This week, Learning and Teaching Scotland issued a draft paper outlining to teachers in early years, primary and secondary the "outcomes and experiences" pupils should have under the new curriculum.
It aims to build on the strengths of current practice, but also to improve mathematical understanding, increase the emphasis on challenge and enjoyment, and ensure that pupils are better equipped to meet the demands of a rapidly-changing world.
Important changes include:
- the introduction of algebraic thinking at an earlier stage;
- more emphasis on interpreting statistical information and on the ability to take account of chance and uncertainty in making decisions;
- a stronger emphasis on the important part mathematics has played, and will continue to play, in society and the relevance it has for daily life.
John MacKenzie, principal teacher of maths at Oban High, welcomed the earlier introduction of algebraic thinking, saying it should aid mathematical understanding and help build confidence. But he warned that the challenge for teachers will be the "unpacking" of the outcomes - especially for young and inexperienced teachers.
"Careful planning, and the time to carry out this task, will be essential to take these outcomes forward. There are implications for teacher development, resources and workload and it will be interesting to note what 'additional guidance' will be provided to support planning, recording and assessment of the outcomes," he said.
Alastair Gillespie, chair of the Scottish Mathematics Council, also welcomed the greater emphasis on handling statistics and chance and uncertainty, along with a greater focus on the importance of mathematics in the world. "No mathematician is going to disagree with that," said Professor Gillespie.
But he said he was uncomfortable with the way the outcomes were written, all in the first person along the lines of "I have explored numbers, understand that ... , and can ... " at the earliest levels, or "Having investigated the practical impact of inaccuracy and error, I can ... " at the fourth level.
"I don't think it helps to get across the message; I don't think it's the right way to write a document."
Professor Gillespie, who lectures in mathematics at Edinburgh University, added that, as he was not a school-based maths teacher, he was cautious about commenting on classroom practice. Nevertheless, he felt that, without more guidance to support their planning, teachers would find it difficult to convert the "outcomes and experiences" as they are portrayed into a coherent programme of study.
If teachers were going to adapt an outcome in the format of "having investigated 'x', I can do 'y' and apply it to related problems", it would take them a lot of time to achieve, he suspected.
Professor Gillespie also picked out one of the third-level outcomes, which reads: "I can apply my understanding of factors to investigate and identify when a number is prime and can explore and explain the application of prime numbers in today's world."
He said: "It is ambitious to get youngsters to understand applications of mathematics today."
While it was true that prime numbers were very important in cryptography and security in general, he said, this was quite a sophisticated concept.
The Scottish Government's insistence that the new curriculum should relate to Scottish culture and heritage is demonstrated vividly in the draft outcomes for classics.
By studying the themes of culture and heritage through classical languages, pupils can gain an awareness of how "vital parts of Scotland's culture, the arts, law, political systems and social values have both direct and indirect links with their classical predecessors and with the classical world in general", states the guidance.
Alan Jones, acting headteacher of Eastbank Academy and a classics teacher, said he had long believed that pupils of the classical languages and classical studies were "ideal candidates to meet the four capacities, long before the concept of A Curriculum for Excellence was born".
He added: "The learners' outcomes proposed for the classical languages are both appropriate and eminently attainable. As there always has been, there is also welcome scope for much valuable inter-disciplinary activity involving classical languages and related areas, particularly English and history, at both primary and secondary school stages."
Gaelic for learners
The Gaelic for Learners paper follows a similar format to that already published for modern languages.
Effective teaching programmes and strategies will include the use of information and communications technology to establish links with Gaelic speakers, it emphasises.
Mary MacKinnon, co-ordinator of Gaelic for Learners in the primary school in Argyll and Bute, particularly welcomed the importance attached to cultural awareness and Gaelic's place as part of Scottish identity in the new guidance.
"The understanding of the background, together with the promotion of active learning through games, storytelling and ICT, make for increased motivation and willingness amongst pupils throughout Scotland to engage with the language at all levels," she said.