Far less is expected of pupils in England, and too much time is spent learning about simple topics like space and shape, rather than algebra, he said.
“The quality of the mathematical knowledge of teachers remains an important influence,” Prof Burghes says in the pamphlet.
“The majority of entrants to the profession have only a GCSE C grade as their highest mathematical qualification.
“The emphasis throughout primary is on numeracy and accessible topics in, for example, shape and space, rather than the provision of a mathematical foundation (including algebra) on which to build in the secondary sector.”
Prof Burghes adds: “We have too few teachers at primary school with a real understanding of mathematics, leading to children not being fully extended; the pupils continue into the secondary stage, where there is a shortage of adequately trained mathematicians so that many of them are either bored or not coping.
“This results in not enough students in the sixth form taking mathematics and low numbers of students undertaking mathematics or mathematics-related degrees at universities. The cycle continues with not enough mathematically well qualified young people entering the teaching profession.”
Prof Burghes sets out proposals for a new maths curriculum that would see children learn their times tables up to 10 times 10 by the end of Year 2, age seven.
By this time they would also have learnt how to use numbers up to 100, as well as add, subtract, multiply and divide.
Algebra should be introduced at an early age, Prof Burghes says, similar to other high-performing nations, and pupils should be able to solve simple equations and inequalities by the time they are eight-years-old.
At this age they should also be able to calculate simple probabilities, he adds.
But he says fractions should not be introduced in the first year of primary school, and left until a year later.
By the time they are 11, and ready to go to secondary school, pupils should be able to multiply and divide fractions, use simple percentages, decimals, as well understand ideas such as radius, diameter and circumference of a circle.
Prof Burghes says that he has gained “enjoyment, inspiration, challenge and, at times, despair” from maths, but adds “it is obvious that many of our school children (and their teachers!) do not experience even a fraction of this emotion and enjoyment but are bored with the subject.
“This is regrettable and not helpful at a time when, in an increasingly technological world, we need young people who are confident, capable and able to use their mathematical skills and knowledge in new and challenging contexts.
“I make no apology for concentrating on primary mathematics. Anything else at any other level is just ‘putting sticking plaster on the cracks’ of lack of understanding of the subject, rather than providing a long-term and sustainable solution.”
Ministers announced plans for a new back-to-basics primary maths curriculum in June.
Under the proposals, pupils will be expected to know all their times tables up to 12 times 12 by age nine, whereas under the current system they should know their tables up to 10 times 10 by the end of primary school.
By the age of seven, children will be expected to have memorised all so-called “number bonds” – simple addition and subtraction sums such as 9+9=18 or 15-6=9 – up to 20.
And by the time they are 11, children will be expected to be able to add, subtract, multiply and divide fractions and decimals.
Many of these topics are not covered by the current curriculum, which means that pupils struggle when they get to secondary school and do not have the right grounding for more difficult concepts such as algebra, the Department for Education has said.
A Department for Education spokesman said: “We place a high priority on providing a solid grounding of arithmetic early on in schools. It is important that pupils are fluent in calculation and have learnt the multiplication tables by heart before they leave primary school.
“That’s why we are driving up standards in schools across the country with plans for a more stretching primary curriculum, which includes banning calculators for Key Stage 2 tests. We are also encouraging more new primary teachers to specialise in maths and we are prioritising funding for graduates with a 2:1 or first class degree in the subject.”
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