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Background: This paper reports on the use of classroom assessment techniques (CATs) by primary school mathematics teachers in China. CATs are short, focused assessment activities that can reveal students' understanding of specific mathematical subjects. The study involved six female third-grade mathematics teachers from Nanjing, China. The focus was on assessing division. Data were collected by teacher interviews, feedback forms and final reports, lesson observations, and student work. Results: The study revealed that the teachers could easily include CATs in their daily practice. By conducting the CATs, the teachers got new information about their students' learning. Most teachers liked using the CATs, especially those with the red/green cards, which is a whole-classroom immediate response format, providing quick information of the students' learning. The teachers also found the CATs feasible to conduct and helpful to engage their students during the lesson. However, no evidence was found that they used the information gained from the CATs for adapting their instruction to meet the students' needs in subsequent lessons. In fact, the teachers only used the teacher guide of the CATs to adapt their instruction beforehand. The CATs, instead of being implemented as assessment activities, were often included as extra exercises in the pre-arranged lesson plans of the teachers. If necessary, the teachers provided their students with instant help in order to assist them to get the correct answers. Conclusions: In general, the teachers were positive about the CATs as a way to reveal their students' understanding of division in an effective and efficient fashion. The teachers recognized that it can be very revealing to challenge their students with questions that are not completely prepared by the content of their textbooks. The results of this study suggest that on the one hand CATs can be helpful for Chinese mathematics teachers' formative assessment practice in primary education. On the other hand, our study also provides some evidence that using CATs, as an approach to formative assessment, to make informed and adequate decisions about further teaching, can be a real challenge for teachers. [ABSTRACT FROM AUTHOR]

We recall the scientific work and professional contributions of Piero Villaggio (b. Genoa, Dec 31st 1932, d. Jan 4th 2014), member of the Editorial Board of the Journal of Elasticity for almost 30 years. [ABSTRACT FROM AUTHOR]

Background: We discuss first experiences with a new variant of self-assessment in higher mathematics education. In our setting, the students of the course have to mark a part of their homework assignments themselves and they receive the corresponding credit without that any later changes are carried out by the teacher. In this way, we seek to correct the imbalance between student-centered learning arrangements and assessment concepts that keep the privilege to grade (or mark) completely with the teacher.Results: We present results in the form of student feedback from a course on functional analysis for third- and fourth-year students. Moreover, we analyze marking results from two courses on real analysis. Here, we compare tasks marked by the teacher and tasks marked by the students.Conclusions: Our experiments indicate that students can benefit from self-assessment tasks. The success depends, however, on many different factors. Promising for self-assessment seem to be small learning groups and tasks in which a priori weaker students can catch up with stronger students by increasing their practising time. [ABSTRACT FROM AUTHOR]