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The issue of students’ difficulties in processing operations with percentages has been addressed in several international research studies from a qualitative perspective. In this study, we analyze students’ difficulties on this topic, focusing on the transition from middle school to high school with a mixed methods research design. We focus on students’ responses in a specific task belonging to the Italian large-scale assessment analyzed through the Rasch model, and we deepen the task analysis thanks to interviews, which enlightened image schemas and metaphors underlying students’ reasoning. From the qualitative point of view, the Rasch model shows that students’ difficulties in dealing with percentages is a macrophenomenon that involves the higher levels of competences. From the qualitative point of view, the metaphoric approach outlines the image schemas that foster the correct conceptualization of percentage and those that hinder their correct learning and can be one of the possible causes of the emerging aforementioned macrophenomenon.

We present an external close replication of the 1985 Fischbein et al. study about intuitive models of multiplication and division. We administered two batteries of mathematics items developed in the original study, via a spiralling process, to a quota sample of 903 students attending grade 7. Compared with the analytic strategy based on the count of correct answers employed in the original research, our study goes a step further as we propose a methodological approach that guarantees measurement invariance, thus allowing for the direct comparison of different groups of students and/or items. The advantages of Rasch estimates compared to percentages of correct answers over the total are critically discussed to show why the former should be considered as more robust than the latter.

Mathematical memes are an Internet phenomenon with an epistemic potential noteworthy for the teaching and learning of mathematics. The aim of this paper is to conceptualize this phenomenon on an em...

National and International standardized assessments have shown sharp differences between native and foreign students’ performance in both text comprehension and mathematics. Based on the data gathe...

In this era of great uncertainty, imagining the future may be challenging, especially for young people. In science education, the interest in future-oriented education is now emerging, research needs, however, to keep eyes on youngsters’ future perceptions and on the development of a future literacy. In this article, starting from a sample of individual students’ narratives about their future daily life in 2040, we aim to delineate which ways of grappling with the future can be observed in the essays and which methodological tools are suited to operationalize their identification and characterization. The analysis led to the definition of “polarization” and “complexification” attitudes that represent the ways in which the students’ narratives are positioned with respect to a bunch of dichotomies: personal–societal, functional–aesthetics oriented, good–bad, natural–artificial, and certain–uncertain. Moreover, with this study, we provide a contribution to the methodological reflection that deals with the collection and analysis of data, when students’ future perceptions need to be investigated. Discussing the limits of the current data collection tool, we introduce the design of a SenseMaker® questionnaire which contributed to feeding a collaboration with #OurFutures project, recently launched by the European Commission to collect future narratives all around Europe.

Differences in performance of native and foreign students in reading comprehension and mathematics emerge in all standardised assessments, both at national and international levels. This study is the continuation of a previous research project in which we examined citizenship-based differences in Italian mathematics standardised assessments, both at item level and in connection with students’ competence in text comprehension. We present a deeper analysis of items which presented a significant Differential Item Functioning (DIF) in favour of native students, and interpret these differences in terms of linguistic difficulties. On the basis of this analysis, we then present a classification of possible item characteristics causing disadvantage to foreign students, going one step further classification of items in terms of reading demand. The results obtained are then supported by further analysis of items similar to those considered in the first part of the present study, but administered in different years: all the results in terms of DIF analysis are confirmed also in the similar items’ analysis.

The research described in this paper focused on the issue of describing and understanding how mathematical discussion develops in a hybrid learning environment, and how students participate in it. The experimental plan involved several classes working in parallel, with pupils and teachers interacting both in their real classrooms and in a digital environment with other pupils and teachers. The research was based on a rich set of data collected from the M@t.abel 2020 project, which was developed in Italy during the Covid health crisis. Based on Complementary Accounts Methodology, the data analysis presented in this paper involved specialists from the fields of mathematics education and inclusive education. In the study we considered the complexity of learning and the different elements that have an impact on students’ activity and participation, when they are engaged in mathematical discussions within the multilevel-digital environment that emerged due to the pandemic. These parallel analyses showed that ‘mathematical discussion in the classroom’ is a complex (and sometimes chaotic) phenomenon wherein different factors interweave. A complementary approach assists in developing a global vision for this dynamic phenomenon and in highlighting local episodes that are crucial in this interplay of factors. It is precisely in these episodes that the role of the teacher is fundamental: these episodes appear as catalysts for the different variables, with the teacher acting as mediator.

