The paradigm change in STEM Education – has it happened already?
Jan Slovák

Department of Mathematics and Statistics

Masaryk University

Kotlářská 2

611 37 Brno

Czech Republic


Abstract. This short paper aims at collecting observations and thoughts related to the Education in
Science, Technology, Engineering, and Mathematics (the so called STEM). In this way we would like
to initiate new studies and experiments. In particular, we shall question how the current trends of
the massified Education, together with the available technologies and the changes in the attitudes
of the new generations of both students and teachers, are reflected in the attitudes, knowledge and
skills of the graduates. The method of the paper consists of comparison of well-known general facts
and conclusions with the author’s own experience in teaching Mathematics. Particular attention is
devoted to the (mis)use of new technologies in these areas.


1. Introduction
Over centuries, the main content of teaching and learning swapped repeatedly, roughly speaking,
between two main phases: ‘teaching facts’ and ‘engaging the intellect’. These are the two basic
approaches to Education and both can be done in a useful and practical way, or the opposite.
Actually, another point of view is that these are rather two parts of the same process and it could
be only a matter of taste or presentation, whether we focus more on the ‘teaching facts’ or the
‘engaging intellect’ part. But definitely, the tendency to stress the first or the latter one swaps
in time.

In recent decades, the tendency to teach facts was perhaps stronger than ever before. Moreover,
there were many further risk factors appearing in parallel – too much specialisation, fit for
purpose training, unrealistic expectation from new web based technologies, etc.

Long back, the Education used to be very individual. There were only a few students, all living
together with their teachers at colleges, and the entire Education was based on individual
learning, and public disputes and discussions with fellows and teachers. Education was very
international at those days too (linked rather to some religion/church than states or regions).

The current massive education platforms are mostly just the opposite – often very regional and very
anonymous. At the same time, the knowledge seems to be available everywhere and for free at the
internet, while the usage of all the engineering and information technology inventions seems to be
easy without knowing the principles why and how they work.

All these circumstances lead to the belief that the Teaching Facts Paradigm seems to be

·         practical (the students perform tasks fast);

·         efficient (the students immediately display the ‘right’ knowledge);

·         manageable (even in massified forms of Education);

·         easily supported by technologies (accessible even in online and distance education
versions).

No wonder that this has been the dominant approach over decades and gets much support now.

But how and why should we engage the intellect then? We should think on the following points:

·         learning vs. understanding;

·         memorizing vs. thinking and deducting;

·         blindly applying vs. developing and experimenting;

·         watching vs. discovering.

All this is hard to achieve in the massified Education forms, and it is linked to the general
problem of perception of information.


2. Impact of personal typologies in Education

In a face to face contact, good teachers always pass their ‘experience and opinion’. This is
perhaps the best way to help the students to understand the topics really. Unfortunately, this
mostly fails with big groups.

One of the reasons is that typology of the individual people varies, which is usually balanced well
in the face to face contact (at least in the presence of reasonable social intelligence). But
unfortunately, there cannot be a universal method for lecturing in large classes since we cannot
address all the types of personalities in parallel. The way out seems to be to invoke thinking and
communication among the students, initialised, supervised and amended by the teachers. This is
exactly the point where smart usage of new technologies together with relevant changes in the
structure of instructions, workgroups and individualised learning should help.

So what is special about the perception during the learning? Perhaps every teacher has noticed that
some people need ‘intuition’ first and only then they can perceive the ‘technicalities’, though
most of the population needs the opposite.

Such questions were addressed by Jung’s typology of personalities, and it is remarkable that these
obvious facts heavily used in the Human Resource management were given little notices in Education
management and practice. There is a rather simplistic version of such typology known as
Myers-Briggs Type Indicators, used heavily by HR people nowadays, see [1]. Here the type is based
on four dichotomies:

·         the attitudes are Extraversion (E) versus Introversion (I)

·         the perception functions are Sensing (S) versus Intuition (N)

·         the judging functions are Thinking (T) versus Feeling (F)

·         the lifestyle is Judging (J) versus Perception (P)

This provides 16 types of personalities, for example ENTJ, ISTJ, etc.

A lot of criticism applies to the MBTI tests and to the use of the typology in the HR practice, see
e.g. [2], pointing out the low re-test reliability (caused perhaps by mechanical splitting of the
results in the individual dichotomies at a virtual central value, though most of the population
displays results close to this value). But for our aim, this seems to be perfect explanation why
any universal effort to teaching in big groups based mainly on the teachers’ presentations has to
be dammed to failure.

