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Making connections to real life, real student interests and contemporary issues makes the subject matter the teacher addresses more compelling for the students. In addition, a teacher cannot assume that an "off-topic" question has no relevance. Sometimes students make connections that we don't recognize, but if given the opportunity to clarify they can make some very good points and show the class how they made this connection. Don't forget to address those teachable "off-topic" moments that crop up either.
When a teacher talks about a particular subject it can be interesting. I however prefer them to link their subject matter to everyday life. In doing this, they make their topic more interesting and applicable. In conclusion, talking about more than one topic at a time, if done correctly, can facilitate the learning process.
Everyone remembers having teachers who were easy to get off topic - in high school, we even liked to try and do that as often as possible. But in both high school and college, teachers are dealing with a limited amount of time to teach a lot of material, so it's best they stay on topic. This doesn't mean the class still can't be taught in a fun and entertaining way.
You can do it either way, but if you introduce (or let students introduce) ideas that are not obviously related to the main topic, make sure you let them know how it relates to the subject. I teach in a 90 minute block system, and I have to be somewhat flexible when a student asks about something that may only be slightly related to the main topic, but is obviously something they've wondered about. For things completely off topic (last night's baseball game or something) I try to give them a minute or two at the beginning of class (What's new, guys? Anything happening this week?)
I tend to think that organization is more important than whether you stick to one topic or move on to others. Particularly if they are organized around a particular theme or if one leads to the other, I think most students have no trouble following those changes.
If things are disorganized, moving on to different topics can feel very disjointed and lead to a loss of focus.
Often students will take the lead in whether a teacher digresses in a relevant direction from a topic. For, those who are creative and analytical and imaginative enjoy discussions from other perspectives on a topic; however, the more concrete thinkers find such venturing down different avenues of thought as irrelevancy and "getting off the topic" since they may not make connections.
I think it depends on how long the class lasts. A 45 minute period is often not long enough to truly go into depth on one topic, however, in 90 minutes in seems several topics/subjects can often be covered.
The key to keeping student attention (in my opinion) is to keep the subjects relevant and applicable to their lives. You know people can sit around talking about one thing for days and days if they are truly interested in it...
I agree with you, but I think that teachers need to be careful so that they don't spend too much time on topics that are not related to the class. It is always good to have a change of pace, but if the teacher spends too much time off the topic you can often feel like you are not learning the things that you need to learn.
i think sticking on a cetain subject will make the student exhausted during the class time and will bring down their intrest!
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