Abstract
The aim of the offered guide is to address teachers who think about how to lead lessons to develop both mathematical knowledge and skills, but also (and perhaps mainly) the personality their students, their autonomy, ability to work in a team, discuss, reflect their learning, formulate and verify hypotheses, their joy of learning, and invite them to cooperate. For such teachers, the handbook offers the sharing of real-class lessons and collaboration in thinking more deeply about lesson preparation, formulating meaningful goals that link cognitive and social components, teaching forms of pupils 'work, reflections on their and classmates' learning, and many other areas of didactic of mathematics that interfere with quality teaching.
Often teachers are looking for other interesting problem tasks for students and an interesting way to present the task to students. Often teachers aim to develop numeracy and agility in calculations as well as in knowledge of effective problem-solving procedures and strategies.
That, of course, is all very deserving. In our experience, the way to work with tasks, and even better with a system of tasks, is more important for achieving the goals - whether he can give tasks a sense that motivates students to solve them, whether it gives students enough space to look for their own solving strategies, to present them, discus them and compare and evaluat them, whether each student has the opportunity to solve a reasonable task for themselves, and thus experience the joy of well done job.