National and international surveys highlight a strong disparity in males and females results in mathematics: boys outperform female in almost all the countries and in all school levels. In the international context, Italy appears to be one of the countries in which the results related to gender differences in mathematics are more alarming and INVALSI tests’ data confirm a very marked gender gap in favour of males at all school levels. In this paper we present the international situation regarding gender differences in mathematics starting from large scale assessment and paying particular attention to the Italian situation. Hence we present a detailed overview of the causes underlying the gender gap in mathematics, analysing the main studies on this issue and trying to provide a complete, though complex, interpretation of this phenomenon.

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.

Research, at both national and international levels, has started to focus on the gender gap regarding student performances in technological/scientific topics. Fervent ideological and epistemological debates have sprung up, particularly concerning the differences in mathematics test results between males and females (with males outshining females in most countries). In this paper, we analyse some questions taken from the INVALSI mathematics tests administered at varying educational stages; emergent didactic phenomena are investigated via one of the key concepts of mathematics education, the didactic contract. From a quantitative analysis, based on the percentage of answers given and Rasch Model results, it is possible to identify the presence of significant gender differences between the performances which can be traced back to the effects of the didactic contract. Furthermore, study of the features which accompany these gender gaps in the case studies allows us to investigate the gender gap in mathematics via a new interpretative method which also takes into account student ability levels.

The paper presents some reflections and activities developed by researchers and teachers involved in teacher education programs on cultural transposition. The construct of cultural transposition is presented as a condition for decentralizing the didactic practice of a specific cultural context through contact with other didactic practices of different cultural contexts. We discuss the background theoretical issues of this approach and also give an analysis of two examples of cultural transposition experiences carried out in Italy. In particular, by means of qualitative analysis of some excerpts, discussions, and interviews, we show that the contact with different perspectives coming from China and Russia fostered educational practices and reflections on whole number arithmetic education.

This study presents a quantitative approach based on Differential Item Functioning analysis within the Item Response Theory framework, to quantify gender differences in tackling specific mathematical items. We use this approach to explore two crucial topics in mathematics education (misconceptions in decimal numbers, and estimation) by analysing answers given by Italian students to specific mathematical items taken from a sample of 1400 items administered in INVALSI tests since 2008. For each item, we have a sample of 30,000 students per year, statistically representative of the entire Italian student population. The results section presents a didactic interpretation of the statistical evidence and shows how interdisciplinarity between statistics and mathematics education, with a mixed-method approach (Johnson & Onwuegbuzie, 2004), represents a good approach to exploring the gender gap in relation to specific constructs of math education. This approach, common in many disciplines, can also make an interesting contribution to mathematics education research.

This study is aimed at exploring how different formulations of the same mathematical item may influence students’ answers, and whether or not boys and girls are equally affected by differences in presentation. An experimental design was employed: the same stem-items (i.e., items with the same mathematical content and question intent) were formulated differently and administered to a probability sample of 1647 students (grade 8). All the achievement tests were anchored via a set of common items. Students’ answers, equated and then analysed using the Rasch model, confirmed that different formulations affect students’ performances and thus the psychometric functionality of items, with discernible differences according to gender. In particular, we explored students’ sensitivity to the effect of a typical misconception about multiplication with decimal numbers (often called “multiplication makes bigger”) and tested the hypothesis that girls are more prone than boys to be negatively affected by misconception.

Many research papers have studied the problem of taking a set of data and separating it into subgroups through the methods of Cluster Analysis. However, the variables and parameters involved in Cluster Analysis have not always been outlined and criticized, especially in the field of Science Education. Moreover, in the field of Science Education, a comparison between two different Clustering methods is not discussed in the literature. Conceptions of students about modeling in physic are investigated by using an open-ended questionnaire. The questionnaire is analyzed through Clustering methods. The clustering results obtained by using the two methods are compared and show a good coherence between them. The results are interpreted and are compared with literature results. A synergism between the two clustering methods allows us to obtain more detailed and robust information about the modelling concept. Looking at the content from a pedagogical point of view, our study allowed us to obtain more detail about the relationship between different student conceptions of modeling in physics.