what can technology add to the mathematics classroom? douglas butler director, ict training centre,...

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) …

Butler – MANSW 2006

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) …


October 2003

September 2005

My last two visits …


Mathematics Education: is there a problem?

What can technology add

to the mathematics classroom?


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)


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”


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?


“Mathematics Society”Average attendance .. .. 17

“Financial Mathematics Society”Average attendance .. .. 89

What do pupils think “work” involving mathematics is all about?


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?


The modern mathematics classroom?


Two types of TABLET to take round the class:


COMPUTERS Geometry Expressions XThink

HAND-HELD Casio Classpad TI Nspire

And what is just round the corner?


Where did it all start?




Let’s look back ...

Pythagoras of Samos (569 - 475 BC)

The Tunnel of Eupalinos


How did we count?

The Mathematics of 1000 years ago


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


… and more portable?

Virtual Slide Rule (Andrew Davie, Tasmania)


So, was Sydney OH built with a slide rule?


So how does Google work?

As of today, Google states that they are indexing 19 Billion distinct web pages.


Find out using “tracert”

How does the Internet get from

Oundle to Brighton-le-Sands?


Exposing some of the mystery




The human bodyand PHI


Credit Card

Parthenon (440 BC)

Gary Meisner’sGolden Number site


Some INTEGER GIANTS




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


The mystery of CALCULUS



Why do we teach it?


“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”


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


mg

kvn

mv

So, if you fall out of an aeroplane …


See “Differential Equations” tutorial on the Autograph InAction page


VECTORS in 2D and 3D



“I hate vectors!”


Now for some MOVIE MATHS



Movies ABOUT mathematics

Movies created with mathematics


•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


See “Starship Enterprise” tutorial on Autograph InAction page

‘Ice Age 2’ trailer

This principle behind rendering 3D shapes


DATA, DATA everywhere




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)


What’s so special about the NORMAL distribution?

See “Central Limit Theorem”tutorial on the Autograph InAction page


Check in: Why don’t they weigh US?


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


Some fun with SPORTS DATA




ONE-DAY CRICKET 2005-2006 InternationalsTotal runs scored per match

0

2

4

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300

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1000

??


ONE-DAY CRICKET 2005-2006 InternationalsTotal runs scored per match

0

2

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ONE-DAY CRICKET 2005-2006 InternationalsRun DIFFERENCES per match

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AUSSIE RULES FOOTIEPoints per match

0510152025303540

0 25 50 75 100

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275

300??


AUSSIE RULES FOOTIEPoints per match

0510152025303540

0 25 50 75 100

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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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23

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67

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0

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??

Australiav.Namibia



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RUGBY UNION WORLD CUP Cup 2003Score DIFFERENCE per game

01

23

45

67

89

10

0 10 20 30 40 50 60 70 80 90 100

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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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RUGBY LEAGUE (misc)Point DIFFERENCES per match

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SOCCER WORLD CUP 2006Goals scored per match

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0 1 2 3 4 5 6 7 8

Goals Data

Poisson

??


SOCCER WORLD CUP 2006Goals scored per match

0

5

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0 1 2 3 4 5 6 7 8

Goals Data

Poisson

SOCCER WORLD CUP 2006Goal Difference per match

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UK SOCCER PREMIERSHIPGoals per match

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Goals data

Poisson

UK SOCCER PREMIERSHIPGoal DIFFERENCES per match

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60

70

0 1 2 3 4 5 6 7 8

Goals data


Spreadsheet Skills


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)

0

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2

3

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6

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1934

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1950

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1974

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1982

1986

1990

1994

1998

2002

2006

2010

Wikipedia articles


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


Data, Data everywhere …

The GCSE Statistics Coursework Project (UK)


Two ways of looking at the same data …

… using Autograph (Statistics page) and varying the class-width.


Sunrise over

Lake Geneva


Using the “Fit Data”

facility in Autograph


Using Google Earth and the Iconico Screen Protractorto find Geometrical objects


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


Using Google Earth:1. Heathrow Airport, London


Using Google Earth 2. Dubai, United Arab Emirates


Using Google Earth 3. Sydney Airport


Using Google Earth:3. Sydney Airport


WIND SUMMARY DIAGRAMS

Other Statistical Diagrams …


Airport runway directions

Measuring Runway directions

MACKAY AIRPORT (Qld)


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 …


Calculus Vectors 2D and 3D

Movie Maths Data, Data Google Earth

And the headlines again …


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




DOUGLAS BUTLERDirector, iCT Training Centre,

Oundle School, Peterborough (UK)

Web:www.tsm-resources.com

Email:

[email protected]

This Slideshow:

www.tsm-resources.com/MANSW.pps



THE END!!

OUT-TAKES ….


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


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.


Some lottery magic

UK Lottery site

All Winning Numbers

Frequency distribution


Even Excel can get it wrong

What do you think π is to 30 dp?

Let’s ask Excel


Trigonometry and Harmony

sinA + sinB =2sin½(A + B) cos½(A – B)


The Occurrence of Conics

Jill Britton (Vancouver, Canada)


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!


GIANT INTEGERS

Powers of 10

Powers of 2


Any rectangular sheet of paper …


Can you find all the angles?


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

How was it done?Butler – MANSW 2006

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


To Bleanau FfestinioggButler – MANSW 2006

747 Maiden FlightButler – MANSW 2006

747 Maiden Flight - 1969


USA: 8.5x 11”

= 216 x 279 mm

A4: 210 x 297 mm

11/8.5 = 1.29…

297/210 = 1.41… [ ]


1:

Good web summary

(Markus Kuhn)


One giant leap for mankind

• One small step for man …


UK Government report 2004”The Post-14 Mathematics Inquiry”

=> National Centre for Excellencein Teaching of Mathematics

a Mathematics Degree => 10% increase in Salary


The Pythagorean scale

Musical scales

The

PythagoreanComma

The‘Fifth’ interval


Virtual Learning Environments

TI-83 … Autograph in 3D


In Ab majButler – MANSW 2006

In A majButler – MANSW 2006

The Triangle in NatureThe Hyptiotes spider


INTERMISSION




To create a paper Tetrahedron


Some ERRORS




A famous mistake … Sept 1999 Mars Orbiter lost


Harmony and chaos


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


And portable?

Museum of Soviet Calculators


Funderstanding Rollercoaster


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


Some TRIGONOMETRY




Trigonometry … and Drains!


or ∞ !!

MIN = 1:60

MAX = 1:16

Trigonometry … and Drains!


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


Norfolk Pines off Mackay


what can technology add to the mathematics classroom? douglas butler director, ict training centre,...

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