1,720,976 research outputs found
Nuovi approcci nei corsi di Matematica per l’Architettura: connettere forme e formule in geometria attraverso esperienze laboratoriali
No full textI corsi di matematica del primo anno in architettura mirano a fornire agli studenti il linguaggio scientifico, aumentare il pensiero spaziale, creativo, insieme alla capacità di riconoscere e creare forme e consentire un uso consapevole dei software di progettazione. Tuttavia, i futuri architetti italiani considerano spesso questi corsi marginali nella loro formazione (Pagano & Tedeschini Lalli, 2005). Per superare questa criticità, abbiamo sviluppato un’officina sperimentale di 4 ore seguendo la metodologia DBR (Brown ,1992; Barab & Squire, 2004). Il contenuto didattico è la parabola, familiare agli studenti del primo anno, riscoperta con attività volte a svelare il legame tra forma geometrica e descrizione analitica. Gli studenti piegano (su carta) l'inviluppo di una parabola, ne verificano la proprietà di riflessione, "scoprendo" così la descrizione algebrica della curva e, infine, la applicano ad un problema di luminosità in architettura. Dopo la fase di progettazione, il laboratorio è stato sperimentato con due gruppi di 75 studenti del primo anno del Politecnico di Torino e dell'Università Roma Tre nell'a.a. 2021-22. Il confronto delle nostre note sul campo con l'analisi comparativa delle risposte di un questionario finale ci ha fornito risultati incoraggianti sull'apprendimento concettuale e sul coinvolgimento, con un impatto sulla matematica al di là dell'esempio specifico considerato nell’officina.First-year mathematics courses in architecture aim to provide students with scientific language, increase spatial, creative, thinking together with the ability to recognize and create forms, and enable informed use of design software. However, future Italian architects often consider these courses marginal in their education (Pagano, & Tedeschini Lalli, 2005). In order to overcome this criticality, we developed an experimental 4-hour workshop following the DBR methodology (Brown ,1992; Barab & Squire, 2004). The didactic content is the parabola, familiar to first-year students, rediscovered with activities aimed at revealing the connection between geometric form and analytical description. Students fold (on paper) the envelope of a parabola, verify the reflection property, thus "discovering" the algebraic description of the curve and, finally, apply it to a problem of architectural luminosity. After the design phase, the lab was experimented with two groups of 75 first-year students from Politecnico di Torino and Università Roma Tre in a.y. 2021-22. Comparison of our field notes with comparative analysis of the responses of a final questionnaire provided us with encouraging results on conceptual learning and engagement, with an impact on mathematics beyond the specific example considered in the workshop
Thinking inside and outside the box: a hands-on paper folding activity leading to optimisation problems
No full textThis paper explores the use of hands-on origami activities to enhance mathematics learning in high school and university courses, improving both student engagement and deeper understanding of mathematical topics. We designed an origami-based workshop to address the concept of domain of a function and its behaviour at the boundary of the domain alongside two optimisation problems, emphasising real-world applications and creative problem-solving. By implementing these activities in various courses and contexts, we evaluated their effectiveness using a design-based research methodology
Challenges in Mathematics Learning at the University: An Activity to Motivate Students and Promote Self-awareness
Full text linkMath anxiety is always just around the corner. At the university, it makes students continuously postpone the Calculus exam, leading them into a vicious circle of low confidence and poor performance. To get out of this situation, students need to be motivated and involved. They also need to master metacognitive strategies that can support their learning process. In this paper, we present a digital activity entitled Advent Calendar, focused on storytelling and proposed through the logic of spacing. The aim is to increase students’ motivation and self-awareness, but also to obtain learning analytics useful to monitor progress and solve any possible weaknesses with appropriate feedback. The activity was proposed using the tools offered by the Learning Management System (LMS) Moodle. It was tested in three university courses at two Italian universities, the University of Milan and the Polytechnic University of Turin, with students’ active participation. This participation had a high impact on the results of the final examination. Feedback demonstrated positive feelings and good results in the motivation process, while the analytics showed a continuous approach to the study of mathematics
Teaching Geometry and Surfaces Evaluation Through Graphic Representation and Dynamic Paper Models
Full text linkTo make the geometrical cognitive process more interactive, we produced teaching aids (tangible models, graphic tablets) that help students in visualiz-ing their geometrical-analytical investigations of the architectural artifacts and enhance their spatial prefiguration and critical form-reading skills, three-dimensional thinking and geometrical reading of shapes. Then, we looked for a medium suitable to create simple three-dimensional models, not only observable, like virtual models, not only tangible, like physical models pro-posed in the design studios, but also dynamic, using multiple media and lan-guages in the same training message.
