i2
Given
SPH = [ c r ]CIR = [ c orient r ]
Compute Results
numIntersectionPoints ( 0, 1, 2, ∞ )point locations i1 i2
Problem-solving methodology
Problem statement
Sketch out a mental solution
Write pseudocode
0: dist (c1, c2) > r1 + r2
Translate algo into Java
if (Vec2.distance(C1.c, C2.c)
Test algo graphicallyalgo
library
Algorithmic Geometry - Project development path Milestone Done?
syllabus / coursebook drafted 2004
course lab software (2D module) 2005
proof-of-concept pilot course (72 h) 2005
NSF grant proposals 2006-7-8
course lab software (3D module) 2008-9
Summer ‘09 course announced 2009
Learning metrics design/capture 2009
Teach-the teachers feasibility 2009-12
Technical expert reviews 2009-12
First 150 student outcomes 2012
NCTM presentation 2008
Algorithmic Geometry summary
Uphill challenges
Student performance elevated beyond level measurable along standard yardsticks (e.g. SAT, TIMSS, NAEPS)…. will “accountability” crowd buy in?
Is is math or computer science? (it’s both)
NSF 9-12 ed research seriously underfunded and somewhat risk-averse
Project could move ahead faster as an academic-industry partnership
Potential benefits
“Seed” next generation of scientists-engineers with sophisticated, operationalunderstanding of 3D geometry applicable to their specialties
Redefine math-problem mastery as ability to devise an automated solution
Influence more young people to consider STEM careers during the critical decision timeframe (grades 11-12), especially girls, under-represented groups
Spatial problem-solving proficiency of students could be raised to a collegiate or grad-student level before leaving high school
Q/A - roundtable discussion
Pierre Bierre [email protected] (White paper on Algo Geom)
Robb Cutler [email protected] www.tutorcrossing.com
Follow-up:
Educating Tomorrow’s Algorithmic Problem-Solvers