Short Tasks for Scaffolding Computational Thinking by the Global Bebras Challenge

Abstract

The short task methodology enhances the Bebras constructive environment, and provides an emotional context that triggers the convolution of initially biased mental models and corresponding emotional reactions into an unbiased set of conceptual models for informatics education. This provides the motivation of our research–to explore the process of pedagogical design of short informatics concept-based tasks from the standpoint of mindset formation, which allows one to build conceptual models for CT education. The aim of the research is to gain a conceptual understanding of what a short task is in the context of the global Bebras Challenge initiative. We explore the principles which should underlie the pedagogical design of short tasks for informatics education that scaffold CT. Exploration of a number of practical examples of the Bebras short tasks is the background of our research methodology. The results include an analysis of the structure of short tasks, focusing on the interaction of mental models, conceptual models, and heuristics inherent in the task design. The discussion provides a comprehensive insight into the issues of the short tasks in relation to CT and the Bebras environment. We conclude with recommendations for organizing an effective pedagogical design of a short task.

Full text

Citation: Dagiene, V.; Dolgopolovas,
V. Short Tasks for Scaffolding
Computational Thinking by the
Global Bebras Challenge. Mathematics
2022,10, 3194. https://doi.org/
10.3390/math10173194
Academic Editor: Jay Jahangiri
Received: 8 July 2022
Accepted: 31 August 2022
Published: 4 September 2022
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mathematics
Article
Short Tasks for Scaffolding Computational Thinking by the
Global Bebras Challenge
Valentina Dagiene and Vladimiras Dolgopolovas *
Institute of Data Science and Digital Technologies, Vilnius University, Akademijos Str. 4,
LT-08412 Vilnius, Lithuania
*Correspondence: vladimiras.dolgopolovas@mif.vu.lt
Abstract:
The short task methodology enhances the Bebras constructive environment, and provides an
emotional context that triggers the convolution of initially biased mental models and corresponding
emotional reactions into an unbiased set of conceptual models for informatics education. This
provides the motivation of our research–to explore the process of pedagogical design of short
informatics concept-based tasks from the standpoint of mindset formation, which allows one to build
conceptual models for CT education. The aim of the research is to gain a conceptual understanding of
what a short task is in the context of the global Bebras Challenge initiative. We explore the principles
which should underlie the pedagogical design of short tasks for informatics education that scaffold
CT. Exploration of a number of practical examples of the Bebras short tasks is the background of our
research methodology. The results include an analysis of the structure of short tasks, focusing on
the interaction of mental models, conceptual models, and heuristics inherent in the task design. The
discussion provides a comprehensive insight into the issues of the short tasks in relation to CT and
the Bebras environment. We conclude with recommendations for organizing an effective pedagogical
design of a short task.
Keywords:
computational thinking; CT; constructionism; CT heuristics; constructivism; informatics
education; the bebras challenge
MSC: 97D50
1. Introduction
Understanding the importance of informatics/computer science (CS) in today’s world
as a necessary condition for the formation of digital competencies not only among in-
formation technology specialists, but also among representatives of other professions in
engineering, industry, medicine, etc., as well as the general public, is widespread. As a
consequence, it is very important to organize an appropriate educational environment
in schools, as a result of which computers and informatics are becoming a common phe-
nomenon not only in school management, but also in the widespread growth of informatics
classes. At the same time, any specially organized top-down education reform, includ-
ing the widespread introduction of informatics in schools, is, as usual, based on some
formality and formalism, but it takes time for the various guidelines and instructions
to be accepted by the educational community and become practically effective. On the
contrary, informal approaches, including game-based and short task-based approaches,
maybe more attractive because they increase motivation and engagement, and may be
easier and faster to implement. Examples include initiatives such as Code academy Code
academy [
1
,
2
], CS Unplugged [
3
,
4
], Hour of Code [
5
,
6
], and Bebras Challenge [
7
,
8
]. Among
the above-mentioned areas, it is important to emphasize that informal approaches are a
kind of platform to ensure equal access of minorities and underrepresented groups to the
digital benefits provided by modern technologies.
Mathematics 2022,10, 3194. https://doi.org/10.3390/math10173194 https://www.mdpi.com/journal/mathematics

Mathematics 2022,10, 3194 2 of 30
The digital age has many demands where computational thinking (CT) is a core
competency, especially for the general public [
9
–
12
]. Despite the fact that the study of
CT has greatly motivated the interest of many educators, and numerous studies have
examined CT from different angles, including its history, definitions, and educational
approaches [
13
,
14
], research on this topic is still looking for its theoretical foundations and
new approaches [
15
,
16
] to develop. Looking at the approaches that have already been
presented, play-based learning and constructivism are the first to be mentioned [17].
We question some of the statements related to the scope and definitions of CT pre-
sented by Stella et al. [
18
]. There is a limited view of CT behind these definitions, which
positions CT as a way of “thinking about the world in terms of data” and that CT skills
include “defining a quantifiable problem” [
18
]. This positions CT as a kind of skill for
crunching numbers or a competency for dealing with computers when “analyzing large
volumes of data or testing theoretical predictions by coding simulations” [
18
]. In our
view, this is rooted in a widespread empirical tradition that views education as a kind of
laboratory for unlocking the mysteries of the objective world. In contrast, CT education is
not just about data and algorithms. It teaches a specific problem-solving process involving a
wide range of relevant skills and computer science related methods such as decomposition,
pattern recognition, abstraction, algorithms, and debugging [
19
]. It is also the cultivation
of individuality and empathy, as well as the application of Papert’s constructionism [
20
],
creativity and their practical values in education [
17
]. As the theory of constructionism
suggests [
21
], learning occurs through a process of insight, a process of reconstructing
initially incoherent information about the world in a personally meaningful way. The
numbers, data, computing, algorithms, simulation, etc., are just an important content and
context here.
While computers and related skills used to be considered the most important aim of
learning, nowadays computer literacy has become a common medium used everywhere
and by everyone. However, this implies certain consequences and raises certain issues that
need to be addressed in educational design practice. How should such a constructionist
context be practically organized? And what are the principles of educational design so that
such personally significant interaction can occur? To summarize this discussion, despite
our debating position, we share the understanding that “a mindset, a definition of com-
putational thinking grounded in cognitive science remains an open question” [
18
]. This
provides the motivation for this study–to provide a bridge from the mindstorms of con-
structionism context to the mindset of CT in a practical way that enables the development
of appropriate educational solutions.
The study focuses on the Bebras international contest [
22
] in connection with an in-
structional approach of solving short informatics content tasks [
23
] as part of constructionist
learning. The aim of the study is to gain a conceptual understanding of what a short task
is in the context of CT and contest-based education based on the context of the Bebras
Challenge. The research question: What principles underlie the pedagogical design of short
tasks for informatics education that scaffold computational thinking?
To conduct the research, we employ the networking of theories approach to develop
the theoretical framework that integrates a number of interdisciplinary domains, such
as cognitive, pedagogical and instructional domains, into a coherent set and enables
methodological reflection for semantic analysis of a short task focused on the issue of CT
education in the context of Bebras.
On the whole, the research itself is based on a way that enables the interaction of Infor-
matics concepts coherent through the personally meaningful “Aha!” discovery. Consider a
practical example of a short task (see Figure 1). First, this short task addresses two disparate
concepts: the concept of number (quantity, sum) and the concept of disposition (between).