As an example, we present here an interdisciplinary lesson between Cal-culus and Architectural Drawing and Survey Laboratory about developable surfaces, experimented on first year students of the bachelor program in Ar-chitecture. The lesson is based on the use of a graphic tablet and some ori-gami inspired models: it summarizes the geometric description of a pyramid and a cloister vault of equal height and equal orthographic projection on the horizontal plane.
We saw that tackling the same topic in both teaching contexts is not a use-less overlap, but a stimulus to compare different languages and methods. 2D and 3D paper models of artifacts – and of projective reduction from 3D to the plane – aid spatial intuition and the subtle exercise of controlling mental images which replace artifacts, turning 3D configurations into signifying im-ages. Moreover, this experience stimulates reading and evaluation of the drawn geometry (ruled surfaces, projections, developments), increasing criti-cal sense in reading the built environmen
Origami, Art and Mathematics at school
No full textWe present a new experience of how the introduction of origami at math classes brings a lot of benefits, viewing origami as a tool that allows to construct cognitive artifacts and also as a clear example of learning by doing strategy. The advantages of the use of origami in mathematics education are clear: visualization, improvement of spatial skills and specific language, tangible approach to problem solving, but also soft skills like self-confidence, patience and concentration. However, this time we add an artistic component, what makes this experience original and cross curricular, and adds other advantages to the previous ones. Specifically, we present a part of a project held in an Italian school, done together with the Italian association “T’immagini” (@asstimmagini), that involved all the levels of studies, from kindergarten to high school, during the scholastic year 2018-2019. In this work we focus on the activities held at the classes of students from 5 to 7 years, giving enough information so that teachers can reproduce the project at their classes. We also sketch how to extend this approach to higher levels of education. For the 5th degree level, the complete work is at the proceedings of Edulearn19. The main idea of the project consisted in chose famous paintings all related by the subject of the sky. Each teacher of each class level chose a painting. After that, we chose the parts of this painting we wanted to cover with origami models, following the shapes on it or making a free interpretation of the elements represented. In this way, we obtained a new 3D collaborative artwork. On each of the origami models, we designed a math lesson, whose topics where all related by some theme, and helped to make connections between different math subjects. • At the kindergarten level, the painting chosen was Castle and Sun, by Paul Klee. The part we decided to cover were the castle and the sun. From the point of view of learning folding and vocabulary techniques, it was a way to introduce two simple origami bases, the Triangular or Waterbomb base and the Preliminary base. This allowed to present different types of shapes and to practice the recognition of triangles and squares. The model to conclude with something to bring at home was a traditional box. At the first level of primary school the goals where similar and the painting chosen was by Paul Klee, too. • At the second year of primary school, the painting chosen was Water Lilies, by Claude Monet. The part we decided to cover were parts of the pound and the water lilies. The origami base showed was the Blintz base and all the math activities were related with symmetries. The model involved was the traditional origami model Fortune Teller. The participants, in total around 200 students, appreciated a lot these activities, as show the results of surveys
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Non degenerate projective curves with very degenerate hyperplane section
No full textWe study the Hilbert scheme of non degenerate locally Cohen-Macaulay projective curves with general hyperplane section spanning a linear space of dimension 2 and minimal Hilbert function. The main result is that those curves are almost always the general element of a generically smooth component H(n,d,g) of the corresponding Hilbert scheme. Moreover, we show that the curves with maximal cohomology almost always correspond to smooth points of H(n,d,g)
- …
