My husband is a secondary mathematics teacher, and he has always said that the children he meets in secondary schooling often struggle with the abstract concepts because they have not had enough play in their primary years. Playing with numbers, shapes, measures and concepts allows children to explore these ideas in their minds and to build their own web of concrete knowledge and understanding on to which abstract concepts can later hang. One of the problems with a very fixed curriculum for maths is the idea that children have to acquire certain concepts at a certain age. In reality, children might come to an understanding of different concepts at varying times. And if they pick up that they ought to be able to do something they cannot yet, then they will become discouraged, even internalising the idea that they are no good at maths. Many of us will know that this perception can stick with a person into adulthood. It may very well be absolutely untrue ... Perhaps a child just isn't ready for a certain concept yet. Let's think about telling the time, and the many ideas which need to come together for a child to understand this .... a concept of the passing of time, the 5 times table, fractions ... one child might be able to put all these ideas together in Year 2, but another child might get there later. How much does this really matter? But building a fascination with mathematics, even a love for the subject, seems to me to be a far more important aim. I honestly believe this is better achieved through play in the primary years.

I have been observing my 4 year old's current fascination with numbers and mathematical concepts. This term, he has been interested in the ancient Egyptians, and from there came questions about pyramids and 2D and 3D shapes. His question was about 'flat' shapes and 'solid' shapes ... We played with Geomag and cocktail sticks and sweets. We looked at platonic solids on YouTube and he built several of those, observing why a square-bottomed pyramid was different.

He has been doing lots of counting, just at random moments, of course when playing hide and seek, but also in the car ... anywhere. Sometimes he now counts in 2s or in 10s. He has been playing with a tape measure, and we have measured things, including making a size chart of various sharks - another of his fascinations. And how big was he compared to all those creatures of the deep?

He has been looking at the clock - numbers, wherever he sees them in his real life - and reading around the clock, then in 2s. This week, he began to add his friends' ages together to add up to other friends, for example: Amelia (who is 3) and Leo (who is 5) make Micah (who is 8). It is clever, the way he is puzzling this out.

He plays with a calculator, and types in 10, then 2 10 ... I show him 20 ... It becomes a game: 3 10, 30 etc. He asks questions like "10 and 10 is ?" or "What's 4 10s, Mummy?" I answer. He puzzles. Sometimes I scribe what he is saying to show him how that looks written down. I remember my third son similarly puzzling out a whole page of self-written sums, so thrilled with the idea that 2 + 2 = 4 and we can write it like this.

Maths Seeds is also a real hit with my tech-loving son with 3 older brothers. He loves the idea that he has 'his work' to do on a tablet, and the immediacy of knowing whether his answers are correct, as well as the opportunity to work independently are both positives of the app. A friend of mine's little girl (age 6) is loving Carol Vorderman's Maths Factor and can't wait to get on with her work on the app every day. Technology provides a whole new way to play with maths.

Lego - and similar toys - are brilliant, too - for space, shape, form and symmetry.

My eldest son, now 15, is naturally good at maths. His brain seems to work that way, and with very little formal maths education prior to starting at a local engineering academy this term, he finds himself at the top of his class and predicted a good grade at GCSE. My husband tutored an unschooled girl of a similar age for a couple of terms once or twice a week. She had had no formal maths education, but worked independently through past papers, bringing to my husband questions about which she was unsure or concepts she was struggling with. She passed her GCSE Maths with a grade B. What our unschooled children are really good at is solving problems and figuring things out, which should stand them in good stead for the new GCSE, if GCSE is something you feel is necessary.

My second son (13) is not so naturally inclined towards maths, in fact, his own assertion that he was no good at maths, after just a year at school, was one of the reasons we decided to take our boys out. It is not actually true. He is very clever at some things which require mathematical thinking .... design and technology, for example. Perhaps all the time he has had to work on his music, at which he is very talented, has helped his mathematical thinking, too. Some people say the two are connected. At any rate, through much play and patience, he has acquired many mathematical concepts over the years, most importantly the belief that if he wants to know how to figure something out, then he can do it. The other day, he wanted to draw a pie chart and wasn't sure how to do that. So he went to YouTube, looked it up and watched a video, going on to produce the required pie-chart. He is just about to start working through a KS3 maths text book because we don't want him to be disadvantaged for GCSE ...(He just does a little bit perhaps every other day) ... and I am sure he will find he can apply himself to the problems presented and figure them out, because being an independent learner is really what it is all about. Real learning has to start with the learner.

My eldest son's teachers don't quite know what to do with him, and I have realised why. It is to do with learning style. The teachers are used to students coming in to the classroom and waiting to be directed as to what to do and how. My son goes in having pre-read the day's lesson, and next week's too, full of his own questions about it. Rather than waiting to be told what grade he should be expecting or working towards at GCSE, he goes to the teacher and asks whether he will be able to achieve the top grade in this class. Self-directed learners. Whatever the subject, keep it fun .... Inspire curiosity, consider the possibilities ... Let them exceed your limited understanding and expectations. And don't worry about it so much.