THE new Labour leader Jeremy Corbyn visited Scotland last week, and like many other Scots, I was interested to hear what he had to say.

By any account, he had a remarkable leadership campaign – beginning as rank outsider and finishing as comfortable winner.

Based on what he said during that campaign, it sounded like there was much that he and I could agree on.

Mr Corbyn seemed to offer a change of direction for his party, after years of Labour running scared of the Tories.

And judging by the convincing victory he secured, many other people got that impression as well.

However, I think it’s fair to say that Jeremy Corbyn has not made the most convincing of starts.

Rather than the new leader changing Labour, it feels more like the deeply divided Labour party is changing its new leader.

So far, he has reaffirmed Labour’s support for George Osborne’s fiscal charter.

That means that cutting the deficit still comes above all else – regardless of how it affects our public services.

He has shied away from trying to change his party’s support for spending £100bn on renewing Trident – and admitted that Labour may go in to next year’s Scottish elections without a clear position.

This is very important, as the key votes on renewing Trident will take place in the next few years, and people must know where Labour stand.

And I was dismayed to learn that Jeremy Corbyn has also now shelved his plans to scrap university tuition fees.

Mr Corbyn has a long history of opposition to fees - so much so that, during his leadership campaign, he issued an apology to past generations of students for Labour’s broken promises.

Labour has a very poor track record on this issue.

Tony Blair famously promised not to introduce fees, but then did so after he became Prime Minister in 1997. Then he broke another promise by trebling them a few years later.

And in Scotland, Labour pretended to abolish fees when the Scottish Parliament was established, but in reality they created back-door tuition fees with the so-called graduate endowment.

It took the election of an SNP Government in 2007 to finally restore our country’s proud tradition of free higher education.

And we’ll continue to oppose tuition fees south of the border as well – not only because it is the right thing to do, but because currently Scotland’s fixed budget is determined by how much is spent on public services in England.

It’s an issue about which I feel incredibly strongly.

I grew up in a working class family in Ayrshire, and was the first in my family to go to university.

I almost certainly couldn’t have gone to Glasgow Uni if I’d faced the enormous financial barrier of tuition fees.

So how could I, who have benefitted so much from an education at one of the finest universities in the world, deprive today’s young people of the same opportunity?

Since we abolished fees in Scotland, our higher education sector has gone from strength to strength.

We’ve got a record number of Scots being accepted to Scottish universities, and UCAS figures for this year show a 50 per cent increase, since 2006, in applications for 18-year-olds in the most disadvantaged areas of Scotland.

And just last week, the latest annual Times Higher rankings revealed that we now have five universities in the world top 200 – more per head of population than any other nation on earth.

Glasgow this year jumped an impressive 18 places.

The lesson from all of this is that if we invest in young people and in our public services, everybody benefits in the long run.

So that is my plea to Jeremy Corbyn.

As I said during the general election campaign, SNP MPs are keen to work with MPs from other parties to provide a progressive alternative on a whole range of issues.

Since the election, the SNP’s large block of MPs has led the way - with David Cameron forced into retreating on issues such as fox hunting, scrapping the human rights act and the timing of the EU referendum.

The Tories don’t have a big majority – and we’ve shown it can be overcome if we work together.

So I would urge Jeremy Corbyn to stick to his principles, not abandon them.

As a new leader, he shouldn't let Labour continue to run scared of the Tories.

If he is willing to stand up and be counted on these and many other issues, he will have a strong ally in the SNP.