Educating Tomorrows Algorithmic ProblemSolvers Pierre Bierre Algorithmic Geometry

Educating Tomorrow’s Algorithmic Problem-Solvers Pierre Bierre, Algorithmic Geometry course developer Algo. Geom. org, founder Robb Cutler, co-founder, Computer Science Teachers Association (CSTA) Tutor Crossing, founder February 10, 2009 SUSE ED 291 Symposium

Today’s outline What is meant by “computer-science fluency”? What is CSTA’s plan impart it broadly via a K-12 model curriculum? 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 meant by “computer-science fluency”? What is CSTA’s plan impart it broadly via a K-12 model curriculum? 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 Pierre Bierre: degrees in physics, CS, Stanford Neuropsychology 4 years, biotech data analysis & robotics 15 years, inventor recognized by Modern Marvels 2007 Why algorithmic geometry? The most powerful medium for solving spatial problems is a blend of paper & pencil + software programming Geometry theory is bending as a result of working in the new medium High school students deserve up-to-date, relevant math-CS education Hart-Rudman Commission said to compete globally via math education

Algorithmic Geometry What is it? Spatial problem-solving done as a human-machine partnership creativity stamina understand meaning error-free arithmetic handle exceptions computational speed human computer + + + Want geometry concepts that make it easy to delegate work to computer

Examples of conceptual shifts Pre-computational ∞ Algorithmic n / 0 = error! [x y] slope = dy / dx use direction vector [ x y ] use angle q to represent 2 D direction use direction vector [ x y ] use angles [ f q ] to represent 3 D direction use direction vector [ x y z ] “=“ sign used ambiguously a == b (comparison) trigonometry don’t use anymore handle pedagogic cases handle all cases closed-form solution number-crunching algorithm pages of complex equations layering of small, bite-sized algos b a (info copying)

Degree-of-difficulty of algorithmic geometry problems 2 D robot arm motor coordination Given: shoulder location sh upper-arm length r 1 forearm length r 2 desired reach-point h, h solve for motor angles [qsh qel ] r 2 el r 1 sh “home” position of motors qsh == 0 qel == 0

Degree-of-difficulty of algorithmic geometry problems 3 D sphere-circle intersection Problem: solve intersection of sphere and circle 3 D SPH i 2 CIR i 1 Given Compute Results SPH = [ c r ] CIR = [ c orient num. Intersection. Points ( 0, 1, 2, ∞ ) point locations i 1 i 2 r]

Problem-solving methodology Problem statement Sketch out a mental solution 0: dist (c 1, c 2) > r 1 + r 2 Write pseudocode if (Vec 2. distance(C 1. c, C 2. c) Translate algo into Java algo library Test algo graphically

Algorithmic Geometry - Project development path Milestone Done? syllabus / coursebook drafted 2004 course lab software (2 D module) 2005 proof-of-concept pilot course (72 h) 2005 NSF grant proposals 2006 -7 -8 NCTM presentation 2008 course lab software (3 D 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

Algorithmic Geometry summary Potential benefits Spatial problem-solving proficiency of students could be raised to a collegiate or grad-student level before leaving high school 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 “Seed” next generation of scientists-engineers with sophisticated, operational understanding of 3 D geometry applicable to their specialties 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

Educating Tomorrow’s Algorithmic Problem-Solvers Q/A - roundtable discussion Follow-up: Pierre Bierre pierre@Algo. Geom. org (White paper on Algo Geom) Robb Cutler robb@tutorcrossing. com www. tutorcrossing. com