"How can my class collaborate in ArcGIS Online?" This is an inspiringly frequent question. The good news is that there are several key ways, but they need careful attention to process to work well.
The number one wrong expectation by ArcGIS Online novices is that the basic Map Viewer works just like a "collaborative word processor," with many people editing a single document at once. It doesn't, for good reason. So, just know that, if ten users log in and open the same map, each is working on his/her own version of that map, and saving happens only when a given user clicks "save," and saves a user-specific document in that user's contents. Now, here's how good collaboration can happen.
 Users can share documents they have created. OK, sharing is not the same as collaborating, unless thought of in sequential terms. User A can create a map and share with her Org, and/or Group(s) in the Org, and/or the Public. Others can use that as a starting point for their own custom work. (Caution: users planning to save modifications should keep good metadata.)
 "Ownership of an item" can be reassigned from one user to another, by an Org admin (or "custom helper" with the privilege to reassign). The admin can go into A's contents, and reassign ownership to B, and so on. (Caution: it passes in the condition last saved, so be sure all saving is completed, including metadata updates, and the current owner has closed the doc before reassigning.)
[2.1] A "shared public login" (Row 3 of http://esri.box.com/agousestrategies) allows users not in an Org to simulate the process above, but extreme caution and self-control must be exercised here, since everyone using the login has equal access to all items at all times. Strictly following a sequence (A starts a map, makes changes, saves it, then closes it; B opens the map, makes changes, saves it, then closes it; more users follow B's strict sequence) in which only one user at a time has the map open, and it is saved and exited before another person opens it, can work. (Having each user quit their browser immediately after saving will ensure there is no "residual version." Alert: Be sure to update and save the metadata before considering it ready to be passed to another user.)
 Users in an Org can create and share data layers as components for others to use in building their own map. User A can make a layer of neighborhood parks, B can do stores, C can do bus stops and bike racks, and so on, for sharing with the Group/Org/Public. Each user can then create their own maps. (Alert: If the layer owner changes the layer, those changes will be visible in every map using the layer, which can be in ways other map creator/s might not anticipate.)
[3.1] Even Map Note layers can be shared this way, if the creator of a given layer accesses the layer properties while in the map, and chooses "Save the layer," and then navigates to "My Content" and shares the layer with the Group/Org/Public. (In a "shared public account," since everyone is logged in as the same user, formal sharing is not required. See this document for a step-by-step process description.) Map Note layers shared this way are a "feature collection" (essentially "ad hoc geolocated graphics, each with custom attributes") and not a true "hosted feature service," so no filtering is possible.
 Users can collaborate on generating data, such as field data collection activities, via Survey123 or Collector creations. Here, process leaders can decide to share with only certain people (Group or Org) or open it up to the world. Data contributors in this process work according to the parameters set by the creator. This is a hugely powerful opportunity (explore the map app in Fun with GIS 223), which demands much forethought to capture the proper content easily, and to imagine all the conditions under which someone might contribute. The "farther" the contributor is from the collection instrument designer, the greater the chance for misperceptions, hiccups, and errors.
[4.1] Survey123 creators can also share the permission to analyze results from within the Survey123 dashboard.
[4.2] Survey123 creators can even share an entire survey form with someone else in the Org by doing "SAVE AS" in design, then having the admin reassign ownership of the newly created folder and contents.
[4.3] Collector requires an Org login and membership in a group which includes the specific Collector map.
 Multiple people can collaborate on a Story Map if, for instance, the group plans out a project, and each person or sub-group is responsible for some of the "raw materials" to be used in different portions of the content, and someone is responsible for pulling the disparate creations into a tidy and sensible whole. For instance, users A,B,C,D,E can collaborate if A,B,C,D each generate independent components and E assembles the final product. (In this case A,B,C,D need to set appropriate sharing, and recognize that any changes made in their contents will appear in E's final product.)
ArcGIS Online software evolves periodically, and collaboration options may change in the future. Be sure to examine the documentation for options. But, for now, focus on the powerful options above. Collaboration is possible, but groups must think through the workflow carefully, understand what is technically possible, and focus on what is good practice under a given situation. Emphasize the steps that will lead to a good result, not necessarily doing everything that is technically possible.