=Paper=
{{Paper
|id=Vol-2770/paper5
|storemode=property
|title=Learners as Extended Minds of the Digital Age
|pdfUrl=https://ceur-ws.org/Vol-2770/paper5.pdf
|volume=Vol-2770
|authors=Alexei Semenov,Vladimir Kondratiev
}}
==Learners as Extended Minds of the Digital Age==
https://ceur-ws.org/Vol-2770/paper5.pdf
Learners as Extended Minds of the Digital Age1
Alexei Semenov1[0000-0002-1785-2387] and Vladimir Kondratiev2[0000-0002-9792-2698]
1
Lomonosov Moscow State University, Leninskie Gory 1, 119991 Moscow, Russia
Axel Berg Institute of Cybernetics and Educational Computing, FRC CSC RAS,
44k2 Vavilova st., 119333 Moscow, Russia
Herzen State Pedagogical University, 48 Moyka Embankment,
191186 St. Petersburg, Russia
Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny,
141701 Moscow, Russia
alsemno@ya.ru
2
National Research University Higher School of Economics, Moscow, Russia
kondratjew239@gmail.com
Abstract. Humanity is going through one of the most important information
revolutions, after the emergence of speech and writing – the revolution of Arti-
ficial Intelligence. It was foreseen by Lev Vygotsky and artistically described
by Andy Clark and Michel Serres. This revolution brings with it an extremely
rapid and radical extension of the human mind. The report examines necessary
implications of this extension for education systems. Neglection of these impli-
cations cause dramatic decrease of effectiveness of learning and teaching as we
see clearly in the Coronavirus epidemy. A key example of mathematics educa-
tion is considered. Today it is oriented on pen-and-paper computational skills
and memorizing geometrical theorems. This cause losing motivation to educa-
tion of millions of kids. Using existing environments of computer-based algebra
and dynamic geometry an extended human can develop computational thinking
along with rigor reasoning, pre-adaptivity and interest to math. Priorities in
math education including assessment should be shifted from accuracy and
speed of hand calculations to sensitivity to feedback self-evaluation and ability
to improve your work.
Keywords: information revolutions, revolution of Artificial Intelligence, ex-
tended human, extended mind, digital technologies in education, mathematics
education, computational thinking, digital competence, digital literacy, digital
ethics, digital culture.
1 What is extended human?
Changes in information technology have led to major cultural and intellectual revolu-
tions in the history of humanity. It is conjectured [1] that the human – Homo Sapiens
emerged miraculously about 500,000 years ago with abilities to think, observe, and
1
Supported by the Russian Science Foundation, grants No. 17-11-01377, 19-29-14202.
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0
International (CC BY 4.0).
Proceedings of the 4th International Conference on Informatization of Education and E-learning Methodology:
Digital Technologies in Education (IEELM-DTE 2020), Krasnoyarsk, Russia, October 6-9, 2020.
learn. According to research [2], this version of the human had the ability to teach as
well.
The first information revolution for humanity was the advent of a new information
technology – speech 50–100 thousand years ago. This resulted in radical changes in
the transmission and reception of information, teaching, and thinking as well. Around
4–6 thousand years ago, writing appeared. So, knowledge and teaching could be
transferred over time and space. About 100 years ago, the third revolution of Artificial
Intelligence started. For the purposes of this paper, it would make perfect sense to call
artificial intelligence any automation of intelligent activity.
According to Vygotsky [3], “the use of artificial means, the transition to mediated
activity, fundamentally changes all psychological operations, just as the use of tools,
limitlessly, broadens the range of activities within which the new psychological func-
tions may operate”. This leads us to the idea that each new revolution extends the
human mind radically. In the case of speech, the expansion is going through a devel-
opment of speech apparatus. In the case of writing, it came with external media of
different forms: stylus with a soft clay tablet, papyrus and reed brush, chalk and slate,
etc. Vygotsky outlines his perspective [4]: “The following may serve as examples of
psychological tools and their complex systems: language, different forms of enumera-
tion and counting, mnemonics, algebraic symbolism, works of art, writing, schemes,
diagrams, maps, blueprints, all sorts of conventional signs, etc.” [5].
