When you create a list -- even one as simple as a shopping list -- you're performing a simple form of brainstorming. Listing ideas as soon as they enter your head is an effective brainstorming strategy because it forces you to condense your thoughts into bullet points that leave little room for critiques or analysis. Brainstorming is about getting as many ideas as possible, not narrowing them down. Put brainstorming ideas in list form to keep them organized and brief without imposing restrictions on your thoughts.
Mapping creates a more visually meaningful arrangement of brainstorming ideas because the placement of those ideas on the page or board also carries information. Write the fundamental concept or problem about which you're brainstorming in the center of the page. Then add ideas around it, clustering similar ideas together. After the brainstorming phase, draw connections, circle and underline as you see fit to show the interrelations between concepts and how they relate to the central theme. Mapping translates the language you probably already use to describe "the heart of the matter" or "the central problem" into a visual system that can highlight new relationships among ideas.
Depending on the nature of the problem, you might find seeing it from different perspectives enlightening. During the brainstorming session, try to see the central concept from other people's points of view. For example, if you were brainstorming about a new brand of car, you might think of it from the perspective of a prospective buyer, a seller, a safety engineer or a designer. Cast yourself in the role of different types of buyers to gain insight about how parents, college students or white-collar workers might view this vehicle. If you're brainstorming about a more personal topic, ask yourself how those close to you might see the problem.
While most brainstorming methods are additive processes, challenging assumptions is subtractive. You start with an idea and systematically dismantle it during a challenging brainstorming session. Begin with a set of statements that describe an issue. Brainstorm challenges to those assumptions and give alternatives to them. If you were deciding on a major in college, you might challenge the assumption that you needed to choose a major yet, that you were limited to a single major or that college was your only option. Challenging brainstorm sessions are more than just negation; they also involve listing alternatives. Instead of college, you might list joining the military, seeking apprenticeship or traveling for a time before continuing your education.