Abstract
Teaching mathematics is much like building a house: if we do not lay a strong foundation, innumerable difficulties appear later. Too often we see a nice facade, with papers done accurately or algorithms copied and performed well, but like a house on a poor foundation, the student's understanding does not hold up when he or she tries to learn the next logically connected concept. The same student who can add and regroup for two-digit numbers cannot seem to understand how to add three-digit numbers. The student who can subtract with regrouping in the tens column is unable to subtract accurately when asked, and even shown how, to regroup in the hundred column.
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