![](bg5.png)
Figure 5: Discrete Fourier Transform gadget.
However, the main use of the gadget in learning
DFT goes in the opposite direction. Given an input
function (drawn in black), a learner should find the
spectrum by himself or herself; a red function that
corresponds to the actual spectrum appears in the
upper window and should match the black one in all
sampling points represented by the vertical lines.
The device provides several levels of hints to
make this difficult task easier (e.g., sets the correct
value of certain spectrum item, or at least indicates
whether the present value is too small or large).
It takes typically several hours of hard work in a
trial-and-error style to find ways to match at least
roughly the black and the red functions, because the
correspondence between a digital signal and its
Fourier image is conceptually rather complex, but
learners find the task challenging and even funny
and eventually get surprisingly high level of
understanding of the essence of DFT.
3.8 Visual Hints
Visual presentations can quite often be enhanced by
visual hints. One source of such hints is a use of
colours when visualising algorithms and protocols
with temporal features. Any displayed object has
typically a particular status; it can be processed
and/or exhausted (dead), new, fresh, pending, active,
etc. In our cultural range such terms are associated
with colors (fresh=green, dead=black, attention or
stop=red, etc.).
Another kind of visual hints uses shapes or
forms. An example of a shape visual hint is used in
the Algovision implementation of AVL-tree course,
where balance of a node is shown using ideas of
Calder's mobiles.
4 CONCLUSIONS
We found that visual learning objects and courses
directed to algorithms and communication protocols
should be constructed to explain the underlying idea,
in other words, why it works in a presented way.
Doing so is more art than science or methodology,
but we listed several paradigms and approaches that
proved to be useful and give good results.
ACKNOWLEDGEMENTS
Work on Algovision was partially supported by
Czech Ministry of Education, Youth and Sports.
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