Abstract:

George Polya's Ten Commandments for Teachers are ten sentences that this Hungarian mathematician and mathematical educator considered fundamental for being a “good teacher”, based on the heuristic approach to education that he advocated. According to the author, the order of these commandments was relevant, the 1st being the most relevant and the 10th the least relevant. These commandments date from the middle of the twentieth century, but they remain current and very appropriate in the context of teacher training.

The author of this study is the teacher of Didactics of Mathematics (2nd semester of 3rd year) of the 1st cycle course in Basic Education, which in Portugal gives access to 2nd cycles of teacher training from pre-school to 6th year of basic education (between 3 and 12 years old). Usually, in this subject, the teacher in dialogue with students reflect together on George Polya's Ten Commandments for Teachers, its meaning and implications for the teaching of mathematics.

This school year, partly due to the covid-19 pandemic, the working methodology usually used has changed, and as far as the approach to Polya's Commandments is concerned, the teacher has decided not to make any prior reference to them and to propose a task to be carried out, individually, with consultation and during a videoconference of about 1 hour. At the end, the students sent the teacher their resolution by e-mail. The task consisted of "Read carefully the following statements [George Polya's Ten Commandments for Teachers, without naming them, so that it would not be easy for students to search in Internet] considered the rules to be a good teacher and choose 4 of these statements, justifying the reason for their choice and explain them".

We believe that this task would allow us to understand what these future teachers think about what they consider a "good teacher" and what their interpretation of Polya's commandments is. This has become the research questions of a qualitative and interpretative study that we present here.

The participants in the study were 21 students from the above-mentioned 1st cycle course of a Portuguese public university. The data consists of the task written answers sent by the students. We carried out a quantitative analysis and a content analysis of these answers.

The results showed that George Polya's Commandments for Teachers 2 and 4 were the most chosen (71%) by students, followed by 5 and 9 with 62%. In other words, these students value the teacher's mastery of the mathematical content to be taught, the students and their expectations, as well as the development of their skills and competences. Students did not choose commandment 8 and five students (24%) mentioned Commandment 1, considered the main one by Polya. It should be noted that in the rationale of the choices, contradictions are recognized between a traditional teaching (which values the transmission of knowledge by the teacher) and a heuristic teaching (which gives the active role to the student valuing heuristic learning). Aspects to develop in the talk.

Keywords:

George Polya’s Ten Commandments for Teachers, teacher training conception of teaching practices.