Canvas Notifications

Each user controls their own notifications. So an instructor can not set notification settings for their students.

Here are text instructions for setting notifications up in Canvas: How do I set my Canvas notification preferences as a instructor? 

Discussion Notifications

For discussions, you need to subscribe to the original discussion post and then go and set your notifications for Discussions. There are two options for Discussion notifications as seen in the screenshot below.

Discussion Notifications

So you would enable notifications for "Discussion Post" to keep up with an existing conversation.  If you want to know when someone creates a totally new discussion thread, then you will edit notifications for "Discussion".Here is the Canvas Notifications Cheat Sheet that covers all you need to know about notifications.