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Journal of Software Engineering and Applications, 2017, 10, 11-40
http://www.scirp.org/journal/jsea
ISSN Online: 1945-3124
ISSN Print: 1945-3116
DOI: 10.4236/jsea.2017.101002 January 23, 2017
Thinking Fast and Slow in Computer Problem
Solving
Maria Csernoch
Faculty of Informatics, University of Debrecen, Debrecen, Hungary
Abstract
Research in spreadsheet management proved that the overuse of slow thin
k-
ing, rather than fast thinking, is the primary source of erroneous end-
user
computing. However, we found that the reality is not that simple. To
view
end-user computing in its full complexity, we launched a project to
investigate
end-user education, training, support, activities, and computer problem sol
v-
ing. In this project we also set up the base and mathability-extended
typology
of computer problem solving approaches, where quantitative values are a
s-
signed to the different problem solving methods and activities. In this
paper
we present the results of our analyses of teaching materials collected in di
f-
ferent languages from all over the world and our findings considering the di
f-
ferent problem solving approaches, set in the frame of different
thinking
modes, the characteristics of expert teachers, and the meaning system
model
of teaching approaches. Based on our research, we argue that the
proportions
of fast and slow thinking and most importantly their manifestation are r
e-
sponsible for erroneous end-user activities. Applying the five-point matha
-
bility scale of computer problem solving, we recognized slow thinking activ
i-
ties on both tails and one fast thinking approach between them. The low m
a-
thability slow thinking activities, where surface navigation and language d
e-
tails are focused on, are widely accepted in end-user computing. The
high
mathability slow thinking problem solving activities, where the utilization
of
concept based approaches and schema construction take place, is hardly d
e-
tectable in end-user activities. Instead of building up knowledge which r
e-
quires slow thinking and then using the tools with fast thinking, end-users
use
up their slow thinking in aimless wandering in huge programs, making
wrong
decisions based on their untrained, clueless intuition, and distributing err
o-
neous end-user documents. We also found that the dominance of low math
a-
bility slow thinking activities has its roots in the education system
and
through this we point out that we are in great need of expert teachers and i
n-
stitutions and their widely accepted approaches and methods.
How to cite this paper:
Csernoch, M.
(201
7) Thinking Fast and Slow in Comput-
er Problem Solving
.
Journal of
Software
Engineering and Applications
,
10
, 11-40.
http://dx.doi.org/10.4236/jsea.2017.101002
Received:
November 30, 2016
Accepted:
January 20, 2017
Published:
January 23, 2017
Copyright © 201
7 by author and
Scientific
Research Publishing Inc.
This work is licensed under the Creative
Commons Attribution International
License (CC BY
4.0).
http://creativecommons.org/licenses/by/4.0/
Open Access
M. Csernoch
12
Keywords
Computer Problem Solving, End-User Computing, Teaching Materials,
Mathability, Meaning System Model, Expert Teachers
1. Introduction
1.1. The State of Art
It is mutually agreed that “real” computer problem solving is mostly related to
professional programmers, so end-users do not have to carry out such activities,
since they are highly supported by “user-friendly”, “full-proof” environments.
Two of the most frequent phrases in end-user computing is “I can use it, that’s
enough” and “I can learn it on my own”. This is in accordance with Panko’s
finding, which claims that end-user computing is “invisible to IT professionals,
corporate managers, and information systems (IS) researchers” [1]. It seems that
most of the participants of the digital world are satisfied with the non-existence
of end-user computing. However, it has been found that this approach(es) leads
to erroneous end-user computing [1]-[11], institutionalized bricolage [6]. The
consequences resulting from incorrect figures cause serious financial losses and
also mean that human and computer resources are used up in vain [1] [2] [8] [9]
[10].
Research found that those involved in end-user computing—central corporate
IT groups, general corporate management, information systems researchers [1]
[2] [9] [10], education policy-makers, teachers, publishers, and end-users [3] [4]
[5] [11]—seem to be blind to effective teaching methods, to error handling, rec-
ognition, and correction, to how the brain works, how it can be utilized effec-
tively in digital environments. Even those methods are not adopted which have
proved effective in real world problem solving in other sciences and in pro-
gramming. Kadijevich’s research in spreadsheets found that the widespread
misconception is that “(1) there are no interesting problems related to spread-
sheets, and (2) teaching spreadsheets is not necessary because spreadsheet
learning occurs naturally through practice.” [7]. Conferences on computer edu-
cation also claim that end-user text management (word processing) is “not really
relevant to computing education”, “not focused on computing education”. We
claim that these findings and statements are alarming and we provide further
proofs that neither education nor end-user programs and their developers sup-
port end-user problem solving and the development of the end-users’ computa-
tional thinking [12], and these approaches lead to erroneous end-user compu-
ting.
1.2. Time for Changes
It is mutually agreed upon that end-users are those participants of the digital
world who do not carry out any “serious” computer related activities, which re-
M. Csernoch
13
mains the privilege of the trained professional of CS/Informatics (Computer
Sciences/Informatics).
As it is mentioned above, end-users are usually untrained or self-trained, and
they seem to be invisible to digital professionals. On the other hand, they can be
self-confident to the extremes, especially those who are trained in Informatics
and find themselves in end-user roles. (The sample of Figure 1 clearly presents
how an overconfident end-user evaluates his knowledge. The list of IT Skills in
general holds the major end-user subjects, but even their classification shows
lack of knowledge.)
To clarify end-user activities and roles in the digital world, we launched a
project focusing on computer problem solving (CPS). Our project is different in
nature from previous studies, where only one aspect of end-user computing is
thoroughly examined—spreadsheet, text, presentation, etc. management. We
claim that CPS is an umbrella project, since end-user activities are considered in
symbiosis, where knowledge transfer plays a crucial role in developing computa-
tional thinking.
In the present paper, we argue that (1) end-user computing should not differ
in nature from any other problem solving, (2) effective teaching methods and
approaches can be adapted from other sciences (3) novel methods can and have
to be invented and introduced, (4) what teachers do matters, and (5) what
“some” teachers, the expert teachers, do matters [13] [14].
1.3. Sampling Process
Considering that we launched a pilot project, our first concern was the data col-
lection and the analyses of the available sources in the subject, in different lan-
guages and countries. The sampling process was planned in advance, but during
Figure 1. The end-user’s lack of knowledge in word processing is clearly presented in Section Research Activities, while his over-
confidence is revealed in the comparison of his product and his knowledge listed in Section IT Skills. It is not clear what he meant
by “internet applications”, “email”, why “multi-media presentations” is listed separately, and what meant by “all” in his first sentence.
M. Csernoch
14
the work, without any previously published guides, we had to reframe our me-
thods and strategies. (Reasons for this: Lack of financial support, lack of availa-
bility, language barriers, the diversity of countries, lack of acceptance of the sub-
ject, etc. However, we would like to express our gratitude for all the volunteers
for helping us.)
