My husband has been busy the last few months, downloading apps for my daughter on the ipad. Some of the educational ones are somewhat
One new app is supposed to teach little ones to add. It launches straight into addition sums, like 4+3= . Although my daughter has been doing some 'school work' at home with me this year, in preperation for her start to school next year, I try where possible to make all the activities 'hands on' and that help her to build her understanding of a concept before she attempts abstract ideas like 'sums' in school next year.
Anyhow.... my dear hubby attempted to 'teach' addition when she found this new app. Of course, I sat smugly in the corner, preparing to witness a train wreck. He lasted a few minutes, told her how to count using her fingers on from the first number. So if it was 3 + 2, she should say 3 and then count 2 more numbers. Luckily she grasps things quite quickly and I was surprised that she did OK with the first few.
My daughter was left alone for a while with the app. I was busy on the computer, my head down working, but I kept and ear out to hear how she was going as she progressed through the sums.
To my amazement I heard her developing a strategy to work out sums that required more fingers than she had on her hands! Totally spontaneous and completely her own attempts to figure out an answer. The question was 9+6. I heard her say "one ten... two eleven.... three twelve.... four thirteen....five fourteen......six fifteen". I was blown away by her creativity and very very proud. I just had to share this with some teacher friends that would understand my excitement.
We have some standard testing here in my state for working out a child's level in maths and we always try to get the children to reveal the 'strategies' they use to work out answers. It is difficult, as most of them have no idea how to explain how they are thinking. I love it when they say 'I just thinked it' in response to my question 'how did you get that answer'.
I am sure if I asked my daughter she would not know how to explain this strategy that she used to solve the sum and perhaps not be able to do it again. I am so glad I was in the room to catch this little revelation into the inner workings of her mind.