Presentations from the workshop Math Education in 2016, August 8-10 2006, Helsinki.

Online proceedings of the first JEM workshop. Lisboa, 8-9-10 February, 2007.

Initially funded by the German Federal Ministry of Education and Research (bmb+f) as a joint project of several German universities within the "New Media in Education Funding Programme", the web-based, interactive learning and teaching environment called EMILeA-stat has been developed and realized since 2001 (cf. http://emilea-stat.rwth-aachen.de, http://www.emilea.de). At the RWTH Aachen University EMILeA-stat supports teaching in introductory courses on probability and statistics for students of Computer Science, Economics, Industrial Engineering and Mathematics. Besides a broad spectrum of topics in stochastics the environment also covers supplementary contents like elementary calculus. In the talk the general structure of EMILeA-stat, its scope and objectives are presented.

We present experiences of using on-line interactive exercises in mathematics learning. These exercises are automatically graded and so give immediate feedback to the learner. Also hints and fully worked-out solution is provided with most of the exercises. The problems are delivered through the Maple T.A. system which is a Maple powered automatic assessment system.

This material has been developed since January 2005 when the WebALT project started. Exercises were created both for the university level and high schools. For university level, exercises for Calculus were created and used in teaching in University of Helsinki and Florida State University. We present some of this material for universities and how it was used in a synchronous on-line Calculus course held in the University of Helsinki in Spring 2006.

High school exercises were first created in Finnish and used in the Helsinki School of Natural Sciences. In summer 2006 a team of students and teachers developed a comprehensive set of exercises for all the long term mathematics courses in the Finnish high school curriculum so they cover a wide range of topics from Calculus to Geometry. Most of this material is also translated into English. We present the pilot projects in some Finnish high schools and experiences obtained from them.

The Helsinki Polytechnic Stadia has used diagnostic testing for the beginning students of engineering with written exams. Starting from January 2007, Stadia has utilized the automatic assessment system to have these diagnostic tests done with a computer. Since the diagnostic tests should also measure how well the students master the level of mathematical skills learned in high schools the automatic exercises done for high school suited well for the tests. We present the arrangements and results of these first diagnostic tests.

Presenting mathematical formulae is a fundamental part of its communication. Authors, and applications, may choose to encode formulae in their documents using presentation markup, as is done in TeX or MathML-presentation. An alternative practice is to encode formulae by their semantics, using OpenMath or Content-MathML and letting an automated process convert the formulae to presentation code.

This last way supports the many value-added services of semantic mathematical encodings, since it exposes the formulae semantics. We present an approach where the rendering process is configurable by author-defined notations that can be interleaved with user-defined notations. This process can be dynamically enriched by new notations of (new) symbols that were just found since it bases on notations documents which are declarative.

Aside of serving of food for the rendering process, the notations documents appear to provide also the right information that can be presented to authors which shop for their symbol.