We planned to collect teaching, learning materials developed both for institu-
tionalized and self-trained educational purposes, user guides, helps for support-
ing daily end-user activities, and sources of widely accepted approaches to
end-user computing and teaching. At the time of the publication, we hold 85 and
23 printed materials in our native and foreign languages, respectively. Beyond
the printed materials we heavily rely on sources available on the Internet and in
the built-in helps. The number of digital sources increases more rapidly than of
the printed sources for at least three reasons: (1) their easy access, (2) the online
versions of the printed materials, (3) and the changing proportion of the printed
and digital sources. Beyond the official supporting sources, we have a huge pri-
vate collection of end-user documents, the results of end-user activities. This
collection consist of several hundreds of documents downloaded from the In-
ternet, sent in emails, collected in our previous projects, and collected by sup-
porting researchers and students.
After collecting, analyzing, and evaluating the content of the sources, the re-
sults were compared to the results of recent studies in education, thinking mod-
es, and problem solving. This comparison clearly revealed the discrepancies
which led us to end-user bricolage, ineffective end-user computing.
In the present paper, we provide samples of the collected sources (Section 5)
and the reason why most of the teaching and supporting materials do not match
the requirements of effective end-user problem solving. Those materials which
are found supporting are mentioned in Section 7, but their number is infinitely
small, compared to the number of the analyzed materials. Here, however, we
have to mention that our collection is only a thin slice of the existing materials,
and consequently, we are open to any further sources which we do not have
access.
2. Problem Solving Approaches
To talk about different computer problem solving approaches we all need a ty-
pology which consists of all the possible approaches and their definitions. At the
beginning of our project, we were faced with the lack of such typology; back
then, there was no available complete typology which consisted of all end-user
problem solving approaches. Consequently, our major concern was at that time
to reveal what other sciences and computer programming had already recog-
nized. We found, by comparing the contents of several typologies, that there is a
considerable overlapping, however (1) the terminology used in the typologies
and (2) the non-recognition of end-user computing would explain that these si-
milarities are not obvious and that the typologies do not cover all end-user
problem solving approaches. The results of our analysis, comparison, and exten-
M. Csernoch
15
sion are summarized in Section 2.1.
In the following phase of our project, we proposed the extended typology of
end-user problem solving approaches, where the mathability levels of the named
approaches were set up. Such ranking of the mathability levels allows us to a
quantitative measuring system of the recognizable methods (Section 2.2).
2.1. Typologies of Problem Solving
Our typology of computer problem solving approaches (published in 2014 in
Hungarian) [15] identifies five clearly distinguishable approaches in two hyper-
nym classes—deep approach (DA) and surface approach (SA) classes (Figure 2,
Figure 3).
Figure 2. Two typologies of problem solving approaches in sciences (Case & Gunstone) and computer programming (Booth) (left
and middle, respectively), which partially cover the end-user problem solving approaches, and our extended typology presented in
2014 (Csernoch & Biró) (right).
Figure 3. The mathability of computer problem solving approaches, introduced in 2015 by Biró & Csernoch, allow us to a quanta-
tive measuring system for developing and evaluating teaching and guiding materiels in end-user computing.
M. Csernoch
16
Some methods of these approaches are adapted from other sciences, while
others are recognizable mainly in computer environments, computer related
problem solving, and in data and information management.
The concept based approach (DA class), the algorithmic and the information
based approaches (SA class), are well defined in Case & Gunstone’ typology for
problem solving in sciences [16] (Figure 2). All three approaches are identified,
with similar contents in Booth’s typology [17] for functional programming a
decade earlier (using different terminology, Figure 2), remained almost unno-
ticed. In her typology, Booth named one more DA hyponym category, which
focuses on building algorithms for programming problems (operational). The
similar contents of the categories made it clear for us that these typologies can be
merged, expanded, and tuned to fit the requirements of the digital era [15]
(Figure 2).
For emphasizing that building algorithms (Booth—operational) and applying
algorithms (Case & Gunstone—algorithmic based) requires different thinking
modes, slow and fast, respectively [1] [25], in the DA hypernym class, we intro-
duced the “Computer Algorithmic And Debugging” expression (CAAD) [15]
[17], instead of Booth’s operational. Our expression also includes the debugging
process, which is essential in the testing and evaluating process of the computer
generated outputs.
Since our concern was to identify all the end-user computing approaches, we
had to expand the already existing typologies and added the Trial-And-Error
Wizard based (TAEW) SA methods [15]. The trial-and-error activities are dif-
ferent in nature from the others, since they are related to problem solving, but
real problem solving is hardly carried out; instead, a surface navigation over-
arches the whole process, where any output, if reached, is accepted. This ap-
proach is not unknown in methodology, but not considered as problem solving,
which would explain not being included in any of the previous typologies.
However, TAEW is so widely accepted and practiced in computer related ac-
tivities that we cannot ignore it anymore. The question is why TAEW and in-
formation based approaches are so popular in the digital world, while they seem
to be the detours of computer problem solving. For the presence of the TAEW
based approach one of the best explanations can be adapted from Polya [18]. He
claimed that
“We know, of course, that it is hard to have a good idea if we have little
knowledge of the subject, and impossible to have it if we have no know-
ledge. Good ideas are based on past experience and formerly acquired
knowledge.” ([18], p. 9)
Considering the information based approach, Polya stated that
“Mere remembering is not enough for a good idea, but we cannot have any
good idea without recollecting some pertinent facts; materials alone are not
enough for constructing a house but we cannot construct a house without
collecting the necessary materials.” ([18], p. 9)
M. Csernoch
17
Rewording Polya’s note in the digital world, we find that computers alone are
not enough for solving problems but we cannot solve problems without “col-
lecting” the necessary hardware and software tools. However, we have to note
here that it is difficult to find the border line between the information and the
TAEW based approaches, since both focuses on the tools, without considering
the problem; “I can use it, that’s enough”. The difference between them is rather
on the proportion of learned materials. The ECDL exams, for example, require
the candidates to follow a long list of familiar instructions, without giving any
thought to the problems. These participants of the digital world mainly carry out
information based activities during the ECDL exams. However, in other situa-
tions, this knowledge is hardly useful, so TAEW based methods are applied out-
side of the exams. We also found that most of those end-users who never had the
opportunity to participate in any formal digital education primarily carry out
TAEW based bricolage and they cause serious financial losses [8]; we have
reached a level which Polya considered as the worst.
“The worst may happen if the student embarks upon computations or con-
structions without having understood the problem.” ([18], p. 6)
2.2. The Mathability of Computer Problem Solving Approaches
The results of one further research let us complete our typology, namely research
in mathability [19] [20] [21] [22]. According to the authors, they apply the con-
cept of mathability to the usage of computer tools.
