and queue up at a teller. or that pos or online electronic payments did not exist. however, innovation also enables agents to create complex and often opaque products, whose risk structure is difficult to understand and whose economic rationale is not always obvious. the greater ease in making payments, borrowing money or investing savings that technology affords is itself not an unmixed blessing, in that it may be conducive to hasty, imprudent or uninformed choices. hence the need to improve all areas of consumer protection, and to increase customers ’ ability to understand risks and rewards, to assess the suitability of products for their particular needs, and more generally to exploit the undisputed advantages of innovation while avoiding its pitfalls. financial education itself, like all kinds of education, can leverage on new technologies that make it possible to reach a much vaster public, to tailor didactic content to specific needs, to use novel teaching tools, and to design efficient and effective surveys to test the results achieved. it must, on the other hand, avoid the risk of turning the digital divide, geographical or generational as it may be, into another source of financial exclusion. 39 the bank of italy has taken on the challenge of digitalisation in its educational projects. our financial education portal, ‘ economics for everyone ’, has been online since the end of 2019, and has over 50, 000 hits per month. the portal ’ s content is supplemented by interactive and multimedia tools meant to encourage the general public to engage and identify with it, especially people who are less expert, and to stimulate them to learn more about personal finance. let me now conclude by mentioning two facts that could make educational challenges even more complex in a digital environment. the first is linked to the well - known ‘ cognitive bubble ’ and ‘ echo chamber ’ 40 effects. the web contains all sorts of information, including academic debates that were once confined to academia, or technical advice that was once the preserve of a selected few. in principle, abolishing the barriers to the circulation of information is a good thing. however, to make sense of the almost infinite amount of information available, a finite mind needs criteria and filters. when choosing from an enormous menu, both human inclination and the logic of search engines tend to act selectively and confirm initial bias. while in theory everyone can access all information, in practice self - contained bubbles may emerge ( naturally or by deliberate action ), whereby many web users receive information, whether

##lana saggi ’, translation by emilio diana, rizzoli, milano. maria montessori, dall'infanzia all'adolescenza, garzanti, milan 1949 ( the french edition had the title ‘ de l'enfant a l'adolescent ’, 1948 ). ‘ a great many people find financial issues difficult and boring. that is a weak foundation for making good financial choices. at least some of those problems originate in the mental block many people encounter when it comes to mathematics. finance is a numbers game. and research by the department for business, innovation and skills suggests there are an incredible 17 million adults in the uk whose standards of mathematics are no higher than those of a primary school child. the way maths is taught may be part of the problem here. for many, maths is a turn - off because it seems unrelated to their everyday lives ; it lacks real - world relevance. sad to say, payday lenders have a greater resonance to many people than pythagoras ’ s theorem. the abstract nature of mathematics, as taught, leads many children to tune out or switch off entirely. others conclude that they simply do not have “ a maths brain ”. this is an educational scar that can last a lifetime ’, andrew g. haldane ( 2016 ), the great divide, cit. pp. 11 - 12 ‘ part of the solution may come from making maths relevant to people ’ s lives, to link it to real - world decisions. and what better set of real - world decisions than financial ones : how to draw up a monthly budget of debits and credits ; how to make sense of an annual percentage rate on a loan ; how to decide between competing savings, pensions and mortgage products. these are big financial decisions that, if flunked, can have big social, as well as financial, consequences ’, andrew g. haldane ( 2016 ), the great divide, cit. p. 12. ‘ my objective in this essay is to try to explain why intellectuals who are interested in economic issues so consistently balk at the concept of comparative advantage. why do journalists who have a reputation as deep thinkers about world affairs begin squirming in their seats if you try to explain how trade can lead to mutually beneficial specialization? why is it virtually impossible to get a discussion of comparative advantage, not only onto newspaper op - ed pages, but even into magazines