An autonomous approach to learning maths

Isobel Bogucki has given me permission to use this description of how her children learned maths in an autonomous environment.  This is from an e-mail which was originally sent to the UK-HOME-ED mailing list.

My 3 children have always been autonomously educated. I have never attempted to 'teach' them anything until they requested input.  I have never required them to do anything but what they have freely chosen to do.

When they were younger we played all sorts of board-games from Snakes and Ladders to Monopoly, Sorry to Triominos.  This gave them a good grasp of number.  Having activities on particular days then later needing to set the video timer etc. gave them a good grasp of time and the 24 hour clock.

Cutting up toast etc.(they knew at a very young age that half of a half was a quarter) and sharing things out brought in fractions.   Pocket money and post office accounts took care of money and interest rate knowledge. Discussing petrol prices brought in decimals. Counting in different bases then cropped up somehow.  Properties of circles when eating bought pizzas (home made ones are usually rectangular).

We never felt the need to write anything down on paper. Only the eldest ever felt inclined to go through some workbooks for a short while when he was about 6ish.  He always enjoyed being with me when I was preparing ideas for maths workshops.  The other two were definitely not.

When the eldest started his GCSE course at a 6th form College I was quite anxious but he easily coped with writing things down in the 'correct' way and never needed my help.

My second who has never been interested in maths has just started a 9 month course.  (She is also taking English, IT, Photography plus an AS level Dance) On the third day she was presented with the first module exam paper and felt it was totally beyond her.  Then we looked at each question. She was really focused on it and very quickly learnt the written language needed.  The way she talked about the question showed a genuine understanding of the written number and real insight into what she was doing.  I have been so impressed with her approach.  I really feel that if written maths had been done too early she would not have the degree of understanding that she now shows.  If drilled she would be faster but would she be so creative?  Children who really enjoy maths would be but if you have no interest ..........


My eldest has read maths books for fun. Recommending any particular ones is difficult.  What one person loves another may hate.

Martin Gardner's books are well known e.g. Mathematical Circus and Mathematical Magic Show.

W.W. Sawyer Mathematician's Delight, Ian Stewart Game Set and Math.

An excellent book on probability is How to take a Chance by Darrell Huff.

E.P. Northrop wrote Riddles in Mathematics.

Two very general books are Mathsemantics - Making Numbers Talk Sense by Edward MacNeal and 200 % of Nothing by A.K.Dewdney.

Ivars Peterson The Mathematical Tourist - snapshots of modern mathematics is a little deeper.