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In this article, we shall not discuss the question "What is the mostly effective method to substantiate solutions of mathematical tasks?". There are lots of theses devoted to this topic, where you can find many answers to this question - with diagrams, graphs, description of experimental techniques and many other interesting things. Let us better consider this problem under the more practical angle, namely: how to use the computer technologies for the most complete substantiation of solutions of mathematical tasks, and how this problem relates to your child.
To clarify the problem, we shall perform a small test. Let us write down the complete substantiation of solution of square equation. The complete substantiation means that you have to write down all formulations, definitions and prove all formulas and theorems used in the course of solution. I can ensure you that this requires a number of written pages. Is it really necessary to substantiate each solution completely? Certainly not, but under one condition - that you possess a skill to carry out this substantiation. If the level of substantiation is low, then "one-type-task-training" is taking place. Such students remember not the cause-and-effect mathematical relations, but a concrete technique applied to one particular structure (course of solution). The result is known: as soon as the structure of a problem is slightly changed, such student cannot solve it. To build up the robust problem-solving skills one needs to build up an ability to substantiate the solution - that is to be able to explain which formulas, definitions and theorems were used in solution. The paper books with such level of substantiation of each example do not exist, simply due to limited power of printing industry.
What this has to do with computer technology? Everything! The point is that the computer allows for solution of this problem. How this is done technically is not interesting. Who is interested in the cycle Karno? We care for horsepowers, the petrol consumption, the driving system, and - let us go for a spin!
About "horsepower" or what you can squeeze out of a training program.
- Briefly:
- A description of the course of solution of an example
- Formulation of purposes of carries out transformations
- Math calculations
- Formulations used in the course of transformations
- Formulas and theorems used in the solution
- Complete proof of formulas and theorems
- Formulations related with the proved theorems
- Questionnaires on the studied topic
- Evaluation of user's performance
Methodical recommendations
"Petrol consumption" or overflow of information
This is easy: if you do not need this piece of information (you have already learnt this topic) - do not call it. However, should you require this info - it is under your hand, just press the button.
About "driving system" or how difficult is to manage a program?
As usual: you have to use lists, buttons, helps. A testing has shown that one needs 10-15 min to cope.
How to try?
Load the free-of-charge version EMSolution Light or EMMentor Light.
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