What can technology add to the mathematics classroom?
DOUGLAS BUTLERDirector, iCT Training Centre,
Oundle School, Peterborough (UK)
Mathematical Association of New South Wales
MANSW Annual Conference 2006Bright Ideas at Brighton
Sydney, Australia 8 – 10 Sept 2006
OPENING KEYNOTE – WEB VERSION9:30 to 10:30 am Friday 8th September 2006
Novotel Brighton Beach, Brighton, NSW
The downward spiral – go there
Classroom Technology – go there
History of Mathematics – go there
Google, etc – go there
The Golden Ratio – go there
Some integer giants – go there
CONTENTS (1) …
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Calculus – go there
Vectors 2D and 3D – go there
Movie Maths – go there
Data, Data – go there
Spreadsheet skills – go there
Google Earth – go there
CONTENTS (2) …
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October 2003
September 2005
My last two visits …
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Mathematics Education: is there a problem?
What can technology add
to the mathematics classroom?
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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)
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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”
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Try the 1966 ‘World Cup’ O level
Boys 14,800 5.1% awarded A grade
Girls 11,400 3.6% awarded A grade
Total: 26,200 4.5% awarded A grade
2005: 450,000 candidates 9.1% A, 4.7% A*
And exams at 16?
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“Mathematics Society”Average attendance .. .. 17
“Financial Mathematics Society”Average attendance .. .. 89
What do pupils think “work” involving mathematics is all about?
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Australia: (June 2004) International Centre of Excellence for Education in Mathematics
USA: (April 2006) National Mathematics Advisory Panel
GB: (May 2006) Centre of Excellence in Mathematics Teaching
What are Governments doing about it?
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The modern mathematics classroom?
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Two types of TABLET to take round the class:
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COMPUTERS Geometry Expressions XThink
HAND-HELD Casio Classpad TI Nspire
And what is just round the corner?
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Where did it all start?
What can technology add
to the mathematics classroom?
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Let’s look back ...
Pythagoras of Samos (569 - 475 BC)
The Tunnel of Eupalinos
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How did we count?
The Mathematics of 1000 years ago
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When did serious calculations start?
• Charles Babbage Difference Engines 1842 - 1871
4000 moving parts, 31 places of accuracy #2 (Science Museum, London) weighs 2½ tons
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… and more portable?
Virtual Slide Rule (Andrew Davie, Tasmania)
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So, was Sydney OH built with a slide rule?
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So how does Google work?
As of today, Google states that they are indexing 19 Billion distinct web pages.
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Find out using “tracert”
How does the Internet get from
Oundle to Brighton-le-Sands?
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Exposing some of the mystery
What can technology add
to the mathematics classroom?
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The human bodyand PHI
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The human bodyand PHI
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Credit Card
Parthenon (440 BC)
Gary Meisner’sGolden Number site
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Some INTEGER GIANTS
What can technology add
to the mathematics classroom?
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Mersenne Primes
Download M44: 2^32,582,657-1It has 9 808 358 digits, still just less than 10 million.
Discovered 4th Sep 2006, Curtis Cooper , USA
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The mystery of CALCULUS
What can technology add
to the mathematics classroom?
Why do we teach it?
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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”
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Volume: 33.96π cm³
Area: 10.90 cm²
The Volume of Harry Potter’s Goblet
See “Volumes of Revolution” tutorial on the Autograph InAction page
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mg
kvn
mv
So, if you fall out of an aeroplane …
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See “Differential Equations” tutorial on the Autograph InAction page
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VECTORS in 2D and 3D
What can technology add
to the mathematics classroom?
“I hate vectors!”
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Now for some MOVIE MATHS
What can technology add
to the mathematics classroom?
Movies ABOUT mathematics
Movies created with mathematics
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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
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See “Starship Enterprise” tutorial on Autograph InAction page
‘Ice Age 2’ trailer
This principle behind rendering 3D shapes
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DATA, DATA everywhere
What can technology add
to the mathematics classroom?
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Who drives on the left?
What proportion of the World’s populationlives in a country thatdrives on the left?
Data from TSM Resources mathematics links page(Statistics section)
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What’s so special about the NORMAL distribution?
See “Central Limit Theorem”tutorial on the Autograph InAction page
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Check in: Why don’t they weigh US?
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Some weight dataButler – MANSW 2006
1 2 3 4 5 6 7 8 9 10 11 12 13 14 lb MEAN = 8.15 lb SD = 0.92 lb
The normal distribution: baby weight
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Some fun with SPORTS DATA
What can technology add
to the mathematics classroom?
