Creative Education
2013. Vol.4, No.9, 557-562
Published Online September 2013 in SciRes (http://www.scirp.org/journal/ce) http://dx.doi.org/10.4236/ce.2013.49081
Algorithmics for Preschoolers—A Contradiction?
Roland T. Mittermeir
Institute for Informatics-Didactics, Universität Klagenfurt, Klagenfurt, Austria
Received May 23rd, 2013; revised June 23rd, 2013; accepted July 1st, 2013
Copyright © 2013 Roland T. Mittermeir. This is an open access article distributed under the Creative Commons
Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the
original work is properly cited.
Developing an algorithm requires expressing it in some (formal) language. The respective language is
usually understood to be textual (conventional programming language) or partly graphical (design lan-
guages, and languages in programming environments for children). As writing and reading are capabili-
ties not to be presumed from preschoolers, many educators claim that confronting such young kids with
algorithmic concepts is beyond their abstraction capability. This paper reports on an experiment with
kindergarten-groups requiring them to discover simple algorithms without resorting to reading and writ-
ing. It clearly showed that limited capabilities of abstractions are not a hurdle at all, if the problems are
posed in a way corresponding to the limited experience base of the children, and if solutions are small
enough to be kept in memory and allow expressing themselves in other forms than writing.
Keywords: Algorithmics; Preschoolers; Capability for Expressing Algorithms; Capability for Abstracting
Motivation and Background
The experiments reported here took place within a funded
project, Informatik erLeben, requiring that at least three age-
groups are involved. These age groups could range from kin-
dergarten via primary schools (Grades 1 to 4; age group: 6 to 10)
to secondary schools I (Grades 5 to 8 or 9) or to secondary
schools II (Grades 9 to 12 or 13).
The aim of the project has been to show pupils and school-
students that Informatics is a technical subject resting on a sci-
entific background of science, physics and mathematics and has
also developed its own distinct contributions in theoretical and
applied Computer Science. Thus, informatics is more than push-
ing buttons on a laptop or on a modern cell-phone; and the lat-
ter is being quite often the core of informatics instruction in
school. Sometimes, fair enough, these topics are labeled as
ICT-instruction. In some countries, Austria being one of them,
unfortunately this instruction is performed under the label “In-
formatics instruction” with “Informatics” referred to as local
synonym for Computer Science (which it is, when comparing
university studies).
In a number of countries movements are against such seman-
tic bending of the term “Informatics” and discussions as to what
kind of knowledge should be introduced in the standard school
curriculum emerged and led to a reversal of this trend. Respec-
tive arguments can be found in documents emanating from pro-
fessional and/or learned societies (c.f. Wilson et al., 2010; Fur-
ber et al., 2012). Engraining algorithmic thinking is always a
key element in such deliberations as well as in arguments raised
by individual scientists, (c.f. Wing, 2006; Hromkovič, 2006;
Mittermeir, 2010). This holds in spite of Dennings (2004)
warning that programming does not circumscribe the complete
wealth of CS and in spite of the difficulties school administra-
tions are facing when demanding informatics-instruction be-
yond ICT-training, pointed at by Sentance, Dorling, & McNicol
(2013) and Tort, & Drot-Delange (2013).
The project Informatik erLeben had a pilot-phase in the
school-years 2008/09 followed by application phases in 2009/
10 and 2010 till February 2012. Its overall aim is described in
Bischof & Mittermeir (2008) and in Mittermeir, Bischof, &
Hodnigg (2010). In the sequel, the paper focuses only on those
parts that took place in kindergarten, i.e., with preschoolers.
In the remainder of the paper, first possible interpretations of
the word “Algorithm” are discussed. On this basis, the details
of the experiment conducted with preschoolers and the insights
obtained are described. As this is definitely not the only ap-
proach to introduce true CS-concepts to preschoolers, and a sec-
tion briefly discussing alternative proposals suitable for pre-
schoolers depending on their relative maturity follows before
drawing conclusions from the approaches described.
