In terms of blogging in the classroom, I see a lot of application of connectivism. When you have a group of students come together with their own knowledge and expertise, it would be awesome to utilize these strengths in our courses. In other words, give students the opportunity to vlog (video blog) rather than write blog posts if the student possesses the knowledge of video production.
However, connectivism could influence more than the medium of an assignment. Allowing students to connect other fields of knowledge to what they are learning in my course sounds phenomenal for interdisciplinary studies. Not to mention the benefits of students being able to orient their learning on their own terms with prior knowledge.
I see many ways connections can yield stronger understandings of material and give students opportunities to invest in their own learning. All that to say, I see connectivism playing a part in the curriculum of a blogging course.