Mathematics for all: sense and nonsense of statistical representations Heleen Verhage, Freudenthal Institute PME25 Summer Institute, July 2001.

Mathematical literacy (OECD/PISA): "Mathematics literacy is an individual’s capacity to identify and understand the role that mathematics plays in the world, to make well-founded mathematical judgements and to engage in mathematics, in ways that meet the needs of that individual’s current and future life as a constructive, concerned and reflective citizen."

Planetary orbits, 10 th or 11 th century

William Playfair ( ) Inventor of: Line graph Bar graph Pie chart Examples of time series and multivariate analysis

Playfair: Trade balance of England,

Playfair: import and export in Scotland, 1786

Playfair: timeseries (250 years: ) of price of wheat and wages of labour

Playfair: area of countries (circles), population (left line seg.) and tax revenu (right line seg.). An example of ‘multivariate analysis’

Tufte: Graphical excellence begins with telling the truth about the data.

USA population piramids, 1874

Charles Minard ( ) New techniques: Use of area as a measure Use of maps

Minard: carrying traffic by train, area proportional with revenues.

1. Tell the story of this graph 2. How many variables in the graph?

Minard: French army on its way to Moscow

Florence Nightingale ( )

Nightingale: original version of the coxcomb graph (1858)

Source: Scientific American

Textbook: ‘Getal & Ruimte”

Nightingale: bar graphs to compare conditions in the army with civilian life

Florence Nightingale in later life

“There are three kinds of lies: lies, damned lies and statistics” (Benjamin Disraeli ( ))

College enrollment Tufte: “the worsest graph ever made…”

Tufte: The number of information- carrying dimensions depicted should not exceed the number of dimensions in the data.

example of lie factor (source: Tufte)

Taken from textbook

Between saying and doing…

Selling of icecream

Manic-Depressive Illness

Timeline of Robert Schumann

Graphical excellence is that which gives to the viewer: - the greatest number of ideas - in the shortest time - with the least ink - in the smallest space

Relevant literature: Darrell Huff (1954). How to lie with statistics. Reprinted in Penguin and Pelican books. Edward R. Tufte (1983). The visual Display of Quantitive Information. Cheshire: graphics Press. M.J. Moroney: facts from figures. First published in Howard Wainer (1997). Visual revealations. New York: Copernicus-Springer

Relevant websites: mhttp:// m