La percezione della numerosità e la sua relazione con le abilità numeriche

La percezione della numerosità e le abilità numeriche

La percezione della numerosità e la sua relazione con le abilità numeriche

6-4 ÷ 2+3 8 6 6 V2Perché è importante: vita quotidiana, scelte di vita, economia, benessere

Parma Ferrara POI Modena Bologna Genova Ravenna La Spezia Cesenao Rimini Pietrasanta O San Marino Firenze Sebenico Pisao Ancona Arezzo 10 ore 7 min Livorno 951 km Ma San Benedetto Italia del Tronto Grosseto E45 Mare Adriatico 10 ore 13 min .008 km Cors @Roma Ajaccio ESS Fiumicino Latina Foggia Barletta Ba 9 ore 41 min 934 km assari Salerno Matera erõ Nuor Sardegna Mar Tirreno

Il contagio in Italia

IL CONTAGIO IN ITALIA

• Indice RT
• Incidenza per 100.000 abitanti 1.823 Soglia di rischio grave ·150 ··· 1,0 1.362 962 848 836 776 717 699 552 510 433 1,15 1,12 1.0 0,83 0,97 0,93 0,89 0,94 0,77 28/1 4/2 11/2 18/2 25/2 4/3 11/3 18/3 25/3 1/4 8/4 15/4 22/4 29/4 FONTE: Iss

L'EGO - HUB

L'EGO - HUB S CIENCE TECHNOLOGY PARTENZE TRENO MILANO C.LE 06:22 90' 3 REG 2178 MILANO G. P. 06:34 90' 3 REG 10572 MILANO G. P. 06:51 80' 3 REG 10574 MILANO C.LE 07:01 80' 3 RGV 2180 MI BOVISA 07:09 80' 5 S13 23106 MILANO C.LE 07:16 80' 3 REG 2160 MILANO G. P. 07:25 90' 3 REG 2162 MILANO CERT. 07:34 90' 3 EC 141 NIZZA 07:35 30' 2 . U VARIAZIONI, PERTUN GUHSTU H ON THE ORARIO RIT BIN DESTINAZIONE ENGINEERING M ATH REG 10576 0,73 0,75 0,96 0,93 725 672 1.24 675 Teramo Terni Spalato Siena Zara Iristano Potenzahttps://www.oecd.org

PISA e le abilità numeriche

Science Mathematics 450 - O 475 - 500 525 550 475 500 - 525- 55 GRC GRC 21 esimi su 23 SVK - C HUN - O ITA - ESP LUX - O LTU HUN - LUX O LTU - 0 SVK - O ESP ITA LVA - OAVG 0 OAVG - PRT AUT - O FRA PRT O LVA DNK - O AUT FRA CZE IRL DEU CZE - IRL BEL - SWE · SWE - 0 FIN DEU - BEL NLD - DNK SVN O SVN C POL - 0 POL O FIN - 0 NLD - EST - O EST - 450 - O 17 esimi su 23 L'italia? PISA is the OECD's Programme for International Student Assessment. PISA measures 15-year-olds' ability to use their reading, mathematics and science knowledge and skills to meet real-life challenges.

Il senso del numero

00 0building blocksApproximate number system THE NUMBER SENSE How The Mind Creates Mathematics 3 9 1 S Stanislas Dehaene 1997 Sistema che permette una stima rapida ma approssimativa del numero di oggetti/eventi presenti nello spazio (e nel tempo) Dominio-specifico 7 Conteggio seriale (lento e preciso)

Esempi di percezione della numerosità

"Percezione della numerosità" ESEMPIO"Percezione della numerosità" ESEMPIO"Percezione della numerosità" ESEMPIO.

Ricerca sulla percezione della numerosità

WHAT ANIMALS REVEAL ABOUT OUR UNIQUELY MATHEMATICAL MINDS CAN FISH COUNT? BRIAN BUTTERWORTH Butterworth, 2022 Nieder 2015, PNAS Rugani 2015, Science Wittlinger 2006, Science Ferrigno 2017, Nature comm Pica 2004, Science Izard 2010, PNASArticle Current Biology The Venus Flytrap Dionaea muscipula Counts Prey- Induced Action Potentials to Induce Sodium Uptake BBC Clicca per ingrandire

