Teaching to the Test and the Italian National Assessment of Mathematics.

Daniel Doz & Jurka Lepičnik Vodopivec

Teaching to the test means to use part of the curricular school hours to prepare students to a test, showing them solving methods and focusing on the topics, which are more likely assessed by the test. In Italy, the INVALSI institute is responsible for preparing national assessments of knowledge for the evaluation of the quality of the educational system. Mathematics is assessed also in grade 8 and grade 10. In the present work, we investigated the presence of the phenomenon of the teaching to the test in North-Eastern Italy. Through an online questionnaire, we gathered the data among N=84 Italian middle and high school teachers, showing that the phenomenon of teaching to the test is present in the majority of those teachers, who teach to grade 8 or grade 10 students. Moreover, we found that more than half of the teachers, who prepare their students for the national assessment, solve some specific exercises taken from old national assessments; some teachers do also include some questions taken from national assessments in their formative and summative tests. When asked about the quantity of school hours invested in preparing their students for the test, we found that, on average, teachers spent M=6.98 hours, which represents 2-3 weeks of regular lessons. Teachers do however believe that national assessments should not influence students’ final grading; statistically significant differences were found among high school teachers who did and did not teach to grade 10 students.

Perceptions des pratiques des enseignants de mathématiques en fin de secondaire: quelles influences sur les choix d’études STIM?

Doriane Jaegers, Virginie Dupont & Dominique Lafontaine

The present research conducted on a sample of 6th year secondary school students in the Wallonia-Brussels Federation aims to study the influence of the perception of mathematics teachers' practices, on the aspirations for higher education with a strong mathematics component on the one hand and, on the other hand, on three motivational variables (self-perception, feeling of self-efficacy and perceived usefulness of mathematics) known to favour this choice of orientation. If the cognitive activation practices are directly favourable to aspirations for mathematical studies, the perception of relevant teaching is positively related to self-perception and the perceived usefulness of mathematics (particularly in courses with low hourly volume).

Problems with Teaching Critical Thinking.

Hasmik Hovhannisyan & Robert Djidjian

This paper outlines main difficulties arising in the process of teaching the different levels of critical thinking. The first of these difficulties concern the basic level of critical thinking, which we consider as the field of laws and rules of traditional formal logic. The principal task here is correcting the thinking of those students who allow invalid inferences in their judgments. The next level is related to the means of analytical thinking and forming the required competence of understanding subjects under discussion. Here teachers confront the problem of understanding the essence of understanding. The most serious difficulties may arise at the level of teaching students the ways of independent thinking. The core problem here is that of the mechanism of idea generation. This paper discusses also difficulties related to the meta-level of argumentation and methodology of scientific revolutions. The final section of this paper demonstrates the method of critical resolution of classical paradoxes – the versions of the “Liar” paradox and Zeno’s aporias. 

BOOK REVIEW.

Lin Wang & Gil Inana

Starting from the recent publication by Crombez Bart 2020 “ LEAN transformations : why LEAN works and how to introduce it with success” special attention is given in the domain of “Education Management” to the"Inconvenient truth" perspective concerning to dare to face, to take into account and to learn to deal with sabotage, thwarting, bullying, brainwashing (of victims). Between others it is crucial to recognize and to learn to deal with bullyboys, dyssocials, hypocrites, perverse narcissists… To be able to tackle efficiently these challenges, one must be aware that such people are rather becoming popular and successful and use these methods to promote their influence…