I like that podcasts and videos allow students to learn the material in a different way than through lecture. Math can be easily taught through daily lecture, but videos (even if they are simply explaining topics) give a good alternative for students. I also like how different each video and podcast is--it provides diverse lesson plans for students (and addresses different learning styles). Also, by using podcasts and videos in the classroom, you can follow up with the students make the videos accessible at home. This way, students and their parents can recall what was taught in the classroom.
You can use podcasts as an alternate form of teaching. Instead of boring your students through writing on the board every day, you can play videos to keep students interested. Some of the podcasts I found also provide interactive activities. Math podcasts often provide examples where students are expected to solve them and then continue the video to see if they answered correctly. Like I mentioned before, podcasts can be used in the classroom and then be made available to students at home so that they can relearn the material. If a student needs further explanation, they can consult the podcast. Also, if a student misses class, they can watch the podcast or video and have a better understanding of the topics.