Basi fisiologiche della numerosità

Basi fisiologiche: neuroni della numerosità nell'animale e nell'uomo a. 1 VIP IPCF IPS Normalized activity 1 2 3 4 0 1 2 3 4 Number of dots b. 1 1 1 Fixation 500 ms Normalized activity 2 3 Sample 800 ms 4 Delay 1000 ms Non-match 2 3 4 0 0 1 2 3 4 1 Number of events Nieder, A., The neuronal code for number. Nat Rev Neurosci, 2016. 17(6): p. 366-82. 0 1 Test 1200 ms Match 1 Test 1200 ms Match TimeNeuron Volume 44, Issue 3, 28 October 2004, Pages 547-555 CelPress Article Tuning Curves for Approximate Numerosity in the Human Intraparietal Sulcus Manuela Piazza 1, Véronique Izard 1, Philippe Pinel 1, Denis Le Bihan 2, Stanislas Dehaene 21 X Solco intraparietale Stream of habituation stimuli (16 dots) 150 ms 1050 ms ....... Occasional deviant stimuli 8 (far) 10 (medium) 13 (close) 16 (same) 20 (close) 24 (medium) 32 (far) Number only B 0.4 Activation 0.2 0 -0.2- Nhabit 16 Nhabit 32 -0.4 8 16 32 64 Deviant numerosity (log scale)

Sviluppo della percezione numerica

Presente alla nascita

2-3 Sviluppo Presente anche alla nascita? 1 12 2 11 3 MOUSE 10 4 5 months 8 6 7 3:9 "Il senso comune sembra suggerire che questa domanda sia assurda; se la mia ipotesi è corretta il cervello umano possiede un meccanismo di comprensione delle quantità numeriche, ereditato dal modello animale, che lo guida nell'apprendimento della matematica. Deve essere presente prima dell'apprendimento delle competenze matematiche ... " Stanislas Dehaene il pallino della matematica capitolo 2 4:5,6º

Sviluppo cross-modale e cross-formato

Sviluppo: Presente anche alla nascita? cross-modale - cross-formato // preferential looking Familiarization (2 min) età 49 ore ... " tu-tu-tu-tu-tu-tu-tu-tu-tu-tu-tu-tu " ... " ra-ra-ra-ra-ra-ra-ra-ra-ra-ra-ra-ra-" .. or ... " tuuuuu-tuuuuu-tuuuuu-tuuuuu " ... " raaaaa-raaaaa-raaaaa-raaaaa " ... Test (4 trials) Fig. 1. Newborn infants were familiarized with auditory sequences containing a fixed number of syllables, and were then tested with images of the same or a different number of items (here 4 or 12). Auditory sequences were equated across numbers on extensive parameters (total duration), and visual arrays where equated on intensive parameters (size of each item, density of the array). *** *** p<0.0001 40 s . p<0.1 Looking time *** 30 20 10 0 4 vs. 12 6 vs. 18 4 vs. 8 Congruent number 2 Incongruent number Fig. 2. Newborns looked consistently longer at the displays that were congruent in number with the auditory sequences presented during familiar- ization, when the numbers to discriminate were separated by a ratio of 3:1 (4 vs. 12, 6 vs. 18), but not for a smaller ratio (4 vs. 8; ratio 2:1). Error bars represent standard errors. During the familiarization phase, the screen stayed black and sounds were played through 2 speakers that were located just behind the infant seat on each side. After 2 min of familiarization with auditory sequences, the infants were presented with test images while the auditory stimulus continued to play in background. Four test images were presented, alternating between the congruent number and an incongruent number. The images stayed on the screen until the infant looked away for 2 seconds, or after 60 s of looking.

Evoluzione della precisione del sistema

Sviluppo Come evolve la precisione del sistema durante la vita? Frazione di Weber > La più piccola differenza percepibile / intensità n1 n2 .: . Scarsa precisione Frazione di Weber Alta precisione Weber Fraction= precisione = risoluzione del sistema ("number-acuity")

Frazione di Weber e tempo di risposta

Sviluppo 10,000 participants ranging from 11 to 85 years of age B A 0.50 0.45 Weber Fraction (w) 0.40 0.35 0.30 0.25 0.20 0.15 B 2000 Response Time (ms.) 1600 - 1200 800 400 10 20 30 40 50 60 70 80 Age (yrs.)