Mathematics 2022,10, 3194 3 of 30
Mathematics 2022, 10, x FOR PEER REVIEW 3 of 30
is an outstanding example for an attempt to combine geometry and algebra by the means
of practical solution the Geogebra software [24])—“the two opposite poles of mathemat-
ics, and the source of historic conceptual conflict”. [25] as “arithmetic is discrete, static,
computational, and logical; geometry is continues, fluid, dynamic, and visual” [25]. How-
ever, during the solving process, which does not lend itself to formal quantification be-
cause it requires operating with something more than data and numbers, namely with a
concept related to spatial arrangement, real creativity occurs–the search for a solution
brings the discovery process to the forefront, evoking the “Aha!” effect and the corre-
sponding mental structure [26] that forms into a CT mindset. Such a discovery process,
however, does not reside in some kind of vacuum. Concepts of informatics provide the
context for such a constructionist process “in action”. At the same time, it enables the ed-
ucational environment to be designed in such a way that there is a process of scaffolding
[17] in the practice of such challenge-oriented education.
Figure 1. Short Bebras task for younger children. Labels A, B, C denote answer choices. Adapted
from www.bebras.org (accessed on 24 February 2022).
The paper is structured as follows. The Background section discusses some basic
ideas of CT education, pedagogical approaches and basic vocabulary. In addition, the
Bebras challenge and the introduction of a short task as a pedagogical approach in chal-
lenge-based educational settings are presented. This is followed by a section describing
the materials and methods associated with the study follows. Here, the theoretical foun-
dations of the implemented methodology are presented, and the experimental settings are
described with the case study of the Bebras Challenge. The Results and Discussion section
presents the results of processing a number of short tasks, including a systematization to
illustrate the mindset associated with short tasks. This is followed by discussion of con-
ceptual interplay as a driving force for enabling mindstorming process and Aha! creativity
as part of CT education within a challenge-based educational environment. The Conclu-
sions section finalizes the study.
Figure 1.
Short Bebras task for younger children. Labels A, B, C denote answer choices. Adapted
from www.bebras.org (accessed on 24 February 2022).
At first glance, it appears that there are no logically meaningful ways to combine
these seemingly non-overlapping ways of thinking–the world of geometry (dispositions,
figures, angles, etc.) and the world of arithmetic (quantities, sums, dimensions, etc.)
(There is an outstanding example for an attempt to combine geometry and algebra by
the means of practical solution the Geogebra software [
24
])—“the two opposite poles of
mathematics, and the source of historic conceptual conflict”. [
25
] as “arithmetic is discrete,
static, computational, and logical; geometry is continues, fluid, dynamic, and visual” [
25
].
However, during the solving process, which does not lend itself to formal quantification
because it requires operating with something more than data and numbers, namely with a
concept related to spatial arrangement, real creativity occurs–the search for a solution brings
the discovery process to the forefront, evoking the “Aha!” effect and the corresponding
mental structure [
26
] that forms into a CT mindset. Such a discovery process, however,
does not reside in some kind of vacuum. Concepts of informatics provide the context for
such a constructionist process “in action”. At the same time, it enables the educational
environment to be designed in such a way that there is a process of scaffolding [
17
] in the
practice of such challenge-oriented education.
The paper is structured as follows. The Background section discusses some basic ideas
of CT education, pedagogical approaches and basic vocabulary. In addition, the Bebras
challenge and the introduction of a short task as a pedagogical approach in challenge-based
educational settings are presented. This is followed by a section describing the materials
and methods associated with the study follows. Here, the theoretical foundations of the

Mathematics 2022,10, 3194 4 of 30
implemented methodology are presented, and the experimental settings are described with
the case study of the Bebras Challenge. The Results and Discussion section presents the
results of processing a number of short tasks, including a systematization to illustrate the
mindset associated with short tasks. This is followed by discussion of conceptual interplay
as a driving force for enabling mindstorming process and Aha! creativity as part of CT
education within a challenge-based educational environment. The Conclusions section
finalizes the study.
2. Background
A key focus of our research is the conceptual interrelationship of CT and scaffolding.
Here, scaffolding is understood as Vygotsky scaffolding [
27
,
28
]. In this respect, scaffolding
is a teaching strategy based on a socio-cultural tradition focused on exploring the zone
of proximal development (ZPD). Since our study aims at teaching CT through related
challenge activities, we are interested in what are the main principles of the pedagogical
design of appropriate scaffolding means such as the Bebras challenge short task.
To clarify this issue, we can consider CT as an approach that is implemented in a set of
concepts and practices students explore during formal learning and informal extracurricular
activities in a specific context, not necessarily related to the context of informatics. Finally,
through reflection, trial and error, this grows into a set of attitudes and heuristics [
29
] for
solving problems the way computer scientists do [
30
]. Moving forward, we suggest that
initially these heuristics are limited in scope and probably based on a set of miss attitudes or
“biases” in the terminology of Tversky and Kahneman [
31
]. Namely, the aim of scaffolding
is to overcome these biases and to keep students in their ZPD.
Next, we will provide some background information and draw attention to a few core
concepts referred in the text or directly related to the topic we are trying to uncover. Al-
though some of these concepts are fairly well known, rather than just describing commonly
known facts, we will try to expose them the perspective of CT. Nevertheless, we do not aim
to be in-depth and will limit ourselves to introductory observations.
2.1. The Intended Audience and Motivation behind the Study
The reader we assume may be interested in some of the theoretical underpinnings of
Bebras. Although Bebras is not as widely represented in the US and UK, it is popular in
many other countries, so we would expect first of all a broad interest from both the broad
community of theorists and practitioners involved in Bebras, especially in the design of
short tasks. As far as other interested readers are concerned, the article is an attempt to
outline some guidelines on theoretical foundations for practical educational activities, i.e.,
we think it may be useful for educators who are interested in providing some theoretical
foundations for the teaching method they implement.
It should also be noted that Bebras’ practical activities are directed and based on a
conceptual understanding of informatics (computer science). However, informatics is an
example of an activity that is both practical and theoretical (a kind of example of the subtle
difference in terminologies that emerged in different languages (cultures), since historically
the European term “informatics” emerged from an activity focused mainly on theoretical
constructs for information processing, and in contrast the US term “computer science”
emerged from a famous “garage” activity focused on the practical design of information
processing instruments. This kind of theory-practice dualism is always (explicitly and
implicitly) present in Bebras. Considered as a practical educational activity (hands-on, chal-
lenge, competition) Bebras’ didactic constructions are extensively immersed in informatics
and draw their inspiration from the discourse of informatics (check at this point the term
informatics in Techopedia [
32
]) (algorithms, interactions, computation, systems and the
various “types” of thinking generated by them, e.g., algorithmic, computational, systems
thinking). Therefore, despite the arguably inductive approach to its implementation, such
theoretical background has always been presented implicitly, so, and this is one of the
motivations of the study, must be disclosed further to become explicitly visible.

Mathematics 2022,10, 3194 5 of 30
2.2. Formal and Informal Approaches to Mathematics and Informatics Education
Although the scope of our paper is informatics and not solely mathematics education,
which corresponds to the scope of the journal in the STEM education section, discussions
and comments related to mathematics education are still relevant. In addition, aspects
related to educational policies and the relationship between mathematics and informatics
education can be discussed.
We are witnessing the dominance of positivist approaches to education, which seek
to model and explore objective reality (no doubt assumed), comparing education with
medicine or other natural sciences. Therefore, in education, by analogy with medicine, it
is assumed that some large-scale and extensive reforms are needed, with corresponding
large-scale experiments, comparative studies, and statistical calculations. As a result, we
have seen many attempts at such reforms in our long professional lives, but none, as
far as we can remember, has succeeded. Of course, within this paradigm, all but the
“scientific” (read: formal, scalable, objectively true, effective, uniform, impeccable, etc.)
and informal are declared unclaimed and even dangerous. In our view, the reason for
this lies on the historical plane, since Western culture has always been oriented towards
knowledge transfer with technology, so some universal and standardized approaches have
been quite attractive.
However, we assume a non-positivist paradigm exists (as far as education is con-
cerned). We could observe this through a kind of kaleidoscope of interpretations, providing
a compelling and unique view of each educational community member. In such an inter-
pretivist paradigm, the goal is not unification, but rather to highlight what is unique about
each country, to move away from utilitarian goals toward the true purpose of education–
the development and growth of the individual (which, from our perspective, can only
be carried out in conjunction with teacher development). Here the process is no less or
even more important than the result, a departure from the utilitarian and pragmatic goals
positioned as an unconditional virtue, to a humanitarian and value-based approach, with
no intention of unifying or scaling. As an example, the Bebras community is a platform for
flourishing and sharing unique ideas.
The contradiction described leads to misunderstanding. For example, if one who
stands on the position of interpretivism considers informal approaches to be an opportunity
value, then one who stands on the positivist position sees it as a problem, because it does
not fit into the holistic picture of the world, which, in his opinion, definitely exists. In such
a positivist world, everything must be systematized, formalized, proven, etc. This ties
in with the meaning of “equal access”—if one views the top-down systems approach as
the only correct one, it should be systemized and coordinated at the policy level. If one
considers a bottom-up approach, every opportunity has value. For example, the Bebras
community provides the ability to use playing cards, meaning a computer is not needed
in such a case. Another way is access through school computers, as Bebras provides the
ability to connect to the server for free.
2.3. Scalability
Overall, scalability as applied to education is a complex and comprehensive topic,
requiring much effort to implement and research [
33
]. Scalability, especially from the
perspective of educational policymakers, is positioned as a solution to unify education and
optimize educational costs. However, that “only addressing quantity is an oversimplified
perspective on scalability” [
33
]. Moreover, innovation is context-dependent, and a success-
ful initiative “in one context might have very different results in other contexts” [
33
]. In
this respect, Bebras can be seen as a kind of context-sensitive platform, a community that
helps educators in their attempts to find unique educational solutions in informatics and
CT. Standardization or formalization of the educational process is not a primary Bebras
goal. In its internal organization, however, Bebras is certainly formalized. It is based on a
number of procedures and formalizations, but this is not aimed at limitations, but rather at
convenience and communication. By analogy, Bebras is a kind of universal language that

