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I know this isn't a math question per se, but I only experience this problem in math courses. I suspect this is because the material and knowledge build on themselves.

Often in math courses—or in sections of a lecture that involve a lot of math—I will be confused. The lecturer might pause and say, "Now does anyone have any questions?" And I won't understand what is being discussed well enough to even frame an articulate question. I'll just feel confused.

What question(s) should I ask in this moment?

Alternatively, is there something I should be doing so as to not put myself in this position? The only thing I can think of is to stop the lecturer constantly. Often, in math, it feels like there is an endless foundation of ideas and knowledge upon which something is built, and I feel like I could spend all day saying, "But yes, why is that true?" Another way to frame my question is: What question should I ask when I have too many questions?

jds
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  • If you have a syllabus or if you can guess what the lecturer will cover next, read the textbook / lecture notes before the lecture. It will take much more time and effort, but if you go into the lecture even with a very loose understanding of the material, the time you spent struggling on your own gives you a great sense of what you don't understand, and the lecturer will end up filling in the gaps in your understanding. This also gives you the chance to find out what you don't know before lecture, and allows you to formulate your questions instead of being in a state of total confusion. – angryavian Dec 01 '16 at 19:10
  • The lecture hall isn’t the best place to deal with that situation, even if the instructor has the kind of interactive style that I preferred when I was still teaching: you probably need an extended session one on one with the lecturer or someone else who can work through the material with you. – Brian M. Scott Dec 01 '16 at 19:10
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    If time is not an issue, you could redo the lecture when you get home the same day. Go through every step, write the math with your own Words. Do not focus so much about how to phrase things or to be rigorous. Play around se what happends. Then you will get a feeling for it. If after this there is something you dont understand, maybe ask the lecturer or here. – Olba12 Dec 01 '16 at 19:10
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    If you aren't able to articulate a specific, targeted question that is likely to be answerable quickly by the lecturer, probably you should not ask it during the lecture. Alternatives: office hours, TA session if available, asking other students outside of lecture, hire a tutor, etc. It's completely normal in mathematics not to be able to follow everything in real time during the lecture. Take good notes and reread (or even rewrite them) after the lecture. If notes/text are available before the lecture, reading ahead of time is a good idea. –  Dec 01 '16 at 19:11
  • This is a rather broad question; it depends from course to course, and the level of expertise you're trying to gain. If you're a math major in a real analysis course, for example, it might be good to ask for good counterexamples to theorems, or perhaps to go line by line through a proof and find the "sticking point," whether that's the step that needs a little more explanation or just seemed to appear out of thin air.

    Counterexamples always helped me get a deeper insight into the ideas behind/motivating the theorem, while explanations gave me more techniques or ideas for future proofs.

     – Giuseppe Dec 01 '16 at 19:15

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Here are two reasonable questions you could ask during lecture.

Could you summarize the main idea?

Can you highlight the key steps?

The former is best when you're missing the overarching concept. The latter is when you miss the procedure. However, neither question may help you if you are completely lost and require extended guidance. You will likely find the best council by heading to your instructor's office hours and being honest about your level of understanding. He or she may help you understand the lesson, but also may advise you to study instead. I also recommend that you seek tutoring services. Many campuses offer free tutoring for large volume undergraduate courses.

During class, actively take notes: not just on what the instructor writes down, but on the questions and comments these generate in your mind. Take these notes with you to office hours for reference.

In order to understand where your difficulties lie, consciously check your level of preparation. Read the material before the lesson. Read the book. Read the course notes. Re-read your submitted homework. Be wary if at any point you're advancing to new material without having understood the prior: that could set up a weak foundation for later learning.

If you encounter difficulty during studying at any particular concept or step, it's likely either because it's a challenging, new idea or it's indicative of a gap in the prerequisite knowledge. One of your duties as a student is to identify these gaps and fill them. Again, an open dialogue with you instructor would be of use.

zahbaz
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    Just to mention that asking "Could you summarize the main idea?" and/or "Can you highlight the key steps?" to a lecturer who most probably just did exactly that can have undesirable consequences. – Did Dec 01 '16 at 19:42
  • @Did then again sometimes they aren't clear, and if so what kind of professor isn't willing to help students learn? Maybe you have ADHD. It might be embarrassing to ask, but when it comes down to embarrassment or understanding choose the latter. And anyways, if the student picks up everything in the lecture they wouldn't need to study. As part of a continued wholesome discussion, I can see asking them to summarize can be useful + keep professor on track. At the same time though I see what you mean. – Pineapple Fish May 30 '20 at 06:11