Douglas Engelbart, in his “Mother of All Demos” [6], was speaking on Augment-
ing Human Intellect on which Wikipedia [7] writes “Augmented intelligence provides
extra support for autonomous intelligence and has a long history of success. Mechani-
cal and electronic devices that function as augmented intelligence range from the
abacus, calculator, personal computers and smartphones. Software, with augmented
intelligence, provides supplemental information that is related to the context of the
user.” Dwelling on the changes up to the era of AI, Andy Clark [8], follows Vygotsky
literally (presumably not being acquainted with the words of the latter): “Mind-
expanding technologies come in a surprising variety of forms. They include the best
of our old technologies: pen, paper, the pocket watch, the artist’s sketchpad, and the
old-time mathematician’s slide rule. They include all the potent, portable machinery
linking the user to an increasingly responsive world wide web. Very soon, they will
include the gradual smartening-up and interconnection of the many everyday objects
that populate our homes and offices… It is because our brains, more than those of any
other animal on the planet, are primed to seek and consummate such intimate rela-
tions with non-biological resources that we end up as bright and as capable of abstract
thought as we are.” Further development of Vygotsky’s and Clark’s ideas is presented
in [5].
The authors we quote did not mention musical instruments and music notation that
definitely add to the range of technologies.
2 Extended human’s learning
We believe that the most important question forming the future of education in the
21st Century is:
Do we teach the extended human schoolchild all the appropriated means of
the digital world,
or
Do we teach our students while depriving them of all means available outside
school?
To illustrate the consequences of the second alternative, we can take a look at
many teachers in our schools this spring of Coronavirus. They were asking students to
do their homework on paper, then to take pictures of all pages and send them via mo-
bile phone. Teachers were printing the received pages, marking them with their red
ink, scanning them, etc. The case of a teacher who checked 1100 homework pages in
a week was reported in [9]. This is an enormous waste of time and contradicts the
essence of digital communication between professionals producing a document. First-
ly, because it does not allow teachers to make suggestions and comments in an effec-
tive way, as happens in professional communication. Secondly, it does not allow stu-
dents to improve their work, using these suggestions and not spending much more
time than needed.
We propose to focus upon the first alternative. We consider the learners and teach-
ers as extended humans, optimally using digital means to achieve their goals. Today,
a learner’s mind is extended not only by a pen, notebook, watch and a calculator, but
also by, for example, an automatic translator, access to the World Wide Web and
other digital means, extraordinarily increasing the power of the human brain.
Today's system of educational goals, planned results, standards and programs
should be addressed specifically to the extended minds of the student and the teacher.
We evaluate the quality of the educational system, taking this into account.
In the following table we sum up the outcomes serving the goals of certain epochs:
Table 1. The outcomes serving the goals of certain epochs.
Epoch Outcomes
Feudal Age Survival through submissiveness
Industrial Age Development through labor efficiency
Digital Age Digital literacy and computational thinking
Learning to be an extended human means to be aware of oneself within the digital
infrastructure and to be able to use digital tools to achieve one’s personal goals effi-
ciently and effectively. This is digital literacy that extends to life-long learning, in-
cluding the integration of new digital means in your extended mind. The naturally
extended mind uses computational thinking. According to Jeanette Wing [10], com-
putational thinking is a concept which involves solving problems, designing systems,
and understanding human behavior by drawing on the concepts fundamental to com-
puter science. Michel Serre interprets computational (algorithmic) thinking as follows
[11]: “The objective, the collective, the technological, the organizational: today, these
depend far more on this algorithmic or procedural cognition than the declarative ab-
stractions to which philosophy, nourished by letters and sciences, has dedicated itself
for more than two millennia”.
What does it mean for a teacher to be ‘digitally extended’? We are convinced that
the key role of the teacher is to orchestrate continuous reciprocal causation in the
classroom and in the digital environment. The concept of the extended human, for the
teacher, starts with commenting on students’ works, presented in digital form, and
discussing with the students, using classroom recordings, originally implemented for
school security, but now also used as a tool for enhancing their interaction in the
classroom or on project work. In the future, more and more important, but routine,
operations will be passed to ‘intelligent agents’, considered and respected as parts of
the extended teacher’s mind. The AI agents can indicate various types of errors in
essays, recognize students’ faces and voices in the records, transcribe records and
extract critical cases of behavior, reaction, or interaction for the teachers’ and stu-
dents’ consideration. Naturally, the agents’ oral messages can be synthesized, based
on the teacher’s speech.
The important mission of the teacher, being a life-long learning extended human, is
to inspire the student for their learning journey and join them in it.