In my own practice, I have been most interested in the polarized (NT) opposed to (SF) subgroups of
students (or teachers). The members of the first group heavily need `intuition’ first, they want to
think on the general picture, on the reasons why to deal exactly with the discussed phenomenon
etc., and only then they can perceive the `technicalities’ and work on real practical tasks. The
people from the (SF) group are just the opposite. Needless to say that there are many more SF’s
than NT’s in the population! We shall return to this point in the realm of my Mathematics courses
in a moment.


3. How are the colleges/schools performing?

Next, we come to the obvious question how the colleges should develop their approaches to curricula
and the teaching/learning standards. Nearly all studies and statistics say that the outcomes are
poor and some of the authors relate this fact with our question raised above: too much of teaching
facts and too little of engaging the intellect. But we can also rephrase this as a perhaps wrong
balance and order of practicing intuition and technicalities. A nice interview with Dr. Jo
Handelsman, Howard Hughes Medical Institute Professor in the Department of Molecular, Cellular and
Developmental Biology at Yale University, can be found in [3]. Roughly speaking, the students of
Biology are getting many fragments of facts in individual sub-disciplines, but they lack both
global picture and understanding. She claims that using the conventional science instruction, only
10 to 20 percent of lecture content is actually retained by students, while the professors spend
hours explaining to them. Opposed to that, active learning schemes have proven to be more
effective, she says.

Actually, there are even much more pessimistic results of recent studies explained in the two books
by two sociologists, Richard Arum and Josipa Roksa, [4], [5]. Their first book is based on the
study of more than 2300 bachelor students in24 schools of different image claiming that, with a bit
of exaggeration, the students learned a lot of bad habits while their critical thinking and
readiness to work got often even worse. In the second book they extend the study to the general
changes in the social behaviour in the last 40 years. Their observations include:

·         earlier, rather introvert people having their behaviour and values copied from their
teachers and parents were admired as wise and serious;

·         now, the immediate response from the colleagues is the guiding principle and the
extrovert people with no values of their own are winning;

·         university teachers are too much under pressure of student evaluations and their
standards have developed in similar way too, and thus, the students have never had studied as
little with as good marks as nowadays.

Although their study is criticised for using exclusively the Collegiate Learning Assessment (CLA)
Performance Task to test the outcomes, which is not believed to cover all the abilities to be
tested, their results match very well the lack of the ‘engaging the intellect’ part of the
educational process, combined with further sociological data.

Let us pose another provoking question. Can the students and teachers mutually understand each
other? We could guess from other studies that, at least, this will not be easy. As shown in the
Generation Z survey, the current teenagers are, unlike their teachers:

·         multitasking across 5 screens;

·         keeping attention for less than 8 seconds only;

·         collaborate better, but more than 10% of them suffer hyperactivity and further
neurological deviations;

·         live in virtual realities.



4. Do the new technologies help?

In the last decade we have witnessed the very wide use of the web based technologies:

·         more communication and working in groups in diverse e-learning collaborative tools (or
just using general tools like Skype, Hangouts, etc.);

·         easy capture of lectures;

·         sophisticated on-line learning schemes provided on large public platforms (Moodle or BB
platforms, all the MOOC’s etc.);

·         virtual web based universities (and virtual diplomas).

All this burst of ideas, approaches and tools has got many good flavours. Watching the popularity
rankings of the tools and platforms on the web, we learn about Adobe Connect, Blackboard, Canvas,
Coursera, edX, ePals, FaceTime, iTunes U, Moodle, Schoology, but also Google Plus Hangouts, Skype,
YouTube and many more general purpose communication platforms. Some of them are used internally at
schools, some of them provide free public service for everybody.

There are many questions in place here. Does this all always lead to real learning? Which part of
the crowd does it support best – the average, the best ones, or the laziest and weakest ones? Does
the technology strengthen the ‘teaching facts’ or the ‘engaging intellect’ parts? Does it help to
balance them right for the different types of personalities? And the most appealing question – will
regional universities need their own real teachers at all?

The answer to the latter question is, of course, yes and the reason is the same as with theatres
and musicians/actors. Although there are all the recordings of the absolutely best ones, still the
people enjoy real live concerts. Simply, they want to experience the emotions, experience, and
passion live, and the same applies to teaching. Let us add a few further observations suggesting
some partial answers:

·         movies are good for initiating interest and more, but it is difficult and extremely
labour-intensive to make them to provoke critical thinking;

·         thinking goes better with still images, schemes or texts which is typical in STEM, but
also in Medicine etc.;

·         the right technology should allow for ‘live’ appearance of teachers/speakers combined
with classical slides displaying the topic to be discussed – this very much imitates the standard
way of consulting in someone’s office;

·         the technology should invoke symmetric discussion the same way in any kind of groups;

·         should allow the teacher to create the messages/lectures easily, in order to keep the
feeling of rather real time discussion than a perfect anonymous performance;

All this can hardly work just with videos from the classrooms or some universal MOOC presentations,
as we mostly know them.


