Most multiplication charts epitomize the worst of traditional elementary arithmetic: teaching numbers and arithmetic rules as abstractions to be memorized rather than as common-sense extensions of the child’s own experience and intuition. CM tried to steer parents away from too-early emphasis on such things by encouraging two principles:
(1) Heavy reliance on word problems that use situations and relationships the children can imagine and through which their common sense and intuition can grasp how the numbers are acting.
(2) Regular use of manipulatives to act out situations and model relationships and to count up answers that are beyond the child’s mental calculation abilities.
One problem we have as parents is that our own education was often so formal (abstract) that it crippled our understanding. Many adults don’t know how to recognize multiplication except in a times table or on a worksheet. Look at the richness of multiplication as expressed in the images linked below, and then make for your children, and encourage them to make for you, multiplication word problems using similar variety:
Multiplication Models
And also, look at this version of the multiplication table, without numbers. Print it out and show it to your chilidren, without explanation. What do they notice? What do they wonder? What do YOU notice that you may not have thought about before?
Multiplication Table to Scale
Finally, here is a link to a multiplication models card game on my blog. You might find it useful—not as helpful at first as word problems and manipulatives, but as an aid for the transition from those to more abstract mental figuring.
Multiplication Models Card Game