“This usage has basically two forms:
(1) In some cases we use existing functions and methods provided by a sys-
tem, and we apply these tools to solve the problems.
(2) Another possibility is, if we, based on existing means of the system, de-
velop new programs and functions for solving new problems.”
In our typology-building process, we recognized that the two approaches to
the usage of computer tools matches the two hypernym classes of problem solv-
ing approaches. The first usage covers the surface approach (SA) methods, while
the second usage the deep approach (DA) methods. This finding of ours, led us
to further consequences: based on our completed computer problem solving ty-
pology [15] and the concept of mathability [19] [20] [21] [22], in 2015, we de-
fined the mathability of software tools [19] [20] [21] [22].
The adaptation of the mathability of software tools to computer problem
solving approaches allows us to create a quantitative measuring system [23] [24].
In this measuring system, the concept based approach is associated with the
highest mathability level, Level 5, while the TAEW based approach with the
lowest level, Level 1. The DA CAAD, and the SA algorithmic and information
based methods are at Level 4, Level 3, and Level 2, respectively, presented in
Figure 3.
With the association of the typology of end-user problem solving approaches
M. Csernoch
18
and the mathability of software tools, we invented the mathability of end-user
problem solving approaches, which provides us guide lines in recognizing the
mathability of problem solving approaches, in teaching methods, in tasks pre-
sented in classes, in teaching materials, in exams, in developing curricula, frame
works, etc. With this measuring tool we would be able to provide comparable
quantitative values associated to teaching and guiding materials.
Due to the facts that our end-user problem solving typology is an extension of
previously published typologies in sciences and computer programming and that
problem solving in general in the digital era is mostly computer based, our ty-
pology would be accepted in other sciences and programming also. The intro-
duction of our mathability associated typology into other subjects is our further
concern.
The arrows in the typology of computer problem solving (Figure 3) indicate
the direction of communication between the different mathability levels. In real
world problem solving there is continuous communication between Levels 5 and
4, until the problem is understood, the relations between the input data and the
required output(s) are recognized, and the plan—the algorithm—is completed.
If the problem is too complicated we can simplify it, until a stage is reached
which leads to discussable or acceptable results. This second option, namely the
acceptance of partial results, is a well-known phenomenon in problem solving.
Polya suggested that if the problem seems too difficult
“…we must look around for some other appropriate point of contact, and
explore the various aspect of our problem; we have to vary, to transform, to
modify the problem. Could you restate the problem?” ([18], p. 10)
What Polya suggested, Kahneman [25] proved, and stated that
“This is the essence of the intuitive heuristics: when faced with a difficult
question, we often answer an easier one instead, usually without noticing
the substitution. The spontaneous search for an intuitive solution some-
times fails—neither an expert solution nor a heuristic answer comes to
mind. In such cases we often find ourselves switching to a slower, more de-
liberate and effortful form of thinking.” ([25], p. 12])
In general, we can conclude that in our typology we can recognize four ap-
proaches which require slow thinking: the DA methods for planning, substitut-
ing, and discussing—concept and CAAD based approaches—and the two lowest
mathability approaches for the aimless usage of the tools—information and
TAEW based. There is only one computer problem solving class which utilizes
fast thinking; this is the algorithmic based approach (SA class). The proportion
of slow and fast thinking approaches is 4:1. Being aware of this number, there is
no wonder that end-user computing is erroneous.
2.3. Increasing the Proportion of Level 3 Activities
Activities at Level 4 have multiple purposes. Beyond building algorithms and
M. Csernoch
19
discussing and debugging the outputs, the construction, association, and ac-
commodation of schemata [26]—schemata construction for short—also take
place at this level. Schemata construction plays a crucial role in the learning
process. Back in 1971 Skemp referred to this process as intelligent learning [26].
In novel research—e.g. in Cognitive Load Theory [27]—the multilevel hierarchy
of schemata is considered the measurement of proficiency.
These findings are in complete accordance with Kahneman, when he states
that System 2 (thinking slow or Attention Thinking Mode, ATM) is the only one
that can follow rules, compare objects on several attributes, and make deliberate
choices between options, and a reliable System 1 (thinking fast or Automatic
Thinking Mode, AUM) requires knowledge built up in learning and practice
[25].
“As you become skilled in a task, its demand for energy diminishes. … the
pattern of activity associated with an action changes as skill increases, with
fewer brain regions involved.” ([25], p. 35). “…repetition induces cognitive
ease and a comforting feeling of familiarity.” ([25]. p. 66)
Applying this rule, we can transfer knowledge from the highest mathability
levels to Level 3, where System 1 can work. For reducing the errors in spread-
sheet management a reliable System 1 should be used, suggested Panko in his
paper, entitled “The Cognitive Science of Spreadsheet Errors: Why Thinking is
Bad” [1].
Consequently, the algorithmic based approach is different in nature from the
information and the TAEW based approaches in the SA class. The algorithmic
based level is where System 1 operates. At this level the stored schemata are ac-
tivated, and decisions are made quickly based on these schemata. On the other
hand, the information and the TAEW based levels heavily rely on System 2,
which Panko claimed as erroneous approaches to spreadsheet problem solving.
Consequently, we can claim that mathability Levels 2 and 1 are pseudo problem
solving approaches. At these levels there is no real problem solving, the goal is to
perform satisfactorily in tests or exams and/or to achieve any kind of output.
The information based approach [16] or habit learning [26] focuses on the de-
tails of the tools, without recognizing or understanding the problems. The
TAEW based approach is pure surface navigation [15]; aimlessly clicking and
browsing until some form of output is produced. In these low mathability ap-
proaches the problem is not determined, plans are not built, and consequently
the discussion of the outputs is not part of the process; in general, leading to er-
roneous end-user computing, documents, conclusions, and consequences. Sys-
tem 2 is heavily used, instead of the fast System 1, however, when System 1 res-
ponses there is no background knowledge to make reliable decisions ([25], pp.
237-239).
Kahneman explains that for a reliable System 1 we need intuition and real ex-
perts who can trust their intuition. (The definition of intuition is from Herbert
Simon and cited in Kahneman ([25], p. 237):
M. Csernoch
20
“The situation has provided a cue; this cue has given the expert access to
information stored in memory, and the information provides the answer.
Intuition is nothing more and nothing less than recognition.”
However, it is difficult to define who the real experts are. Even Klein and
Kahneman took time to find the sources of their misunderstanding.
“He [Klein] was more willing to trust experts who claim an intuition be-
cause, as he told me, true experts know the limits of their knowledge. I ar-
gued that there are many pseudo-experts who have no idea that they do not
know what they are doing (the illusion of validity), and that as a general
proposition subjective confidence is commonly too high and often unin-
formative. ([25], p. 237), [28]
The illusion of validity is not unknown and has been researched extendedly.
