Mathematics is often taught by explaining an idea, then giving students practice in applying it. Tutoring systems can increase the effectiveness of this method by monitoring the students' practice and giving feedback. However, math can also be taught by having students work collaboratively on problems that lead them to discover the idea. Here, teachers spend the bulk of their time orchestrating collaborations and supporting students in building productively on each other's contributions. Our research question is: Can tutoring technology somehow make teaching-by-eliciting more effective? Using tutoring technology, we developed an intelligent orchestration system named FACT. While students solve problems in small groups, it makes recommendations to the teacher about which groups to visit and what to say. Data from over 50 iterative development trials (study 1) suggest that FACT increased neither the collaboration nor productivity of the students' struggle compared to paper-based classes. However, the data also suggest that when there is just one teacher in the classroom, then only a few of the groups that need a visit can get one. We modified FACT to directly send students the provocative questions that it formerly sent only to teachers. A pilot test (study 2) suggests that this version may increase productive struggle, but increasing collaboration remains an unsolved problem.