Thirty-nine descriptions were related to working independently to make a conjecture, and 19 descriptions were related to sharing and discussing a conjecture.
Further on, the solution of the stabilizing control is extended as a geometric control for the EHS tracking problem, but given the extreme difficulty of the problem, the proposed solution works only as a conjecture, well confirmed by numerical simulations.
The animation The Square gave participants a context to discuss students' independent work making a conjecture.
"We may only put a question in mathematics (or make a conjecture)," he adds (PR §151), "where the answer runs: 'I must work it out'".
While students are working on crafting a conjecture, the teacher has the opportunity to guide and observe each dimension of the task; namely, the resources that students use, the operations that students perform, and the goals that students work toward.
For example, a mathematician working on a proof regards a conjecture as plausible if it "has some chances of success" (Polya 1954 (v. 2): 148).
We end by sharing a conjecture about how teachers' perception of students' work in conjecturing task might inform the exchange teachers need to make of students' work on conjecturing tasks for claims that students have learned a bit of the geometry curriculum.
This conjecture suggests in turn that in exchanging students' work on conjecturing tasks for claims that students have learned a bit of the geometry curriculum, teachers might deem that particular work valuable on account of the resources used.
Insights gained from these research questions will be used to inform the question of how teachers manage the exchange of students' work on conjecturing tasks for claims that students have learned a bit of the geometry curriculum.
"We have only been guess working and conjecturing and making what appears to us to be intelligent deductions – in light of the facts available to us, especially the fact that when they rode out on the jet ski Janet Bandu was not wearing a life jacket … We are in unimaginable pain and shock and we will give anything to Castro and Janet back".