Mathematics 2022,10, 3194 6 of 30
allows members of the community to communicate. Thus, considering Bebras as a language
or platform, this problem of scalability is diminished, in contrast to considering it as a
universal educational solution, where, as mentioned, such universality must
be developed.
2.4. Computational Thinking
In general, CT is well known, especially within the CT and informatics education com-
munities, as a paradigm, educational method, and approach to problem
solving [7,9,11,30,34]
.
Although there are several directions and several specific definitions, there is nonetheless
some consensus on the general line. Therefore, we assume that the reader is either familiar
with what CT is or can easily check it out in the literature. This raises the question: is it even
possible to define what thinking is? Typically, such “definitional” approaches originate in
the deductive (or other formal) approaches to reasoning, equating reasoning with logical
assertions and evaluating predicates. However, does this explain creativity and insight?
The other way is “definition” through examples, the transmission of experience, craft, and
practical activity (theoretically based on the meaning of “grounded” cognition [35]).
Another aspect is the connection between CT and informatics education [
36
]. The
key idea here is to move from specialized knowledge and skills to a set of universal
competencies (as an example, the CS for All movement [
37
] could be mentioned), where
CT can be seen as one of the components. This leads to a consideration of CT pedagogy,
seeing it as a kind of CS-inspired approach to problem solving. This results in a number of
misconceptions that lead to preconceived attitudes toward particular CS concepts. People
usually apply heuristic processes familiar to them from everyday experience, adapting
them (which is not always correct) to solve problems in a manner such as computer
scientists do. This is why the scaffolding process is important here [
17
,
28
]. The process
of such scaffolding must be comprehensively designed, including proper pedagogical
considerations and effective instructional support.
The challenge-based pedagogical approach provides a socially meaningful environ-
ment for the student, immersing them in a kind of constructionist environment that
provides a context for “mindstorming” or “re/discovering” powerful ideas, as Papert
presents [
20
]. In terms of instruction, the concept of the short task can be illustrated by
the concept of microlearning, balancing the cognitive load and complexity of the concept
being taught, but this is only an illustration, since instruction using the short task involves
a different context than is typically found in microlearning. In this respect, the following
aspect may be discussed. There is a certain contradiction between formal, abstract and
experiential knowledge. Most often, the former is considered as true or objective, while the
latter is associated with heuristics and usually has no objective meaning. This is also true
of CS because “computation in its strict mathematical sense is an abstract concept whose
relationship to experience is indirect” [
38
]. CT, however, offers a perspective to broaden
the “the semantic frame of interest” [
38
], by viewing the formal as a kind of context in
which experience occurs. This dualism, inspired by Papert, provides the motivation for
developing short task-based instruction within CT’s challenge-based pedagogy.
2.5. Constructivism vs. Constructionism
As for constructionism, Papert, the originator of the term, also introduced the term
CT [
34
]. Since he referred to Piaget’s constructivism [
39
] as the core theory of his research,
these three basic meanings (constructivism, constructionism, and CT) are sometimes con-
sidered in conjunction. Constructivism is a theory of child development with the basic idea
of presenting the growing child in terms of (a) interconnection and interaction with the
surrounding environment and (b) considering a series of successive stages of development.
Constructivism refers to developmental theory. Constructionism deepens into construc-
tivism by focusing specifically on the practice of interaction in a socially meaningful context,
while at the same time focusing on self-interaction with artifacts of various types, including
computers. In this way, CT (from Papert’s point of view) can be seen as an approach to

Mathematics 2022,10, 3194 7 of 30
interact more effectively (from a developmental perspective) with the computer (considered
as a tool of interactive educational technique).
2.6. Situated Constructionism
Most development theories consider child development as a process aimed at develop-
ing a perfect “intellectual mechanism” and “higher forms of perception” [
40
] and reasoning.
All of this is purely “mentalistic”, that is, situated and processed in our heads, so the
aim of child development is to develop an intellectual, logical thinker capable of moving
from the concrete to the abstract and generalizing [
39
]. On the contrary, Papert’s situated
constructionism shares the idea that knowledge by itself is not abstract and universal,
but “it lives and grows in context” [
39
], so cognitive development approaches encourage
individual and culturally specific learning styles, and we “should prefer the more concrete
forms of knowledge favored by constructionism to the propositional forms of knowledge
[favored by traditional epistemology]” (Papert 1991, p. 10 as cited in [39]).
2.7. Mindset
Considering CT as a kind of cognitive tool, a thought technique, then we move on to
the notion of mindset. Generally speaking, in the common meaning mindset means a set of
attitudes, sometimes emphasizing certain traits, such as mathematical mindset, engineering
mindset, growth mindset, etc. This leads to the “introduction” of CT mindset as a type of
mindset developed through interaction with computers in a constructionist sense.
2.8. Mindstorms
Papert referred to “Mindstorms” in the title of his core book [
20
]. A programmable
Lego construction kit was later named after the book [
41
]. From the CT perspective, Mind-
stroms refers to an attempt of convey a “view the computer and its associated technologies
as a coherent source of experience” [
38
]. It is important to emphasize that Mindstroms
aimed at “epistemological reflection” [
20
] through the direct experience of the learner.
This brings us to the plane of instruction and highlights the following concepts such as
microlearning and scaffolding.
2.9. Microlearning, and Scaffolding
Although there is some “tension” between constructivism and microlearning [42], as
the former is based on emphasizing self-interaction and requires time to “tune” a learner’s
attention, while the latter is promoted as beneficial by reducing the instructional time by
dosing the portion of information conveyed, in general the two approaches are compat-
ible [
17
]. Instructional scaffolding is the support provided to a student by the instructor
throughout the learning process. In this sense, “scaffolding” refers to the practice of guid-
ance and support in the process of construction and deconstruction [
23
]. It is important to
emphasize that the goal of scaffolding (and education in general) is to enable the child’s con-
tinued collaborative development toward encompassing the zone of proximal development.
Scaffolding efforts diminish when the zone of proximal development becomes covered.
2.10. Computational Thinking and Powerful Ideas
We can observe at least two main directions for academic understanding of CT–the
positioning of CT as a (problem solving) approach and the positioning CT as an approach
to (constructionist) pedagogy [
34
]. The former, perhaps, has its origins in Wing and the
latter in Papert. The other is the semiotic approach to CT, positioning CT as a semiotic
mediator [
15
,
16
]. Here we will focus on the first two. The CT-style approach to problem
solving postulates some unique features of the problem-solving process when viewed from
a computer science perspective. It employs some vocabulary specific to computer science,
such as algorithm, abstraction, decomposition, pattern recognition, and others. CT-style
constructionist pedagogy positions computational artifact (e.g., computer) as a tool for
“getting things to work” [
23
] (in the educational sense). In this case, the computer is just a

Mathematics 2022,10, 3194 8 of 30
tool incorporated into the learning process, which itself is quite specific in its purposes and
instructional means, namely, that it aims at teaching the real through the interaction with
the virtual and the artificial. This leads us to the sense of creativity arising from interaction
with “microworlds” where the real is conceptually driven, and such concepts (such as
laws of nature or mathematical concepts) reside in a form of powerful ideas that can be
comprehended through constructionist educational efforts.
2.11. Aha! Creativity
The meaning, the essence of the concept of creativity per se is imposed in contradiction
to logic or reasoning and mostly as its unsystematic antipode. Nevertheless, there have
been many attempts at a kind of systematization, from developing a kind of approaches
to forcing creativity to constructing models of what the creativity is on the cognitive
level. Many efforts have been made to link the concept of CT (seen as an approach) and
creativity. The following interesting observation is inspired by Martin Gardner [
43
]. If
you look closely at the guidelines of Aha! approach [
43
] (rewritten by the authors in a
math-neutral manner):
•Can the problem be reduced to a simple case?
•Can the problem be transformed to an analogue one that is easier to solve?
•Can you develop a simple algorithm for solving the problem?
•Can you apply an approach or theory from another branch or discipline?
•Can you check the result with good examples and counterexamples?
•
Are the aspects of the problem given that are actually irrelevant for the solution, and
what presence in the problem description serves to misdirect you?
One can see obvious similarities with Wing’s inspired definitions of CT [
34
]. It should
be noted that for Gardner, inspiration Aha! is not an abstract thing, but something definite,
an insight that comes through the right way to solve a problem (actually a short problem,
or one with a non-obvious or surface-level solution). This brings us to the notion of short
task and challenge-focused education. It is interesting to note, that, according to Gardner,
actually there is no correlation (or there is, but negative) between high intelligence and
Aha! thinking, which can be a headache for educational policy aimed at high scores on
standardized educational tests. The dilemma here is whether we are seeking an intelligent
or smart child, because in the latter case, formal requirements are likely to kill curiosity
and Aha! creativity in favor of a high I.Q. as an educational policy requirement. It seems
that Gardner was one of the first in the modern history of educational science to offer short
problems to scaffold a kind of creative thinking, as we might call it today by analogy with
CT. A special way of solving problems was presented—“[...] if you can free your mind from
standard problem solving techniques [...] that leads immediately to solution”, without any
prerequisite of prior knowledge of mathematics and “intended for any reader, with a sense
of humor, capable of understanding the puzzles” [43].
2.12. Conceptual Content of Short Tasks
First, we need to clarify what we are talking about: the organizational aspects of the
Challenge itself, the pedagogical aspects related to CS and CT, or the instructional aspects
related to the concept of the short task. The Challenge can be considered as a platform
that provides a socially meaningful educational context, the pedagogical aspects include a
reflective approach [
19
] to education based on problem solving and “developing the high-
level knowledge and skills needed to become an effective learner” [
19
], and the concept of
short task itself is based on providing an instructional unit for the CT pedagogy process.
It is important to emphasize that the short task is not limited to the task itself, but
includes the whole set of features, such as the background, reasoning behind the solution,
justification of the informatics aspects, and contains a certain structure based on a formal
pattern, which ultimately leads to the formation of a pool of tasks. The short task here is
a reservoir for informatics related content, while at the same time allowing CT pedagogy
to kick-start the problem-solving process, which is a bridge from biased to unbiased that