Some of the earliest works is the paper of Kruger and Dunning [28], who cited
Confucius claiming that
“Real knowledge is to know the extent of one’s ignorance.”
Further considering the subject of true experts Kahneman explains that ac-
quiring a skill is fundamental.
“If subjective confidence is not to be trusted, how can we evaluate the
probable validity of an intuitive judgment? When do judgments reflect true
expertise? When do they display an illusion of validity? The answer comes
from the two basic conditions for acquiring a skill: (1) an environment that
is sufficiently regular to be predictable (2) an opportunity to learn these re-
gularities through prolonged practice. When both these conditions are sa-
tisfied, intuitions are likely to be skilled.” ([25], p. 240)
3. Hypotheses
Considering the different approaches to end-user computing and the education
of end-users, our hypotheses are the following:
[H1] End-user teaching materials do not support high mathability end-user
computer problem solving.
[H2] Teachers unconditionally accept low mathability end-user computing
teaching materials.
[H3] Computer Sciences/Informatics Education research does not consider
end-user computing and problem solving as important as programming.
[H4] End-user-program developers and end-user-programs do not support
understanding and effective computer problem solving.
In our hypotheses the generally accepted views, the main tracks, the most
widely accepted, and institutionalized approaches are in the focus. However, it is
also expressed in the present paper that there are teachers, teaching materials,
approaches which realized the dangers and consequences of the institutionalized
bricolage, and try to introduce their findings.
M. Csernoch
21
4. The Meaning System Model Applied to End-User
Computing
The question we need to address is what it is that leads to low mathability end-
user activities. To find an explanation we have analyzed both the direct human
participants in the teaching-learning process—teachers and education policy
makers—and the indirect human participants—ICT (Information Communica-
tion Technology), IT (Information Technology), CS (Computer Sciences) curri-
cula, teaching materials, and software supports.
It is wildly accepted that end-user computing is boring [35], comprising low
level routine tasks [36], nothing more than computer skills [32]; consequently, it
is not suitable for developing students’ or end-users’ computational thinking
[12], and as such it is restricted to serious programming. These opinions are in
accordance with the software companies’ “user-friendly” slogans, and rest on the
assumption that low mathability approaches are sufficient and effective in
end-user computing.
It is obvious that low mathability approaches are not in accordance with those
opinions and approaches which claim that there are various tools beyond de-
clared programming languages which would serve the development of algorith-
mic skills and the computational thinking of students [37]-[42], and their prob-
lem solving skills.
The meaning system model of Chen
et al
. [43] (Figure 4) explains the con-
nection between teachers’ belief in the nature of science, their goals, and the re-
sults achieved by students in the teaching-learning process.
Figure 4. The meaning system model [43].
M. Csernoch
22
End-user activities are mostly taught with a belief in the fixed nature of
science—if it is considered science at all. In this framework the various software
tools are separated from each other, and emphasis is placed on toolbars, menus,
and the programming languages as something unique to each application and
their different versions. This approach is well presented by the teaching mate-
rials which we have analyzed (Figures 5-17) and also by the Spreadsheet Com-
petency Framework, launched in 2016 [44].
5. Low Mathability End-User Activities and Training
5.1. Low Mathability Tasks
In end-user computing the steps of problem solving are reduced to one: “carry
out” something, use the computer, the software, the Internet. In end-user termi-
nology this is usage. Most of the end-users are convinced that this is what mat-
ters. However, in practice it is nothing more than surface navigation [15],
i.e
.
bricolage [3]. As it was mentioned in the previous sections, on the mathability
scale these approaches are at the lowest levels [23]. In educational environments
we can distinguish two different approaches to software usage (software usage ≠
problem solving): (1) apply whatever is available, regardless of whether the con-
tent requires it or not (Figure 5, Figure 9, Figure 17), if there is any content
(Figure 6, Figure 10, Figure 11, Figure 12), (2) follow the instructions step-by-
step regardless of their correctness or of their functionality (computer cooking
for short) (Figure 7, Figure 8, Figure 10), and the combination of the two
(Figure 6). In the following we present samples of low mathability tasks, where
the focus is on the software tools.
In end-user text management, Level 2 activities are present when end-users
are forced to learn how to apply various font and paragraph formattings to piec-
es of texts—they learn the tool—, but they do not plan or design the document
Figure 5. An example of low mathability problems, focusing on the software tools and
features. Star Wars Family Tree. The sample is part of a lesson plan, written by a
pre-service teacher of Informatics.
M. Csernoch
23
Figure 6. A text without any specific content, created only for the manipulation of soft-
ware tools (sample text of a lesson plan written by an in-service teacher of Informatics).
according to its content; they do not know whether applying these tools leads to
a typographically correct document or not. In Figure 5 a Star Wars Family Tree
was created, however the over- and misuse of tools (table, alignments, colors,
font types, font styles) leads to the loss of the content.
The task in Figure 6 is borrowed from a lesson plan of an in-service teacher of
Informatics. However, this piece is not unique, since several similar ones can be
found on the Internet. The greatest problem with this type of tasks is that they
have no content, and without content we cannot associate any format, conse-
quently, the task is completely meaningless.
According to the lesson plan, the teacher gave instructions which the students
had to follow: (1) the teacher wrote the text on the board, (2) the students had to
type it, (3) and then the lines and pseudo lines had to be formatted according to
the “computer cooking” instructions of the teacher and/or the text, without giv-
ing any thought of typography and content.
Unfortunately, one of the greatest institutionalized computer cooking is the
ECDL exam system, where long lists of demands have to be performed in pre-
practiced tasks (Figure 7, Figure 8). Beyond licensing low mathability end-user
activities, one further serious consequence of this approach is that both non-
expert teachers and students are misled;
“…they identify computer science with a computer driving license. They
think that studying computer science is not a challenge, and that anybody
can learn it. Computer science is not considered a scientific discipline but a
collection of computer skills.” [30].
In Figure 7 and Figure 8 an ECDL Excel and PowerPoint sample is presented,
respectively. Without further details, the samples clearly demonstrate that the
primary purpose of these tasks is forcing the students to follow instructions and
giving marks for pure software usage. In PowerPoint Task 8 even the picture is
distorted by changing both the height and the width. We also have to call atten-
tion to the inattentive terminology usage: spreadsheet application is opened
(Figure 7), while presentation application is started (Figure 8).
M. Csernoch
24
Figure 7. An ECDL Excel example of computer cooking [29].
Figure 8. An ECDL PowerPoint example of computer cooking [29].
In Figure 9 the picture is positioned behind the text. The author used the tool,
but did not pay attention that with this setting of the picture the text would be-
come unreadable.
