Mathematics as the Language of nowadays Science, Technology and Engineering Jan Slovák

1. Mathematics as the Language of nowadays Science, Technology and EngineeringJan Slovák

2. What is the role of Mathematics? Often we hear: • Mathematics should be the common base for Science, Technology, Engineering (and elsewhere) = the source of the STEM paradigm. • Mathematics should help to “real understanding” part of the learning proces. • Mathematics is „weird and hardly necessary“! Mathematics as the Language of STEM - Tomsk - 2017

3. What is the paradigm of STEM Education? • Teaching facts? • Engage the intellect? = two swapping phases in Education approaches? or two parts of the teaching and learning process? And what is the role of Mathematics really? Mathematics as the Language of STEM - Tomsk - 2017

4. What is Mathematics? mathematic (n.) late 14c. as singular noun, replaced by early 17c. by mathematics, from Latin mathematica (plural), from Greek mathematike tekhne "mathematical science," … from mathema (genitive mathematos) "science, knowledge, mathematical knowledge; a lesson," literally "that which is learnt;" related to manthanein "to learn," … (cognates: Greek menthere "to care," Lithuanian mandras "wide-awake," Old Church Slavonic madru "wise, sage," Gothic mundonsis "to look at," German munter "awake, lively"). As an adjective, 1540s, from French mathématique or directly from Latin mathematicus. Mathematics as the Language of STEM - Tomsk - 2017

5. But how is Mathematics perceived really? • Counting with numbers? • Set of rules how to reshuffle letters? • … difficult to convince people that it is a way of thinking! Mathematics as the Language of STEM - Tomsk - 2017

6. Even worth – how do people remember Maths? Mostly as meeting people and topics they did not understand: • `Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different.’ ~ J. W. Goethe • `The good Christian should beware of mathematicians and all those who makeempty prophecies. The danger already exists that mathematicians have made a covenant with the devil to darken the spirit and confine man in the bonds of Hell.’ ~ St. Augustine (De Genesi ad Litteram, Book II, xviii, 37) • Medicine makes people ill, mathematicsmake themsadand theology makes them sinful. ~ M. Luther Mathematics as the Language of STEM - Tomsk - 2017

7. Mathematics as a language • Goethe‘s observation is pretty good, indeed! Mathematics should be understood, and thus taught, as a foreign language. • This in particular means: • try to learn by using it, as much as possible; • do not insist in too much of perfection, until reaching reasonable level; • the absolutely best way is to see the „mathematical approach“ without naming it this way (and recognize the concepts later in the Maths lectures). • All this is behind the STEM paradigm. Mathematics as the Language of STEM - Tomsk - 2017

8. How do we teach (Mathematics)? • Most of my colleagues try to do everything completely „right“ and they believe, one daythe students will themselves understand how beautiful and useful Maths is. • The other possibility is to focus on the „right things“and to present them as useful tools (and the best students will come to understanding finally too). • Usually we tryto provide „complete” exposition the first time already. • But we could also touch topics in a simpler way first and„come back“with new understanding later again. Mathematics as the Language of STEM - Tomsk - 2017

9. What about the perception by the students? • We want/should pass `experience and opinion’ as in a face to face contact. This often fails with big groups.Why? • Since typology of the individual people varies very much, there is no `correct method’ for lecturing. On the contrary, „prescribed methods“ increase risks heavily. • Some people need `intuition’ first and only then they can perceive the `technicalities’, though most of the population needs the opposite. • This was addressed by Jung’s typology of personalities, cf. the practical version in the form of the MBTI indicators used heavily by HR nowadays. Mathematics as the Language of STEM - Tomsk - 2017

10. Distribution of the MBTI types in US (figures from 2010) Mathematics as the Language of STEM - Tomsk - 2017

11. Mathematics as the Language of STEM - Tomsk - 2017

12. How did our own experiment go … • My initial strategy for teaching the Maths for our Computer Science Faculty (back in 2004) was: • To focus on practical topics with easy going intuition and rather simple algorithms. • To work in spirals, i.e. to come back to the topics with a better supply of tools and more tasks to be solved. • To experiment with the format of the lecturing in order to match as many types of personalities as possible. • Consequences: • Build discrete models first, the continuous analysis comes later to deal with convergence and robustness. • Avoid splitting Maths into Algebra, Analysis, etc. Mathematics as the Language of STEM - Tomsk - 2017

13. The goals and the conditions: • The students should master the following • to formulate precise definitions of basic concepts and to prove simple mathematical results, • to perceive the meaning of roughly formulated properties, relations and outlooks for exploring mathematical tools, • to understand the instructions and algorithms creating mathematical models and to appreciate their usage. • The standard approach to lectures and tutorials seems to be outdated – the young generation come with different habits and abilities to work compared, say, to 50 years back. Mathematics as the Language of STEM - Tomsk - 2017

14. The goals and conditions: • As generally known, the students • are able/used to focus for very short time only • they are used to follow several parallel processes • they have got very different understading of „face to face“ communication. • Thus, we should addopt a reasonable rough and active approach. In particualr, the students have to find their own paths. • Following our experience over more then 10 years, we are preparing a textbook called `Brisk Guide to Mathematics’(to appear with Springer soon). Mathematics as the Language of STEM - Tomsk - 2017

15. The uncoventional layout of the book Mathematics as the Language of STEM - Tomsk - 2017

16. Thanks for attention!!! Mathematics as the Language of STEM - Tomsk - 2017