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What can technology add to the mathematics classroom? DOUGLAS BUTLER Director, iCT Training Centre, Oundle School, Peterborough (UK) Mathematical Association of New South Wales MANSW Annual Conference 2006 Bright Ideas at Brighton Sydney, Australia 8 – 10 Sept 2006 OPENING KEYNOTE – WEB VERSION 9:30 to 10:30 am Friday 8 th September 2006 Novotel Brighton Beach, Brighton, NSW

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The downward spiral – go therego there Classroom Technology – go therego there History of Mathematics – go therego there Google, etc – go therego there The Golden Ratio – go therego there Some integer giants – go therego there CONTENTS (1) … Butler – MANSW 2006

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Calculus – go therego there Vectors 2D and 3D – go therego there Movie Maths – go therego there Data, Data – go therego there Spreadsheet skills – go therego there Google Earth – go therego there CONTENTS (2) … Butler – MANSW 2006

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October 2003 September 2005 My last two visits … Butler – MANSW 2006

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Mathematics Education: is there a problem? What can technology add to the mathematics classroom? Butler – MANSW 2006

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Despite a record number of graduates entering the job market this year, many will lack the basic skills in grammar and mathematics needed for employment … … they make basic mistakes, write illiterate memos and need constant supervision. THE TIMES’ newspaper (London, 7th February 2006) Butler – MANSW 2006

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A level Mathematics (England): 75,000 in 1991 [13,500 = 18% awarded top Grade A] 56,000 in 2006 [24,080 = 43% awarded top Grade A] “Mathematics Downward Spiral”Downward Spiral Butler – MANSW 2006

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Try the 1966 ‘World Cup’ O level Boys 14,8005.1% awarded A grade Girls 11,4003.6% awarded A grade Total: 26,2004.5% awarded A grade 2005: 450,000 candidates 9.1% A, 4.7% A* And exams at 16? Butler – MANSW 2006

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“Mathematics Society” Average attendance “Financial Mathematics Society” Average attendance What do pupils think “work” involving mathematics is all about? Butler – MANSW 2006

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Australia: (June 2004) International Centre of Excellence for Education in Mathematics International Centre of Excellence for Education in Mathematics USA: (April 2006) National Mathematics Advisory Panel National Mathematics Advisory Panel GB: (May 2006) Centre of Excellence in Mathematics Teaching Centre of Excellence in Mathematics Teaching What are Governments doing about it? Butler – MANSW 2006

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The modern mathematics classroom? Butler – MANSW 2006

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Two types of TABLET to take round the class: Butler – MANSW 2006

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COMPUTERS Geometry Expressions XThink HAND-HELD Casio Classpad TI Nspire And what is just round the corner? Butler – MANSW 2006

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Where did it all start? What can technology add to the mathematics classroom? Butler – MANSW 2006

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Let’s look back... Pythagoras of Samos Pythagoras of Samos ( BC) The Tunnel of Eupalinos Butler – MANSW 2006

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How did we count? The Mathematics of 1000 years ago Butler – MANSW 2006

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When did serious calculations start? Charles Babbage Difference Engines moving parts, 31 places of accuracy #2 (Science Museum, London) weighs 2½ tons Butler – MANSW 2006

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… and more portable? Virtual Slide Rule Virtual Slide Rule (Andrew Davie, Tasmania) Butler – MANSW 2006

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So, was Sydney OH built with a slide rule? Butler – MANSW 2006

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So how does Google work?Google As of today, Google states that they are indexing 19 Billion distinct web pages. Butler – MANSW 2006

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Find out using “tracert” How does the Internet get from Oundle to Brighton-le-Sands? Butler – MANSW 2006

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Exposing some of the mystery What can technology add to the mathematics classroom? Butler – MANSW 2006

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The human body and PHI Butler – MANSW 2006

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The human body and PHI Butler – MANSW 2006

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Credit Card Parthenon (440 BC) Gary Meisner’s Golden Number site Golden Number site Butler – MANSW 2006

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Some INTEGER GIANTS What can technology add to the mathematics classroom? Butler – MANSW 2006

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Mersenne Primes Download M44: 2^32,582,657-1 It has digits, still just less than 10 million.M44 Discovered 4th Sep 2006, Curtis Cooper, USA Butler – MANSW 2006

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The mystery of CALCULUS What can technology add to the mathematics classroom? Why do we teach it? Butler – MANSW 2006

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“The decline in attacks over the past two years has slowed down” Pottengal Mukundan, Director of The Piracy Reporting Centre at the International Maritime Bureau The Times July 26, 2006 “Pirates are back on the map” Butler – MANSW 2006

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Volume: 33.96π cm³ Area: cm² The Volume of Harry Potter’s Goblet See “Volumes of Revolution” tutorial on the Autograph InAction page Autograph InAction Butler – MANSW 2006

