The opposite of divergent teaching is convergent teaching. Convergent teaching focuses on helping students bring together material from a variety of sources in order to produce a "correct" answer. Convergent teaching is particularly useful in the hard sciences, mathematics and technology-related fields. Purely divergent teaching, while helpful in getting students to think outside the box, can do little in the way of helping a student in breaking down chemical formulas or lines of computer code, as these don't leave themselves open to multiple interpretations.
An exclusively divergent teaching approach can leave a student relatively unprepared for standardized intelligence tests and national exams, which require and measure a stable and reliable set of results. These types of tests, in which multiple choice questions are favored, don't cater to students who are exposed only to a divergent teaching style. If you are trained to view a problem as having no particularly "correct" answer, yet are given problems that do, in fact, contain only one possible right outcome, you might find yourself quite at a loss.
Divergent teaching methods deviate from the conventional convergent teaching model. This is not a bad thing in itself, however, without a significant change in the methods by which tests and assignments are graded, divergent teaching and learning will always find itself subject to conventional grading standards. What makes grading the things students learn via divergent teaching difficult is the problem of how precisely to assess and grade creativity. Without a grading scale or system that caters specifically to a divergent teaching approach, divergent thinking can be hard to measure.
There are clear restrictions to be found in teaching exclusively convergent methods or exclusively divergent methods. In many fields, there are many routes by which one can travel to discover any number of possible outcomes. In other fields, a more rigid approach is necessary. A purely convergent model of teaching may not encourage people to have original thoughts. A purely divergent teaching model, on the other hand, might foster creativity and originality, but might also leave out the facts. Ultimately, divergent teaching requires a certain amount of the convergent approach to balance it out to make it effective and vice versa.