To teach mathematics in the school of tomorrow Thomas Lingefjärd University of Gothenburg

The school of tomorrow is already here

The technical evolution The technical evolution moves faster and faster and more and more humans use resources such as , Skype, word processors, spreadsheets, and so called cloud computing in their daily life. The concept of cloud computing describes when we humans do not know or care about where the computers we use really are. Facebook, Flickr, Picasa, Skype are such resources for our daily (?) communication and to organize parts of our daily life. Google, Wikipedia and other sources of data for fact searching Google Docs if we want to write something together WolframAlpha for calculations and information Internet bancs for economy

The possibility to buy small and affordable computers as well as almost all (young?) people having an mobile telephone has created a huge change of the school we used to know.

Around the world: One computer – one student - projects are growing exponentially in Sweden and in many other countriescountries

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Around the world: Free software as GeoGebra, Maxima, WolframAlpha together with the rapid development of handheld technology is reshaping the way we can do mathematics.GeoGebraMaxima WolframAlpha

Mathematics in an iPhone

WolframAlpha is more than just an answer: Lingefjärd & Jönsson

WolframAlpha is more than just an answer: Lingefjärd & Jönsson

WolframAlpha is more than just an answer:

Lingefjärd & Jönsson WolframAlpha is more than just an answer:

Lingefjärd & Jönsson WolframAlpha is more than just an answer:

Thomas Lingefjärd Mathematical Formulas & iPhone

Thomas Lingefjärd SpaceTime & iPhone

Lingefjärd & Jönsson

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Obviously there are many new resources for learning and teaching mathematics. I will go a little deeper into the use of GeoGebra…

GeoGebra – a tool for teaching and learning mathematics Downloadable from Translated to more than 50 languages!

Basic ideas behind GeoGebra: Euclidian geometry… Algebraic representations Tools for different mathematical areasGeoGebra

Swedish teachers are hard to convince, but… General positive responses from teachers regarding GeoGebra:

Generality: When teachers learn that GeoGebra can not only be used for introducing basic arithmetic on a number line, but can also be used to demonstrate more advanced geometry, algebra, calculus, number theory or statistics, they become more confident that they will have many other teachers to discuss the use of GeoGebra with.

Portability: The fact that GeoGebra is installed over Java has two major benefits. First, GeoGebra looks and acts the same whether you are running it on under Windows, Macintosh, or Linux. Since students can run GeoGebra at home, it is important for teachers that it makes no difference what kind of operating system the students have at home. If necessary, GeoGebra can be launched via the Internet or run from a USB stick.

Connectivity: The fact that GeoGebra allows you to put two points (for instance) in the Graphics view and immediately see them represented in the Algebraic view and also in the Spreadsheet view is probably the most beneficial feature from a cognitive point of view.

More specific positive responses: The possibility to use sliders in order to vary mathematical constructions in various ways The possibility to use images within GeoGebra and perform various mathematical activities with these images

Example 1a Example 1a & Example 1bExample 1b

GeoGebra can also connect to free resources and practice concepts as area, scale, map technique, geographical coordinates, etcetera.

GeoGebra together with Google Maps or any national geographic information system.

Teachers can provide students with local problems What is the area of this lake?

Teachers can provide students with different Contexts – Example 3Example 3

Example 4

There are immense resources of applets, GeoGebra files, articles and demonstration movies on the Internet. Some teachers have created their own resource center, as for instance:

GeoGebra can be used all way through the school curriculum and up to university level Integrals Complex spiral Complex Squaring Taylor approximations