Description of the Experiment
Algorihms—Central Elements of Computing for All
It needs to be mentioned that preparing preschoolers for a
professional career as software developer it is neither the au-
thor’s intention nor, hopefully, an intention of parents or educa-
tional decision makers. But algorithmic thinking (or according
to Wing (2006) computational thinking) is a capability impor-
tant for all contemporary school graduates indeed. This is a
position, though phrased differently, already taken by Harel
(1987) when arguing for the importance of algorithmic con-
cepts in many disciplines. Based on this claims, algorithmic
concepts should be gradually introduced already early in a pu-
pils education. However, for a substantial number of teachers
describing and developing an algorithm requires such a high
level of abstraction that students have to have passed at least
the n-th grade (n being quite often quoted as a number between
8 and 10) before they can write an algorithm.

R. T. MITTERMEIR
558
Such statements quite often equate the concept of algorithm
with the concept of computer programming, ignoring that learn-
ing programming consists of two quite different capabilities:
1) Developing an algorithmic solution in order to transfer a
statically given problem statement into a statically specified
solution;
2) Translating the algorithmic solution, given precisely, but
nevertheless in a (sub-) language the pupils are familiar with,
into some formal language, eventually a programming language
or a data manipulation language.
The description of how to reach some well-known target
within the school house starting at the class-room as proposed
by Kolczyk’s (2008) spiral teaching model clearly distinguishes
between these two tasks intermixed in traditional programming
instruction.
It is hard to blame teachers falling into the trap of this mis-
conception. When looking at certain dictionaries or handbooks
of Computer Science, one finds definitions such as “Given both
the problem and the device, an algorithm is the precise charac-
terization of a method of solving the problem presented in a
language comprehensible by the device. In particular…” (Korf-
hage, 1983). It is interesting that this definition is placed in the
context of small FORTRAN programs apparently intended to
explain the concept. A shorter definition following the same
line of arguments is given by Maly (1984) in the Handbook of
Computers and Computing. “An algorithm is a finite sequence
of well defined instructions each of which can be carried out
mechanically within a finite amount of time; furthermore, an
algorithm always halts”. It is noteworthy that the chapter on al-
gorithms introduces also concepts of programming languages
such as procedures or how to program recursion.
It has to be seen though, that the person who’s name is hon-
ored by this term, Al Khowarizmi1 focused in his books (origin-
als destroyed when the “House of Wisdom” in Baghdad has
been destroyed) in the early ninth century on algebra and
arithmethic. He also introduced the Arabs to the number system
used by Indian astronomers (Williams, 1997). The computa-
tions used for developing astronomical tables were basically to
be executed on sand tablets, quite comparable to sheets of
(erasable) paper (Berggren, 1986, 2011). So is the supposedly
first algorithm ever published, Euclid’s algorithm for finding
the greatest common devisior between two integers, (presumeb-
ly Euclid, according to Shipley et al. (2006) between 5th and 3rd
century) precisely defined, but independent from any particular
device.
A definition commensurate with this traditional concept can
be found in Marciniak’s Encyclopedia of Software Engineering
(1994). Here, one can read “1) A finite set of well-defined rules
for the solution of a problem in a number of steps; for example
a complete specification of a sequence of arithmetic operations
for evaluating sine x to a given precision; 2) Any sequence of
operations for performing a specific task (IEEE).”
The Experimental Group
The experiment reported here took place in a kindergarten in
Klagenfurt, Austria. The group, following the full agenda of
four interventions consisted of 10 pupils in the age from 3 years
to 6 years. During the first intervention, the one dealing with
search algorithms, only 6 pupils took part (4 girls and 2 boys).
They fell into the age group of 4 to 6 years.
The intervention has been performed by Ernestine Bischof, a
member of this department. The kindergarten teacher responsi-
ble for the children, Ms. Horn, was present during the full time.
So was the director of this kindergarten, Ms. Krenn-Wache, dur-
ing the initial unit.
