Teaching Mathematical Modelling National Network Project Matti Heiliö, LUT Robert Piché and Seppo Pohjolainen Institute of Mathematics, TUT

Piché, Finnish Network for teaching MM, slide 2 National virtual university network a pilot project of Finnish Virtual University course methods and contents IT tools student and expert comments conclusions, future directions

Piché, Finnish Network for teaching MM, slide 3 The Finnish Virtual University Started in 2001 by ministry of education Goals: improve networking between universities develop pedagogical skills support innovative uses of ICT in education make VU an attractive alternative

Piché, Finnish Network for teaching MM, slide 4 Good choice as a national pilot project modelling skills useful to industry & science curriculum not established experts & students scattered emphasis on independent study and communication

Piché, Finnish Network for teaching MM, slide 5 Brings together teachers and students across the country Participating institutions: Tampere University of Technology Helsinki University of Technology Lappeenranta Univ of Technology University of Helsinki University of Joensuu University of Jyväskylä University of Kuopio University of Oulu University of Tampere Centre for Scientific Computing

Piché, Finnish Network for teaching MM, slide 6 Course structure students and 9 teachers A&O: sign-up, schedule, links, uploads, discussion videoconferenced opening lecture local tutor & tech support streaming video lectures, synchronised slides weekly assignments, student comments project, videoconference presentation

Piché, Finnish Network for teaching MM, slide 7 Accessible anytime, anywhere

Piché, Finnish Network for teaching MM, slide 8 Project themes are open-ended Design the flow control for a fountain in a windy square Predict the population of Finland in 2100 Does toast tend to fall buttered side down? Are fingerprints unique?

Piché, Finnish Network for teaching MM, slide 9 Courses cover a range of topics Introduction to MM mathematics applications the modelling process numerical software continuum models differential equations dimensional analysis discrete models fitting data probabilistic models decision analysis Modelling with PDEs fields, flows and waves FEM for multiphysics tractor cabin acoustics melting and solidification silicon crystal growth impedance tomography Modern Data Analysis fuzzy & multivalued logic neural networks genetic algorithms data mining decision analysis Statistical Modelling MCMC for process parameter estimation statistical methods for pattern recognition mixed models for forest harvester operation multivariate regression and DOE for process optimization. Modelling Randomness Brownian motion in finance and communications stochastic diff eqns time series analysis inverse problems filtering Modelling visual motion How to reconstruct motion and shape from a video sequence: feature extraction, optical flow and visual velocity field, projecting 3d rigid body motion onto image sequence, statistical calibration. Methods for Continuum Modelling linearisation, asymptotics, regularisation, model fitting, model based optimization and control

Piché, Finnish Network for teaching MM, slide 10 Student feedback generally positive Would you like to take a similar course again? Would you recommend this course to a friend? How many lectures did you watch? How many hours did you work? * Were technical problems a significant obstacle? Overall grade?

Piché, Finnish Network for teaching MM, slide 11 Pedagogical experts’ evaluation Term projects support meaningful learning contexts are novel & authentic students are active collaboration structure & apply theory oral presentation & comments Good technical implementation A&O learning environment simple to use, good visual layout, easy navigation, schedule use of widely supported file types (HTML, PDF) local tutors & tech support in video lectures, the lecturers’ train of thought was supported rhythmically with motion and articulation

Piché, Finnish Network for teaching MM, slide 12 Cooperation of teachers & practitioners in math modelling steering committee meets 4-5 times/year Finnish students to ECMI Modelling Week Study Groups in Tampere ‘02, Helsinki ‘04 graduate school proposal EU project application

Piché, Finnish Network for teaching MM, slide 13 What next? Courses are now integrated into the standard curriculum at 7 universities Textbook project International network alpha.cc.tut.fi/mallinnus/