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MathAid Teaching Methodology
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MathAid teaching methodology combines maximally interactive
teaching methods with a system of evaluation and tests. Every
product will include two major parts:
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Basic Blocks activities teach basic concepts and
develop problem-solving skills. One block normally covers one
important topic, such as a particular theorem, formula, or
standard problem. Basic blocks are designed to build
understanding of the topic, to teach solution methods for
relevant elementary problems, and to provide the student with the
opportunity for control of the learning process. In order to
attain these objectives, Basic Blocks are built of the
three standard types of lessons:
- Concepts,
- Interactive Examples, and
- Drills
(all three types do not necessary have to be present
in each Basic Block).
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Concepts are reference material containing central
formulas, definitions, claims, and theorems. These are not
interactive lessons and serve only as a basic theoretical review
and reference.
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Interactive Examples are interactive lessons, which
usually contain graphical illustrations. They give the student
an opportunity for hands-on exploration of a mathematical
concept, for example, a function and its dependence on numerical
parameters. In some cases, when it is helpful for understanding,
Interactive Examples use animation of parameters to dynamically
illustrate this dependence in a certain parameter range.
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Drills are collections of interactive problem-solving
lessons which provide the student with an opportunity for
evaluation and meaningful control of the learning process. Drills
also serve to build problem-solving skills. The problems which
the system generates in the Drill section of a Basic Block
correspond to the subject matter covered in the Concepts and
Interactive Examples sections of the Basic Block. The system
accepts answers to the problems as input from the student. The
student may check his or her answer and if it is incorrect, may
give and check a new answer an unlimited number of times. The
student also has the opportunity to view the correct answer, and
in the case of more difficult problems, to obtain a full
solution.
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Tests contain problems associated with the different
chapters and topics of the product. The system gives a teacher
(or student) an opportunity to choose the topics covered by the
test, the number and degree of difficulty of the test problems,
and the time allocated for the test; the system then generates
the test according to the user's specifications. When the test
is finished, the system generates a report and provides the
correct answers and solutions, if desired.
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It is worthwhile to note that this teaching methodology is
particularly conducive to the future expansion of existing
products. Products can be easily upgraded by adding new Basic
Blocks or Problems or by updating existing ones. This makes
MathAid products very flexible and easily adjustable to the
user's needs.
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