“No child should use a multiplication table until he has made one”
- Mary Everest Boole.
Can we talk about the reason why we have our children memorise the multiplication table? We do it so our children can be efficient in their Arithmetic. We believe that children will make fewer mistakes, understand other concepts easier and finish their sums faster if they have memorised the multiplication table. In the traditional school system, we teach children the concept of multiplication, make them memorise their multiplication tables and then criticise them for using the concept of multiplication. This is plain ridiculousness. But I digress.
Charlotte Mason advocated play lessons before real lessons. Before a child sits down with a list of sums or gets to write and Math, the child should be encouraged to play maths. We teach the four elementary operations using coins or counters or situations that he is accustomed to. We do not use written notation until the child understands the operation.
Caleb Gattegno mentioned something similar. He said that the Cuisenaire rods should form the basis of the students’ introduction to new topics. He also noted that the initial introduction to the Cuisenaire rods should be via a period of free play.
By adhering to these principles, we are allowing our children to discover Maths. That which is discovered stays forever. During a period of free play, my five year old discovered that 9 plus 1 equals 10. I’m sure he will never need to memorise that fact. I will never need to teach him. My job is to ensure that more discovery happens in our Maths journey.
The first step is for the child to grasp the notion of a number as a collection of co-existing units. Caleb Gattegno did this by inviting the child to make different arrangements of rods, end to end, that will make up the length of any one rod exactly. The child will learn that the black rod can be made by a train of a pink rod and a light green rod. The child will also learn different combinations and, in so doing, will see that 4 and 3, 5 and 2, 6 and 1 all make 7. He will thus learn to perform without conscious effort any separation of these groups for subtraction or union of them for addition.
In one of the P.N.E.U articles, Rev. R. H. Quick, describing expectations of the first year of Arithmetic, said that he was firmly in favour of teaching numeration without notation for at least the first two years.
It is of the greatest consequence that the pupils should take pleasure in Arithmetic ; the lesson should therefore invariably cease before they become inattentive or fatigued.
- Horace Grant
I know what you’re thinking. You’re wondering if it’s okay for your Maths lesson to last only 5 minutes. I’m permitting you to have a one minute lesson. I’m reminding you that Charlotte Mason’s methods require concentrated effort and attention for short periods.
For the young child, Maths must be conversational. There are various Maths picture books here.
I know Charlotte Mason advocated that you don’t buy unique manipulatives. On this matter, I tend to agree with Caleb Gattengno. Purchase the Cuisenaire rods. You’re going to buy toys anyway. You can as well make a decent investment.
If you need a script for introducing your children to Maths, this book by Horace Grant is brilliant.
Our goal is a thorough understanding and love of the subject.
Now, a child who does not know what rule to apply to a simple problem within his grasp, has been ill taught from the first, although he may produce slatefuls of quite right sums in multiplication or long division.
- Charlotte Mason
We aren’t trying to turn our children into calculators. We are trying to raise children that understand the logic behind calculators. We need to demonstrate everything demonstrable or, in Montessori’s words,’ move from the concrete to the abstract.’
Best Regards,
Olufunmike