Sviluppo rapido entro i 10 anni

Sviluppo Anche e sopratutto entro i 10 anni lo sviluppo è molto rapido 1. 아 Estimated w, linear scale 1.0 0.8 0.6 0.4 F 0.2 - 0 10 20 30 40 50 Estimated w, logarithmic scale 0.5 0.4 0.3L 0.2| 0.1 0 0.1 0.5 1 5 10 50 Age in years, logarithmic scale Age in years, linear scale Occidental infants, children and adults Mundurucu people Piazza et al., 2004 4 Pica et al., 2004 O Halberda et al., 2008 V Piazza et al., submitted Infants (Izard et al., submitted; Xu & Spelke, 2000; Xu & Arriaga, 2007) - Power function fit

Influenza della cultura: i Munduruku

Popolazione Munduruku

Influenza della cultura (popolazioni indigene) Equator L Brazil Munduruku main territory Transamazonian Rio Tapajós Highway Jacareacanga Sai Cinza Katō Rio das Tropas Missão Velha Rio Juruena Rio Cururů Rio Teles Pires 40 km Adults Children · n=9 (55.5 y) · n=10 (59.3 y) O n=9 (4.7 y) Monolingual, no instruction Bilingual, no instruction n=7 (8.6 y) Monolingual, with instruction · n=7 (38.7 y) O n=13 (9.6 y) Bilingual, with instruction Mundurukù. Popolazione "isolata" con scarsissimo linguaggio per i numeri e scarsissima scolarizzazione anche aritmetica A Mundurukú house (pilot study of 2001) A child participating in the computerized tests under supervision of the first author (Pierre Pica) An adult demonstrating how he refers to numbers by pointing to his fingers and toes (pilot study of 2001).

Linguaggio numerico dei Munduruku

Naming task scarsissimo linguaggio per i numeri, hanno parole fino al 5 Nessun lessico definito per numerosità superiori a 5 !!! -pug/pug ma =one -xep xep = two -ebapug = three 100.0 -ebadipdip = four 90.0 -pug pogbi = one hand 80.0 -xep xep pogbi = two hands 70.0 -adesu/ade gu = some, not many 60.0 -ade/ade ma = many, really many 50.0 40.0 30.0 20.0 10.0 0.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Stimulus numerosity Fig. 2. Number naming in Munduruku. Participants were shown sets of 1 to 15 dots in random order and were asked to name the quantity. For each quantity on the x axis, the graph shows the fraction of times that it was named with a given word or locution. We only present the data for words or locutions produced on more than 2.5% of all trials. For numbers above 5, frequencies do not add up to 100%, because many participants produced rare or idiosyncratic locutions or phrases such as "all of my toes" (a complete list is available from the authors). Response frequency

Capacità di approssimazione dei Munduruku

If the Munduruku have a sense of number, they should succeed in approximation tasks with quantities beyond the range for which they have number words >5 n1 n2 French controls 1 Prop correct peggio dei controlli ma comunque ben capaci di svolgere il compito Prop correct Come I controlli !! 0 All Mundurukú B Approximate addition and comparison Indicate which is larger: n1+n2 or n3 n1 n2 n3 - French controls All Mundurukú

Effetto dell'educazione sulla precisione numerica

EDUCATION ENHANCES THE ACUITY OF THE NON-VERBAL APPROXIMATE NUMBER SYSTEM Manuela Piazza, 1,2,3,4 Pierre Pica,5 Veronique Izard, 6,7 Elizabeth Spelke, 8 and Stanislas Dehaene9,1,2,3 a Mundurucú, Uneducated - Mundurucú, Some Education Italian Participants (Group Means) 0.5 2.0 1.5 0.4 1.0 Weber Fraction 0.3 Weber Fraction 0 0.2 . -0.5 -1.0 0.1 -1.5 0 -2.0 0 10 20 30 40 50 60 70 0 2 4 6 8 Age (years) Level of Education The curve derived from Italian participants fits the data from educated Mundurucus, with an initial delay plausibly due to less intense schooling in the Amazon. The performance of uneducated Mundurucus does not seem to develop beyond the 6- year-old level. B, Weber fraction, age-corrected, as a function of education in the Mundurucu. The data suggest that the second-to-third year transition might be a particularly important period for the development of precision in numerical estimation. Contrary to the numerosity task, there was no effect of education (F(5,26) = 0.77, p = . 58) over and above age (F(1,26) = 3.33, p =. 08). Indeed, the size WF was equal for Mundurucu adults with vs. without education (0.033 and 0.034, p = . 91). These results indicate that culture and education have an important effect on basic number perception. We hypothesize that symbolic and nonsymbolic numerical thinking mutually enhance one another over the course of mathematics instruction. b A child participating in the computerized tests under supervision of the first author (Pierre Pica) (standardized age-corrected residuals) · . 0.5 -