QJFRCCAL
QJFRCCAL EDUCATIONAL
SYSTEM “LUMEN”

EDUCATIONAL
SYSTEM “LUMEN”
Presented here is an example of one session works with the system
“Lumen”. The arbitrary algebraic equation
is given to “Lumen” to solve it but the system needs to find a method for
solving the equation. The system explains in details every step of obtaining
the solution. This way of explanation does not use the interactive way of
solving, very disturbing by asking questions in the form of “insert a
number”. It is assumed that, after training on many nontrivial examples of
mathematical problems, a student will be able not only to understand and
solve a problem but also to explain each step of solving the problem. The
system can also generate algebraic tasks with the similar difficulty level or
solve the algebraic tasks that are given by user. At this stage the system
“Lumen” is subjected to the complex testing procedure and will be developed
to solve and to explain problems from the different domains such as physics
or chemistry. There is a big stress to enrich the ability of Lumen to solve
the text tasks as well as to understand explanations given by a student. The system “Lumen” is intended to be part of the explanatory module of
SUS. In the first version this module was used for explanation of problems to
the other machine or to the user (student). For this reason, in the contrast
to the Paris Group which stresses the importance of solving of the tests, our
proposal is focused on teaching/learning of the explanatory ability of solved
problems. Our definition of understanding consists of two parts, the first is
referring to solving problems and the second to explanation of the solving
process and obtained results. In this context the ability to explain the
process of solving problems appears to be the most important part of
understanding of the problem. Leaving the detail discussion of issue of
teaching/learning of explanatory abilities that will be presented elsewhere,
it is important to point out to one important aspect of this topic. It is the
matter of “polishing” of the acquired knowledge during teaching/learning
process. In the example
that is shown, it is easy to notice that complex problems can be decomposed
into subproblems that could be solved independently. Deep understanding of
the solving process is the best guarantee for obtaining the proper solution.
Deep understanding assumes the ability to explain each step of obtaining the
solution without paying too much attention to obtained result. Even when the
result can be wrong as the result of, for example, some computational
mistake, the proper explanation of the solving process will be assessed as
the top mark. In the professional practice this type of complex problems will
be solved by application of the special software packages such as Mathematica. To conclude, learning the
ability to understand the process of solving problems that culminates in
acquiring the very good ability to explain the way of obtaining the solution
can put into end so fast spreading testing madness. Copyright the Queen Jadwiga
Foundation 
Finding the solution – with interactive
explanation Level
0 L1, L2, L3, L4, L5 Level 1 L1_1, L2_1, L3_1, L4_1, L5_1 Level 2 L1_2, L2_2, L3_2, L4_2, L5_2 Example  Interactive model L4_1_Int 