Do the institutes promote propaganda or are they instilling appreciation of rich culture that was quashed?
It is only natural China should turn to its wisest son, Confucius, who lived from 551 to 479 BC, to lend his weight to the country's most ambitious efforts to spread Chinese language and culture around the world, including Ireland.
When Spain wanted to promote its culture, it turned to Cervantes, the author of Don Quixote, and the Germans had Johann Wolfgang von Goethe.
In China, Confucius is best known for a complex value system based on the principle of humanity and how people interact with the broader community. The goal is to achieve harmony, with everyone knowing their place within the broader social order.
Confucius is best known in China for revolutionising the education system and for inventing a ruthless system of examinations that remains a key plank of tuition in China today.
But there is another dimension. China is keen to match its formidable economic strength with diplomatic and political influence, and the Confucius institutes are central to Beijing's efforts to promote this soft power.
"The Confucius institutes are just one of the building blocks in the drive for soft power," says June Teufel Dreyer, a professor of political science at the University of Miami. "The Confucius Institutes do have a Confucian ethos, because they will typically present lectures for the community, what a true Confucian scholar recently referred to as "pop Confucianism"," she says. "They were set up in universities but also teach in primary and secondary schools, which is very unusual. The Chinese Confucius institutes have been characterised by a lot of things that are just factually erroneous or just give a very skewed or misleading impression," she says.
The institutes' headquarters, in Beijing, is run by the Office of Chinese Language Council International, more commonly known as the Hanban, which is closely linked to the Chinese ministry of education.
But many critics have a problem with the institutes' links to the United Front Work Department, whose numerous duties include handling Tibet policy for the Chinese government.
Dreyer cites a couple of examples where the official Chinese version of events differs from the western one. In one cartoon in a schoolbook, the Korean war (1950-3) was depicted as being started by the US. China was North Korea's ally in that war. There have also been signs of anti-Japanese bias: another school textbook had a story of a Chinese child heroically killing a Japanese soldier.
"Propaganda is a loaded word; what every country does is propaganda. What concerns me about these is that they are blatantly misleading and sometimes counterfactual. They do include in their ambit some very young children who won't be able to independently assess what is going on here," says Dreyer.
During the period of ideological extremism known as the Cultural Revolution (1966-76), ultra-leftist Red Guards turned on any bourgeois decadence they could find, and Confucius was a prime target. Red Guards destroyed Confucius's family home, his family's grave plot and a temple in his honour in his eastern hometown of Qufu, destroying more than 6,000 priceless relics.
However, as in many other areas of society in China, there has been a change in thinking on Confucius. The leadership believes burgeoning wealth and the rise of consumerism have seen many traditional Confucian values of honour and decency slip away in favour of self-serving, money-grabbing behaviour. Also, Confucian thinking is secular, which sits easily with Marxist thinking.
Scholars and, increasingly, the Communist Party believe following some sound Confucian principles would be conducive to the building of a "harmonious society".
Steven W Mosher, the president of the human-rights organisation Population Research Institute, says the United Work Front is all about "subversion, co-option and control" and that its ultimate aim is to control all western academic discourse on China.
"It is ironic that Communist leaders, who for nearly a century vilified Confucius as the very embodiment of feudalism, should now seize upon the name of the ancient Chinese sage for their own purposes," he said in an address this year, during which he described the Confucius institutes as Trojan horses.
Peter Mattis, the editor of China Brief at the Washington-based Jamestown Foundation, believes that the Confucius Institutes are aimed at allowing Beijing to determine how China is discussed internationally and how students learn about it.
"China's leaders, after all, belong to a party based on a foreign ideology that once tried to wipe out traditional Chinese culture. The country's rich cultural heritage stands on its own merits, and many foreigners can learn a great deal from it. Depoliticising foreigners' exposure to China's culture and history can be only a good thing," he says.