5. Mathematics and STEM

All the questions raised above are particularly urgent within the STEM programmes. Moreover, there
are the following observations to make:

·         the individual components (Science & Technology & Engineering & Mathematics) should not
be taught separately, rather we should like to build a global picture;

·         the ‘understanding’ part of the process is the more important one, while mere memorizing
of facts can be even dangerous;

·         it is extremely hard to manage the STEM education in big crowds due to various perception
schemes (and abilities) of the individual students;

·         the technologies can be very helpful here, but they also can spoil the game completely.


Mathematics is a quite specific part of the STEM which could be understood as the common language
or one of the possible approaches. Unfortunately, this often is not the way how it is presented.
Mathematics should help to the ‘engage intellect’ part of process.

I am intensively teaching Mathematics for big classes of Informatics students and my own experience
says that the videos with lectures or further similar material are very appreciated by the
students, but they do not help much to their real understanding. Rather, their existence is often
misleading them in the belief that they will be able to browse through the videos before the exams
like they watch the sitcoms. Just the really serious students use them the right way, coming back
to unclear points when revisiting or filling gaps later.

Thus, I was rather seeking for a structure of the teaching process and the exploited support
technology which would allow for a combination of the following parts:

·         a flipped-classroom approach based on up to date prepared presentations amending the
practical aspects of the lectures, available to the students short before the main lectures;

·         standard lectures (in the rather classical big lecture hall standard, coming with usual
tutorials in smaller groups) combining the practical use of the mathematical tools with rather
intuitive explanation of the methods and procedures;

·         practical seminars devoted to the numerical and computational aspects (computer based
activity in small groups with a tutor);

·         individual problem solving (perhaps in small groups, invoking mutual discussion between
students).

In general, there are many ways how to teach Mathematics. Mostly, the instructors try to do
everything completely ‘right’ (from the pure Mathematics point of view) and they believe, one day
the students will themselves understand how beautiful and useful the Mathematics is. The other
possibility is to focus on the ‘right things’ and to present them as useful tools and we hope that
the best students will come to understanding of the tiny details too, while the average students
will at least remember the usefulness of Mathematics.

Another point is the overall structure of the exposition. Usually the instructors try to provide
‘complete’ exposition of the phenomena the first time already. But this makes it nearly impossible
to gain complete understanding. The other approach is touching topics in a simple way first and
‘coming back’ with new understanding later again.

Perhaps, we should like to specify what we mean by Mathematics first. Since Mathematics became also
the name of one of the subjects taught at Grammar School level, the people obviously think that
they have met Mathematics, they have perhaps hated it, and they believe Mathematics is just playing
with numbers or, even worse, the abstract letters representing them. The etymology of the word
Mathematics displays a quite different picture. The Online Etymology Dictionary reveals (abridged):

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.

The etymology itself suggests that Mathematics should be following rather the questions of “WHY”
then those of “HOW” and it should be rather understood as many diverse ways of consistent thinking.

So why do people remember Mathematics so much differently, even those very knowledgeable ones? For
example, J. W. Goethe said `Mathematicians are like Frenchmen: whatever you say to them they
translate into their own language and forthwith it is something entirely different’; or St.
Augustine wrote in his book (De Genesi ad Litteram, Book II, xviii, 37) `The good Christian should
beware of mathematicians and all those who make empty 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.’; even  worse, M. Luther wrote ‘Medicine makes people ill, mathematics make them sad
and theology makes them sinful.’


6. The `Brisk Guide to Mathematics‘ project


Following the wish of the Faculty of Informatics management at the Masaryk University in 2004, I
took up the challenge to reshape the Mathematics instruction for the entire faculty.

My initial strategy was:

·         to focus on practical topics with easy going intuition and rather simple algorithms (and
be aware that the intuition is too difficult to perceive without any knowledge);

·         to work in spirals, i.e. to come back to the topics with a better supply of tools and
more tasks to be solved (and be aware that this might also lead to “spirals of misunderstadings”);

·         to experiment with the format of the lecturing in order to match as many types of
personalities as possible.

The immediate consequences included:

·         we are building discrete models first, the continuous analysis comes later to deal with
convergence and robustness;

·         we avoid splitting Mathematics into Algebra, Analysis etc.;

·         we use innovative technology to invoke the thinking part of the process and to activate
the students.

All this is following the main goals of the four semester long course:

·         the students should be able to formulate precise definitions of basic concepts and to
prove simple mathematical results;

·         the students should perceive and understand the meaning of roughly formulated properties,
relations and outlooks for exploring mathematical tools;

·         the student should master tools and algorithms behind mathematical models and they should
appreciate their usage.