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ONE-DAY CRICKET 2005-2006 InternationalsTotal runs scored per match
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ONE-DAY CRICKET 2005-2006 InternationalsTotal runs scored per match
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ONE-DAY CRICKET 2005-2006 InternationalsRun DIFFERENCES per match
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AUSSIE RULES FOOTIEPoints per match
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AUSSIE RULES FOOTIEPoints per match
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AUSSIE RULES FOOTIEPoint DIFFERENCES per match
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RUGBY UNION WORLD CUP Cup 2003Total points per game
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RUGBY UNION WORLD CUP Cup 2003Total points per game
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Australiav.Namibia
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RUGBY UNION WORLD CUP Cup 2003Total points per game
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RUGBY UNION WORLD CUP Cup 2003Score DIFFERENCE per game
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RUGBY LEAGUE (misc)Total points per match
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RUGBY LEAGUE (misc)Total points per match
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SOCCER WORLD CUP 2006Goals scored per match
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Goals Data
Poisson
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SOCCER WORLD CUP 2006Goals scored per match
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SOCCER WORLD CUP 2006Goal Difference per match
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UK SOCCER PREMIERSHIPGoals per match
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UK SOCCER PREMIERSHIPGoal DIFFERENCES per match
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Spreadsheet Skills
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WORLDCUP Goals per match
2006 Germany 2.30
2002 Korea-Japan 2.52
1998 France 2.67
1994 USA 2.71
1990 Italy 2.21
1986 Mexico 2.54
1982 Spain 2.81
1978 Argentina 2.68
1974 W. Germany 2.55
1970 Mexico 2.97
1966 England 2.78
1962 Chile 2.78
1958 Sweden 3.60
1954 Switzerland 5.39
1950 Brazil 4.00
1946 -
1942 -
1938 France 4.67
1934 Italy 4.12
1930 Uraguay 3.89
GOALS SCORED per match (SOCCER WORLD CUPS)
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Wikipedia articles
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ExcitementLeague Table! Averages Excitement
A+B |A–B| (A+B)/|A–B|
1-day Cricket 418.88 27.58 15.2
Aussie Rules 187.98 29.73 6.3
Rugby League 32.70 9.69 3.4
Rugby Union World Cup 59.06 32.85 1.8
Soccer World Cup 2.30 1.42 1.6
Soccer World Cup Knockout 1.88 1.25 1.5
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ExcitementLeague Table! Averages Excitement
A+B |A–B| (A+B)/|A–B|
1-day Cricket 418.88 27.58 15.2
Aussie Rules 187.98 29.73 6.3
Rugby League 32.70 9.69 3.4
Rugby Union World Cup 59.06 32.85 1.8
Soccer World Cup 2.30 1.42 1.6
Soccer World Cup Knockout 1.88 1.25 1.5
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Data, Data everywhere …
The GCSE Statistics Coursework Project (UK)
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Two ways of looking at the same data …
… using Autograph (Statistics page) and varying the class-width.
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Sunrise over
Lake Geneva
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Using the “Fit Data”
facility in Autograph
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Using Google Earth and the Iconico Screen Protractorto find Geometrical objects
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What was MY ROUTE to get here from Oundle?1. Heathrow Airport, London
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Using Google Earth:1. Heathrow Airport, London
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Using Google Earth 2. Dubai, United Arab Emirates
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Using Google Earth 2. Dubai, United Arab Emirates
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Using Google Earth 2. Dubai, United Arab Emirates
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Using Google Earth 3. Sydney Airport
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Using Google Earth:3. Sydney Airport
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WIND SUMMARY DIAGRAMS
Other Statistical Diagrams …
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Airport runway directions
Measuring Runway directions
MACKAY AIRPORT (Qld)
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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 …
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Calculus Vectors 2D and 3D
Movie Maths Data, Data Google Earth
And the headlines again …
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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?
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DOUGLAS BUTLERDirector, iCT Training Centre,
Oundle School, Peterborough (UK)
Web:www.tsm-resources.com
Email:
This Slideshow:
www.tsm-resources.com/MANSW.pps
What can technology add
to the mathematics classroom?
THE END!!
OUT-TAKES ….
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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
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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.
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Some lottery magic
UK Lottery site
All Winning Numbers
Frequency distribution
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Even Excel can get it wrong
What do you think π is to 30 dp?
Let’s ask Excel
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Trigonometry and Harmony
sinA + sinB =2sin½(A + B) cos½(A – B)
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The Occurrence of Conics
Jill Britton (Vancouver, Canada)
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Queen Victoria (2007)Length: 294mTonnage: 90,000Passengers: 2014
Titanic (1911)Length: 269mTonnage: 95,000Passengers: 1316
Queen Mary 2 (2004)Length: 345mTonnage: 151,400Passengers: 3090
QE2 (1967)Length: 294mTonnage: 70,327 Passengers: 1792
Two Queens in New York!Butler – MANSW 2006
A couple of topical graphs!
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GIANT INTEGERS
Powers of 10
Powers of 2
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Any rectangular sheet of paper …
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Can you find all the angles?
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So let’s chase some angles!Butler – MANSW 2006
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How was it done?Butler – MANSW 2006
How did the Victorians do it? [2 km long, started at both ends] – Robert Fairley 1853
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To Bleanau FfestinioggButler – MANSW 2006
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747 Maiden FlightButler – MANSW 2006
747 Maiden Flight - 1969
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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… [ ]
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1:
Good web summary
(Markus Kuhn)
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One giant leap for mankind
• One small step for man …
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UK Government report 2004”The Post-14 Mathematics Inquiry”
=> National Centre for Excellencein Teaching of Mathematics
a Mathematics Degree => 10% increase in Salary
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The Pythagorean scale
Musical scales
The
PythagoreanComma
The‘Fifth’ interval
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Virtual Learning Environments
TI-83 … Autograph in 3D
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In Ab majButler – MANSW 2006
In A majButler – MANSW 2006
The Triangle in NatureThe Hyptiotes spider
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INTERMISSION
What can technology add
to the mathematics classroom?
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To create a paper Tetrahedron
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Some ERRORS
What can technology add
to the mathematics classroom?
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A famous mistake … Sept 1999 Mars Orbiter lost
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Harmony and chaos
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That GOLDEN RATIO: φ = 1·618…The Parthenon – built around 440 BC
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And portable?
Museum of Soviet Calculators
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Funderstanding Rollercoaster
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210
220
230
240
250
260
270
1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
1 mile = ? meters
4-minute mile
The Record for running a MILE
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Some TRIGONOMETRY
What can technology add
to the mathematics classroom?
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Trigonometry … and Drains!
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or ∞ !!
MIN = 1:60
MAX = 1:16
Trigonometry … and Drains!
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20,000 m³ litres daily = 400 litres of water per person daily50 km length
Slope of the Roman Aqueduct (19BC)
(Pont du Gard) Average slope: 34 cm/km
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Norfolk Pines off Mackay
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