While a little bit of group learning and guiding-on-the-side is good in the classroom, too much poses an obstruction to effective dialogue between teacher and students as well as to the efficient transfer of knowledge from teacher to students. In such a climate, gone is the possibility that the teacher can share with students his or her insights or warn them against pitfalls, or that students can learn enthusiastically from their teacher in class and do the mental construction at home — with or without a group of friends. Right now all the learning must take place instantly in school. But can any substantive mathematics be learned this.
