R. T. MITTERMEIR

Copyright © 2013 SciRes.

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

izmi, is another transliteration often found.