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This paper focuses on the importance of covariational reasoning within the processes of mathematics teaching and learning. Despite the internationally recognized relevance of covariation, research shows that only a small percentage of students and teachers is able to adopt covariational reasoning and the majority of mathematics curricula do not contain explicit references to covariational skills. In particular, when covariational reasoning manifests as conceptual knowledge, it becomes challenging to assess, and the need for innovative methods of assessment emerges; there is a need for suitable assessment to highlight the characteristics of covariation and capture the various features that characterize conceptual understanding. Comparative judgement (CJ) is an innovative assessment method based on collective expert judgements of students' work rather than requiring scoring rubrics. Due to its holistic approach, CJ is particularly suitable for assessing complex mathematical competencies, and, as we shall see in this study, it proved to be appropriate for the covariation's assessment. In details, our study aims to investigate the perception and relevance attributed by mathematics teachers to covariation as a theoretical construct and the way CJ can help in the assessment of covariational reasoning skills underlying a less structured modelling task. [ABSTRACT FROM AUTHOR]

National and international large-scale assessments of mathematics show that, in most nations, males achieve better results than females and Italy is one of the countries with a greater gap. Many research studies in mathematics education have analysed this issue, using both quantitative and qualitative methods to understand the sources and characteristics of this gap. This study focuses on a specific Grade 10 task that requires algebraic manipulations of powers with the same base. Item-level analysis enables the study of gender differences on specific content, before using the lenses of mathematics education theories to interpret macro-phenomena emergeing from standardized assessment results. The quantitative analysis, carried out using the Rasch statistical model, highlights a gender gap in favour of males in this task and, furthermore, a variance in choices of incorrect options between males and females; the interviews conducted provide a key to understanding this phenomenon in terms of didactic contract. [ABSTRACT FROM AUTHOR]

In this paper we provide some relationships between Catalan's constant and the 3F2 and 4F3 hypergeometric functions, deriving them from some parametric integrals. In particular, using the complete elliptic integral of the first kind, we found an alternative proof of a result of Ramanujan for 3F2, a second identity related to 4F3 and using the complete elliptic integral of the second kind we obtain an identity by Adamchik. [ABSTRACT FROM AUTHOR]