As part of an active approach to learning, read ahead for each lecture and class. In particular, identify those concepts that are the most troubling for you so that you can better prepare yourself for when they arise in discussion.
Do not be afraid to read more than is required of you, especially if you are unable to find answers to your questions in your lecture notes. Lecture notes are not typically intended to be exhaustive, and we expect you to actively read about the subjects you have chosen to study. Many courses will provide reading lists with both core and further reading to facilitate this.
Learn to read with a critical eye. Aim to understand the main ideas behind a topic rather than with the intention to reproduce a given result or statement. You will learn and retain more if you actively question the texts you are reading, rather than simply trying to memorise them.
Questions you might ask, for example, are:
❏ Why is a certain definition given the way it is? What is the effect of changing things (e.g. allowing weak inequalities instead of strong inequalities)?
❏ Why does a theorem contain exactly those conditions and those conditions only? What happens if we were to drop some conclusions? Or if we were to strengthen some?
❏ Why does a worked example follow those particular steps? Could we drop some, or mix the order up? Are there alternative approaches available to us?
❏ When reviewing a model proof, do not ask yourself how they came up with a solution, but rather what makes that solution work. Does it look similar to other proofs you have seen? If so, what do they have in common?
Critical reading will require you to constantly review what you have read and reflect upon your understanding of it.
These activities are crucial to active learning, but are not limited to just your reading.
For more on how to review and reflect, see Review and reflect on your learning|.