Do you agree with Keith Devlin that multiplication should not be taught as repeated addition?
Keith Devlin is a mathematician who has written a number of pop math books and is NPR’s “math guy.” I usually enjoy following his work, but I disagree fairly strongly with the idea expressed here
My feeling is that, as much as possible, teachers should make use of students’ intuitive grasp of the material. Thinking of multiplication as repeated addition makes it easier to understand some basic arithmetic properties. For example, to show that a*b = b*a, arrange items it rows and columns and then rotate the collection by 90 degrees to show rows and columns exchange roles, but the total remains the same. To teach the distributive law, look at 5(3+4) as (3+4) + (3+4) +(3+4) +(3+4) +(3+4) = 5*3 + 5*4.
In a similar way, exponentiation is easier to understand if it is first introduced as repeated multiplication. (a^b)(a^c) = a^(b+c) makes perfectly good sense if you think of combining b multiplications of a with c multiplications.
Historically, whole numbers were understood before fractions and decimals. It is certainly not necessary to teach things in historical sequence, but the history does provide a guide to the order in which understanding can be achieved. It seems perfectly natural to me to look at the arithmetic of real numbers as an extension of the arithmetic of whole numbers.