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mg kv n m v So, if you fall out of an aeroplane … Butler – MANSW 2006

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See “Differential Equations” tutorial on the Autograph InAction page Autograph InAction Butler – MANSW 2006

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VECTORS in 2D and 3D What can technology add to the mathematics classroom? “I hate vectors!” Butler – MANSW 2006

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Now for some MOVIE MATHS What can technology add to the mathematics classroom? Movies ABOUT mathematics Movies created with mathematics Butler – MANSW 2006

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Numb3rs (CBS tv, now) Proof (2005) A Beautiful Mind (2001) PI (1998) Good Will Hunting (1997) Sneakers (1992) Stand and Deliver (1987) Movies ABOUT Mathematics Butler – MANSW 2006

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See “Starship Enterprise” tutorial on Autograph InAction page Autograph InAction ‘Ice Age 2’ trailer This principle behind rendering 3D shapes Butler – MANSW 2006

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DATA, DATA everywhere What can technology add to the mathematics classroom? Butler – MANSW 2006

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Who drives on the left? What proportion of the World’s population lives in a country that drives on the left? Data from TSM Resources mathematics links page (Statistics section) Data mathematics links page Butler – MANSW 2006

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What’s so special about the NORMAL distribution? See “Central Limit Theorem” tutorial on the Autograph InAction page Autograph InAction Butler – MANSW 2006

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Check in: Why don’t they weigh US? Butler – MANSW 2006

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Some weight data Butler – MANSW 2006

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lb MEAN = 8.15 lb SD = 0.92 lb The normal distribution: baby weight Butler – MANSW 2006

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Some fun with SPORTS DATA What can technology add to the mathematics classroom? Butler – MANSW 2006

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?? Butler – MANSW 2006

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?? Butler – MANSW 2006

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?? Australia v. Namibia Butler – MANSW 2006

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?? Butler – MANSW 2006

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?? Butler – MANSW 2006

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Spreadsheet Skills Butler – MANSW 2006

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WORLD CUPGoals per match 2006Germany Korea-Japan France USA Italy Mexico Spain Argentina W. Germany Mexico England Chile Sweden Switzerland Brazil France Italy Uraguay3.89 Wikipedia articles Butler – MANSW 2006

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Excitement League Table! Averages Excitement A+B|A–B| (A+B)/|A–B| 1-day Cricket Aussie Rules Rugby League Rugby Union World Cup Soccer World Cup Soccer World Cup Knockout Butler – MANSW 2006

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Excitement League Table! Averages Excitement A+B|A–B| (A+B)/|A–B| 1-day Cricket Aussie Rules Rugby League Rugby Union World Cup Soccer World Cup Soccer World Cup Knockout Butler – MANSW 2006

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Data, Data everywhere … The GCSE Statistics Coursework Project (UK) Butler – MANSW 2006

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Two ways of looking at the same data … … using Autograph (Statistics page) and varying the class-width. Butler – MANSW 2006

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Sunrise over Lake Geneva Butler – MANSW 2006

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Using the “Fit Data” facility in Autograph Butler – MANSW 2006

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Using Google Earth and the Iconico Screen Protractor to find Geometrical objectsGoogle EarthIconico Screen Protractor Butler – MANSW 2006

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What was MY ROUTE to get here from Oundle? 1. Heathrow Airport, London Butler – MANSW 2006

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Using Google Earth: 1. Heathrow Airport, London Butler – MANSW 2006

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Using Google Earth 2. Dubai, United Arab Emirates Butler – MANSW 2006

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Using Google Earth 2. Dubai, United Arab Emirates Butler – MANSW 2006

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Using Google Earth 2. Dubai, United Arab Emirates Butler – MANSW 2006

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Using Google Earth 3. Sydney Airport Butler – MANSW 2006

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Using Google Earth: 3. Sydney Airport Butler – MANSW 2006

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WIND SUMMARY DIAGRAMS Other Statistical Diagrams … Butler – MANSW 2006

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Airport runway directions Measuring Runway directions MACKAY AIRPORT (Qld) Butler – MANSW 2006

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The downward spiral Classroom Technology History of Mathematics Modern applications, eg Google The mystery of the Golden Ratio Some integer giants And the headlines again … Butler – MANSW 2006

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Calculus Vectors 2D and 3D Movie Maths Data, Data Google Earth And the headlines again … Butler – MANSW 2006

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FRIDAY Session # 4 [Endeavour 1] 3:00-4:00 Making WORD mathematically friendly SATURDAY Session # 8 [Endeavour 1] 12:40-1:40 AUTOGRAPH for Coord. Geometry 2D/3D SUNDAY Session #13 [Endeavour 1] 10:00-11:00 AUTOGRAPH for Probability and Statistics What can technology add to the mathematics classroom? Butler – MANSW 2006

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DOUGLAS BUTLER Director, iCT Training Centre, Oundle School, Peterborough (UK) Web: This Slideshow: What can technology add to the mathematics classroom?

