Every child, by nature, likes learning just as he likes eating. Children reluctant to eat, and parents using promises and threats in order to make them eat, are not rare, yet they constitute perhaps rather an exception than a rule. In teaching, the situation is worse: to attach rewards and punishments to learning is more a rule than an exception. It is an institutionalized practice supported by social conditioning and by decrees. This practice exerts an unfavorable influence on the natural process of learning.
W.Servais, T.Varga: Teaching School Mathematics, A UNESCO Source Book, 1971
A good teacher supports the natural learning process of each student. Then everything is simple. Even when it comes to subjects that are “a little unusual,” like math. Each student has their own preferences and their own pace of acquiring knowledge, and all that changes through growing up. Of course, the environment in which the learning process takes place, in addition to limiting working conditions, usually puts significant pressure on this naturalness of learning. This environment often requires that the student is assessed, categorized, to achieve “results”. On the other hand, it requires the teacher to fulfill plans, achieve learning outcomes, …. I personally have never believed in acquiring knowledge and teaching under pressure. I believe that the only quality knowledge is that knowledge that is freely acquired and which becomes part of the human personality. Knowledge is a noble feature of the human race. By trivializing knowledge, we also trivialize ourselves. I have always strived to teach such knowledge Of course, I came up with a whole host of tricks on how to present to the authorities that everything is going according to the plan and that students will eventually be ready for the “labor market”.
Fortunately, you who visit these pages, come here and get out of here completely freely, guided by your natural desire for knowledge. Thus, in this medium, my ideal of free knowledge is automatically fulfilled.
Learning math shares all the characteristics of any learning. Perhaps it is only because of the strangeness of the objects mathematics deals with and the methods by which it does so that it is shrouded in more false myths than other subjects. You can read more about this in Preface-to-Circle-1, the preface to the first book in the Understanding and Doing Math series.
As with many other things, we will get to know math best by hanging out with it. All the books I have written are intended for that. They are an invitation to friendship with mathematics. On the Teaching Math Examples page, there are links to some presentations that at various gatherings were an invitation to students to associate more freely with mathematics than what strict school plans prescribe. The presentations are currently in Croatian, but I intend to translate them into English in a due course.
On the About Teaching Math page there are some articles (written in Croatian) that I presented at various conferences, and which are intended for mathematics teachers, with the aim of making a certain shift towards freer teaching of mathematics. I intend to translate them into English in due course, too.