Mathematics 2022,10, 3194 9 of 30
leads to the replacement of misconceptions and the identification of valid heuristics for
coherent conceptual reasoning. All of these (challenge-based environment, CT pedagogy
and short-task instruction) form a set that is important to view and understand as a whole.
The Bebras Challenge focuses on short, multiple-choice quiz-style tasks. The “short”
here refers not to the possible short answer, as one might expect based on Gardner, but to
the length of the task and the time in which it must be solved. This instructional trick is
due to the challenge format, which encourages students to look for solutions on their own
without resorting to a computer or Internet search engines. On the other hand, the multiple-
choice format gives a kind of hint for the right solution, and the context itself simulates a
competitive environment to increase motivation to participate. Proper implementation of
the CT heuristic allows the right answer to be found. If the solution is not found during
the competition hours, follow-up observation and reflection simulates the Aha! insight in
understanding the correct answer. This connects CT and creativity, and provides a kind
of scaffolding for CT, promoting the rejection of misconceptions and biases that a student
may have.
2.13. Mental, Conceptual Models, Heuristics, and Aha! Convolution
Mental model can be defined as the “image of the world around us, which we carry
in our head” [
44
]. It is a model that is based on our experiences and beliefs, expectations,
and fears and is within the realm of the cognitive. It is usually the unconscious cause for
biased attitudes and actions based on heuristics, which, as demonstrated by Tversky and
Kahneman [
31
], do not always corresponds to the real state of affairs, and it is precisely
such biases that create obstacles to the development of conceptual models.
While mental models refer to the cognitive domain, the conceptual model, which
can be defined as a set of “simplified representations of real objects, phenomena, or situa-
tions”. [
45
] refer to the disciplinary domain. Therefore, the educator’s task is to provide
a bridge from a possibly biased mental model to a conceptual to mental model that is
represented by the disciplinary domain.
Heuristics can be defined as “mental shortcuts that allow individuals to quickly select
and apply schemas to new or ambiguous situations” [
46
]. It is important to understand
that heuristics usually originate from mundane norms and everyday experiences, and this
should be taken into account by the educator in appropriate pedagogical constructions.
The neural theory of Aha! creativity–is a concept developed by Taggard and Stew-
art [
26
,
47
] in studying the cognitive domain of mental model development. The most
important aspect for us is that such a convolution process is based specifically on mul-
timodal representations “encompassing information that can be visual, auditory, tactile,
olfactory, gustatory, kinesthetic, and emotional, as well as verbal” [
26
], which makes it
important for the instructional designer to arrange an appropriate environment for this
process to occur.
3. The Bebras Challenge for Scaffolding Computational Thinking
3.1. Computational Thinking: Towards Participatory Solutions
Historically, the introduction of the concept of CT has its origins in Seymour Papert,
who introduced CT in connection with the use of computers in reforming mathematics
education [
48
]. Computers, according to Papert, can provide great opportunities for a
deeper understanding of mathematical concepts, including an improved way of solving
and analyzing problems and tracing conceptual relationships between them. Worth men-
tioning is another approach presented by Vee [
49
]. She defines “computational literacy”
as the “mass” skill “to break a complex process down into small procedures and then
express or write those procedures using the technology of code that may be read by a
non-human entity such as a computer” [
49
]. However, it is still difficult to predict whether
programming as public literacy will become commonplace and if ever. Continuing the
historical retrospective of CT, the real popularity of the term and the concept started when
Jeannette Wing introduced a new look at the topic, namely considering CT as “a universally

Mathematics 2022,10, 3194 10 of 30
applicable attitude and skill set everyone, not just computer scientist, would be eager to
learn and use” [
30
]. From this, the history of CT as precondition for a mass computer
literacy began. To refine her definition, Wing provided a more specific one, proposing that
CT could be considered “as the thought processes involved in formulating problems and
their solutions so that the solutions are represented in a form that can be carried out by an
information-processing agent” [50].
Continuing such historical retrospective, we will further compare these approaches.
Both Papert and Wing developed the foundations of CT by foregrounding computers and
computation. Although Papert saw CT more as a tool to help develop “powerful ideas” [
20
]
and Wing focused on the cognitive and thought process, both emphasize the importance of
reasoning. While CT is being promoted as a computational tool, it is also being positioned,
according to Papert, as a cognitive tool to improve analytic and explanatory abilities or, even
more radically, according to Wing, as a new approach to problem formulation (a crucial
competence for which the innovation economy struggles). At the same time, both tried
to promote CT beyond computation, as a kind of mediator between cognition and the
information processing agent as introduced by Wing [30].
Despite the seeming similarities, the two approaches have some fundamental dif-
ferences. This may be one reason for the rather wide range of current views on CT [
51
]
and numerous attempts to develop some kind of “consensus” definition [
52
]. In general,
Wing focuses on a unidirectional approach focused on computer and computation imple-
mentation, asking “what would I have to do to get a computer to implement an existing
solution to the problem?” [
30
]. In contrast, Papert emphasizes a bi-directional approach,
giving computers a supporting role and emphasizing the importance of interdisciplinary
interaction between computers, CT and other problem-solving approaches, and allowing
alternative approaches at the intersection of computing and other disciplines to emerge
(for a broader discussion of the comparison of the two underlying approaches, see, e.g.,
Lodi and Martini [34]).
CT has received further attention from the world’s leading organizations supporting
education, such as the International Society for Technology in Education (ISTE) and the
Computer Science Teachers Association of America (CSTA). Both organizations made an
effort to conceptualize CT skills and create a set of CT teaching materials. As a result,
updated definitions of CT with a focus on skills and competencies were developed, defin-
ing CT as “data collection, data analysis, data representation, problem decomposition,
abstraction, algorithms and procedures, automation, parallelization and simulation” [
53
].
It is important to emphasize that, following Papert and Wing, such skills are positioned as
universal, not exclusively related to CS or science, technology, engineering, and mathemat-
ics (STEM), but enabling and enhancing broader and interdisciplinary participation in the
modern digital agenda.
In addition, ISTE gave the following “operational” definition for CT focused on
problem-solving: “formulating problems in a way that enables us to use a computer and
other tools to help solve them; logically organizing and analyzing data; representing
data through abstractions such as models and simulations; automating solutions through
algorithmic thinking (a series of ordered steps); identifying, analyzing, and implementing
possible solutions with the goal of achieving the most efficient and effective combination
of steps and resources; generalizing and transferring this problem-solving process to a
wide variety of problems” [
54
]. Further, some auxiliary agentic characteristics “[
. . .
] such
as confidence in dealing with complexity, persistence in working with difficult problems,
tolerance for ambiguity and ability to deal with open ended problems” were emphasized,
(www.csta.asm.org, cited in [
55
], accessed on 30 August 2022). Another area addressed
by CSTA has to do with the question of how to implement CT in K-12, educate and train
educators, and incorporate CT into curricula, targeting both the school and university
community [56].
Despite the popularity and wide acceptance of CT, some critical views still exist
(see, for example, [
57
]). The main objections are: (1) CT is simply a new name for a