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THE END!! OUT-TAKES …. Butler – MANSW 2006

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Some concepts can be tricky... Speed of Sound: Most movie makers think the time between lightening and thunder = 0 sec Density of a Pulsar (Rotating Neutron Star) Mass of the sun, and the size of London Speed of India (moving North) 5cm per year Butler – MANSW 2006

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Some lottery magic The UK Lottery plays on Wednesday and Saturday You may as well play the Wednesday Lottery as the chance of winning on Wednesday is greater than the chance of surviving to Saturday by not being knocked down in a traffic accident. Butler – MANSW 2006

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Some lottery magic UK Lottery site All Winning Numbers Frequency distribution Butler – MANSW 2006

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Even Excel can get it wrong What do you think π is to 30 dp? Let’s ask ExcelExcel Butler – MANSW 2006

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Trigonometry and Harmony sinA + sinB =2sin½(A + B) cos½(A – B) Butler – MANSW 2006

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The Occurrence of Conics Jill Britton (Vancouver, Canada) Butler – MANSW 2006

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Queen Victoria (2007) Length: 294m Tonnage: 90,000 Passengers: 2014 Titanic (1911) Length: 269m Tonnage: 95,000 Passengers: 1316 Queen Mary 2 (2004) Length: 345m Tonnage: 151,400 Passengers: 3090 QE2 (1967) Length: 294m Tonnage: 70,327 Passengers: 1792 Two Queens in New York! Butler – MANSW 2006

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A couple of topical graphs! Butler – MANSW 2006

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GIANT INTEGERS Powers of 10 Powers of 2 Butler – MANSW 2006

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Any rectangular sheet of paper … Butler – MANSW 2006

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Can you find all the angles? Butler – MANSW 2006

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So let’s chase some angles! Butler – MANSW 2006

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How was it done? Butler – MANSW 2006

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How did the Victorians do it? [2 km long, started at both ends] – Robert Fairley 1853 Butler – MANSW 2006

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To Bleanau Ffestiniogg Butler – MANSW 2006

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747 Maiden Flight Butler – MANSW 2006

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747 Maiden Flight Butler – MANSW 2006

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USA: 8.5x 11” = 216 x 279 mm A4: 210 x 297 mm 11/8.5 = 1.29… 297/210 = 1.41… [ ] Butler – MANSW 2006

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1: Good web summary (Markus Kuhn) Butler – MANSW 2006

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One giant leap for mankind One small step for man … Butler – MANSW 2006

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UK Government report 2004 ”The Post-14 Mathematics Inquiry” ”The Post-14 Mathematics Inquiry => National Centre for Excellence in Teaching of MathematicsNational Centre for Excellence in Teaching of Mathematics a Mathematics Degree => 10% increase in Salary Butler – MANSW 2006

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The Pythagorean scale Musical scales The Pythagorean Comma The ‘Fifth’ interval Butler – MANSW 2006

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Virtual Learning Environments TI-83 … Autograph in 3D Butler – MANSW 2006

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In Ab maj Butler – MANSW 2006

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In A maj Butler – MANSW 2006

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The Triangle in Nature The Hyptiotes spider The Hyptiotes spider Butler – MANSW 2006

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INTERMISSION What can technology add to the mathematics classroom? Butler – MANSW 2006

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To create a paper Tetrahedron Butler – MANSW 2006

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Some ERRORS What can technology add to the mathematics classroom? Butler – MANSW 2006

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A famous mistake … Sept 1999 Mars Orbiter lost Butler – MANSW 2006

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Harmony and chaos Butler – MANSW 2006

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That GOLDEN RATIO: φ = 1·618… The Parthenon – built around 440 BC Butler – MANSW 2006

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And portable? Museum of Soviet Calculators Butler – MANSW 2006

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Funderstanding Rollercoaster Butler – MANSW 2006

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1 mile = ? meters 4-minute mile The Record for running a MILE Butler – MANSW 2006

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Some TRIGONOMETRY What can technology add to the mathematics classroom? Butler – MANSW 2006

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Trigonometry … and Drains! Butler – MANSW 2006

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or ∞ !! MIN = 1:60 MAX = 1:16 Trigonometry … and Drains! Butler – MANSW 2006

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20,000 m³ litres daily = 400 litres of water per person daily 50 km length Slope of the Roman Aqueduct (19BC) (Pont du Gard) Average slope: 34 cm/km Butler – MANSW 2006

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Norfolk Pines off Mackay Butler – MANSW 2006

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