E took B off and they did some LISP together, and I played with K downstairs. First, she wanted to build towers with the nesting blocks, and I noticed that she was paying attention to sorting them into groups (by shape) after I had modelled it. She also carefully built a tower with one of each of the different colours available. After that, she did a jigsaw, without hesitation over which piece went where, but with still a little clumsiness fitting the pieces in the base. Then she wanted to play with the magnetic letters and numbers, so we got a baking tray and used that as a base for exploration. I started out by handing her letters and seeing how many of them she knew – for about ten, she identified them without hesitation, and could even provide an example of words starting with the letter for some. I noticed that somehow she has even picked up lowercase – for those letters she knew, she knew them in lower or uppercase, which surprised me! Then we did the same with the numbers. Although she can count to ten (if she feels like it – when B was trying to get her to repeat her earlier feat she shouted “No seal!” *snicker*), she doesn’t yet recognise the numerals. Eventually she just decided to pack as many letters as she could onto the tray, but she would find multiples of the same letter, some of which came from different sets so were different sizes, and group them together (often she would pretend they were kissing, and declare that they were friends *g*). She would also describe some of them which she could name as, eg. “Big C an’ ittoo c”, which was unbearably cute. Then she went off with Daddy for books, stories and songs before sleep.
E. adds: when we were playing hide and seek earlier tonight, I coaxed her into counting on my fingers, and she managed 1, 2, 3, 4, 5, and 6. After that, everything seemed to be eight, except for 8, which was 2. Still not bad for a 2-year-old!
Tried a more pictoral tack on the LISP with B tonight. Started with a subject close to her heart — money — and got her to work on an equation ($14 + 5 x $2) – ($23 + 20 x 5c), which was pocket money + five hours babysitting, spent on a $23 robot (her idea!) and 20 5-cent lollies. She worked it out arithmetically without any trouble of course, and then we tried drawing a diagram with the various parts of the equation inside bubbles. This gave her the breakthrough she needed, and she picked up the process of translation from mathematics -> bubbles -> LISP without making any mistakes. This is the key aspect of LISP that she wasn’t getting: that expressions can be arbitrarily complex, so 14 and 5 x 2 and (14 + 5 x 2) – (23 + 20 x 0.05) are all expressions, some of them composed of other expressions, which are in turn composed of more expressions… it’s turtles all the way down, if you like.
After that we did some revision of non-mathematical lisp, the car and cdr operators. Even though it’s been ages since we did this, it came back to her without much trouble.
Next time (finally!) we may be able to get into the fun part: writing functions. Now that I’m on a real operating system, I should be able to find some useful third-party libraries for graphics and sound so she can write functions to play music.