Mathematics 2022,10, 3194 11 of 30
long history that was previously recognized as “algorithmic thinking”; (2) CT is simply a
renaming of the term “computer science”; (3) CT is more a practice, a set of heuristics, than
a foundational concept, and its roots go back many years, “evolved from ancient origins
over 4500 years ago to its present, highly developed, professional state” [9].
3.2. Bebras Challenge as a Global Endeavor
CT, considered as an intermediate between social literacy and specialized knowledge
of computer science, has contributed to the emergence of a new approach, the Bebras
(Lithuanian word for “beaver”) informatics challenge as a global challenge-based edu-
cational activity [
22
]. The Bebras challenge is founded by a research group from Vilnius
University in 2004. Currently 77 countries are in the Bebras network with over 3 million
students participating annually [
22
]. The event is held annually (main Bebras week in
November and second round in March), and the focus is on solving and discussing the
informatics-based tasks.
The challenge is conducted annually and in parallel in the schools of the participating
countries. Summarizing statistics are collected according to the results. The geography of
participants covers countries from all continents, such as Australia (20,790 participants in
2021 [
22
]), Canada (25,970), Israel (1594), Indonesia (26,831), Japan (5139), Malaysia (5235),
New Zealand (2756), Germany (428,857), Singapore (551), Taiwan (175,818), the United
States (102,115), and many other countries around the world with more than three million
participants worldwide [
22
]. The challenge is based on the creation of a playful, informal
educational environment (contact and online) that encourages students to engage in short,
interactive tasks presented in an engaging way [58].
In general, the challenge is aimed to engage and develop students’ interest in informat-
ics and CT in an attractive, informal school activity [
22
]. Years of experience organizing this
activity in more than 70 countries in previous years has confirmed a high level of acceptance
among participants, including children and teachers of all ages, and has promoted the
active involvement of female students [
36
]. The reason for this is that the task presents tra-
ditionally considered difficult-to-learn topics, such as informatics and programming [
59
], in
an engaging way, focusing on problem-solving activities presented as a specially designed
and challenging task. The design requirements include items such as the content of the
assignment should be related to one or more informatics concepts and presented in such a
way as to exclude comprehensive technical aspects. At the same time, it should be solvable
in a few minutes and have attractive problem content.
Teaching informatics and programming is a complex task that requires a systematic
and holistic approach to educational efforts in order to succeed [
59
]. Thus, it is important
to focus on different ages, starting at a very early age. Bebras provide this opportunity,
covering virtually all groups of students from elementary school through high school, and
include the following age groups [
22
]: Mini Beavers (grades 3–4), Benjamin (grades 5–6),
Cadets (grades 7–8), Juniors (grades 9–10), and Seniors (grades 11–12). At the same time,
teachers have the opportunity to assess students and cross-check their teaching methods
against the country, the region, or even the world.
Another important point to emphasize is that the challenge provides a place for the
emergence of relevant communities, including global communities of students of interest
and professional communities of educational practitioners and university theorists. At
the same time, the challenge encourages broad public participation, including parents,
funders, and educational policymakers. This motivates an in-depth look at the problems
and challenges of informatics education, as well as a rethinking and redesigning of teaching
materials and curricula for more engaged informatics teaching.
One more attractive feature of the task is that the emphasis is not on competition, but
on participation. For example, problem-solving in pairs (e.g., Germany) or in teams is
encouraged. In general, the goal of the contest is to encourage problem-solving activities
and “storming of the mind”, including activities of discussion and communication with
peers and teachers.

Mathematics 2022,10, 3194 12 of 30
The results allow evaluation of various aspects of student performance, including a
comparative study of different teaching methods as well as comparisons between countries
on the same activity. For example, it has been observed that pairs perform better than
single students [
60
,
61
]. Another interesting trend relates to the problem of why women
are an underrepresented group in informatics. A study of the task results confirmed the
problem and may provide insight into how to design an informatics course that remains
appealing and motivating to female students throughout their school years. For example,
a comparison of girls and boys between the ages of 10–13 showed that girls were not
inferior to boys at this age [
62
]. As for junior high school students, an international study
showed that “there was no significant difference between boys and girls” [
63
], but that in
high school boys began to outperform girls in problem-solving results. This showed the
direction for improving the informatics curriculum, as it is very important to look for the
right motivation and tasks that appeal to girls [64,65].
3.3. Mindstorming Short Tasks—A Pathway towards CT Mindset
The concept of a short task to introduce schoolchildren to the central ideas, principles,
and concepts of informatics/computer science was introduced in the Bebras challenge
many years ago. This kind of microlearning serves well to motivate students’ interest in
various informatics topics. Short tasks and small problem-solving activities help students
and teachers develop CT skills while also promoting an interest in informatics [
7
]. One
of the most important requirements is that these short tasks should not necessitate any
prior knowledge of computer programming or informatics. This means that students
should construct their informatics knowledge and mental structures by actively solving
these tasks.
When solving short tasks, students need to think about information, data, algorithms,
computations, data structures, data processing, programming constructs, and many other
informatics concepts and principles. In more than 20 years of experience working with the
concept of short tasks for the Bebras challenge, thousands of such short tasks have been
created and used on various informatics concepts. In addition, Bebras tasks are used as a
tool to assess CT skills [66–68].
A typical short task consists of a title, a description (body), one or more questions,
the reasoning behind the solution(s), and most importantly includes an explanation of the
concepts used in the task–named “It’s Informatics” and other official information (see the
Bebras task template presented in Figure 2).
The basic idea behind the Bebras assignment concept is that it is a collaborative effort
between informatics educators from each participating country. This is important because
any effective educational solution must be integrated into the local educational content and
fit into the local educational culture, which is unique in each case. However, to maintain
a coordinated approach, a joint event, the international Bebras Workshop, is organized
annually [
22
]. The aim of the workshop is to develop a collaborative strategy, review the
state of the art, and develop a pool of tasks to be shared among community members. Tasks
are categorized by levels of difficulty (easy, medium, difficult) and can be positioned as
corresponding to high cognitive skill domains according to Bloom’s taxonomy [63].
The purpose of task design is to encourage creativity and support conceptual un-
derstanding of informatics and programming. Despite its apparent simplicity, the design
process is quite complex, since it is based on a set of formal requirements in the form
of mandatory criteria that are met by a number of educational experts who form an in-
ternational team of task creators. Some of the mandatory criteria are as follows: (1) the
problem must be completed in three minutes or less; the problem statement must be easy
to understand; (2) presented on a single screen; (3) solvable as presented without the
use of additional software or paper and pencil; (4) independent of specific computing
systems [22].

Mathematics 2022,10, 3194 13 of 30
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Figure 2. Template for creating a short Bebras task. Retrieved by permission from www.bebras.org
(accessed on 24 February 2022).
The basic idea behind the Bebras assignment concept is that it is a collaborative effort
between informatics educators from each participating country. This is important because
any effective educational solution must be integrated into the local educational content and
fit into the local educational culture, which is unique in each case. However, to maintain a
coordinated approach, a joint event, the international Bebras Workshop, is organized annu-
ally [22]. The aim of the workshop is to develop a collaborative strategy, review the state of
the art, and develop a pool of tasks to be shared among community members. Tasks are
categorized by levels of difficulty (easy, medium, difficult) and can be positioned as corre-
sponding to high cognitive skill domains according to Bloom’s taxonomy [63].
The purpose of task design is to encourage creativity and support conceptual under-
standing of informatics and programming. Despite its apparent simplicity, the design pro-
cess is quite complex, since it is based on a set of formal requirements in the form of man-
datory criteria that are met by a number of educational experts who form an international
team of task creators. Some of the mandatory criteria are as follows: (1) the problem must
be completed in three minutes or less; the problem statement must be easy to understand;
(2) presented on a single screen; (3) solvable as presented without the use of additional
software or paper and pencil; (4) independent of specific computing systems [22].
Figure 2.
Template for creating a short Bebras task. Retrieved by permission from www.bebras.org
(accessed on 24 February 2022).
The idea of task design is based on the concept of microlearning [
23
] as applied to
informatics training and problem solving. The emphasis is not on technical details, but on a
deeper conceptual understanding of the ideas and principles that underlie the information
system. In fact, the task involves a combination of some static and interactive design
elements combined to provide easily visible and understandable content. At the same time,
the task should be solvable with mental effort and a reasoning process that does not require
any additional tools, such as paper or pen, as all the necessary information is presented on
the computer screen and only a few reasoning steps are required to solve it, because a short
task is usually designed as a multiple-choice question.
Another important aspect to be addressed in the task design process is how to design
content that is related to the concept of informatics and simultaneously elicits an emotional
response from students in the form of excitement and fun. This is because only personal
involvement in a new, previously unseen situation can provide the emotionally rich context

Mathematics 2022,10, 3194 14 of 30
necessary for creativity to emerge. The designer’s approach is to be involved in a kind
of simulated reflection, trying to emulate the conditions and approaches the child will
encounter and apply in solving the problem.
Although implementation requires a lot of effort, the interactivity inherited from the
task is very important because it enables a sort of virtual communication while solving the
task. At the same time, it embeds the content in a playful environment with which students
are already familiar, thereby maintaining their confidence and providing a kind of virtual
scaffolding for communicating with the content. Attractive content is critical to successful
task development.
At the same time, it is important to design content in such a way that it reflects real-life
concerns, including examples and supported by data related to scientific and societal issues.
To ensure this requirement, in addition to the individual assignment development process,
an accompanying process of selecting the most appropriate assignment is organized. In the
selection process, educational experts consider various aspects of the assignment in terms
of education and attractiveness.
To maintain consistency with the informatics curriculum, informatics-related content,
including basic informatics concepts such as algorithms and data structures, should be
incorporated into the task content. This provides a parallel venue for informatics teacher
training. This training, in addition to the annual Bebras workshop, takes the form of local
workshops and online conferences where teachers can independently test their knowledge
and conceptual understanding of informatics content that the task creation process requires.
A further important aspect is that the pedagogical design of the problem focuses on
formulating it in such a way that it “can be answered without prior knowledge of CS” [
69
].
This is important because, first, it allows us to attract a broad range of students who do not
study informatics at school, and second, it stimulates new ways of reasoning that lead to
a deeper conceptual understanding rather than simply memorizing already known facts.
To ensure high-quality content, the competition implemented a selection procedure in
which assignments are discussed, evaluated, and selected by members of the professional
community-experts in pedagogical task design–to meet a number of formal requirements,
including attractiveness, creativity, and CT support.
4. Materials and Methods
4.1. The Purpose of the Study
The purpose of the study is to explore the concept of the short task in terms of CT and
contest-based education based on the context of the Bebras Challenge. We are particularly
interested in the principles of effective pedagogical design that leads to overcoming biases
in CT heuristics that the child may have. The idea is that while solving the quizzes, the
child, using constructionist and peer-supported trial-and-error methods, will move toward
finding the right solution and eventually acquire unbiased CT-related heuristics, discarding
the misconceptions and incorrect preconceptions that they are likely to have. Specifically,
we explore the connections between biased and unbiased heuristics [
29
,
70
] and the mental
and conceptual model [
45
] that the child will operate and construct during problem solving.
In addition, we emphasize the role of the Aha! insight [
26
,
43
] as the impetus for the
eventual formation of conceptual understanding.
4.2. Methodological Assumptions
To further clarify the methodology, we discuss the difference between the analog and
digital entities in relation to cognition and learning, while defining the place of CT in this
landscape (Figure 3).