The particular research question behind teaching algorithmic
concepts to preschoolers has been how early, i.e. at how low an
age group, one might start teaching informatics as a technical
subject to children. The question came up during the piloting
phase. There we determined that with most classes of primary
school, more advanced topics could be addressed than origin-
ally anticipated.
Agenda of the Experiment
The intervention reported here lasted for one hour. It started
with the algorithmic part, find and describe a simple search
algorithm, and concluded by opening a PC, showing pupils the
components and allowing them to disassemble the device.
The algorithmic part required pupils to identify within a bag
of cotton (prohibiting visibility) the shortest among a set of
colored pencils of different length just by sensing using one
hand only. (The other hand was needed to hold the bag.)
Readers considering this to be too trivial a task for showing
and discussing algorithmic concepts might pause here a little
and define two different strategies to find a solution. As these
doubtful readers are grown up, it seems fair to require from
them also voicing arguments, why their strategy (their algo-
rithm!) necessarily leads to the correct result.
The later requirement would obviously be totally inadequate
for preschoolers. They were just required to remember how
they solved the problem and not to mention their approach till
everybody had her or his try. All of them had a chance to find
the smallest one.
The sample is too small to generalize any gender differences
out of the result. Nevertheless it is worth mentioning that all 4
girls presented a correct solution while both boys missed the
target. Moreover, the girls had the result a little faster than the
boys. However, all pupils worked concentrated and were able
to describe their approach. Here again, two categories could be
identified. One used rather an (almost) random approach, others
worked according to a particular strategy.
This initial experiment has been conceptually repeated by
asking the kids to identify the longest pencil. This task was a bit
more difficult, as the difference in length among the longest
and second-longest pencil was minor. Considering this differ-
ences, several rounds of trials were made. Nevertheless, some
succeeded right away. In order to further help those, who did
not find the solution on their own; director Krenn-Wache pro-
posed to use a wooden brick to adjust the pencils to a common
bottom-line and another one to measure their height. This
eventually led to full success for all participants.
Evaluation of the Experiment
Obviously, the experiment suffers from a small sample size.
Consequently, one has to be extremely careful with interpreta-
tions, especially those concerning the gender differences ob-
served. But, the results are clear enough to state the following.
 Children from an age group ranging from 4 to 6 years are
capable of pondering about a good strategy, i.e., of devel-
1There exist several transliterations for the shortened name of Mohammed
ibn Musa Al-Khowarizmi, depending on how the Arab letter “ڡ” is tran-
scribed. Hence, Khwa
r
izmi, is another transliteration often found.

R. T. MITTERMEIR
oping some algorithm.
 Children of this age group were able to verbalize the algo-
rithm they devised.
 Children of this age group could reflect on different solu-
tions and apply hints to improve or revise their algorithm
productively.
One has to mention that a set of various evaluative measures
has been applied in experiments targeted for pupils of primary or
secondary school. In the case of preschoolers we were limited to
the reports from the kindergarten teacher. Fortunately, she was
highly cooperative and provided us with very informative reports
that were helpful in re-interpreting the experimenter’s observa-
tions during the intervention.
In this context it is worth mentioning, that she returned to the
issues dealt with during the experiment the day after. This was
certainly instrumental to keeping some aspects and terminology
for a long time, as noted in her report after the end of the project,
more than half a year after this experiment.
Related Experiments
Before concluding, the paper wants to shed some light on
approaches similar to the one reported. Most of them are not
targeted specifically for preschoolers. However, notably the
approach reported by Futschek & Moschitz (2011) seems to fit
perfectly the topic of this paper, even if the authors have de-
veloped it for primary school.
Tim the Train
The approach to familiarize very young children with algo-
rithmic concepts proposed by Futschek & Moschitz (2011) uses
a short wooden train (2 to 3 wagons) to be loaded by differently
shaped and differently sized blocks of wood. The target is that
no carriage is overloaded and no block remains.