Further examples of Level 1 activities in text management are when Space,
Tabulator, and Enter characters are typed until end-users think that the ar-
rangement of the text is “not too bad”; it would look acceptable or quite well in
the printed form (Figure 1, Figure 9, Figure 15). In spreadsheet management,
the argument list of a function is filled in until there is no syntactic error in the
formula. In presentations, animation sequences are created, loaded with annoy-
ing entrances and exits and/or with redundancies. Software independent features
are the meaningless and misleading cell coloring, alignments, and diagrams [31],
as well as animations, transitions, and mismatching pictures and figures [32].
One further consequence of not using real contents is that we are losing an ef-
fective motivating tool. Contemporary students want to acquire knowledge
which is directly adaptable to the real world around them. They do not necessar-
ily like purely educational purpose software, in spite of its good quality. Students
want immediate links to everyday life [33] [34] and end-user problem solving
would be a link between programming and document management.
5.2. Low Mathability Teaching Materials
If teachers believe in the incremental nature of science, this changes their teach-
ing goals, and developing a deep understanding and appreciation of science in
the students becomes the focus of the teaching. However, even with this teach-
er-belief the teaching-learning process can go astray if passing exams is the main
M. Csernoch
25
Figure 9. The sample presents (1) an example of using a tool (picture positioned behind
the text, making it unreadable) without checking its effect and (2) an example of the un-
rational use of Space and Enter characters from item 10 on the list.
goal in this process, rather than the use of methods to reveal the dynamic nature
of science.
In computer problem solving the dynamic nature of CS/Informatics can be
revealed through knowledge transfer, which is primarily based on the high ma-
thability approaches to problem solving.
Real world problem solving, presented through authentic contents, is designed
to increase motivation and give opportunities for practice, and ultimately to en-
able the building of concepts. Students who are interested in the contents are
more likely to be interested in the problems based on them. For the development
of concepts practice, problem solving, and repeated activities are needed. Similar
to other sciences,
“A concept requires for its formation a number of experiences which have
something in common. … Concepts of a higher order in a hierarchy than
those which a person already has cannot be communicated by definition.”
[26].
In the following end-user activities, we have found, in the comparison of
teaching materials which aim is to support office document management, re-
peated contents general ICT knowledge, over tens or hundreds of pages: how to
start the program, what are in the window, in the toolbars, in the menus, what
the new features are, how to color, how to create a border, how to open a file,
how to save a file, how to save a file in older formats, how to make a selection,
and how to copy and move, etc. There is no reference to the fact that these are
M. Csernoch
26
basic ICT skills, which are commonly found in all software tools, and as such,
clearly presents the teachers’, publishers’ and software companies’ fixed belief in
the nature of science, that the different applications should be taught, handled,
and used in seclusion. The connections and the common features of these simi-
lar programs are not discovered, the knowledge transfer between them is ruled
out, the revelation of knowing from other situations is never reached, and these
programs are not only tools, but the only and ultimate purpose of the teaching
and guiding process. Consequently, they do not fulfill the requirements of text-
books [45]. According to Chen
et al
. [43], this approach results, in the best case,
in students passing the required exam.
The other feature of low mathability teaching materials is that there are no
problems presented at all, no real world problem solving, and no design; only
surface navigation and computer cooking. We have also found that if tasks are
presented, they are mostly meaningless—with no content at all, or at most a
couple of lines of fictitious content. These types of pseudo-contents are ex-
tremely boring (Figure 6, Figure 10, Figure 11). The second set of tasks of Fig-
ure 10 is even more spoon-feeding than the first one, since here the functions
are named. Students do not have to think and do not have to make the least
mental effort; there is no problem to solve, the only requirement is to follow
meaningless orders. This teaching approach is in complete accordance with the
requirements of the ECDL and the school leaving exams of our country. The
students pass these exams to everyone satisfaction. However, due to the low
Figure 10. Boring, meaningless, computer cooking tasks from an official Informatics
course book for grades 9 - 10 [47].
Figure 11. Boring, meaningless tasks from a French online tutorial [48].
M. Csernoch
27
mathability teaching approaches, their knowledge and problem solving methods
stay at low mathability levels, which we found in the TAaAS project [56] by
testing first year students of Informatics in tertiary education.
In Figure 10 and Figure 11 we present the same low mathability tasks in
printed and online forms. Recently, most of the teaching materials published on-
line, proposing that that form matches the requirements of the digital children,
the way they think, the way they learn. However, we claim that it does not mat-
ter in which form low mathability materials are presented, since they would not
help the understanding and the appreciation of the science.
The sample of Figure 12, copied from another tutorial, tries to explain for-
mulas on an empty table. In this example not even pseudo-data is typed, not
even computer cooking is required, making it completely meaningless and use-
less.
It is also remarkable that these meaningless tasks are country and language
independent; similar “tasks” can be found in different teaching materials, re-
gardless of language and location. The spreadsheet examples of Figures 10-12
are from teaching and tutorial materials of three different places of the world, in
three languages, and they are in complete accordance with the ECDL exam sam-
ples of Figure 7, Figure 8.
5.3. Low Mathability Help Materials
Help features and materials are the specialties of the digital world, representing
both a blessing and curse. These materials are mainly written by programmers
untrained in psychology and education, using language understandable to pro-
fessionals in Computer Sciences and programming.
In the following spreadsheet examples (Figure 13, Figure 14), concepts are
used which end-users have not mastered; consequently they will not understand
the functions described in the wizards.
In the definition of both the IF() (Figure 13) and the MATCH() functions
(Figure 14) concepts are mentioned which end-users usually do not have (e.g.
Figure 12. Formula created on an empty table [46].
Figure 13. The definition of the IF() function in MS Excel.
M. Csernoch
28
Figure 14. The definition of the MATCH() function in MS Excel.
“argument”, in IF(): “logical test”, “condition”, “any value or expression”, “eva-
luated”, in MATCH(): “array”, “relative position”, “item”, “specified value”,
“specified order”, “logical value”, “reference”).
It also frequently occurs that these definitions are not correct, and further-
more, the published teaching materials repeat the errors, and teachers also ac-
cept them without any more thought.
Presented in Figure 14, in the definition of the MATCH() function, “loo-
kup_array” is mentioned as the second argument; however, any array cannot be
entered, only a vector, which is a one-dimensional array. In the analysis of the
teaching materials, we only found two books which correct this error [49] [50];
all the others go along with the help. A further problem with the help features is
that they use meaningless, empty, misleading, longish descriptions and informa-
tion which is irrelevant when making decisions, and in some cases, incorrect and
ambiguous expressions, sentences, and samples.
We also found in the helps that the examples focus on the details of the lan-
guage. In the sample of Figure 17 a composite function is presented just for the
sake of showing that the language allows one to do so. There is no problem pre-
sented, just the code and the output.
5.4. Spreadsheet Competency Framework
The Spreadsheet Competency Framework was launched in 2016 at the EuSpRIG
Conference. It also consists of the framework specification, where spreadsheet
skills are listed [44]. The skills are organized in eleven groups and four levels of
proficiency is defined.
