A maths textbook asking schoolchildren to solve problems with Nike shoes and Oreo biscuits has re-ignited the debate about corporate advertising in the American classroom.

Although the book was first issued in 1995, a parent’s recent complaint has led a legislator in California, one of 15 states where it is in use, to sponsor a Bill banning corporate logos in textbooks.

News reports have prodded the Texas Parent-Teacher Association to promise a “textbook alert” on the book via the Internet. “It’s not appropriate to have a commercial promotion to a captive audience,” said the Texas PTA’s legislative action chair Karen Miller.

Critics say commercialism is now rampant in US schools. In a well-publicised case last year a Georgia boy was briefly suspended for wearing a PepsiT-shirt on a “Coke in Education” day at his school. The Texas PTA features a list of corporate sponsors on its own Website.

The maths book is “hardly the most egregious example of commercialism infiltrating schools”, wrote Steven Manning, a research fellow at the Open Society Institute, in the New York Times recently. “Eager to attract a captive audience of young customers, marketers are showering schools with advertising and hucksterism.”

The textbook, Mathematics: Applications and Connections, from McGraw-Hill, a prominent US education publisher, asks students in one problem how long it will take to save for a $68.25 (pound;42.50) pair of Nike shoes.

Its 1995 and revised 1999 edition, aimed at sixth-graders (around 12 years old) has numerous references, photos and logos for Barbie dolls, Monopoly, Sony PlayStations and even Kellogg’s Cocoa Frosted Flakes. Disney characters and McDonald’s also appear.

The publisher’s editors and authors said these were not paid advertisements. Brand-name products were included simply to make maths “real” to children, they said.

The past year has seen isolated protests over the level of corporate sponsorship in US classrooms. Critics say the current trend began with Channel One, which offered schools free televisions and a stream of commercial programming.

In Seattle, Washington, on the West Coast, parents who staged walk-throughs in schools to check for examples of advertising found many examples, from soft-drink stands to posters. But it did not prevent a Seattle school district signing a $10 million deal with Coke to stock its drink machines exclusively.

In Colorado, a leaked memo on another Coke deal concerned a promotion that would qualify schools for annual payments of thousands of dollars.

A total of 8,000 schools have signed up for free computers from Zapme!, a Silicon Valley company, with the proviso that ads border the screens at all times, and the computers are available for use at least four hours a day. These and similar deals are ardently defended by school administrators as a means of re-equipping classrooms.