The suitability of the approach for preschoolers is due to the
fact that the algorithm is not to be given in writing. It is rather
to be specified by a set of symbols burned into wooden pieces
(like domino stones). The set of symbols available encompass:
empty the full train (reset), image of a wagon with errors point-
ing left or right (move train forward or backward), and errors
putting up or down (load or unload the piece placed after this
command stone).
The trick with this conceptually already rather complex ap-
proach is the limited language. The narrow vocabulary reduces
the complexity sufficiently such that pupils in primary school,
and supposedly also preschoolers, are able to solve such tasks.
Other Units Performed with Preschoolers
During the project Informatik erLeben further units present-
ing informatics as technical subject were made with the chil-
dren. They also had to pay a visit to the university as well as to
a company working in informatics. As these units were not
specifically related to algorithmic thinking, they are mentioned
here only briefly.
 A hardware unit. The children could open and disassemble
a PC no longer in use in the department. This was probably
the unit most exciting to them. Gender roles were switched
in so far as boys took a leading role. But girls nevertheless
were very interested and had their part in this unit. The
dominance of boys in the hardware unit has been observed
also in primary and secondary schools. Since there the
groups were larger, we insisted that disassembling hardware
was done in at least two single gender groups.
 Synthesis of color. The unit has been almost a direct copy
of the unit for primary school classes. Children got glasses
filled with diluted acrylic colors of yellow, magenta, and
cyan. Posed with the question, how a printer can produce
arbitrary colors if it is only loaded by these three, the pre-
pared classes sufficed to generate the answer “by mixing”.
Then, children could experiment on their own, intermittent
by further questions and input from the teacher.
 During a visit to the usability lab of the HCI-group of the
university the children could explore various alternatives to
remotely control a user interface or to control the movement
of a swarm of butterflies.
Analysis of Algorithms
Part of the repertoire of the Informatik erLeben units are va-
rious sorting algorithms. One or the other of O(N2)-algorithms
will have been intuitively known already by some of the chil-
dren (usually a specific one playfully explored with sorting
some toy-bricks or similar material, but a given child usually
strictly follows the approach once identified). Quite expectedly,
O(N log N)-algorithms are not known. Hence, they are intro-
duced under the motivation “think before sweating”.
The unit consists of analyzing two sorting algorithms of dif-
ferent complexity. It is advisable, though not necessary, to work
on this unit after the children or students are already familiar
with some basics of computer technology such as the unit “exe-
cuting a simplified ‘human’ computer” mentioned below. Know-
ing basic hardware aspects helps them to better appreciate why
comparisons are only possible between two elements. Thus, at
the elementary level, the computer cannot do some pattern
matching considering several pieces at a time, as a human
would do. In order to stress this, students/ children play various
roles. Among them, one child serves as index pointing to the
element (child in the arrangement to be sorted), one serves as
intermediate memory (register) to keep the value against which
the currently considered element is to be compared, and an-
other child remembers the position of the element serving for
the comparison. One child might serve only to ask for the
values involved, compare them and initiate the next move.
Different algorithms might necessitate different roles from
those just mentioned. All children not playing one of the spe-
cial roles are lined up as elements (data) to be sorted.
With students attending higher grades, a given student can
play various roles simultaneously (e.g., remembering value and
position). With pupils of lower grades in primary school, it is
important though, not to overload them with too many duties.
With primary schools, the classes are usually large enough, that
even a fair spread of the special roles leaves enough persons to
be (re)sorted. In kindergarten the groups are smaller. Conse-
quently, it might be advisable to perform the unit with children
from two or even three groups at a time. About 15 children
appear to form a well sized group.
After each of the two sorting experiments, a discussion about
the activities that took place is held with the class in order to
identify characteristics of the algorithm. In this discussion, all
children should be involved. But one could assign to some of
them the special role of observer, if the group tends to become
too large. Otherwise, especially those children serving as
items to be sorted are particularly invited to voice their ob-

R. T. MITTERMEIR
560
servations.
