It would be difficult to decide unambiguously whether the success of educational process depends more on the teacher or pupil. Of course, nobody doubts about dominant influence of a teaching style. The teaching style is significantly influenced by the teacher´s values and aims. Generally, teaching styles can aim at pupils´ development or pupils´ performance. The teaching style focused on pupils´ performance is called transmissive.
The teaching style focused on pupils´ development is called constructivist. There are many more criteria which can show the differences between the two styles. According to M. Hejný these are: value of knowledge, motivation, permanence of knowledge, teacher-pupil relationship, atmosphere, bearer of activity, activity of pupil, piece of knowledge and carrying question.

I suppose that, for many reasons, another crucial criterion is the way of evaluation. During his/her teaching career almost every teacher has to correct and than evaluate pupils´ oral or written performance, especially primary school teachers. But how often does the teacher try to discover deeper meaning of spoken or written words and pupils` thoughts? Often the teacher has got time only to decide whether the performance is right or wrong. This information is valuable but it should not be the main source for evaluation. Of course there are techniques of assessing the work, which require similar processes. Maybe mostly stereotype and simplicity contribute to using this kind of evaluation. Also this attitude is certainly influenced by the teacher´s values and the understanding of wider mathematical aims. It is this analysis of pupils` performance that is often stimulation and possibility to come closer to pupils, empathy to their situation and thinking.

For the realization of the constructivist teaching style I have used individual treatment through teaching tasks. I have made a set of graded tasks and let pupils solve them. The tasks will be a part of the presentation.

When a pupil who was solving a given task had difficulty with it, remained at the same phase of solving, was lost and was not working systematically, I could provide him/her with a various degree of help. This help could be meaningfully used during the work with set of tasks graded according to their difficulty. The tasks were differentiated by the number and quality of helping information. Then, advanced solver was able to work on his/her own. He/she was able to use his/her experience and knowledge aquired by the solving of previous tasks. So there were more opportunities to help solvers who did hesitate and make mistakes. It was important to find each pupil´s difficulty and allow him/her to overcome it. It was suitable to offer a task in which the solver could easily discover the principle of solution, then was able to return to the previous task and apply the principle by him/herself. Of course many other ways and degrees of help exist. But a huge contribution of individual help is indisputable.

In consequence of this individual help, pupil´s attitude to tasks, the subject and her/himself can change. The aim is to develop the attitude as it is described by E. Gruszczyk-Kolczynska: ”I failed, because I may have done something wrong, I just have to correct my mistakes and try again.” She comments on this attitude: ”This interpretation does not lower self-esteem and the person makes further attempts to solve a difficult task and is not afraid of new, intellectual challenges.”

Literatura:

GRUSZCZYK-KOLCZYNSKA, E. Why the solving of mathematical problems is so difficult for children? Intellectual and emotional conditions of mathematics education. In: SEMT. Praha: 2001.

HEJNÝ, M. Číselné představy dětí. Praha: UK, 1999.