Ah, that subject much beloved by many, mathematics!
We are still finding our way on this one… At the start of homeschooling, a friend recommended I read The Three R’s by Ruth Beechick which gave me many helpful ideas. She introduced me to the concept of three different stages in maths – small children work with manipulatives, in other words using physical objects for counting etc. Then perhaps at about 6 years they move onto mental work, where they are able to work with images of objects in their head. Finally, around secondary school age they move onto abstract calculations, simply working with the figures without them representing anything.
The important thing is to always start with the manipulative mode, and if ever a child gets stuck in the next stage, to move back to that to consolidate. I have therefore been trying to use manipulatives far more, especially with CassCass, and it is not only effective but great fun for her. Again, ten minute lessons work well, after that she will lose attention.
For example, here is our method of learning what I discovered is now called ‘place value’ – tens and units does me just fine! Here she has worked out twenty seven in lolly sticks, or 2 tens and seven units. Our friend laminated squared paper for us and she loves working with those too.
The book also highlights how we tend to merge together the different modes in our maths learning. They are given a picture of objects in their book (manipulative), then underneath are the symbols for the calculation (abstract). She therefore suggests we leave textbooks aside more often and simply work on the manipulative and mental maths. Great advice! But once more it challenges that feeling we have to have something to show for our child’s day/week/year of work. I am gradually overcoming that and to help me out, I have made a list of goals for CassCass, various suggestions of how to study them, and then I note down what we do and when. There is also plenty of maths popped into our day in other formats, or as we go out for a walk.
With LissaLou, I did invest in a maths programme called Maths Mammoth. It had the advantage of being a pdf document that I can print out as and when I like – great for using for each child. This also helped with a problem I have – I hate leaving pages undone in a book! They always have a proviso that you can skip what your child already knows, but ouch, that is hard for me! The downside is that I keep forgetting to order more printer ink…!
However, LissaLou has found some basic maths like adding and subtracting a bit of a struggle, so recently we have just focused on mental addition and it has made a great difference. She is so proud of her achievements and loves explaining how she worked something out! We have also started memorising the times table, which I never really did at school, but can now see how useful a tool it is. So I am wondering if leaving the text book behind for a while is the way to go? Does mean more work for me though…