Mathematics 2022,10, 3194 15 of 30
Mathematics 2022, 10, x FOR PEER REVIEW 15 of 30
discarding the misconceptions and incorrect preconceptions that they are likely to have.
Specifically, we explore the connections between biased and unbiased heuristics [29,70]
and the mental and conceptual model [45] that the child will operate and construct during
problem solving. In addition, we emphasize the role of the Aha! insight [26,43] as the im-
petus for the eventual formation of conceptual understanding.
4.2. Methodological Assumptions
To further clarify the methodology, we discuss the difference between the analog and
digital entities in relation to cognition and learning, while defining the place of CT in this
landscape (Figure 3).
Figure 3. Empowering the learning landscape with CT (elaborated by the authors).
The methodology we implement is based on such concepts as “mental simulation”,
“mental model”, “conceptual model”, “modelling” and “heuristics”, which form an edu-
cational discourse that allows for purposeful learning practice. The following remarks
should be made. The cognitive domain is related to practices such as mental modelling
and mental simulations, while the disciplinary domain is related to conceptual modelling
and computer simulations [45]. Mental models do not “end up as a perfect copy of con-
ceptual models” [45]; they are mostly heuristic, aimed at interpretation and prediction. In
general, these models can be seen as an “analogical structure” [71], seen as a mediator for
communication with analog and probabilistic world. Conceptual models, by contrast, are
propositional, logically constructed models. While the conceptual model can be consid-
ered as a simplified representation of the phenomenon under study, the mental model
“represents” the learner herself, her beliefs, biases, or fears (see, for example, [70]), aimed
at making analogies, creating mental simulations, making idealizations and general ab-
stractions [45].
We can consider the learning process itself as an attempt to “construct mental models
that are coherent with the conceptual models” [45] in the process of such construction
based on a kind of “simulation heuristics” [70,72]. At the same time, understanding the
features and issues associated with “mental models would allow us to understand why
the so-called misconceptions resist change so much” [45] (on the meaning and discussion
on misconceptions in relation to informatics and CT, see, for example, [73–75]).
As an example, considering the probabilistic context, the goal of the heuristics is [70]:
prediction; assessing the probability of a specified event, estimating conditioned proba-
bilities, counterfactual assessments, and assessments of causality. It is important to em-
phasize that, in practice, this heuristic is based on “explicit construction of scenarios” [70]
and “should be subject to characteristic errors and biases” [70]. The biases the learner is
Figure 3. Empowering the learning landscape with CT (elaborated by the authors).
The methodology we implement is based on such concepts as “mental simulation”,
“mental model”, “conceptual model”, “modelling” and “heuristics”, which form an ed-
ucational discourse that allows for purposeful learning practice. The following remarks
should be made. The cognitive domain is related to practices such as mental modelling
and mental simulations, while the disciplinary domain is related to conceptual modelling
and computer simulations [
45
]. Mental models do not “end up as a perfect copy of con-
ceptual models” [
45
]; they are mostly heuristic, aimed at interpretation and prediction.
In general, these models can be seen as an “analogical structure” [
71
], seen as a mediator
for communication with analog and probabilistic world. Conceptual models, by con-
trast, are propositional, logically constructed models. While the conceptual model can
be considered as a simplified representation of the phenomenon under study, the mental
model “represents” the learner herself, her beliefs, biases, or fears (see, for example, [
70
]),
aimed at making analogies, creating mental simulations, making idealizations and general
abstractions [45].
We can consider the learning process itself as an attempt to “construct mental models
that are coherent with the conceptual models” [
45
] in the process of such construction
based on a kind of “simulation heuristics” [
70
,
72
]. At the same time, understanding the
features and issues associated with “mental models would allow us to understand why the
so-called misconceptions resist change so much” [
45
] (on the meaning and discussion on
misconceptions in relation to informatics and CT, see, for example, [73–75]).
As an example, considering the probabilistic context, the goal of the heuristics is [
70
]:
prediction; assessing the probability of a specified event, estimating conditioned probabili-
ties, counterfactual assessments, and assessments of causality. It is important to emphasize
that, in practice, this heuristic is based on “explicit construction of scenarios” [
70
] and
“should be subject to characteristic errors and biases” [
70
]. The biases the learner is con-
cerned about “are characteristics of the cognitive operations by which impressions and
judgments are formed” [31].

Mathematics 2022,10, 3194 16 of 30
It should further be noted that “people apply heuristic rules to their has no deliberate
to fallible impressions” and “have little deliberate control over the process by which these
impressions are formed” [
31
]. Most important for us within the purpose of this study,
in order to analyze the pedagogical process of designing the short task, is the following
statement: even though people cannot consciously control their emotions, “they can learn to
identify the heuristic processes that determine their impressions, and to make appropriate
allowances for the biases to which they are liable” [31].
This allows us to formulate the main pedagogical principles underlying the design
of a short task: effective design should allow learners to overcome biases to identify valid
heuristics to coherent conceptual reasoning. This is based on processes of strong emotional
involvement and socialization that provide a kind of trigger to reconfigured biased cognitive
structures within a combined challenge-based and constructionist learning process.
4.3. Research Approach
As a research approach, we employ networking of theories [
76
]. In general, the
integration of theories provides the basis for comprehensive analyses conducted in an
interdisciplinary research environment such as educational research. The approach is
based on combining underlying theoretical principles (P), methods (M), and paradigmatic
research questions (Q) [
77
] in order to deepen understanding of the problem, analyzing the
issue from different theoretical and methodological perspectives, resulting in an improved
theoretical construct.
This “can lead to deepening insight into a problem and to methodologically reflecting
the process of connecting theories” [
76
] and at the same time provides an approach to the
emergence of research results. To develop our study, in addition to the theoretical analysis,
we conduct a qualitative case study [
78
]. We explore conceptual aspects of the pedagogical
design of short tasks by conducting a semantic analysis of a number of practical examples
of such tasks, exploring their internal structure. As a part of this analysis, we develop a
conceptual understanding focusing on transferability and universality to develop students’
CT competences and skills, resulting in a kind of CT mindset.
There were no specific selection criteria; random tasks were chosen for analysis.
However, tasks in which it was difficult to identify a set of underlying heuristics were
excluded from the selection. A table with five columns, namely heuristics (biased, unbiased,
CT) and model/Process (mental, conceptual), was developed as a qualitative data collection
tool in order to extract implicit information that we expect may be embedded in the task
design. At the same time, the goal of such qualitative data analysis was to demonstrate an
approach to task design.
An interesting aspect is that the research approach is pragmatic rather than theoretical
in that it provides a set of research tools that, in our case, can be transformed into method-
ological tools for instructional scaffolding of CT. In practice, this is based on the inherent
feature of instruction as pragmatist [79] reflection of pedagogy (theory) and learner’s cog-
nition (beliefs). This is consistent with the practice of networking theories of “producing
concepts with an empirical load that is not empty” ((Jungwirth, 2009) as cited in [
76
]). A
coherent set of principles and methods leads to the following paradigmatic questions for the
development of the networking of theories construct: (Q1) What is the interconnection at
the cognitive level-identifying inherent heuristics and associated models? (Q2) What is the
interconnection at the pedagogical level-identifying the transition of models? (Q3) What is
the interconnection at the task design level-identifying the interplay of concepts? A general
view of the implemented methodology is presented in Figure 4.

