I will check with the TERC staff to get an official reply.
It is difficult to find a balance between discovery and focusing in to fluent and efficient approaches. The goal of course is not to see how many ways we can solve the problems, but to develop a few very efficient ways to think about division. I think the expectations are very different at each grade level.
I've been working quite a bit lately with division and multiplication in 4th and 5th grade classrooms. I am very pleased with how the students are developing their understandings and strategies to solve the problems. We spend quite a bit of time sharing ways to solve one or two problems. The kids can't wait to share their strategies at the board. We discuss how their ways are similar and different. I ask students at the end if they observed a way they'd like to try on another problem. It seems through this process the classes are really settling in over a few very efficient ways to divide.
I think students are developing their own personal efficient algorithms through their experiences. Will they ever use the traditional algorithm? That's not an end goal I have for the students. I want them to be comfortable with a variety of efficient ways to solve a computation problem. I want them to think about the numbers in the problems they are solving and make good decisions about the best way to solve the problem.
I just finished working with a group of grades 3-5 parents. They were very impressed with how their students were looking at multiplication and division. Their major concern being able to help their children work at home without imposing their ways. We worked with a number of problems and practiced some of their students procedures.
I think you'll find the following article to be helpful.
Developing Computational Fluency with Whole Numbers in the Elementary Grades by Susan Jo Russell