Levels of proficiency: (1) basic user, (2) general user, (3) creator, and (4) de-
veloper.
Groups of skills: (1) Design and best practice, (2) Reviewing and team work-
ing, (3) Basic skills, (4) Efficiency of use, (5) Formulas, (6) Formatting, (7)
Charting, (8) Protection and errors, (9) Data analysis, (10) Macros and automa-
tion, (11) Development and problem solving.
Since the analysis of the framework is beyond the scope of the present paper,
only three of the features are mentioned here. The Basic skills consist of only
three items, Access and save files, Read and enter data, and Set up printing. Two
and a half of these are not spreadsheet skills, but general ICT skills, while read-
ing data is a skill, which would be essential for problem solving. However, prob-
lem solving is only the skills of creators and developers. Even such framework
M. Csernoch
29
does not require any problem solving from end-users.
Creating formulas are also essential in problem solving. In this framework, the
focus is on the functions and formulas, not on the complexity of the problems. A
list of groups of functions are presented, without mentioning that the formulas
and functions can be used at any level, but the problems should match the level
of the students. In this framework, we are again faced with the problems men-
tioned and listed in connection with the teaching materials and teaching ap-
proaches to problem solving: the focus is on the tools, not on the problem solv-
ing and not on the effective problem solving approaches.
5.5. What Teachers Do Matters
It is obvious that the low mathability methods, wildly accepted, supported, and
influenced by teachers, software companies, teaching and help materials, ex-
amination forms, etc., are clearly recognizable in the erroneous document han-
dling, in the lack of knowledge regarding transfers between applications, and in
computer problem solving in general. It is clear that low mathability computer
solving approaches have a negative impact on students. It is not widely accepted
that end-users are not the low quality participants of the digital world. They are
just not professional programmers, on one hand, on the other hand, they seem
to be misjudged, mistreated, and misguided.
Several of low mathability samples are displayed and discussed in the paper.
However, a sample of one of the victim’s work is presented in Figure 15 (left).
The example is selected from a lesson plan of a pre-service teacher of Mathe-
matics in the final year of her tertiary studies. The non-printable characters of
the document clearly reveal the bricolage, which is obviously a TAEW based ap-
proach. However, the footnote added to the formula clearly reveals that she is
not aware of the lack of her knowledge: “At the end of the lines the ‘=’ sign can-
not be entered because of the Word program.” She even blames the software not
allowing the entering of the “=” at the end of the lines, instead of creating the
equations with an Equation Editor (Figure 15, right). (In the second line she
created the “=” by applying double underline font style on two Space charac-
ters.)
She is a victim of low mathability teaching approaches in various senses: (1)
her knowledge in computer problem solving is so low that she cannot use com-
puters effectively, (2) as an in-service teacher, she would not be able to use
computer tools for real problem solving and to motive her students, (3) and
Figure 15. A sample from a lesson plan of an overconfident pre-service teacher of Ma-
thematics (left).
M. Csernoch
30
finally, based on her note added to her formula, she is not aware of her lack of
knowledge.
An example of misleading Microsoft messages is presented in Figure 16. Our
testing of students of Informatics in the TAaAS project (Testing Algorithmic
and Application Skills) [56] proved that even students whose major is Informat-
ics are convinced (99%) that if we changed the extension of a file it cannot be
used any more. End-users do not realize that by changing the filename, the con-
tent does not change. (With data files only the program assigned to them is
changed, but the files can be opened in any previously initiated suitable pro-
grams. While the .exe files are just not recognized as executable.) However, the
extensions can be renamed to the original, while the same warning message is
displayed.
How different teachers can handle this warning message?
Microsoft and experienced teachers want to protect end-users and students.
Both know that if there is no extension, there is no problem. Consequently, Mi-
crosoft decided a couple of versions ago that it is better to hide the extensions,
and most of the teachers accept this setting. This is a low mathability approach.
However, there are teachers who display the extension intentionally and teach
its role and importance. They also provide various examples of file conversions
and cases when the extension is changed intentionally. (e.g. a .csv extension is
changed to .txt for a more convenient opening in a European Excel or the .exe
extension is deleted to attach the file in an email.) With this high mathability
approach students would understand the different file types, the connection be-
tween them, their conversions, and that extension can be changed without doing
any harm to the content of the file. In Chen’s meaning system model these are
the teachers with belief in the incremental nature of science and high teaching
self-efficacy, the experts.
Another type of Microsoft low mathability example is presented in Figure 17,
where the power of embedded IF() functions is demonstrated, the focus is on the
tool. The task is to calculate the grades based on marks stored in A2:A4.
However, grading should not be solved with embedded IF() functions, be-
cause Excel has solutions which are more suitable for this type of problem (e.g.
the INDEX(MATCH()) composite function) [50] [51] [52].
Another two low mathability aspects of the MS solution are that in the help
three four-level composite functions are presented for the three inputs, which
contain A, B, C, D, and F and 89, 79, 69, and 59 as constants.
Figure 16. Misleading warning message from Microsoft.
M. Csernoch
31
Figure 17. A help example for only the sake of language details. This problem can be
solved a lot faster, safer, and flexible solution with the INDEX(MATCH()) composite
function.
For calculating the grades a more expert solution can be provided with the
following settings:
• Instead of the four-level IF(IF(IF(IF()))), the INDEX(MATCH()) two-level
composite functions is created.
• Instead of the constants, a side table is set up (e.g. D1:E5) which holds the
grade limits and the alphabetical grades, arranged in vectors (D1:D5 and
E1:E5, respectively).
• Instead of the three functions for the three inputs, an array formula can be
used [50] [51] [52], [53] [54] [55] (with the array formula the copying and
the absolute and relative references can be avoided which are the major
sources of erroneous documents [1]).
• The solution is {=INDEX(E1:E5, MATCH(A2:A4, D1:D5))} formula.
One can argue that the HLOOKUP() and VLOOKUP() functions would be
faster. However, we claim that there are so many restrictions on these two func-
tions that from the high mathability problem solving and the meaning system
model aspects, they do not worth mentioning. They are another low mathability
solution.
While Microsoft’s is a low mathability, ours is a high mathability solution.
Non-expert teachers can argue that the {INDEX(MATCH())} array formula is
difficult, and students, end-users would not understand it.
However, expert teachers can develop students’ understanding of algorithms
and building and applying schemata which support their flexible problem solv-
ing. The {INDEX(MATCH())} solution presents integrated knowledge, the ap-
plication of previously learned algorithms, flexible and high-efficacy solution.
These are the features which experts teachers have and are able to develop with
their students.