It needs to be mentioned that sorting units have not been ap-
plied to preschoolers so far. They were applied to children at-
tending primary school, even from lowest grades onwards, up
to students attending upper grades in secondary school. For all
these groups, reading capability can be presupposed. Hence
motivating the quest for different algorithms, notably for search-
ing and sorting, can easily be obtained by asking, how learners
would look up the phone number of their school in a phone-
book or search for some particular information in a dictionary,
given their preferred internet-source has broken down tempo-
rarily.
For children knowing the alphabet and the collating sequence
of letters, defining the sorting task is easy in so far as they are
asked to form a line sorted on tallness. Since the size of a per-
son can be assumed to be statistically not related to the name of
this very person, applying different algorithms to re-sort them
by given name seems to be a fair task. Analyzing assumes data
currently in random order with respect to the new criterion.
With higher grades, one might discuss the effect of pre-sorted
data. With lower grades, we were happy if the children saw that
different algorithms, though producing the same result, had
different resource (here: time) consumption. Below, the modi-
fications needed for preschoolers are described.
 Sorting for preschoolers. As alphabetization cannot be pre-
supposed with preschoolers, the concept of sorting by name
is no option. Instead of name, domino-like (one sided)
stones can be used. Children would first pick randomly a
stone that has been placed face-down on a table. Then
they line up according to their tallness like in a gym-
class. The student controlling the algorithm by asking
each child for the value of its sorting criterion asks now
for the number of dots on the stone instead of asking for
the given name.
 Number systems. The domino-like stones just introduced
could also be used to familiarize students with different
number systems, including the binary system.
Normally one would think about a domino like stone as an
arrangement as shown in Figure 1. However, one can also dis-
solve the plain number (5 in this case) into a sum of powers of
two as shown in Figure 2.
The crossed off empty field might be disturbing for the ex-
pert. However, it is introduced to remain compatible with the
empty domino field. It seems advisable to keep it initially and
let the children discover the effect of crossing off the field with
only one dot. Thus, the empty field is not needed. Crossing off
everything will lead to the same number “0”.
From having those stripes with some fields present, some
crossed off; it will be an easy step to write underneath a crossed-
off field “0” and underneath a still existing field “1”. For each
“1” the number of dots are counted and added. The number of
dots in “0”-fields are ignored during this summation. (See also
discussion of the unit related to why computers could perform
calculation, detailed below.)
More Advanced Units
Though results from the literature and our experience of
vastly differing capabilities among age groups results rather
from school classes, it seems fair to assume that this holds at
least to some extent also for groups of preschoolers.
Another experience we made was that with 5 to 6 years old
Figure 1.
Example of a one-sided do-
mino-like stone.
Figure 2.
A stripe consisting of images showing domino-like stones of increasing
value from right to left with invalid elements crossed off to prepare for
binary numbers.
children the capability to read and write numbers is present to a
larger extent than the capability to write characters or words
(smaller set of symbols, simple construction rule). Further,
simple arithmetic (addition, subtraction) over a small range of
numbers (1 to about 20) might be presumed. Thus, future ex-
periments might include also units demanding some arithmetic.
Candidates are the following.
 Executing a simplified “human” computer. With this unit
defined for primary school pupils, a program containing I/O,
load and store operations and operations to be performed by
the arithmetic logical unit (ALU) are performed. The role of
the devices involved (input and output channel, bus, storage,
ALU, program counter, and in a more involved version also
registers) are assumed by pupils. The current version of this
unit requires reading the assembly program to be executed.
A variant for preschoolers might use graphic symbols in-
stead.
