One day after getting all provinces and territories on board with the Canada Job Grant, Employment Minister Jason Kenney says he will be pushing the provinces to make new pledges this fall to spend more on training.

Nunavut signed a deal with Ottawa on Monday to deliver the job grant.

The agreement marked the end of a lengthy and often heated federal effort to get all provinces and territories to take part in the program, which was announced in the 2013 budget.

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The training grant was part of a major reform of a federal training transfer worth about $500-million a year.

But the federal Employment Minister is now setting his sights on two much larger transfers.

Mr. Kenney wants a new deal by the end of the year on the renewal of labour market development agreements worth about $2-billion a year that use Employment Insurance revenue for skills-training programs.

Mr. Kenney said he will also seek more detail on how the provinces spend the Canada Social Transfer, a $12.6-billion arrangement that supports postsecondary education, social assistance and social services. The Canada Social Transfer grows by three per cent a year.

"I think we have every right as a federal government to ask questions about how our transfers are being spent," Mr. Kenney said after delivering a keynote speech to the Canadian Club in Ottawa.

"There's no reporting back to Ottawa from provinces about how those postsecondary transfers are being spent.

"I'm simply asking reasonable questions."

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Provincial education ministers made skills training the main item of their recent meeting in Charlottetown in July.

At that time, the provinces promised to work on more timely labour market information to help students make decisions about their education.

Mr. Kenney used his speech to question why some colleges, such as Edmonton's Northern Alberta Institute of Technology, are turning away students because they do not have enough provincial funding to meet the demand from young Canadians who want training in the skilled trades.

The minister said some provinces, including British Columbia, are already doing more in this area and he wants other provinces to follow suit.

Mr. Kenney's push looks likely to lead to a fight with the provinces. Ontario Finance Minister Charles Sousa's office accused Ottawa of stepping on provincial jurisdiction.

"Trying to dictate how transfers are used by the provinces is taking federal disregard for how this country operates to a new level," Susie Heath, Mr. Sousa's spokeswoman, wrote in an email.

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Nobina Robinson, the chief executive officer of Polytechnics Canada, which represents colleges that offer hands-on training and, for some programs, a university degree, said it is true that many of her organization's members are fighting for provincial funding.

"The provinces receive the social transfer and have many different, competing demands on that lot of money," she said.

"I think all postsecondary institutions have been seeing certain kinds of cuts over the last few years, but our view and our thoughts are certainly that the leading colleges have not had their fair share of that funding as compared to, let's say, the leading universities."

Mr. Kenney – who jokes about the fact that he studied philosophy in university – has argued that Canadians need to shake the view that a university education is more valuable than learning a skilled trade.

Universities have pushed back on that view, insisting that stories of university-educated youth working in coffee shops are exaggerated.

Ms. Robinson said the benefit of this debate is that governments, colleges and universities are now looking to produce better and more comparable information on the success of graduates and the demand for certain skills.

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"We need more data," she said.

"Everything from economic impact studies to tracking the graduates and the alumni, every institution is doing that for their own marketing purposes, producing it for the provincial capital, but there's no vehicle by which to put this into a national [picture]."

With files from Adrian Morrow