Interdisciplinarity for learning and teaching mathematics

Complex problems need interdisciplinary approaches. Thinking in an interdisciplinary way asks for changes in learning and teaching and hence in our views on pedagogical problems. An interdisciplinary approach could provide a new framework also for dealing with disciplinary didactical problems. In this paper, we propose a methodology which we call globally interdisciplinary laboratories as an effective way to practice interdisciplinary teaching at the high school level. We discuss the possibility of applying this methodology to the learning and teaching of mathematics. Globally interdisciplinary laboratories are designed by a pool of researchers in collaboration with high school teachers of several disciplines and they are delivered in the classroom by a pool of teachers in co-presence. This has been experimented in Italy in many classes which are part of a national educational project called Liceo matematico. In this paper, we discuss the general design principle of a GIL and exemplify the methodology by considering the one we have called educate the sight, which aims at stimulating, within an interdisciplinary framework, intellectual curiosity, the ability to spot the prominent features of a problem and, in mathematics, the ability of conjecturing, which should be one of the fundamental concerns of mathematical teaching, according to Polya’s decalogue for mathematics teachers (POLYA, 1981)

Pompilj, Giuseppe

Voce biografic

Decomposition of variance in terms of conditional means

We test against two different sets of data an apparently new approach to the analysis of the variance of a numerical variable which depends on qualitative characters. We suggest that this approach be used to complement other existing techniques to study the interdependence of the variables involved. According to our method the variance is expressed as a sum of orthogonal components, obtained as differences of conditional means, with respect to the qualitative characters. The resulting expression for the variance depends on the ordering in which the characters are considered. We suggest an algorithm which leads to an ordering which is deemed natural. The first set of data concerns the score achieved by a population of students, on an entrance examination, based on a multiple choice test with 30 questions. In this case the qualitative characters are dyadic and correspond to correct or incorrect answer to each question. The second set of data concerns the delay in obtaining the degree for a population of graduates of Italian universities. The variance in this case is analyzed with respect to a set of seven specific qualitative characters of the population studied (gender, previous education, working condition, parent's educational level, field of study, etc.)Comment: 3 figure

Ci sono tanti modi per essere aleatori

Possiamo immaginare dei criteri che ci aiutino a distinguere sequenze binarie finite generate dal lancio ripetuto di una moneta da altre immaginate da un agente umano o simulate con una calcolatrice che usa un algoritmo deterministico? Si possono individuare proprietà caratteristiche delle sequenze delle diverse classi considerate? Intorno a queste domande abbiamo costruito un percorso, proposto in una classe terza di liceo scientifico, che ha stimolato gli alunni a riflettere criticamente sulle loro convinzioni relative alla probabilità e al caso

Alcune applicazioni della Matematica all'analisi dell'elettrocardiogramma

Questo lavoro si propone di far conoscere due importanti applicazioni della Matematica all'analisi dell'elettrocardiogramma(ECG). La prima è quella del riconoscimento delle principali caratteristiche dell'ECG e in particolare del picco R, che corrisponde alla sistole. Si considerano due metodi: i filtri lineari e l'analisi multiscala basata sulle wavelet. La seconda riguarda l'analisi della serie temporale degli intervalli che separano due picchi R consecutivi dell'ECG (sequenza RR), che descrive l'andamento nel tempo della frequenza cardiaca. Qui i metodi considerati sono quelli dell'analisi spettrale e dell'analisi simbolica. Di quest'ultima si illustra un'applicazione all'analisi di sequenze RR di fibrillazione atriale

Uso di un software di Geometria Dinamica nella formazione dei futuri insegnanti

In this paper we make some considerations about using a dynamic geometry software for teaching history of mathematica at university level. After a short introduction to the software GeoGebra, we discuss four activities. The first is an exploration of the menu of the tools menu following the first part of the first book of the elements of Euclid. The second is an activity about pentagons and pentagrams which aims at finding a more natural way of discovering their properties than that suggested by Euclid as an illustration of the method of synthesis and analysis. The third is an activity on circle inversion and its connection with polarity and the construction of the fourth harmonic point after three given point on a line. The activity continues with the reading of Poncelet's ideas about ideal secants of conics and how to use GeoGebra to make sense of them. The fourth activity shows how to use the possibility to move objects in GeoGebra to make sense of the geometric intuition behind Cremona and Hirst letters about the Bellavitis-Hirst inversion of a circle. We discuss the reasons why we believe that these kind of activities may help students to read and understand original writings in projective geometry and why we believe that they may be very effective in the training of prospective teachers of mathematics.Comment: 38 pages, in Italian, 44 figure

La matematica come collante culturale nell'insegnamento

In questo lavoro presentiamo il progetto di ricerca dell'Università di Salerno che ha portato alla sperimentazione per tre anni del Liceo Matematico in 18 classi del Liceo Scientifico in Campania. Questa presentazione vuole essere un contributo al dibattito sui Licei Matematici che, in diverse forme, sono stati attivati nel 2016 anche in altre regioni d'Italia