Mathematics 2022,10, 3194 17 of 30
Mathematics 2022, 10, x FOR PEER REVIEW 17 of 30
Figure 4. General overview of the implemented methodology (elaborated by the authors).
5. Results and Discussion
This section is organized as follows. We begin with the results, where we process
some samples of short tasks in order to identify inherent heuristics and associated models,
situating CT as an approach that allows a smooth transition from biased to unbiased and
from mental to conceptual. The purpose of this is to demonstrate the extraction procedure
and to provide a tool for an instructor to practice scaffolding. We make no claim for an in-
depth analysis; this is simply an outline demonstrating an approach that can be applied
and tested in practice. This is followed by a discussion that raises more complex questions,
demonstrating interrelationships at the cognitive level and revealing the transition of
models as well as at the task design level and identifying the interplay of concepts. This
provides an introductory discourse and emphasizes the interconnectedness of the con-
cepts, which will facilitate more comprehensive design of short tasks aimed at the devel-
opment of CT.
5.1. Results: Processing a Short Task to Scaffold CT Mindset
As mentioned above, the purpose of the analysis is to demonstrate how CT heuristics
support the transition from mental to conceptual and from biased to unbiased. This can
serve as a guide for scaffolding of CT in the practice of task design. To demonstrate this,
several illustrative examples from Bebras challenge short tasks were examined and pro-
cessed. The aim of such examination is to extract interconnection at the instruction level–
identifying inherent heuristics and associated models. We will start with an illustrative
example of the following short task for young (8–10 years old) children (see Figure 5). The
Figure 4. General overview of the implemented methodology (elaborated by the authors).
5. Results and Discussion
This section is organized as follows. We begin with the results, where we process
some samples of short tasks in order to identify inherent heuristics and associated models,
situating CT as an approach that allows a smooth transition from biased to unbiased and
from mental to conceptual. The purpose of this is to demonstrate the extraction procedure
and to provide a tool for an instructor to practice scaffolding. We make no claim for an
in-depth analysis; this is simply an outline demonstrating an approach that can be applied
and tested in practice. This is followed by a discussion that raises more complex questions,
demonstrating interrelationships at the cognitive level and revealing the transition of
models as well as at the task design level and identifying the interplay of concepts. This
provides an introductory discourse and emphasizes the interconnectedness of the concepts,
which will facilitate more comprehensive design of short tasks aimed at the development
of CT.
5.1. Results: Processing a Short Task to Scaffold CT Mindset
As mentioned above, the purpose of the analysis is to demonstrate how CT heuristics
support the transition from mental to conceptual and from biased to unbiased. This can
serve as a guide for scaffolding of CT in the practice of task design. To demonstrate
this, several illustrative examples from Bebras challenge short tasks were examined and
processed. The aim of such examination is to extract interconnection at the instruction level–
identifying inherent heuristics and associated models. We will start with an illustrative
example of the following short task for young (8–10 years old) children (see Figure 5). The
aim of the study is to provide insight into the design structure in relation to the theoretical
considerations previously described (see Section 4). The results are presented in Table 1.

Mathematics 2022,10, 3194 18 of 30
Mathematics 2022, 10, x FOR PEER REVIEW 18 of 30
aim of the study is to provide insight into the design structure in relation to the theoretical
considerations previously described (see section 4). The results are presented in Table 1.
The presented analysis makes it possible to assess directions for further improvement
of the task design. First, the advantage of the design is that the picture is colorful, pleasant
design, allowing you to respond emotionally [80], while evoking emotional responses to
the biases described earlier. The issue to discuss is that the branding is quite formal. If the
branding were real, it would allow students to group items by brand before the elimina-
tion process occurs. This illustrates the importance of accounting for the mindset that must
be developed in the task-solving process by replacing biased heuristics with unbiased
ones that are consistent with the target conceptual model.
Figure 5. A sample of the Bebras short task on logics for primary level (age 8–10). Retrieved by
permission from www.bebras.org (accessed on 24 February 2022).
Table 1. A case of the Bebras short task on logics aimed at scaffolding CT mindset (elaborated by
the authors).
Heuristics Model/Process
Biased Unbiased CT Mental Conceptual
Usually goods, clothes are
judged emotionally by
fashion, color, design, or
indirect evaluation (“it
suits me”). This forms a
barrier to the transition
from a humanitarian, artis-
tic point of view to a digi-
tal and technological one.
Even fashion
items are “tech-
nological objects”
so they have ele-
ments and as-
pects that can be
meas-
ured/counted.
Even textual de-
scriptions can be
combined into
compound state-
ments that allow
for a binary as-
sessment (“true”
or “false”).
Construction of a
composite logical
statement in accord-
ance with the prem-
ises, grouping tasks
(by brand), evalua-
tion and exclusion
of inappropriate ele-
ments.
Logical statements: AND, OR,
NOT. Formal logic, evaluation of
logical statements. Application
to mathematics and engineering.
Logical reasoning: combining
various non-mathematical asser-
tions and ordinary assertions as
a set of initial conditions to build
a model based on technology.
The second example of a short task refers to the pre-primary level (age 5–8) and is an
illustrative example of a short task related to CT (Figure 6). The structure of the task design
according to the Bebras short task mindset model is presented in Table 2.
Figure 5.
A sample of the Bebras short task on logics for primary level (age 8–10). Retrieved by
permission from www.bebras.org (accessed on 24 February 2022).
Table 1.
A case of the Bebras short task on logics aimed at scaffolding CT mindset (elaborated by
the authors).
Heuristics Model/Process
Biased Unbiased CT Mental Conceptual
Usually goods, clothes
are judged emotionally
by fashion, color,
design, or indirect
evaluation (“it suits
me”). This forms a
barrier to the transition
from a humanitarian,
artistic point of view to
a digital and
technological one.
Even fashion items are
“technological objects”
so they have elements
and aspects that can be
measured/counted.
Even textual
descriptions can be
combined into
compound statements
that allow for a binary
assessment (“true”
or “false”).
Construction of a
composite logical
statement in
accordance with the
premises, grouping
tasks (by brand),
evaluation and
exclusion of
inappropriate elements.
Logical statements:
AND, OR, NOT.
Formal logic,
evaluation of
logical statements.
Application
to mathematics
and engineering.
Logical reasoning:
combining various
non-mathematical
assertions and ordinary
assertions as a set of
initial conditions to
build a model based
on technology.
The presented analysis makes it possible to assess directions for further improvement
of the task design. First, the advantage of the design is that the picture is colorful, pleasant
design, allowing you to respond emotionally [
80
], while evoking emotional responses to
the biases described earlier. The issue to discuss is that the branding is quite formal. If the
branding were real, it would allow students to group items by brand before the elimination
process occurs. This illustrates the importance of accounting for the mindset that must be
developed in the task-solving process by replacing biased heuristics with unbiased ones
that are consistent with the target conceptual model.

Mathematics 2022,10, 3194 19 of 30
The second example of a short task refers to the pre-primary level (age 5–8) and is an
illustrative example of a short task related to CT (Figure 6). The structure of the task design
according to the Bebras short task mindset model is presented in Table 2.
Mathematics 2022, 10, x FOR PEER REVIEW 19 of 30
Figure 6. A sample of the Bebras short task on pattern matching for pre-primary level (age 5–8).
Retrieved with permission from www.bebras.org (accessed on 24 February 2022).
Table 2. A case of the Bebras short task on pattern matching aimed at scaffolding CT mindset (elab-
orated by the authors).
Heuristics Model/Process
Biased Unbiased CT Mental Conceptual
Nowadays children are accus-
tomed to the environment of
cartoons, which influences
their behavior [81]. It is usu-
ally associated with emotions,
actions, way of communica-
tion and play activities. This
emotional context can be a
barrier on the way from emo-
tional to logical, evaluative
behavior.
Even a cartoon
character has a
pronounced emo-
tional coloring
,
in
an informatics con-
text they are repre-
sented by a dataset
associated with
their numerous
characteristics.
Even virtual
entities can be
processed by a
set of inherent
data enabling
logical/algorith-
mic data pro-
cessing process.
Construction of
appropriate de-
scriptions asso-
ciated with the
representation
of colors,
shapes, behav-
ior.
Construction of clustering algo-
rithms. The clustering process is
possible even for different kind of
virtual entities. Connection/classifi-
cation is based on abstract geomet-
ric concepts. However, it can be
based on various descriptive con-
cepts represented by a dataset.
It is possible to formulate the following observations on the pedagogical design of
the task. An advantage is the implementation of a cartoon environment already familiar
to the child, colorful characters that provide an emotional phone to trigger biased mental
models. The direction for design is related to the clustering algorithm, a conceptual un-
derstanding of which the task is aimed to develop. Since there is only one representative
in each category, the direction might be to present more representatives of each group to
provide more advanced clustering in the same short task context.
Another example relates to optimization problem, optimization algorithms and
graphs (Figure 7) and relates to the secondary level (age 12–14). The structure of the task
design according to the Bebras short task mindset model is presented in Table 3.
Figure 6.
A sample of the Bebras short task on pattern matching for pre-primary level (age 5–8).
Retrieved with permission from www.bebras.org (accessed on 24 February 2022).
Table 2.
A case of the Bebras short task on pattern matching aimed at scaffolding CT mindset
(elaborated by the authors).
Heuristics Model/Process
Biased Unbiased CT Mental Conceptual
Nowadays children are
accustomed to the
environment of
cartoons, which
influences their
behavior [81]. It is
usually associated with
emotions, actions, way
of communication and
play activities. This
emotional context can
be a barrier on the way
from emotional
to logical,
evaluative behavior.
Even a cartoon
character has a
pronounced emotional
coloring, in an
informatics context
they are represented by
a dataset associated
with their numer-
ous characteristics.
Even virtual entities
can be processed by a
set of inherent data
enabling logi-
cal/algorithmic data
processing process.
Construction of
appropriate
descriptions associated
with the representation
of colors,
shapes, behavior.
Construction of
clustering algorithms.
The clustering process
is possible even for
different kind of virtual
entities. Connec-
tion/classification is
based on abstract
geometric concepts.
However, it can be
based on various
descriptive concepts
represented by
a dataset.
It is possible to formulate the following observations on the pedagogical design of the
task. An advantage is the implementation of a cartoon environment already familiar to the
child, colorful characters that provide an emotional phone to trigger biased mental models.
The direction for design is related to the clustering algorithm, a conceptual understanding

