This work is part of an investigation conducted in Italy, which aims to explore the effects of instruction on secondary school students' combinatorial reasoning. We gave a questionnaire adapted from Navarro-Pelayo's research to two groups of students with and without instruction on combinatorics in order to analyse the students' performances and…

This study investigates the relationship between students' problem-solving skills in solving mathematical problems and asynchronous collaboration in digital learning environments. The research focuses on the Digital Math Training (DMT) project, designed by the DELTA research group at the University of Turin, which aims to enhance students' digital…

In this paper, we describe an experiment in using history to work on problem-solving and the relationship between arithmetic and algebra. The students involved attended the first year of the Italian upper secondary school (grade 9). The original sources we used are problems from Italian treatises on arithmetic and algebra that appeared in the…

We present a model for roleplaying (RP) for university students that is aimed at fostering the interactions of each learner with the teacher and coursemates, self- and peer-assessment, as well as an awareness and meaningful learning of mathematics. Specific features of our model are its focus on metacognition and individualized learning, based on…

Operations Research (OR) is a branch of applied mathematics that deals with optimization problems arising from different real contexts. The solving process of its problems is based on the construction and resolution of mathematical models, showing the possible connections between mathematics and the real world. Nevertheless, OR is not typically…

In this paper the results of a questionnaire about mathematics teachers' inclusion in their teaching of mathematical modelling and problem posing are presented. To make teachers able to choose a coherent teaching method for a mathematical topic, teachers' knowledge of valuable methods for the teaching of mathematics should be fostered. In this…

After some studies on students with Down syndrome (DS) who learned algebra and problem solving and few single case studies on analytic geometry, here the experience on analytic geometry was extended to 6 adolescents with DS, who attended mainstream schools. They were taught individually in the afternoon, one day per week, for 9 months by the same…

Introducing the distributivity property of multiplication over addition is a well-known challenge in mathematics education, especially in primary school. As a contribution, this paper presents the results of a cycle of design research that focuses on the design, implementation and evaluation of a modelling activity in which 2nd-grade students are…

This paper focuses on difficulties that primary school students have in facing mathematical word problems. In particular, we are interested in exploring how they develop in the transition from grade 2 to grade 5. The research basis of the hypothesis is that some difficulties detected in grade 5 are already predictable in grade 2. Starting from the…

Self-assessment, in the education framework, is a methodology that motivates students to play an active role in reviewing their performance. It is defined as "the evaluation or judgment of 'the worth' of one's performance and the identification of one's strengths and weaknesses with a view to improving one's learning outcomes". The goal…

In this paper we analyse the role of the teacher in a Digital interactive Storytelling in Mathematics (DiST-M) activity. involved in the story as a character (the Guru, a math expert), the teacher acts as a mediator in students' problem-solving process. We analyse how the teacher may orchestrate the mathematical discussions to allow students…

A more motivating way of introducing students to probability theory is through real-world problems. Since heuristics play an important role in our probabilistic judgement, knowing how to avoid incorrect probabilistic reasoning, which leads to several biases, could help students to develop more critical thinking skills. In this paper, we present a…

This longitudinal study aimed to identify specific executive function (EF) profiles in 5-year-old children and to examine the association between these profiles and later math achievement. Six EF measures were administered to 175 children who were then tested in Grades 1 and 3 on math tasks. Using a cluster analysis, four EF profiles were…

Educators and several national standards highlight the role that problem solving should play in students' mathematics education: problem solving is recognized as one of the most significant activities of doing mathematics. From the research point of view, nowadays, it is well established that cognitive and affective factors come into play in…

A classroom activity for high-school students, aiming at introducing space geometry from plane geometry has been introduced back in 2009 by Mammana, Margarone, Micale, Pennisi and Pluchino (2009a). The activity was based on the use of a Dynamic Geometry System and of the analogy between figures. Several aspects of the activity have been studied in…