Mediated Learning with two Grade 4 students (10 yo). Their teacher was concerned about their mental arithmetic work. We spent a bit of time talking about the aim of mental arithmetic. We concluded that the the aim was to
Previously their aim was to get a few right answers on paper any way you can. Whether they understood anything didn't really matter!
The next question that arose was: How to do this? The answer was
Pretty simple and straight forward but not always obvious to young minds. We worked with this for a while and refined the process a little:
But what if you still can't find the answer to the question? Then we discovered a new and important question: What to do when you don't know what to do?
A more general question! We discovered some really good steps to follow the above:
(eg, 3X40= ? well we know that 3X4=12 so perhaps .... 3X40=....) This was fun!!!
Prior to this exercise these children were going from a half hearted attempt at step 1. straight to step 10. missing out steps 2. to 9. So they were highly demanding and making little or no real progress. One of the boys' previous teachers laughed at her previous attempts to make similar gains.
Cause and effect can indeed be remote from each other in place and time even in learning systems.
Has it made a difference? Absolutely. These students have probably increased their overall productivity by 500%. Their independence has increased even more (conservative estimates). They are much better behaved, happier and in fact life is easier for them.
Children at RPS finish primary school at the end of Grade 6. Prior to this experience anyone who knew two of the boys would have scoffed at the idea that they would master long multiplication of decimals before leaving primary school.
In fact both boys were doing just that one month after learning how to manage these two important strategies:
We published the whole process in the school Newsletter and suddenly several students were working with family and teachers to greatly improve their own performance in a whole host of areas.
Another example. One grade six boy who would give up on virtually any task before he even started (he was quite good at getting others to do things for him and his mother and teachers were at desperation levels) is now well and truly in charge of his own actions and making good progress across the board. And all because now he knows what to do when he does not know what to do