Various materials for primary school teacher training

Bjørn Smestad,Oslo University College

http://home.hio.no/~bjorsme/prague.htm

My context:Teaching teacher students (for primary school)

- my students have no previous knowledge of history of mathematics- ”no” time for history of mathematics (in itself)- the mathematics is mostly at the level of lower secondary school or lower- my students (mostly) only studies in Norwegian- should be interested in anything that can enhance teaching

(Most of the bullet points should also hold for pupils in school.)

What (I believe) is important for teachers:

-To see that pupils’ problems have also been present in history- To get a general sense of the development of mathematics and see the human dimension- To see different ways in which history of mathematics can be included in teaching (even as a game!)- etymology – teachers should know (a little about) the origin of words in mathematics(and more)

Some results on history of mathematics in schools:

- history of mathematics often is reduced to biography (textbook study + TIMSS Video Study)

- history of mathematics is easily seen as ”taking time away from the mathematics” (interviews with teachers)

Therefore I want:

- a clear mathematical focus and- a clear focus on why working with the history adds value (on this particular topic)

My ways of including history of mathematics:

• as part of a lecture• working on original sources• projects• tasks from history• games

as part of a lecture

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Hoved-”regler”

• Rette linjer i virkeligheten blir også rette linjer på tegningen.

• To parallelle linjer som også er parallelle med billedplanet, blir parallelle også på tegningen.

• Linjer som er parallelle med hverandre men som ikke er parallelle med billedplanet, vil møtes i et punkt (forsvinningspunkt).

as part of a lecture

forsvinnings-punkthorisontlinje

as part of a lecture

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http://www.bjorasen.gs.oslo.no/galleri/1punkta.htmhttp://home.hio.no/~bjorsme/geogebra/perspektiv.htmlhttp://home.hio.no/~bjorsme/geogebra/perspektiv2.htmlhttp://home.hio.no/~bjorsme/geogebra/perspektiv_sal.html

as part of a lecture

as part of a lecture

as part of a lecture

Bilder hentet fra Alseth og Lindegaard. Tangenten 2/2004

”Anne” tegner bord, før og etter

as part of a lecture

”Samantha” tegner hus, før og etter

as part of a lecture

Other examples:

• Al-Khwarizmi• Measurement – development of standard measures• Platonic solids• Erathostenes and the circumference of Earth• Equations (Tartaglia, Abel…)• Florence Nightingale

as part of a lecture

Working with original sources:

Fibonacci (Leonardo Pisano)’s Liber abaci

Projects

Architecture, the golden ratio, calculation of heights, navigation at sea, origami, pi, the pyramids of Egypt, Pythagoras, measuring units, Escher, da Vinci…

Discussion

What do teachers really need?

Which of my ideas may work? Which may not?

• see that pupils’ problems have also been present in history• get a general sense of the development of mathematics and see the human dimension• see different ways in which history of mathematics can be included in teaching (even as a game!)• etymology – teachers should know (a little about) the origin of words in mathematics(and more)