Rachel Wolf is a director of Public First. She was an education and innovation adviser at Number 10 during David Cameron’s premiership, and was founding director of the New Schools Network.

The recently published industrial strategy is one of the main planks of the government’s domestic agenda. It has been criticised for being insufficiently new or bold. This is unfair: the strategy raises radical and important possibilities; it just doesn’t yet commit to them. We don’t know whether the Government will go for marginal iteration or systemic change. In my view, it must pursue the latter.

Let’s take skills, one of the strands of the industrial strategy. The Government has correctly identified basic skills, mathematics, and technical education as the major problems that need to be addressed.

In technical education, we struggle with a system that prioritises low-level qualifications with poor labour market returns. Far fewer of us study mathematics to an advanced level than in many other countries – including those with higher productivity. Meanwhile, we are woefully uncompetitive in basic skills – the only country in the OECD where young people have no better literacy and numeracy than older people. In England, one third of 16-19 year olds have low basic skills. That means they struggle to read the back of a medicine packet and know how to take it safely, or look at a three-quarters full petrol gauge and say how much petrol is left.

During the last few months, I have been working with The Coalition For A Digital Economy (Coadec), the organisation that represents start-ups across the tech sector, to investigate what post-Brexit policies are necessary for rapid growth. The sector represents three million jobs and 16 per cent of domestic output. It is growing fast, and spans many of our potential areas of strength – digital, AI, biotechnology.

The report, of which I am a co-author (leading the skills and talent chapters), will be launched in Parliament today. In it, we analysed the major skills shortages the sector faced, and found (perhaps unsurprisingly) that they were the same as the national challenges identified by the Government. Companies are held back by poor STEM, basic skills, and bad routes into technical disciplines.

What, then, should we do?

First, we need to move to higher skill apprenticeships – the kind common in Germany, but a small minority in this country. In tech, the biggest need is developers. Software Development and engineering are perfectly suited to apprenticeships with its requirement for intensive off and on-the-job training.  The Government has shifted to an apprenticeship system – but the vast majority of funding is still going to low skill courses. This will continue without further reform.

The problem is illustrated by the superb, advanced private sector courses in software development – such as that run by Makers Academy – that had grown rapidly despite students and employers paying thousands to attend. These are locked out of government support and cannot expand to less wealthy participants. At the same time, courses with poor graduate employment rates and poor reputations among employers we spoke to were given government subsidy and backing.

This is a sign of a Government system gone wrong.  If we gave funding support for high quality courses and used the market-leading process of coding tests to determine if apprentices had succeeded, we could dramatically increase the number of developers trained. This model could also be applied to other disciplines, and would be part of a shift to advanced technical training.

Second, we need to move to a system where some mathematics – at a basic, intermediate, or higher level – is expected at 16-19. This is the norm in many countries. It has been raised as a policy many times, but never done. This is usually because officials point to the lack of maths teachers – failing to acknowledge that we don’t have enough maths teachers because not enough people studied maths five years earlier! This is a vicious cycle we must break out of.

I know there will be people reading this who disliked maths at school. There will probably be people who studied history or PPE at Oxford without much maths and find the idea that they were insufficiently educated insulting. But the truth is the world is changing. The number of jobs where an understanding of statistics, an ability to analyse numbers, or just an understanding of what those strange scientists in their labs are talking about, are irrelevant are declining rapidly. We owe it to 16 year olds to give them an education that gives them the best chance in that world.

This shift won’t happen overnight. But there are some interim steps the government could announce immediately. One option would be to introduce an SAT, as is required for American universities, for those applying to universities. It would be up to individual universities what standard to set for entry – as it is in America – but it would send a clear signal to schools and have a direct impact on behaviour. It would mean that excellent new courses like Core Maths would become useful to students, and take up would increase.

Third, we need to make GCSE level of English and maths a prerequisite for Further and Higher Education. Again there has been recent action – people now have to retake GCSEs if they fail – but insufficient radicalism. There is no strong incentive to turn up to class, let alone succeed at retakes. Students can pass their courses without it. Again, this is very different from competitor countries where English and Maths are expected up to the end of school (and where basic skill levels are, unsurprisingly, much better than the UK) and where you cannot go to university without upper secondary certificates which include maths and your home language.

The Government has the opportunity to pursue a radical domestic agenda in a range of fields. For the tech sector, and for the country at large, skills should come high up that list. Our hope is that this report, and its analysis, will encourage the next phase of the industrial strategy to pursue large-scale change. If we do that, we can become one of the most productive and innovative countries in the world.