I'd suggest two things: first, don't look for proficiency in a timed manner. Studies have shown again and again that the negative results of expecting kids to perform in a certain amount of time are too numerous to list (but I will list a couple)...it fosters math anxiety and doesn't necessarily result in learning. For me, the big one is that it serves to remove math from any real-world connections the kid might be forming. When you're an adult, it is very infrequent (if at all) that you are expected to multiply or divide a bunch of questions in a certain amount of time. Kids are pretty savvy. Doing this just becomes more evidence that "math is something we do in school".
Second, instead of focusing on facts per se, there are some wonderful constructivist activities through which students can construct their own meaning. In other words, they can get a solid picture of what multiplication and division really mean. Once they have that (and maybe their own personal algorithm they've developed), the facts are no longer a chore to learn. Generally, they have absorbed most of them and the rest follow suit shortly.
A lot of the stuff we do with kids is because that's the way it was done with us when we were in school. Learning facts is an example of this. We all did it. But was it worthwhile? In most cases, we were able to learn the facts. It didn't make a lot of sense to me or my friends and we sure weren't told why or how the operations worked. If anything, this is reflective of the procedural approach to math: here's how to do it, now go practice. We need to stop and ask ourselves a couple of things. Why am I doing this in my classroom? (Is it because I've always done it? Is it because everyone is mindlessly doing it? Is there research to support it?) Are kids truly learning? (Not just memorizing but really learning?)
I would interpret fluency to be reflective of understanding. I'd consider a student fluent if he or she was able to answer something like "Can you show me, using a couple of different ways, why 5 times 6 is 30?" Or if the student is able to use arrays (for example) to demonstrate why 45 divided by 9 is 5, I would be delighted. In other words, I wouldn't focus on the acquisition of facts but rather understanding the deeper concepts. If understanding is there, the facts will come (more easily and sooner than you might expect).
I definitely think a constructivist approach to introducing multiplication/division is worthwhile and necessary. However, I really think they need to have quick recall of math facts (at least multiplying 1-11). I teach 5th grade and their ability to do long division and work with fractions is seriously impaired if they're not fluent with their math facts. I think understanding the algorithm behind multiplication and knowing your math facts is two totally separate things. We work toward 100 math facts in 5 minutes--timing only eliminates counting on fingers and working the problems out manually. This year, I dedicated two class days a week to math fact practice (using games and timed speed drills) and saw dramatic growth--in some cases 86% growth in math fact proficiency from beginning of year assessments. I do think we need to make math as real-world as possible, but, from what I've seen, not providing adequate math fact practice just sets kids up for failure later on. Again, not because they don't understand the algorithm, but just because they haven't learned 8x6...
Our kids understand multiplication. They can show me WHY 6x7 is 42 in many different ways. But since I teach grade 7/8, I've noticed that a lot of kids are having problems with later concepts because basic math facts are not memorized. I think it's really important to make sure that students first learn multiplication through constructivist activities. But once they have a full understanding of how multiplication works, learning those basic facts until they are second nature makes later math easier.
I totally understand and agree that understanding why something works in math helps them to see more value in it, use it in different ways, etc. HOWEVER, we can't give up on memorization entirely. I am currently teaching math summer school to 8th graders. I gave them an untimed multiplication test of 100 problems (0-9). It took them an average of over 20 minutes to complete. I asked them to evaluate themselves at the top and write "memorized" or "not memorized." Most of them put not memorized. I only had two or three out of twenty finish in what I would consider a reasonable amount of time with all of the problems correct.
When I got into working with each student, I discovered most of them did not have the upper numbers memorized. A few students only had 0, 1, and 2 memorized. I have one child who has memorized to 5, but has to count out on her fingers anything higher.
My point is this: my math coordinator vehemently told me that multiplication was not a grade-level standard and therefore I should not review this with them in summer school. I asked her, "OK, so how are they going to do four years of math in high school, get through algebra, trig, etc. if they don't know their multiplication?" She responded with, "It should have been taught in 3rd and 4th grade." I said, "I'm sure it was, but they have not memorized the material."
She basically kept coming back to "It's not your problem." If you cannot remediate something like multiplication in summer school, what is summer school for, I ask?
Constructivism is great, but it is necessary for the children to actually memorize their math facts after they understand the concepts of the operation. If they don't, they are seriously impaired when they get into algebra, trig, calculus, etc.