I've moved my workflow, task, and idea lists to Trello. This is a good tool and I see others use it effectively for project and task management. Also, it is a fast web app and they have mobile apps, all free.
Project and Idea Management with Trello
Use of Trello is meant to improve my project management and workflow. Everything is spread out across email, text documents spreadsheets and hard to see, search for, organize, prioritize, and track. Also, I tend to bounce around a lot between different areas of focus, and sometimes it is days, weeks, or months before I revisit the information. Many times I simply have lost track of part of what I need to know, and don't have the visual overview of where things are anymore. While I usually produce some kind of text document of notes, sometimes a blog post, and usually email, there is no central place to have these things organized.
Trello and Kanban
Trello has been around for five years (as of 2016) with 10m+ users. It was created by a software company for their own project management, then they spun it out into its' own company, which has venture funding (and paying customers). Basically, Trello is a kanban board which is a project management tool used for knowledge work, that was originally developed at Toyota for lean manufacturing.
Lists, Tasks, Workflow
I've had an account since it was released in 2011, and have used it on and off over the years. My wife and I use it as a shared shopping list, which works great when one of us is at the store (with the mobile apps, which also work offline).
Basically a board displays a vertical list of cards. Each card has a title and can have attachments, assignees, due date, comments and a checklist -- all of which are optional. Cards can be dragged from one list (column) to another. Cards can have labels on them as well, though I don't find that as useful, or just time consuming.
The two main ways boards are configured are for workflow (left to right, start to finish) and ideas in categories. I've set up a board for each of these types for you, and am moving everything into these. So far this helps a lot, and for one-off tasks, it is quick for me to add a new card to the Done list in tasks. Each card, list, and board has a complete history of changes automatically.
Project and Workflow Management
Any kind of process can be kanban-ized and it is especially useful for sharing and tracking information and processes for a group. The visual organization of lists and cards (and boards) can be very helpful for any kind of resource management as well. For example, a given course could have a board for student payment status, e.g., interested, deposit, paid in full, for a given course. It is helpful that cards can be moved between lists (and between lists on boards), so that someone who was interested in a particular course date could be moved to a different one if they change their mind.
Another board be the course schedule for a month (20 lists, one per day), with teachers assigned to different topics/times. Another board could have a list for each student, and their progress would be configured as a card. This would allow different teachers to view other teachers feedback and assessment, and enable chatting about the particular topic in terms of student needs and how to help.