Your point:
>>But my point is that the
curiosity of some students could lead them to study more math, through
casting out nines.>>
is personally very appropriate.
I remember at a fairly young age being absolutely thrilled when I
figured out why this worked. I am quite sure it did motivate me to study
math.
When I taught math for pre-service teachers, I had them work in groups
to figure out why this process works. It is a nice problem for
prospective teachers, both as an illustration of base 10 numeration, and
an application of the distributive property.
In general, I think this is similar to the divisibility rules. The only
justification I see for teaching the divisibility rules is in the
context of asking the students why they work.
Cheers,
Kathy Burgis
Lansing Community College
Lansing, Michigan
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