Maria Knobelsdorf, University of Dortmund, Germany - Didaktik der ...

of answers management is important in practice. The question
does not allow us to construct consequent questions
straightforwardly with the same principle. Yet, after being
reminded of binary system, students are able to realize the
connection. They are doing almost the same as bisecting,
only reversed. The value of these thoughts lay in the fact
that they were driven mostly by students themselves.
Disturbing (however expected) finding is low level of understanding
of certain parts of mathematics among students.
Logarithms are taught intensively, yet no (!) student have
seen a direction to calculate the depth of a tree. Our guidance
had to be very explicit. A few months later, most of
the students actively knew that it is related to exponential
growth and therefore also to logarithms.
Some of the ideas encountered in the first module were
needed again during the school year. More than a half of
students (in both groups) recalled them actively. This includes
bisection, decision trees, binary numeral system and
efficiency modeled using some kind of elementary step.
5.2 Test results
Further explanations and remarks are based on collected
test sheets examination and our own notes from the lessons
and consecutive discussions with students. We have not used
any formal pre-test. It was more than clear from the initial
discussions held for this purpose that students had difficulties
to even understand the given questions. Student can
get a certain amount of points for each task. Furhther given
percentages indicate the average ratio of acquired points,
illustrating the success on each task.
Brief explanation.
Students were to explain briefly the meaning of the term
information. Any meaningful answer was rewarded with
points. Definition or equally complete description got all the
points, less precise expressions or examples got only partial
score. The resulting success is lower than expected, given
that it is a question of knowledge and outer resources were
available. We see the reason in the lack of communication
skills. Most of the students understood the term well, as we
have seen during other tasks. To express it was however too
difficult.
Information and logarithm.
This was a double task. First was to determine how many
yes/no questions does one need to reliably identify a Czech
deputy (they are 200). The second was to determine the
minimal sufficient length for their hypothetical binary ID
code. Very few students have used logarithm for any of the
tasks. Majority of them chose to simulate the known process
(sequential halving and doubling, respectively. Only two
students have realized that the result is the same for both
questions and the second calculation is not needed.
Suboptimal decision tree.
There was a small (7 leaves, 4 levels) decision tree with
given rates per leaf. First task was to calculate the expected
number of questions asked. The second was to lower
that number by adjusting the tree.Those who made some
calculations usually got both parts right. Less than a quarter
of students (in both groups) passed the calculation, as
it was still too mysterious for them. The bigger surprise is
then that some of them understood the situation well enough
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to optimize the tree (swapping frequent nodes towards the
root).
Inquiries comparison.
Students were to sort seven given questions (such as “Is it
a prime?”) according to the expected amount of information
provided by the answers. All the questions were bound to
the same situation, identifying an integer number between
0 and 255. This task was very dependent on mathematical
skills, therefore the results are rather poor.
Statements comparison.
This last task was not included in the same test with the
others. We put it into another test six months later. There
were four different smiley-like crime suspect faces and four
statements regarding the offender, such as “The offender has
no hair”. The task was to sort these statements according
to the amount of information included. Unlike with the
previous task, here it was obvious enough that those who had
a mistake in their resulted did not understand the matter
at all. Hence we gave all the points or none. The success
rates were unexpectedly high, considering the time passed.
We can conclude that the educational results hold well.
6. CONCLUSION
Based on the results above, we may conclude that students
are capable of understanding the notion of information and
its basic applications. The goals of the module were set
surprisingly close to the real need. The limiting factors lay
mostly in students mathematics skills. The teaching methods
are found useful and efficient by the students, although
they have recommended some tweaks, mostly in activities
distribution in time.
We described the concept of an introductory CS course
for Czech grammar schools and gave more detailed specification
about the module about information. Then we could
proceed to the results obtained during the first testing year
of the course.
We intended to find out whether the module is feasible in
the given constraints and conditions. The result shown here
is that the proposed concept works, although it needs a few
adjustments. The most distinctive feature of the proposed
course is the shift in goals from CS itself to key competences
and connections to other grammar school subjects.
7. REFERENCES
[1] Framework Education Programme for Secondary
General Education (Grammar Schools). V´yzkumn´y
ústav pedagogick´y v Praze, 2007.
[2] M. R. Fellows, T. Bell, and I. Witten. Computer
Science Unplugged... offline activities and games for all
ages: Original Activities Book. Computer Science
Unplugged, 1996.
[3] J. Hromkovič and B. Steffen. Why teaching informatics
in schools is as important as teaching mathematics and
natural sciences. In Proceedings of ISSEP, ISSEP’11,
pages 21–30, Berlin, Heidelberg, 2011. Springer-Verlag.
[4] D. Lessner. Computer science curriculum proposal for
czech grammar schools. In Zborník príspevkov, ITAT
2011, pages 99–104, Seňa, Slovakia, 2011. PONT s. r. o.
[5] A. Verno. Supporting k-12 computer science education.
J. Comput. Sci. Coll., 23(3):145–146, jan 2008.