The structured derivations method is a proof language which promotes the use of explicit logical notation and logical argumentation in proofs and has been developed since the mid-nineties by E-Math project leader Professor Ralph-Johan Back and Professor Joakim von Wright at Åbo Akademi University. The system has been tested in several different contexts in the Turku region with positive results.

The system can be used for any kind of mathematics and provides a fixed format for writing down mathematical proofs and derivations in a user friendly way. Structured derivations, simply put, require students to carefully explain each step of a calculation as opposed to just doing the traditional calculations.

Because of the standard format, computer support for structured derivations is easy to build. The standard format makes it possible to create editors that support writing structured derivations and have support for i.e. syntax checking, automatic checking of derivations as well as integration with teaching environments. Given these possibilities, it was natural to use the method when developing the e-books.

This little guide for structures derivation includes the following parts:

1. Basic structure – what is the basic structure of derivations?
2. Assumptions – how to include known facts and solutions?
3. Observations – how to make new information based on existing facts?
4. Cheat sheet – a short reference to structured derivations.

Research on structured derivations

Interactive e-books

The E-Math project has developed software for a new kind of interactive e-books that work as a frame for the substance written in the project. The e-books have several interactive functionalities and are the first in the world to enable the writing of higher level mathematics on a computer. The content in the book has been written by researchers and mathematics teachers at Åbo Akademi and the University of Turku and follow the maths curriculum in each country. The books cover the maths for the first year in high school and a total of 16 books have been written during the project. To read more about the e-books, please click here.

Demo of the book