 Another unit even more banking on calculation capabilities
of the children would be to give them an answer why the
computer could do calculations even if it works only on a
bi-state, i.e. binary, basis. The tasks can be done either in-
dividually or in small groups. To have enough pre-know-
ledge in order to motivate this example, children should be
familiar at least with the numeric range from 0 to 20; 0 to
30 would be preferable. The approach would use single
field domino stones having no, 1, 2, 4, 8, and if possible 16
large marks. Below, each field contains 4 bars (in case of 16
marks 5 bars), containing either no mark, one mark on the
rightmost bar, only one on the bar left to the rightmost, only
one on the bar right to the leftmost, and finally only one on
the leftmost. Apparently, the marks on the bars indicate the
position of a “1” in the binary code representing the number
of large marks in the field above them. Given this equip-
ment and pencil and paper, students could build a decimal
number by noting the number of large marks on the stones
available as decimal numbers and summing those after-
wards. Then each one might place the stones that would add
up to this number in a column and put below marks in those
positions that had marks in the bottom line of the stones
now forming a column. Thus, two versions of the number

R. T. MITTERMEIR
sought were obtained: a decadic one and a binary one. That
both systems rest upon positions indicating the respective
power of the base, in one case 10, in the other case 2 should
be mentioned only by persons possessing an adequate
background in mathematics and mathematics didactic. But
one does not need to go so far, it suffices to mention the
similarity of the system and to convince the children that an
algorithm ensuring the proper conversion between those
systems does exist.
It needs to be mentioned though that both proposals rest on
our experience in primary school and in kindergarten. But so
far they have not been put into practice.
Discussion
The various approaches described in the previous subsections
seem simple enough that teachers or kindergarten teachers can
easily adapt them to the particular situation in their class or
kindergarten-group. Such modifications are foreseen and in-
deed intended by the designers of the Informatik erLeben pro-
ject (Mittermeir, Bischof, & Hodnigg, 2010). Though not ex-
plicitly mentioned, the continuation of the approach by having
pupils write Scratch or BYOB programs is apparently also part
of the approach presented by Futschek & Moschitz (2011).
Doing so, however, requires utmost care.
With Tim the Train it seems almost natural to define the
problem in such a way that not either the train or the blocks are
moved but that only a crane is serving as robot controlled by
the pupil’s algorithm. The suggestion is obvious. However the
simplification has the price that the length of the algorithm
would markedly increase and, therefore, its perceived complex-
ity would increase too.
Similar considerations might be raised for the searching
problem of Informatik erLeben detailed the previous section.
E.g. the choice of algorithms to be selected depends largely on
whether the bag is placed on a table or is freely held by one
hand of the experimenting child.
The example solutions given below should show that irre-
spective of the details the teacher finally decides upon, she or
he should first establish a list of expected solutions, both wrong
or correct, before deciding on the particular variant of the ap-
proach chosen. The list should be rich enough to contain sev-
eral legitimate solutions allowing discussing merits and weak-
nesses of competing approaches. It should also contain some
anticipated mistakes in order to explain not only the child who
fell into such a trap but make the whole group aware why such
errors do occur and what should be considered to avoid them.
Especially with very young children it is important to not blame
them for errors but to make them learn and grow from under-
standing why a particular error occurred.
 Pick an arbitrary pencil.
This is basically ruled out since it would demonstrate lack
of cooperation and motivation by this child.
 Pick a pencil; compare its length to another one. If it is
smaller than keep it, if the other one is smaller take this for
further comparison. Stop after you made as many compari-
sons as there are pencils in the bag.
The approach does not guarantee a correct solution, since
the pencil to be chosen might be used several times while
others are not compared at all. The fact that equality is not
considered in this solution should be discussed, but is of
minor importance. That the stopping criterion will be
reached after n-1 instead of n comparisons might be con-
sidered irrelevant for preschoolers. It is important, though,
that some stopping criterion is mentioned. In several cases,
it is mentioned only after questioning for it.
 Same as before, but pencils still to be used for comparison
are placed on one side of the bag, after having been used,
the pencil not serving as new smallest element is placed on
the other side.
This algorithm will, if correctly performed yield the correct
result. The stopping criterion discussed above becomes ob-
vious (no further pencil left for comparison) and has a bet-
ter chance of being voiced by the respective child itself. It is
to be noted that it would be very difficult to come to this
solution, if the bag with pencils is not placed at least partly
on the table.
 Sorting all pencils and finally picking the first one on the
end containing the small pencils.