3 School Mathematics of the digital era
It was worth fostering neatness, accuracy and computational skills in life and in teach-
ing math 100 or 200 years ago. Today our life is different: knowledge economy
needs, as the priority, sensitivity to feedback, debugging, agile-development. Apply-
ing terms of cybernetics, we can say that the key abilities of an individual of 21 st
century are adaptivity and even pre-adaptivity (see [12]). So, the priorities in math
education have to be changed as well: we need more independent reasoning, readiness
to solve completely new problems, ability to find and correct mistakes. “Moreover,
what went wrong, namely the bugs, are not seen as mistakes to be avoided like the
plague, but as an intrinsic part of the learning process” [13].
The main educational goals are to ensure that the students effectively master:
modeling real world phenomena to solve real world problems,
solving mathematical problems with computer tools, rational,
logical reasoning and acting inside and outside mathematics.
The innate curiosity and adaptation mechanisms should be brought into play.
4 What do we have in schools?
The main problem of mathematics education in schools is the absence of understand-
ing of the essence and the area of applicability of mathematical knowledge. This leads
to a low level of mathematical competence, low performance in exams, inability to
apply the mathematical tools in everyday life. Schoolchildren often ask themselves:
“Do I actually need mathematics in my life?”. The absence of a reasonable answer to
this question causes an outright loss of interest for mathematics both as a school sub-
ject, as an area of knowledge and profession.
Mathematicians, when they solve a new research problem, freely exchange
knowledge, using available means, including digital. At school, the collaborative
solution of a problem becomes almost impossible due to ‘academic ethics’: solving
problems in a limited time, limited resources and limited ability to interact with the
world is a moral must. The child can develop a painful, learned helplessness, which
plays a significant role in weakening interest in mathematics. This state of affairs
significantly reduces the level of trust in teachers and respect for the school.
We profess that geometry teaches students how to think. Well, it could teach think-
ing, if they proved theorems on their own. Currently, they have to memorize some-
body else's proofs, and it is not the best way to learn.
5 What is happening with math in extended learning?
The productive solution to these problems and a way out of this situation could be a
conscious and purposeful formation of a psychological attitude of extended human to:
experiment with mathematical reality, especially exploiting the visualization power
of digital technology,
solve research problems using all available means and resources, including digital
tools and the help of, not only classmates, but also other experts, who are currently
engaged in similar research issues,
model the real world, with your extended mind, using all the power accumulated
by centuries of math and decades of computing.
Dynamic geometry (see https://en.wikipedia.org/wiki/List_of_interactive_geometry_
software) is an environment that is the full implementation of a powerful opportunity
to experiment, to guess and discover a fact, to make hypotheses, obtain evidence –
witness for it and then – to prove it. This is a classical way for scientific discovery.
With hand drawing, you will almost never reach this in school. But dynamic geometry
is really a paradise when used properly for:
geometry constructions,
transformational geometry,
using coordinates and algebra in geometry – analytic geometry.
Computer algebra system (CAS) is an environment where you can graph any function
and use the graph to check your analytic solution of an equation. You can also con-
centrate on modeling the real world and passing the obtained equations to the system
(see https://www.computerbasedmath.org/). Before digital means we asked students
to solve only contrived problems. For the extended mathematical mind, the whole
paradigm of application of math is completely different. Not specifically chosen
numbers, not ‘tractable’ equations are possible, but everything that we can express in
formulas and find parameters, via measurement, have a solution. The problem is how
good our model is and how well we can interpret the results. Of course, this is not
100% accurate but we believe it is a fine approximation that produces a proper atti-
tude for learners. Even more, sometimes we cannot write any equation but can de-
scribe local rules of behavior for the system and model it, not analytically but numeri-
cally, discretely.
Digital environments of computer algebra systems and dynamic geometry provide
the scaffolding for a child that allows them to work in the zone of proximal develop-
ment. Algorithms to deal with mathematical objects can be invented, then taught to
the computer by the child and then integrated to the child-extended mind and used
when needed.
An important feature of mathematics is that it can provide a student with problems
completely new for them personally. So, math is the royal road to preadaptation to
uncertainty that we spoke of [12].
The work was supported by: Russian Science Foundation, grant number 17-11-
01377 (A. L. Semenov, parts 1, 2 and 3), Russian Foundation for Basic Research,
grant number 19-29-14202 (V. V. Kondratiev, parts 4 and 5).
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