Here we explain what is a methodical feedback, why these feedbacks are pivotal in the learning process and how methodical feedbacks are modelled in the EMTeachline mathematics software.

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”. This can be done with the help of a special system of interactive training exercises designed to build critical thinking skills. Such exercises are referred to as training techniques or methodical schemes.

Higher-level thinking skills imply a clear understanding of internal mathematics cause-and-effect relationships – ends and means of math transformations. This includes an ability to understand problem situation and objectives of solution steps, a skill of application of formulas and rules and a skill of verbal formulation of math transformation. Given that you have learnt all necessary definitions, rules and formulas, this complex of skills and abilities is sufficient to solve math problems on your own. Each of these skills can be trained.

There is no universal training technique. One system of methodical exercises “works” on one person and does not on the other. The reasons are the difference in age, psychology, skill level, etc. An experienced math teacher easily finds proper exercises by the try-and-error method.

An **important point**: math training is effective only if student’s performance is analysed, the main errors obstructing the learning process are detected and correcting exercises for building up missing skills are formulated. This is a pivotal element of math training which we call a methodical feedback.

## Now let us explain how this training process is modelled in the EMTeachline mathematics software:

- The software provides a number of interactive training techniques. Each technique approaches the training process from a different learning angle. The choice of a suitable training technique is reduced to a simple try-and-error procedure
- The techniques are arranged in the order of increasing complexity. This facilitates your choice
- Performance of each task and/or any group of tasks is comprehensively analysed. Joint multifactor error analysis reveals main gaps in knowledge and skills
- Based on the results of error analysis, an optimal set of exercises for error correction is generated

The described training process is very effective. After you solve a number of tasks within a selected scheme, you will cope with similar problems without thinking twice. Try training techniques online or download a **trial software version**.