What is a problem? In the context of design, a problem is any situation where you have an opportunity to make things better. And problem solving is converting an actual current situation (the NOW-state) into a more desirable future situation (a GOAL-state you want to achieve),
You can make a difference by “making things better” when you choose one aspect of life and increase its quality in some way, or minimize a potential decrease of quality.*
Here is an example in education: For teachers, it's especially exciting when students are motivated to pursue their own Personal Education so they "adopt a proactive attitude of problem solving (trying to ‘make things better’) with the objective of converting their actual current state (of knowledge) into a more desirable future state (of improved knowledge)."
What is design? During a problem-solving process of design, your objective is to design (to find, invent, or improve) a product, activity, strategy, or theory. { Notice that design can be a noun or verb. }
* Positive Changes and Negative Changes: You might recognize that a problem exists because you have looked at a current situation, and you can imagine that in the future it has changed and improved. Or maybe you imagine a future in which things have changed but have become worse, and you want to avoid or minimize these changes, so you respond with timing that is proactive (to prevent, or minimize, a negative change that might occur) or reactive (to minimize the negative effects of a change that has occurred or is occurring). Thus, you can solve a problem and "make things better" by producing (or increasing) a positive, or by avoiding (or decreasing) a negative.