On Trapezoid Inequality Via a Grüss Type Result and Applications

In this paper, we point out a Grüss type inequality and apply it for special means (logarithmic mean, identric mean, etc... ) and in Numerical Analysis in connection with the classical trapezoid formula

Deepening the mathematical knowledge of secondary mathematics teachers who lack tertiary mathematics qualifications

A professional learning program for unqualified practising secondary mathematics teachers regarding senior secondary mathematics teaching is described in this paper. The VCE (Victorian Certificate of Education) mathematics professional learning program for senior secondary mathematics was designed for practising secondary teachers of mathematics who had no experience of teaching advanced senior secondary mathematics and who had not completed the recommended qualifications. Professional learning episodes, artefacts and reflections of three teachers who participated in the program are analysed to identify the development of these teachers\u27 mathematical and pedagogical content knowledge (PCK). The PCK framework developed by Chick et al. was used to analyse teachers\u27 knowledge, and the cases of teachers\u27 knowledge presented in the paper illustrate the entwining of knowledge of mathematics and knowledge of teaching and learning The findings indicate that a program designed for senior secondary mathematics can enable practising teachers to deepen and broaden their understanding of junior secondary mathematical pedagogy