Given the time frame and the available formats of the instruction, these goals are ambitious and
they require a very rough and active approach. The students have to find their own paths and they
should be enforced to do so.

With a wider team of collaborators, we have prepared the unconventional textbook underlying this
course which we have called ‘Brisk Guide to Mathematics’ and we hope this book should also help to
push the students to their own paths. The book is printed in two columns which are rather
independent of each other, one focused exclusively on practical tasks and examples, while the other
column provides a complete exposition of theory and usage of the individual concepts and tools.
Moreover, the theoretical column is very inhomogeneous in both the details and the complexity of
the exposition and the readers should be self-navigated by the so-called emoticons acting as
switches between the characters of the individual blocks of text. The electronic version of the
Czech book is available at http://www.math.muni.cz/Matematika_drsne_svizne.html and we are working
on the English version now.

The instruction itself has been supported by software tools allowing for easy capturing of any
presentation, based on the full resolution slides (as they appear on the screen) combined with a
full audio-video recording of the speaker. The result is an open format html5 web presentation
available freely on all platforms.

The screen-shot on the right hand side illustrates one of the practical presentations prepared
before the main lectures and displaying the main algorithms and tools to be discussed soon. These
presentations are available[1] to the students a few days in advance, so that the people who need
the practice first can watch them in time. Indeed, the students have reported the extreme
usefulness of such presentations before the lectures (perhaps the “SF” subgroup of types, in
particular).

Next, the theoretical lectures are presented and their recording by means of the same technology is
available to students too, followed by regular tutorials. This is usually followed by wide
discussion on the individual practical problems supported by the general e-learning platform
provided by the university.

In general, the exploited technology allows for completely symmetric mutual communication combining
audio-video and slides, which is very lean and effective, since the slides remain in their jpg
format full resolution all the time and thus the data flow of the presentation is very low.
Unfortunately, the university has not acquired a multilicense for this technology solution and so
this form of communication is not yet widely spread.

The experimental teaching within the “Brisk Guide to Mathematics” project has got the graduates for
several years already and the responses are diverse, quite as expected.

Clearly the new model of structuring and presenting Mathematics teaching is more than welcome by
the best students. We have not got a detailed statistics, but the general university questionnaires
reflecting the opinions and feelings of students suggest at least those in the 1^st quartile of
students by their results of study find the model very good (at Masaryk University we are still
strict with having about 1/3 drop rate in Mathematics in general, and the ‘A’ or ‘B’ marks are
rather exceptional). Also their skills seem to be very good, while the average students (or those
less motivated ones) have not got worse. This was exactly my main goal.

In general, it seems that the existence of the practical presentations (closely related to the main
lectures and tutorials in both topics and time) and the recordings of the lectures, together with
the consequent returning to topics in spirals and with different complexity of the parts of the
exposition, help to find the individual paths for each student. Some of them might come back to the
practical parts after they enjoyed the theoretical lectures (the NT subgroup), others enjoy the
practical presentations before the lectures already (the SF subgroup) and all of them can gain a
lot from the mutual discussions among the students themselves.

There are two typical complaints. The first one is pointing out the lack of explicit lists of
detailed simple tasks to be mastered in order to pass. This is exactly what the students are often
used to in other courses, cf. the comments in section 3 above. The students also complain about a
too wide scope of the course making it too difficult and demanding.

The students report positively on the unconventional use of the technologies and would like to see
it spread more widely across the faculty.


References


[1] Myers, Isabel Briggs, Mary H. McCaulley, Naomi Quenk, and Allan Hammer. (1998) MBTI Handbook: A
Guide to the development and use of the Myers-Briggs Type Indicator Consulting Psychologists Press,
3rd edition. ISBN 0-89106-130-4

[2] Hunsley, J.; Lee, C.M.; and Wood, J.M. (2004). Controversial and questionable assessment
techniques. Science and Pseudoscience in Clinical Psychology, Lilienfeld SO, Lohr JM, Lynn SJ
(eds.). Guilford

[3] Fischer, C. N., Changing the Science Education Paradigm: From Teaching Facts to Engaging the
Intellect, Science Education Colloquia Series, Spring 2011, Yale J Biol Med. Sep 2011; 84(3):
247–251.

[4] Arum, R., Roksa, J., Academically Adrift: Limited Learning on College Campuses, Chicago:
University of Chicago Press, 2011.

[5] Arum, R., Roksa, J., Aspiring Adults Adrift: Tentative Transitions of College Graduates,
Chicago: University of Chicago Press, 2014.

[6] Generation Z survey, Sparks & Honey, USA, April 2014 (< 18, compared to 20-30 and elder)

________________________________

[1] I have been using the software EduArt^TM developed and distributed by Polymedia Technologies,
see www.polymedia.cz for more details.