6. Expert Teachers
6.1. Attributes of Expert Teachers in Computer Problem Solving
In the following, mainly citations of different sources are presented to prove that
there are effective, high mathability teaching methods which can be adapted and
applied in end-user computing. As it was mentioned in the previous chapters,
we are in lack of approaches which modify the proportion of fast and slow
thinking, banish low mathability interface navigation, and focus on high matha-
bility problem solving and schema construction, to build up knowledge.
In the Meaning System Model [43] Chen
et al
. claimed that “Teaching by pro-
viding students opportunities to understand and appreciate science deeply,
M. Csernoch
32
[which] likely use [s] methods to reveal the dynamic nature of science” is the
approach to effective teaching, and this has been proved by Hattie’ research, in
his biggest ever research project on teaching strategies [13] [14].
In the present paper we focus on teaching approaches and teaching materials
for end-user computing and problem solving. Within this framework we have
selected from Hattie’s 16 attributes of expert teachers those which are relevant in
this context [13] [14].
Expert Teachers [13] [14] Computer Problem Solving
“Experts and experienced teachers do not differ in
the amount of knowledge [they possess] … Experts
possess knowledge that is more integrated, in that
they combine new subject matter content knowledge
with prior knowledge; [they] can relate current lesson
content to other subjects in the curriculum.”
The different subjects of Informatics and
Computer Sciences are thought of and taught
in exclusion. End-user computing is taught
without real contents and problems, relying
heavily on concepts which novices and
end-users usually do not have.
“Expert teachers teach and are prepared for a
greater store of algorithms that students might
use when solving a particular problem.”
This characteristic of expert teachers plays a
crucial role in guiding students when they
develop intuitive expertise. Intuitive expertise
is the knowledge which System 1 needs for
making reliable fast decisions [25]. Expert
teachers are able to teach how knowledge at
mathability Level 4 can be transferred to Level 3.
“Both expert and experienced teachers perform better
than novices … because their cognitive skills become
automatic with extensive practice” (Chase & Simon,
1973; Chi
et al
., 1981 in [13]), [25].
“The difference, rather, is that experts develop
automaticity so as to free working memory to deal
with other more complex characteristics of the
situation, whereas experienced non-experts do not
optimise the opportunities gained from automaticity.”
Expert teachers are much effective in activating
System 1 and System 2 in the right proportion
and within the right time frame, which has great
importance in effective problem solving, in
lightening the load of working memory, and in
our case, in reducing the number of erroneous
and demanding documents.
“The expert teacher more often than the
experienced teacher seeks further information,
whereas experienced teachers focus more on
directly available data…”
Typing data, presenting meaningless and/or low
mathability formulas, l’art-pour-l’art formattings,
etc., and the acceptance of low mathability
materials are widely accepted.
“Experts are more adept at anticipating problems
and then improvising. They tend to spend a greater
proportion of their solution time trying to
understand the problem to be solved as opposed
to trying out different solutions.”
In this aspect, the difference between experts
and the others in computer problem solving
is that they prefer high mathability and TAEW
based approaches, respectively.
“They [experts] are better able to filter relevant from
irrelevant information, and are able to monitor,
understand, and interpret events in more detail and
with more insight than experienced teachers.”
This is the aspect mentioned in connection with
the definition and description of functions,
where irrelevant information is focused on.
“Expert teachers aim for more than achievement
goals. They also aim to motivate their students to
master rather than perform, they enhance students’
self-concept and self-efficacy about learning, they
set appropriate challenging tasks, and they aim for
both surface and deep outcomes”,
This statement is in complete accordance with
the Meaning System Model [43].
“Expert teachers are more likely to set challenging
rather than “do your best” goals, they set challenging
and not merely time consuming activities, they invite
students to engage rather than copy.”
This high mathability approach was hardly found
in the analyzed materials; they primarily expected
copying and surface navigation from students.
M. Csernoch
33
6.2. Utilizing Fast and Slow Thinking Effectively
Finally, we return to the computer problem solving approaches, to the two
hypernym categories. Hattie found in his research that
“We can make a distinction between surface and deep learning. Surface
learning is more about the content (knowing the ideas, and doing what is
needed to gain a passing grade), and deep learning more about under-
standing (relating and extending ideas, and an intention to understand and
impose meaning). The claim is that experts are more successful at both
types of learning, whereas both experienced and expert teachers are similar
in terms of surface learning.”
Experts are more aware of when there is a need to activate System 2 than ex-
perienced but non-expert teachers. To be able to find the right proportion of
System 1 and System 2 requires being an expert in our major, which is pedagog-
ical content knowledge: Hattie argues that
“…content knowledge is necessary for both experienced and expert teach-
ers, and is thus not a key distinguishing feature… We are not underesti-
mating the importance of content knowledge—it must be present—but it is
more pedagogical content knowledge that is important: that is, the way
knowledge is used in teaching situations.”
Being aware of the characteristics of the deep and surface approach problem
solving methods and the attributes of expert teachers, we go one step further and
claim that the problem is not with “overuse of ATM thinking”, since this is
needed in real world problem solving to build strategic procedures—imple-
mented in System 2 (ATM thinking)—, but using ATM thinking when AUM
thinking would do better. As we have seen, expert teachers are those who can
teach students how to build schemata and when they can be recalled, and how to
find the right proportion of deep and surface learning.
One further reason to find the right proportion of thinking fast and thinking
slow is explained by Polya [18] and is in complete accordance with Kahneman’s
[25] and Hattie’s [13] [14] findings: “If you cannot solve a problem, then there is
an easier problem you can solve …” Expert teachers are those who have the abil-
ity, based on their attributes, to teach this.
6.3. Sunk-Cost Fallacy
Why is there a shortage of expert teachers in Informatics? Why can teachers not
see that being experienced is not enough; they have to be expert? Kahneman’s
sunk-cost fallacy is one explanation [25]:
“The decision to invest additional resources in a losing account, when bet-
ter investments are available”.
Teachers have invested a lot in being experienced, most of them are self-
taught—similar to spreadsheet developers and users [7], which was found in the
M. Csernoch
34
TAaAS project regarding teachers of Informatics [56]—, and it is not easy to ac-
cept that they have to leave behind everything and change their teaching ap-
proach to a completely new and more demanding one(s). If we can call attention
to the problem and make teachers and education policy makers listen, we can
avoid the mistake which companies make:
“All too often a company afflicted by sunk costs drives into the blizzard,
throwing good money after bad rather than accepting the humiliation of
closing the account of a costly failure.”
We practice in end-user computing, in general, and research focusing on
spreadsheet errors proves that in end-user computing pseudo-experts outnumb-
er the true experts [1] [2] [9] [10]. The environment is not sufficiently regular,
since software companies boast new features, instead of regularities, which is
accepted unconditionally by teachers, education policy makers, curricula devel-
opers, etc., however, it is not accepted that the regularities have to be learnt
through practice. Schema construction is not accepted/used in end-user com-
puter trainings, even though it is necessary for reliable fast thinking and conse-
quently error-free problem solving.
