If you don't want to show recent forum posts on your course page, click on the Edit settings icon associated with the forum and deselect the option to Display recent posts on course page as shown below. New posts will still be indicated in blue on your main course page and will be highlighted with a New! icon within the forum when you open it.
Bonus Tip #1: If you don't see new forum posts highlighted in yellow on your course home page as shown in this example, check out these instructions for updating your forum preferences.
Bonus Tip #2: To view the time and date stamp for a student's forum post, hover over the notice of elapsed time (e.g., 3 hours ago) with your mouse and the actual time the post was made will be displayed in a pop-up window. (We'd wave our Moodle magic wand over this if we could to have the time stamp displayed instead of elapsed time, but at least it's possible to ascertain when a post was made.)