Inquiry is not a method but something that students do. In almost all lessons, students should be inquirying, i.e., thinking and reflecting upon their understanding of the content. Alternate terms for inquiry are meta-cognition, self-reflection and self-assessment. It appears to me that all successful methods promote inquiry on the part of the students.
On the contrary, lecture works really well if students are inquirying and attentive. In fact, inquiry works well with any method, including lecture.
The problem is that the lecture method, by itself, does not promote inquiry. Rather, it assumes students can already inquire and have a desire to inquire. While this may be the case in a scientific conference full of scientists with Ph.D.'s, it may not be the case in a K-12 or college classroom.
Another problem with lecture is that lecture provides very little opportunity to assess whether students are following the logic during the lecture. If the students don't think like the instructor (which is usually the case), it is very likely that the main concepts of the lecture were not mastered.
Inquiry only means that students must question and evaluate their understanding. Certainly, such inquiry must be present for students to successfully "discover" things on their own. However, students do not have to discover in order for inquiry to be present.
As mentioned above, inquiry is more something the students do than something the teacher does. Since most students are unfamiliar with inquiry, the teacher must provide activities that allow students to master it. This usually, but not necessarily, means that the teacher must sacrifice time spent on content. However, once students have mastered inquiry, material can be presented more efficiently because (a) less repetition is needed and (b) time no longer needs to be spent on teaching inquiry skills.
In fact, the oppposite is true. Students must still be given proper scaffolding so that they can build on their previous knowledge. The key is to provide the scaffolding without limiting their ability to reflect on their learning and understanding. For many teachers, scaffolding is equivalent to direct instruction and so when they move toward encouraging more inquiry they end up dropping the scaffolding. This is a mistake.
Disclaimer: These are just my thoughts. Take them for what they are.
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