Development of methodical materials

One of the problems in math training is teaching of groups of students with different backgrounds and thus different levels of knowledge. One way to deal with this problem is to use a variety of alternative courses in math.
However, there are not so many math courses, and moreover, the existing ones are quite often not suitable for such varied groups of students. As a result, teachers are forced to create their own methodical materials; on the other hand, they do not have any appropriate tool to do this work. The teachers have either to compose examples and tasks themselves - which is a long story or to rework the existing books - which is slow and costly. A natural question arises: is it possible to develop such a universal math book that would enable you to make an easy selection of educational materials to your own liking. The answer to this question is NO. Imagine kilometers of shelves with the existing textbooks and problem-books! Think about limitation of printing industry! - And you must agree that such universal book cannot be developed. However, with the advance of computer technologies, especially with the appearance of Internet, the situation has changed.
Now the problem of fast creation of the target methodical books has an easy solution: a standard computer-based database with various selection criteria. Clearly, to make a process of book development effective, this database should be large - the larger, the better. There are however problems.

• First of all, there is a problem of input of mathematical information. Those, who have an experience of filling in the mathematical texts in the existing editors, will immediately recognize the problem. Those, who have escaped such a pleasure, should know that the typing of just five A4 pages of math text in eight working hours is a good result. Considering that the detailed solution of an example of middle complexity takes about two pages, one can estimate how many person-hours is necessary to create a database with thousands solved examples (one thousand of examples is not a complete collection at all, and cannot anyhow be considered as a database). The situation will hardly change in the close future because the problem lies in the complex structure of mathematical record and not in a drawback of the editors.
• The size of files with mathematical information is huge. Just as a test - try to input one mathematical line in "MS Equation" and save it as a file, and you will get kilobytes. Any decent database (of about hundred thousand examples) will take gigabytes.

One way to obtain the necessary math information lies in integration of resources of the Internet. These resources are however limited, sketchy, and besides, the information is usually organized by a single selection criterion that forces you to process a lot of unnecessary information.
If someone will attempt to create a general database with various selecting criteria based on the existing resources, he will face a number of problems, such as the absence of the standard format of representation of math information, complexity of "introduction" of math text, large size of files with math information, etc. Not the least, large investments are needed for realization of such project at a decent level. Eventually, I am sure, such project will be accomplished, and the main math-related resources of Internet will be integrated. At present, however, I see the only affordable way to solve the considered problem: to create specialized mathematical databases. Let us describe the database of EM Teachline complex. We managed to create an economic format of storage of mathematical information: one Mb contains about 30 thousand pages of math texts. Such compression of information opens the door to development of a large database fitting in a small place on the local computer. Consequently, the teacher gets an opportunity to develop his own methodical materials by pressing just a few buttons.
In our database, the system of data selection operates in two modes:

• "Automatic"
• "Manual"

To create a collection of math problems in an automatic mode, you have to select the desired themes and levels of complexity of examples. It is a matter of a few minutes. As a result, you have:

• Collection of 30 similar variants, which you can print at once.
• Detailed solutions of all examples in this collection, which you can print at once.
An opportunity to prepare variants and keep them for further use.
• An opportunity to create and support your own database of variants.

The manual mode of data selection is intended for those who consider the computer as being "stupid". The control is somewhat more difficult than that for the automatic mode. This is natural, considering that you have to evaluate the quality of examples yourselves. The result is similar to the previous case.
You can also apply the "combined" way of development of variants: you may create variants in the "automatic" mode and later use the "manual" mode to correct variants.
Now let us emphasize the volume of data in our database from which you choose. At the moment, the database of problems of our complex comprises more than 5 000 000 of solved examples.
The last thing to be mentioned: it is always better to try once than to read hundred times. The way to try is extremely simple: just load the free-of-charge full-functional version EMSolution Light and try it in work.