Antonia is whizzing through her maths book so fast these days, I thought we would try something different as well. A lot of the other homeschooling families I know in France use Mathematiques des Freres Lyons. It’s a free program from Canada, for children aged 5-7, especially home-educated kids, and I suspect it’s only available in French, because I’ve never heard of it elsewhere on the net. It turns out that anyone who can read French well could use this program with their child, even if the child doesn’t speak French.

I sent off an email and received the first six chapters of the program in pdf format. Each chapter contains a series of exercises based on manipulatives that you can easily make, or that you probably have around the house, like a pack of cards. There is very little writing or recording, and the emphasis is on the child developing their own thought processes through working with the manipulatives.

The first chapter is just for the parent’s information and is a series of exercises to see if the child is still a pre-operative thinker. The program tends to assume that they will be. The first test is quite well known: it involves half filling a clear bottle with water, sealing it, showing it to the child, then tipping it on its side. Many young children will believe that the bottle no longer contains the same amount of water.

These tests were interesting to me. Antonia is mostly a post-operative thinker. She can quantify large groups of objects in her head and does so automatically, and can explain all the conservation tests. With one big exception: she has not mastered the intersections. When shown a picture of 3 lions and 2 donkeys she will say that there are more lions than animals, even if previous discussion has established that lions and donkeys are both animals. I was surprised enough that I did the test again, in English with other categories and got the same result. I think that explains a lot about her thinking, as she often seems very adult in her reasoning, and then there will be a sudden black hole of comprehension. Strangely enough, she can do Venn diagrams, presumably because she’s been alerted to the need to pay extra attention in that exercise.

Based on the expectations of the program, it might have been more appropriate to start it a year or two ago, but I’m still finding it useful for us. Antonia has this tendency to leap to answers that seem obvious to her and flounder if they are not obvious. She finds it hard to deal with situations with multiple answers or no answer at all. She also finds it hard to prove or explain things that seem obvious to her with a physical demonstration, or to manipulate objects and experiment with them. I think it’s really good for her to learn all those things, even if she already has the numeration skills. It’s also fun, more like games really. We’re both really enjoying it so far.