In this article, we discuss the development and the administration of a multiple-choice test, which we named Test of Calculus and Vectors in Mathematics and Physics (TCV-MP), aimed at comparing students’ ability to answer questions on derivatives, integrals, and vectors in a purely mathematical context and in the context of physics. The comparison between the two contexts was achieved by using parallel (isomorphic) questions in mathematics and physics. The final version of the test contains 34 items (17 in a purely mathematical context and 17 in the context of physics) involving different representations (graphs, words, numbers, and formal expressions) of the concepts covered by the test. The test was administered in Spring 2018 to 1252 first-year students enrolled in 23 different degree programs of the School of Science and the School of Engineering of the University of Padua. We assessed the validity, reliability, and discriminatory power of the test both as a whole and at the single-item level, obtaining values within the desired ranges. The analysis of students’ answers to individual items and the comparison between parallel mathematics and physics items provides insights into the factors that affect students’ ability to use derivatives, integrals, and vectors in the context of introductory physics. We believe that the instrument we have developed can be useful not only for research purposes, but also for instructors and for students.

Instructional design is an essential part of teaching practice: both researchers and teachers are engaged in finding strategies to deal with this complex work. We propose the use of storytelling as a skeleton to structure a long-lasting teaching unit, maintaining coherence and giving meaning to its various elements. We refer to an interpretation of storytelling for educational purposes as a role-playing game, drawing inspiration from the Digital Interactive Storytelling in Mathematics framework. Designing a learning unit based on storytelling means integrating every moment of the teaching–learning process within the narrative: the teacher and students are all part of the same story, which motivates every activity carried out in the unit and contextualizes the tasks performed. Moreover, the assessment is also integrated into the narrative flow. In this study, we designed an exemplary Storytelling Learning Unit (SLU) model for the study of light, promoting modelling and argumentation skills in mathematics and physics. This unit, intended for ninth-grade students in an Italian scientific high school, was co-designed by the teacher of the class in which it will be implemented. This work particularly focuses on the design process. From reflection on the specific unit developed, general design principles for creating a SLU were hypothesized.

In this study, we compare students’ performance in solving mathematics and physics exercises with their confidence level in answering them. Accurate self-assessment of confidence is known to positively correlate with academic achievement, yet confidence is often neglected when designing teaching interventions. The research presented here aimed at investigating the relationship between students’ confidence levels and test scores and its evolution over a short lesson cycle. We also examine the presence of gender-based differences. The study was first conducted with a pilot group of 43 secondary school students and later expanded to 260 students. A modified version of the Test of Calculus and Vectors in Mathematics and Physics was used, incorporating confidence assessment for each item. Results suggest that, while test scores and confidence levels improved overall following the lesson cycle, this did not translate into a better “calibration” of the students (i.e., the alignment between confidence level and actual performance). Specifically, male students became more overconfident, whereas female students became more underconfident. These findings support taking into account confidence when designing teaching interventions and using confidence assessment practices to train students’ self-assessment skills.

Information about the paper titled "SUPPORTING STUDENTS' MATHEMATIZATION SKILLS FOR PHYSICS: A TEST AND A LEARNING PATH FOR SECONDARY SCHOOL" at IATED Digital Library

This article reports on the design and classroom implementation of interdisciplinary worksheets aimed at strengthening the relationship between mathematics and physics in upper-secondary education. Grounded in complementary theoretical perspectives—including the structural role of mathematics in physics, interdisciplinarity, covariational reasoning, and specific disciplinary topics—we developed six research-based activities on vectors, derivatives, and integrals and implemented them within a teacher learning community. Data from 203 grade-13 students include a baseline quantitative-reasoning assessment, a post-test on calculus and vectors, and item-level confidence ratings, complemented by teacher focus-group evidence. Results show improved alignment between confidence and performance and suggest a possible threshold effect, with gains emerging primarily for students who completed all six activities. Teachers reported that the worksheets acted as concrete boundary objects that made mathematics-physics connections instructionally actionable, while the community structure supported adaptation, reflection, and sustained interdisciplinary practice.