This again yields a correct solution. The investment seems
high. During the discussion phase of the experiment one
should discuss in which situation this investment will pay
off. Apparently, this solution will hardly appear, if the bag
cannot be placed on a table.
 “Sorting” with the aid of rulers or wooden blocks as sup-
porting device.
This comes close to the aid proposed by the head-master of
the kindergarten where the experiment detailed in the pre-
vious section took place. She proposed two wooden blocks
for the second version of the experiment, looking for the
longest pencil. Here, we first consider only one such block
for marking the common base-line for all pencils. This
would not change the algorithm but it would at least speed
up finding a solution. Above, “sorting” is put under quotes
to indicate that sorting need not necessarily be done by a
conventional sorting algorithm. Physical objects, pencils in
particular, can be moved quasi-parallel in a synchronous
manner defeating the algorithmic complexity of computer-
ized searching and sorting algorithms.
 Using one wooden block as base and one as tally.
This will not work well for finding the shortest pencil, but it
works well for finding the longest pencil. As one block en-
suring a common base, the other one can be gliding down
slowly, remaining parallel to the block defining the base.
The first pencil blocking this movement will be longer than
the longest found so far. One might note that two analogous
formulations from the computer scientist’s point of view
(find shortest, find longest) give way to quite different solu-
tions with different algorithmic complexity.
 Using the flexibility of the bag.
The previous operations can all be performed inside the bag.
However, at least the final one might suggest that the glid-
ing block is moved outside the bag. If this is permitted, one
might as well align the pencils as discussed above and then
visually inspect how the bag shows the profile of its content
defined by the length of the individual pencils. Some edu-
cators might consider this cheating and prohibit this ap-
proaches or variations thereof. However, it in no way vio-
lates rules of the problem specification and it still requires
an algorithmic solution in the preparatory phase before us-
ing the pattern recognition capability of the human visual
system. It is just an innovative solution not foreseen by the
problem’s designer (nor seen during or experiments).

R. T. MITTERMEIR
562
Conclusion
The main conclusion of the experiment reported here is that
preschoolers are capable of designing algorithms, expressing
them, and understanding them if presented properly. Thus,
arguments such as “children below some already advanced age
are incapable of abstracting to the extent of designing and
working with algorithms” need to be revised by adding the
suffix “if not properly introduced in a way conforming to their
age and general non-algorithmic capabilities”.
This conclusion should not be overly surprising, since one
can give preschoolers already a small set of tasks they have to
(and they can) organize themselves. Likewise, one might ask
them to follow a sequence of tasks in unspecified or moderately
defined (open alternatives) order and they will perform them in
an efficient, non-redundant way.
Identifying loop structures is certainly easier if some written
representation as in Tim the Train exits, since repetition will
become more obvious if visible. But even in the strictly verbal
approach followed by having kindergarten-children sorting
pencils, those who had a strategy did not report an overly long
story but mentioned that they repeated a certain subsequence of
steps until a stopping criterion had been reached.
In comparison with experiments or interventions held in
school, it needs to be mentioned that the relative freedom kin-
dergarten teachers have in comparison to school teachers prov-
ed positive. Deepening an intervention on the day thereafter is
much easier in kindergarten than in school with an already
crowded schedule.
Acknowledgements
The contribution of Karin Hodnigg to the overall design of
the project during the piloting phase and of Ernestine Bischof
who conducted the interventions in the Kindergarten-group,
refined many units and held many interventions is gratefully
acknowledged. So is the excellent cooperation of Ms. Horn-
Hohenegg, the person responsible for the Kindergarten-group
we were working with. The indirect contribution of Peter Holub,
who challenged me to “downgrade” some already existing units
adapting them for preschoolers, needs special mention.
Funding of the project by “generation innovation”, a venture
of the Austrian Ministry of Traffic, Innovation, and Technol-
ogy is gratefully acknowledged. The piloting phase of the pro-
ject has been supported by KWF, the Kärntner Wirtschafts-
förderungs Fonds.
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