Numbers Work With Zoodie

Here's a glimpse of the numbers work I'm doing with Zudie.  He has to work really hard to make sense of abstracts, so up to now it's been a lot of groundwork with connecting the abstract numbers, written and spoken, with concrete amounts.  Montessori is great for this and we've been working with Montessori materials since he was very little but even more since we gave up on his special school a couple of years ago.    We used the spindle boxes first, wooden spindles have a lovely feel to them and very nice to handle. The spindle box has 10 compartments where the spindles go, not 1-10 but 0-9.   The empty zero compartment is a nice visual of what zero means and by now Zudie has a very good grasp of that.    The number rods Lots of real-life counting of stuff and adding on or taking away whenever the opportunity arose of course, that's ongoing for all home-edders.



We worked on bead material a lot over the last couple of years, sometimes with Zudie on his own and sometimes with his brother; making the bead triangle, laying out the bird's eye view of numbers with bead amounts beside them, 1 down to 9, 10-90, 100-900, 1000-9000 in columns from right to left (the way the numbers would be written, units at the far right).   This is laying down lots of foundations, for example Zoodie knows that 5 ten bars make 50, although he wouldn't necessarily respond correctly if I ask him randomly “what's five tens?”.    That will come later insha'Allah.   Since he is able to recognise numbers into the hundreds I decided to extend the bird's eye view activity into a partitioning exercise, eg get him to lay out all the numbers in their columns, with or without the corresponding bead amounts and showing him a card with a 2 or 3 digit number – say 24.   He has to make the number 24 by taking the appropriate cards from the columns – 20 and 4 and place them on a tray, place the corresponding bead amounts underneath, and then put the two numbers together so it looks just like the written number 24 (so the 4 goes on top of the zero of the 20).    Zudie was able to do this activity and even 3 digit numbers, so that is something I'm hoping to build on in the future.   It seems a bit advanced in comparison to his arithmetical skills (see below) but then again an uneven skills profile is common enough in LD children and his older brother hates doing very basic sums but manages more complicated stuff like fractions with relative ease.    We worked on the teens (seguin) boards as well, wooden boards with 9 number 10s painted on, and a slot where single digits can be slipped in to cover the zero so as to make 11, 12, 13 etc up to 19.     It's a nice partitioing exercise showing how the numbers 11-19 are made up with one 10 and a number of units.   


Early in the term I was doing “one more, one less” with Zudie, thinking it was a fairly simple concept to work with.     I had tried this before the summer but he obviously wasn't ready then so I thought I'd try again.    It was a bit hit and miss, although funny enough when we do it in real-life situations he seems to understand okay (like demanding another sweet when he's been given one less than his brother, or understanding “one more time”.    Although it seems so straightforward as a maths lesson it obviously isn't for him After demonstrating the concept with concrete amounts like counters, or buttons, or toys or whatever – here's three counters on the table, if I put one more how many will that be? Four (giving child lots of opportunities to answer of course).    When he seemed to “get that”, giving the answer fairly consistently although with some puzzling exceptions (4 pens, if I put one more how many? “7”) - I maybe a little optimistically attempted to introduce the concept of “one less” which didn't go over quite as well and so I abandoned it when I saw frustration setting in a bit.


So what we've been doing for the last couple of weeks is early addition.    It's something I've attempted previously but not had a lot of success with, until now.     Clearly the lesson for me – again – is that when the child is ready they will fly but there's no point pushing them off the branch until then.


We started off by adding counters – here's 2 counters, and here's another 2 – if we add them together how many counters will there be?    Remembering to vary the language – you take these 3 counters, I've got 2 counters here, how many counters is that altogether? - 4 counters, plus 2 counters, equals......and all the time demonstrating very visually and concretely with the counters, pointing to them, putting them together. Then, “how many counters have you got?    I've got x amount, can you count how many it makes altogether?”


You really have to demonstrate the basic concept you're trying to get across hundreds of times in lots of different ways.    That's the nature of many learning disabilities and especially those where abstract concepts are difficult to grasp – this applies whether teaching numeracy or language skills.   Sometimes the child can only take 5 minutes of this, that's fine, there might be another 5 minutes later on when he'll be amenable. When you home educate you learn to spot the teachable moments and make the most of them.


Anyway we've been doing this for a couple of weeks, me and Zudie, and he's really getting the hang of it. He's even using the terminology plus and equals.   I got some really nice addition books, flip books of lots of sums – 2 numbers to five, 2 numbers to 10, and 3 numbers to 10 all in one nice neat and colourful folder type book.    And another wipe-clean book with sums that you do, filling in all the numbers of the operation and then pulling a tab to see the correct answer.    So what with that and all the brightly coloured counters, balls and chess pieces we've been using he hasn't shown any signs of boredom although it's not his favourite activity either.


I think next we'll use the Montessori bead material to do the adding, using the addition strips for him to write on.   I also have an iPad app using visuals of the bead material for addition which would be good for extending the activity to something a bit more abstract.    Ultimately the aim is for Zoodie to be able to do the sum in his head, or even using his fingers, when it's written simply (eg) 4 + 2 =