Mathematics 2022,10, 3194 20 of 30
of which the task is aimed to develop. Since there is only one representative in each
category, the direction might be to present more representatives of each group to provide
more advanced clustering in the same short task context.
Another example relates to optimization problem, optimization algorithms and graphs
(Figure 7) and relates to the secondary level (age 12–14). The structure of the task design
according to the Bebras short task mindset model is presented in Table 3.
Mathematics 2022, 10, x FOR PEER REVIEW 20 of 30
Figure 7. A sample of the Bebras short task on optimization for secondary level (age 12–14). Re-
trieved by permission from www.bebras.org (accessed on 24 February 2022).
Table 3. A case of the Bebras short task on optimization problem aimed at scaffolding CT mindset
(elaborated by the authors).
Heuristics Model/Process
Biased Unbiased CT Mental Conceptual
The context associated with
nature, and insects in partic-
ular, is always emotional
[82], so the process of reflec-
tion that supports such tasks
involving mathematical
problems is disrupted by
this emotional context.
We should model the
flow, by mentally con-
sidering cartoon ants
and their movements as
abstract members of the
flow independently of
their size and appear-
ance.
A continuous dy-
namic flow can
be modeled by
discretization
and computation
at each discrete
step.
Flow modeling by men-
tally observing the move-
ments of ants, considering
the natural queue as part
of the flow, mostly analog
representation, mentally
modeling the analog repre-
sentation
Construction of a
discrete model, dis-
crete simulation, ap-
plication of logical
reasoning and opti-
mization algorithms
The following observations can be made about the pedagogical design of the task.
Although the task is related to a mathematical problem, it is immersed in personally
meaningful content as an application to the experience that everyone had while visiting
the forest, observing ants in an anthill. At the same time, water and the water stones are a
familiar context for Lithuanian students (the region where the task was composed). To
make the task more emotionally responsive, it could be reworded to include some alter-
natives for crossing a water barrier, such as inside and outside a straw, which would make
the task more probabilistic, since crossing always involves the risk of falling into the wa-
ter, which is not present in the current task wording.
5.2. Discussion: Bebras Short Task for CT Mindset as an Interplay of Heuristics and Modelling
In general, the mindset we study is anchored in a number of key concepts, the inter-
play of which is a key driver of creativity corresponding to CT education. At the same
time, it forms the discursive landscape of our study. These concepts are creativity, mental
modelling, grounding and scaffolding, CT and constructivist/constructionist’s educa-
tional context. To systematize this insight, the corresponding discussion questions are
next posted: Why the challenge in relation to educational environment? Why mindstorm-
ing in relation to creativity? Why computational thinking in relation to creative mindset?
Why design a task for the interplay of concepts?
Figure 7.
A sample of the Bebras short task on optimization for secondary level (age 12–14). Retrieved
by permission from www.bebras.org (accessed on 24 February 2022).
Table 3.
A case of the Bebras short task on optimization problem aimed at scaffolding CT mindset
(elaborated by the authors).
Heuristics Model/Process
Biased Unbiased CT Mental Conceptual
The context associated
with nature, and insects
in particular, is always
emotional [82], so the
process of reflection
that supports such
tasks involving
mathematical problems
is disrupted by this
emotional context.
We should model the
flow, by mentally
considering cartoon
ants and their
movements as abstract
members of the flow
independently of their
size and appearance.
A continuous dynamic
flow can be modeled
by discretization and
computation at each
discrete step.
Flow modeling by
mentally observing the
movements of ants,
considering the natural
queue as part of the
flow, mostly
analog representation,
mentally modeling the
analog representation
Construction of a
discrete model, discrete
simulation, application
of logical reasoning and
optimization algorithms
The following observations can be made about the pedagogical design of the task.
Although the task is related to a mathematical problem, it is immersed in personally
meaningful content as an application to the experience that everyone had while visiting
the forest, observing ants in an anthill. At the same time, water and the water stones
are a familiar context for Lithuanian students (the region where the task was composed).
To make the task more emotionally responsive, it could be reworded to include some
alternatives for crossing a water barrier, such as inside and outside a straw, which would
make the task more probabilistic, since crossing always involves the risk of falling into the
water, which is not present in the current task wording.

Mathematics 2022,10, 3194 21 of 30
5.2. Discussion: Bebras Short Task for CT Mindset as an Interplay of Heuristics and Modelling
In general, the mindset we study is anchored in a number of key concepts, the interplay
of which is a key driver of creativity corresponding to CT education. At the same time,
it forms the discursive landscape of our study. These concepts are creativity, mental
modelling, grounding and scaffolding, CT and constructivist/constructionist’s educational
context. To systematize this insight, the corresponding discussion questions are next posted:
Why the challenge in relation to educational environment? Why mindstorming in relation
to creativity? Why computational thinking in relation to creative mindset? Why design a
task for the interplay of concepts?
5.2.1. Why the Challenge in Relation to the Educational Environment?
In answering this question, we will first analyze how some “powerful ideas” [
20
]
can support our vision of education. Constructivism “summarizes the epistemological
view that knowledge is built by individuals” [
83
]. The constructivist teacher serves as a
mediator between educational content and the learner. At the same time, this construc-
tion of knowledge is linked to a learning context rooted in the cultural, the social and
the ethnical. Such an educational context is not a predetermined, but an evolving and
emerging phenomenon that is an object for the instructional designer to influence. The
goal is to facilitate a cognitive conceptual shift, from non-systematic and experience-related
knowledge towards scientist alike mindset. The idea for instruction is a developmentalist
approach based on “ability to extract rules from empirical regularities and to build cogni-
tive invariants” [
39
], effectively reflecting the positivist view of a systematically organized
world to be discovered through interaction.
How to position a non-formal educational environment such as the Bebras chal-
lenge [
7
,
17
] from the point of view of the constructivism educational theory? Is it possible
the cognitive invariants to be developed and the processes of cognitive development of a
child [
84
] to be effectively instructed? In any case, informatics, as a scientific discipline, is
based on its own and related foundations, laws, methods, etc. which requires providing
guidance for the learning process. Moreover, as Kirschner et al. argue, “it may be an error
to assume that the pedagogic content of the learning experience is identical to the methods
and processes (i.e., the epistemology) of the discipline being studied and a mistake to
assume that instruction should exclusively focus on application” [
85
]. To discover abstract
disciplinary meanings, learning must support a process of “separateness through progres-
sive decentration as a necessary step toward reaching deeper understanding” [
39
]. Can
we really achieve this by focusing on non-formal educational settings such as informatics
challenges? The following discussion aims to clarify this question.
Papert’s constructionism [
21
,
39
] actually advances a pragmatist agenda, conclud-
ing that knowledge is always a matter of experience, of personal engagement with the
phenomenon being studied and, as a consequence, context-dependent. Cognitive devel-
opment takes place in a continues dynamic of change, “experiencing a momentary sense
of loss” [
39
], and a challenge-based environment suits this best. In practice there should
be an integration of these two approaches. In this sense, such a non-formal educational
environment can be positioned as a kind of integrative means between detachment and
situated immersion. However, it should be rather shortsighted to position a challenge
based educational environment as a “non-guiding”. The process of scaffolding is inherent
and integrated into this non-formal environment (Figure 8), thereby providing appropriate
instructional guidance [17].

Mathematics 2022,10, 3194 22 of 30
Mathematics 2022, 10, x FOR PEER REVIEW 21 of 30
5.2.1. Why the Challenge in Relation to the Educational Environment?
In answering this question, we will first analyze how some “powerful ideas” [20] can
support our vision of education. Constructivism “summarizes the epistemological view
that knowledge is built by individuals” [83]. The constructivist teacher serves as a media-
tor between educational content and the learner. At the same time, this construction of
knowledge is linked to a learning context rooted in the cultural, the social and the ethnical.
Such an educational context is not a predetermined, but an evolving and emerging phe-
nomenon that is an object for the instructional designer to influence. The goal is to facili-
tate a cognitive conceptual shift, from non-systematic and experience-related knowledge
towards scientist alike mindset. The idea for instruction is a developmentalist approach
based on “ability to extract rules from empirical regularities and to build cognitive invar-
iants” [39], effectively reflecting the positivist view of a systematically organized world to
be discovered through