Published on January 7, 2008
Why robots cannot teach mathematics (but are excellent ballroom dancers) : Why robots cannot teach mathematics (but are excellent ballroom dancers) Steven de Jong [email protected] MMM Competition 28 January 2006 Edgar Degas: The Rehearsal c. 1873-78 (120 Kb) Oil on canvas, 41 x 61.7 cm (18 1/2 x 24 3/8 in) Fogg Art Museum, Harvard University, Cambridge, MA Content: Content PART I Computers and math teachers PART II Artificial Intelligence (AI) PART III Robots, soccer… and the ballroom DISCUSSION PART I: Computers & math: PART I: Computers & math Better at mathematics than you (and me, obviously) Bad at almost everything else humans are good at Speech recognition Visual information Understanding The juggler… Math teachers: Math teachers Do you see something wrong? Math teachers: Math teachers Cellphones in your classroom… Math teachers: Math teachers What did the girl just say? What would you do? So…: So… Being good at mathematics is something else than being a good teacher… The same applies to computers good at fixed procedures and raw calculation bad at anything else Is this a bad thing, actually? It is if you still call computers ‘intelligent’ And it is if you blindly rely on computers Computers in math education: Computers in math education “Modern” math education increasingly makes use of computers Goal: Students do understanding and abstraction Computers do standard calculations However: Students place so much trust in these devices that they start behaving like one abilities and understanding are immediately replaced by automatic procedures Computers in math education: Computers in math education Examples from remedial teaching Example 1 At which values of x does (x-2)(x+1)(x+5) = 0 hold? (2,-1,-5) One of my students said: x = 2 and x = -1 because the ‘window’ of the calculator was set to [-2,2]. It took 2 minutes of typing to find this answer. Example 2 After two months of working with normal distributions, one of my students could do every assignment perfectly, but she still did not know what a normal distribution was! Only procedural abilities, no understanding Just like a computer… Computers and humans: Computers and humans The problem with computers… Computers were developed to help us However, they seem to make us “stupid” because we adapt to their rigidity Ever called a helpdesk and heard the apology “the computer made a mistake?” So how can we make computers (and ourselves) more intelligent? PART II: Artificial Intelligence (AI): PART II: Artificial Intelligence (AI) Philosophical issues What is intelligence anyway? How do we know for sure whether someone is actually intelligent? Do we take emotion, physical, social behaviour into account or is rationality sufficient? Classical view Rationality is the key (think IQ tests) computers Modern view (simplified) Intelligence is the ability to respond aptly Thus, intelligence includes or even requires emotional, physical and social behaviour Artificial Intelligence: Artificial Intelligence Enhancing the computer’s current abilities Calculation Reasoning Logic “Trying to make computers do what they were not meant to be doing” (T. Pratchett) Learning Creativity Interaction Physical (embodied) tasks The need for embodiment & robots: The need for embodiment & robots Knowledge engineering / AI = (inter-)acting in the real world Natural language processing Computer vision … Applications for robotics Smart cars “are you sure you want to use your breaks?” Storage facility management Robo Soccer Robots: Robots Non-autonomous vs. autonomous Learning vs. routines Designing behaviour vs. understanding behaviour Thinking vs. acting (i.e., chess vs. walking) PART III: Robots, soccer and ballrooms: PART III: Robots, soccer and ballrooms Why Robo Soccer? Entertainment Many challenges for AI Computer vision object recognition Planning and team sports Handling the ball Even ‘trivial tasks’ are hard! Robots, soccer and ballrooms: Robots, soccer and ballrooms Let the game begin… Entering the field Robots, soccer and ballrooms: Robots, soccer and ballrooms Let the game begin… Kick that ball! (very short clip) Issues in robot soccer: Issues in robot soccer QUICK PERCEPTION The environment is highly dynamic Light, spectators’ clothing Very fast game Robots must see what happens very quickly PLANNING & TEAMWORK Score many times and allow very few counter scores Calculate path to interception point Roles: attacker, midfielder, defender, keeper, et cetera Tactics: defensive, offensive, plan attacks, block opponents RELIABLE ACTION Keep up with the ball Dribbling Giving the ball direction Passing to other players Shooting at goal (without falling) My opponents are blue and white: Where are my opponents? 1-0 The confused soccerbot My opponents are blue and white Ah yes, there! And finally, the ballroom dancers…: And finally, the ballroom dancers… Conclusion: Conclusion Regarding mathematics: Computers are not mathematicians Computers are tools that should be used only after one understands what happens Regarding artificial intelligence and robots Making computers work in the physical world is extremely difficult Robo Soccer is an entertaining and difficult testbed for this Quite remarkable things can already be done And quite remarkable things have to be done… Slide22: Questions?