7. Examples of High Mathability Materials
Some attempts to change end-users’ computational thinking, their approach to
problem solving have been made. However, it seems that without institutiona-
lized support—both from education policy and education research—they will
remain isolated and forgotten.
It was declared around three decades ago that functional programming is
more effective for developing students’ algorithm skills than imperative lan-
guages, due to the simplicity of the languages [17]. This programming approach
focuses on problem solving instead of the language details. The idea has recently
emerged again, entitled as Functional Model, and been accepted in some of the
states of Germany, based on Hubwieser’s research [57]. His finding, however,
clearly shows the isolation of researchers working in the field. In 2004 he
claimed his model as novelty [57], not realizing that it had been around since
1992 [17]. Similar research is being conducted in Hungary, where Sprego—
Spreadsheet Lego—has been introduced [53]. The Sprego language is similar to
Logo, but in a spreadsheet environment. It serves both as a functional language
and office application. However, at present it is completely isolated for various
reasons: (1) the Hungarian language, (2) teachers’ reluctance to switch from low
to high mathability approaches, (3) the fact that it takes several years to prove its
effectiveness 100%. Both Hubwieser [57] and Csernoch [50] [51] [52] focus on
real world problems with high mathability approaches. Sprego is similar to
Hubwieser’s approach in that it builds the functional models for the problems,
but goes one step further and does coding in its simplified language to introduce
programming concepts to novice users.
A problem solving approach is also present in spreadsheet management in the
M. Csernoch
35
“Succeeding in Business with Microsoft Excel” series [49]. However, the authors
use a made-up company and made-up examples, mix spreadsheets with ICT,
and do heavy computer cooking, not able to distinguish problems from language
details.
Also in relation to spreadsheets we must mention, as a good example, the at-
tempts in France. They teach spreadsheets as part of Mathematics, and as such
focus on the fundamental formulas and functions, and this knowledge is tested
in the “Brevet des colleges” [58]. This approach is present in many spreadsheet
teaching materials, but even French education is not free of low mathability
teaching materials. It must also be mentioned that some of the French maths
course books offer math-oriented real world problems, but most of the on-line
materials are meaningless, empty “examples”, without tables and without real
problems to solve, focusing on the language details. In spite of this effort, several
papers have been published lamenting the low spreadsheet knowledge of French
students [59] [60]. Our own studies within the framework of the TAaAS project
[56] revealed that most French students of Informatics do not even understand
the concept of spreadsheet formula. Research beyond spreadsheet errors focuses
on spreadsheet design and programming in spreadsheet [40] [41] [50]-[55] but
just as with other sources, they are hardly known [7] [62] [63].
Ben-Ari focused on text management [3] [6] and found that most of the text-
based documents are bricolage. Similar results have been published since 1997,
but have remained unnoticed [4] [5] [61]. In presentation and webpage man-
agement the situation is similar; it seems that only a very few listen.
The list of good practices is obviously not complete, just like the low matha-
bility examples in the previous section, but this cannot be the goal of the present
paper. In general, the overwhelming proportion of low mathability tools and
teaching approaches in end-user computing is clearly present.
8. Conclusions
In this paper we focus on the training and problem solving approaches of the
non-professional participants of the digital world, end-users for short. We report
the results of our findings based on the collection and analyses of the available
end-user teaching, guiding, self-learning, testing materials, along with the dif-
ferent teaching approaches in different languages and countries. We also sum-
marize our base and mathability-extended typology of the computer problem
solving approaches (published in 2014 and in 2015, respectively), which is a
quantitative measuring system for evaluating educational contents.
Our analyses of end-user materials led us to the following conclusions:
• End-user educational sources primarily support low mathability slow think-
ing activities, where surface navigation and usage of software tools are in the
focus [H1].
• There are hardly any traces of high mathability slow thinking activities,
where real world problem solving has to be carried out [H1], [H4].
• Intuition based reliable fast thinking activities are scarcely supported and
M. Csernoch
36
carried out, due to the lack of true expertise [H2], [H3], [H4].
• End-user computing lacks expert teachers who have the appropriate attitude
to maximize the impact on learning. The majority of the CS/Informatics
teachers are novice and/or experienced, who do not possess the necessary
pedagogical content knowledge. As such they themselves do not know and
consequently they are not able to teach their students when and how to apply
fast and slow thinking effectively. These teachers focus on tools, on surface
navigation, and accept low mathability and frequently erroneous teaching
and guiding materials [H2], [H3].
• Sunk-cost fallacy further deepens the problem. The experienced participants
of end-user training and support invested so much that they do not want to
or are not able to give up their achievements, but stick with them [H2].
We also found during our analytical process that researches in CS/Informatics
education have already recognized some of the problems in end-user computing.
However, they decided that end-user computing should be banished from
CS/Informatics, and only pure programming has to be taught, that is the only
way for developing the students’ computational thinking [H3].
However, we claim that end-user computing in the digital world is not less
important than traditional CS/Informatics studies. We found that the results of
recent researches in educational studies would provide guidelines for funda-
mental changes in end-user education, training, and support.
• With expert teachers end-user computing can be taught as effectively and ef-
ficiently as programming and other majors in CS/Informatics.
• The path to professionalism in CS/Informatics and to professional problem
solving in other sciences starts at end-user computing.
• End-users outnumber professionals, so they cannot be ignored and/or ba-
nished. Well trained end-users would be those participants of the digital
world who have great impact on developments.
We have a large number of experienced teachers (and also a large number of
unexperienced and novice teachers), but that is not enough. The enormous
number of erroneous documents, the wasting of human and computer re-
sources, the low mathability teaching materials focusing on technical and lan-
guage details, ill-titled and misleading coursebooks and many other teaching
materials, as well as the fact that teachers unconditionally accept these circums-
tances, all outline the necessity of change. The effect of experienced teachers and
software developers on end-user computing is obvious: what they do matters.
However, we are faced with a very unfortunate situation in that they have a neg-
ative effect on end-user problem solving.
We are in great need of expert teachers to develop students’ computational
thinking, the skills required for the digital era, effective end-user computing and
computer problem solving. We must emphasize that “it is excellence in teachers
that make[s] the greatest differences, not just teachers” [14]. We do not claim
that our teachers of CS, IT, ICT, Informatics, or whatever we choose to call it,
are poor teachers; we only argue that for various reasons they are non-excellent,
M. Csernoch
37
and it is high time for change.
We need teachers who are ready to give up their “experienced” status and are
open to novel high mathability approaches. Avoiding the sunk-cost fallacy [25]
might be a humiliation for some, but a great opportunity for the next generation.
Expert teachers are needed who can provide students with opportunities to un-
derstand and appreciate science deeply, and who will likely use the methods re-
quired to reveal the dynamic nature of science [43].
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