In the articles, we explain our approach to both learning and teaching mathematics and present our views on the use of computer technologies in education.

## EMTeachline Mathematics Software Articles

Ordinary task-books versus training software Apart from standard schoolbooks that are selected by a teacher and are mandatory for a student, many people have to buy additional task-books and tutorials. Prior to visiting a book store, consider new opportunities opened by the world of training software… |

Math theory in training software Why we must learn math theory? How training software can help in studying theory? The difference between mathematics and all other sciences is… |

Level of substantiation in math training What is a substantiation of solution? This is the in-depth theoretical explanation of each solution step. Let us look at the substantiation under the more practical angle… |

Methodical feedback – what is this? Teaching students to solve math problems independently, on their own, presents the most challenges for teachers. Theoretical material is limited and must be simply learnt. Practical tasks cannot be just learnt because their number is infinite. The only way is to teach students “to think”… |

Interactive training of problem solving skills How we learn problem-solving skills? Let us consider typical math tasks, such as “solve an equation”, “prove an identity”. In these tasks we deal with symbolic records. A formal indicator that the task is solved is a set of consecutive calculations proving the solution. To produce this set we should be capable… |

Who needs lexical functions in math software, and why? The language of mathematics is a professional slang with specialized lexicon. The EMTeachline mathematics software offers the following lexical options… |

How does the EMTeachline mathematics software help math teachers? Once upon a time, when I was a math teacher I knew little about the world of training programs and was extremely skeptical about training potentials of mathematics software. Although I still firmly believe that no program can replace a good math teacher, I am positive that training programs can help math teachers a lot in the following areas… |

How does the EMTeachline mathematics software help math tutors? As a tutor, you work typically with one person, dealing mainly with vacancies in his/her knowledge and skills… |

Preparation of tests, variant tests and other methodical materials To prepare various tests, exams, revision exercises and homeworks, math teachers have to either compose examples themselves – which is a long story – or use the existing task-books – which is slow and costly. The EMTeachline mathematics software provides an ideal cost-effective help in these areas… |

Why all EMTeachline modules are not integrated in one training program? Any training program is a tool to facilitate your work. The quality of a tool is defined by its performance and convenience of use. With this in mind, we have developed a number of program lines with different sets of user options… |

Further development of the EMTeachline mathematics software This article presents the strategic directions of the EMTeachline software development… |

Why there is no “Solver” in the EMTeachline mathematics software? You didn’t develop a Solver – then do it now! Many developers did – and look how popular their Solvers are! MATHEMATICA being an example. However, the truth is that any Solver is stillborn as a training program… |

Why we support “Light” versions? The programs EMTask Light, EMSolution Light and EMMentor Light are fully functional trial versions of the EMTeachline mathematics software… |

How to select a training program? EMTeachline Software offers a range of training programs. The programs are arranged in topics. Within each topic, the programs differ in sets of available user options, in number of included math problems and hence in prices… |

How many math examples should contain an ideal software? There are mathematics programs with no single example at all and there are programs with huge repositories of math examples. Both program types have their advantages and disadvantages… |

Solving methods in training software …a proportion between the general and special solution methods in training programs. This proportion was verified by almost a century of pedagogical practice… |

Organization of an educational material in training software An educational material, both practical and theoretical, can be arranged in different ways, depending on methodical aims… |

Criteria for assessing the teaching capabilities of training software Any training program is a tool designed to build specific knowledge and a suit of practical math skills. It would be useful to have some quantitative and qualitative parameters reflecting the training capabilities of software… |

## Characteristics and Technical parameters

- Characteristics representative of general program capabilities

**Group of characteristics representative of pedagogical potential **

- Characteristics reflecting possibility to manage educational material in accordance with the accepted in pedagogics means of material presentation
- Characteristics representative of program capability to form knowledge, basic for studying internal mathematical relations
- Characteristics representative of program capability to built up skills, basic for studying of theoretical material
- Characteristics representative of program capability to form knowledge, abilities and skills necessary in math training

**Types of training capabilities **

- Training potentials ensuring an acquiring of concrete knowledge, abilities and skills necessary in studying math
- General educational capabilities
- Capabilities provided by different ways of organization of educational material
- Capabilities related with lexical functions