Mike, I agree with much of what you're saying. I think there is a place for "page-of-twenty-problems" in a constructivist classroom to give students more practice so they can develop efficiency. TERC stresses that students need to eventually settle on a small set of efficient algorithms for each operation that make sense to them, although those need not include the standard algorithms. Most students are not going to get quick enough with their facts or with these algorithms unless they get a lot of practice. How much is "a lot" is a judgment call that teachers have to make based on observing their students.
My concern with "page-of-twenty-problemsÃÂ is that they shouldn't be used too early, while students are still in the exploring phase, but later when they are in the settling on/consolidation phase. This isn't easy for teachers to pull off, because some students, as you mention, get through the exploring phase faster than others.
Some research that is relevant here: a 1998 study compared three groups of 2nd grade students-- some receiving Investigations instruction, some receiving traditional math instruction, and some receiving a combination. The three groups did about the same when it came to basic facts and two-digit addition. But with two-digit subtraction requiring re-grouping, the Investigations group did best, the traditional group was next, and the combination group did the worst. I believe these students in the combination group were introduced to the traditional subtraction borrowing procedure too early. (See Study 3 in http://www.lab.brown.edu/investigations/resources/studresults/iccuwno.html)
I couldn't agree more that leaving the number fact practice and other consolidating work to parents is a bad idea: an abdication of responsibility and a big blow for equity for all children. Parents can do extra work with their students in this area, but teachers should not be counting on this.