When the Scottish Survey of Literacy and Numeracy 2013 was published last month, it did not provide the good news that the government and educationalists might have hoped for.
Attainment in numeracy at primary school level has collapsed since the previous survey in 2011. Whereas 76 per cent of P4 pupils in 2011 performed well or very well at first level, that figure has fallen to 69 per cent in 2013. Likewise, the percentage of pupils in P7 performing well at second level has dropped from 72 to 66 per cent.
At secondary level the story is not much better: the percentage of students who do well or very well in S2 at third level has flatlined at 42 per cent.
And the bad news doesn't stop there. The performance of children from the most deprived backgrounds is significantly worse than that of their richer peers.
The report certainly makes for difficult reading. Larry Flanagan, general secretary of the EIS teaching union, says it should force the Scottish government to stop assuming that "everything is done and dusted in the primary sector".
And Alan McKenzie, acting general secretary of the Scottish Secondary Teachers' Association, says the figures "vindicate" the belief of some of his members that young people coming into S1 do not have the maths knowledge they should.
Change of direction
But beyond the snap judgements and headline figures, the story is a little more complicated. Closer analysis reveals results that raise as many questions as they answer.
Significantly higher levels of secondary maths and non-maths teachers report feeling confident about delivering numeracy under Curriculum for Excellence, for example. This is in part likely to be because CfE has had two more years to embed in secondaries. However, why this increased teacher confidence has not led to gains in student attainment is less clear.
Flanagan suggests that one possible explanation is that as teachers become more confident, they also become more vigilant in assessments.
But the pupil progress figures also highlight the fact that a great deal has changed in the teaching of numeracy in Scottish schools since the implementation of CfE, and the effect of those changes may not always be as desired.
Tom Macintyre, senior lecturer in maths education at the University of Edinburgh's Moray House School of Education, says the survey shows the frequency with which certain ways of learning are changing.
In primary, pupils now have more opportunities to explain in their own words how they solved a problem, as well as to engage in "exploring or investigating" and "interpreting and analysing". But with less time being spent on actually solving problems and "giving a talk to the class or a small group", Macintyre wonders what impact that might have on students' attainment "when considered alongside the drive for breadth, challenge and application".
At secondary school level, in contrast, students now spend more time solving problems and talking about what they are learning in pairs or in groups, and less time using textbooks and completing worksheets.
Macintyre believes that the increased exposure of secondary children to these sorts of practices, and perhaps problem-solving in particular, is "what distinguishes the sectors and may lie behind an overall difference in attainment over time".
Lio Moscardini, senior lecturer at the University of Strathclyde's School of Education, says that regardless of the priorities of CfE, the focus in maths must remain on children understanding the subject. It should not just become "part of active learning", he stresses.
He adds that activities such as those where children must walk from one part of the classroom to another to answer questions are no different from filling in an old-fashioned worksheet, and do not encourage comprehension of the underlying mathematical principles.
He says the key is for teachers to focus on getting children to understand how they solve maths problems. Although this does not require vast resources, it does demand "a lot of dedication on the teachers' part to process what is going on".
"In the past, part of the problem on the teaching of maths was that [students] had to carry out procedures they did not really understand," Moscardini adds. "Only looking at attainment is problematic, because it does not tell you how high the understanding of maths actually is. I would be much more interested to know: `What is their actual understanding?' "
The amount of research on children's maths has been steadily increasing over the past few years, much of it focusing on how students learn and effective ways of teaching them.
"Some say we need primary teachers who are actually better at maths themselves," Moscardini says. "I would agree with that to a point. What is actually needed is the knowledge of children's mathematical thinking. That requires professional development." He adds that some local authorities are now starting to focus their attention on this.
Indeed, CPD was thrust into the spotlight soon after publication of the survey results. On 30 April, the Scottish government quickly announced that funding for the "numeracy hubs" programme, which aims to share best practice between schools and local authorities, would increase by pound;1 million over three years.
Similarly, Graeme Logan, strategic director for school years at Education Scotland, says his organisation is developing a new national progression framework for numeracy, due to be published later this year. This will "complement the provision of extra resources and support on numeracy" that the body is already implementing.
"We will work with education authorities to provide support to teachers to ensure that children achieve the high standards set out within Curriculum for Excellence," he says.
One area benefiting from the funding for numeracy hubs is Midlothian. Under the terms of a partnership with East Lothian, staff are trained at a numeracy academy for five days, before returning to their own schools to pass on what they have learned to other teachers.
Suzanne Thayne, schools' group manager for Midlothian Council, is "running a number of different approaches to provide as much support as possible" to staff. Overall, the council's approach to numeracy has become much more focused, she says, with information given to schools on how classes should be structured and how often numeracy lessons should be delivered in primary schools.
Thayne adds that Midlothian is taking a number of other measures to upskill its teaching force, to ensure that they can meet the needs of children and of the new curriculum. The local authority has set up a development programme for schools, helping them to identify where children may have gaps in their learning and to access suggestions for appropriate resources and information. Each school has a numeracy coordinator, and training takes place at the council as well as at individual school level.
This strategic approach is absolutely essential, Thayne says, and has to be implemented all the way from the early years. "If they don't have the grounding and the building blocks early on, they will fail later on."
While admitting that the numeracy survey results are disappointing, she insists that the results of much of the work in the region are yet to become apparent. "In a strategic way, this has only really been in place for a couple of years," she says. "In the schools that have been implementing this consistently we have seen really good progress."
There are many in Scotland - in schools, local authorities and government - who will be hoping that Thayne is right.