It's perhaps worth noting that there are (at least) two distinct reasons why your students might offer no reply when you ask them if they understand what you've just explained:

They might not understand what you've told them, or even **understand enough to know what it is that they don't understand**. This typically happens when the students lack (or have failed to properly internalize) some prerequisite knowledge that you're assuming they have.

For example, if your students have *never seen a differential equation before*, and have no idea what the notation even means, asking whether they've understood your explanation of phase plane analysis and Jacobians is, most likely, going to be met by blank stares. They may even assume that, since they don't know those things that you're clearly assuming they should know, the class is clearly not meant for them, and they should just keep quiet and not interrupt the other students' learning with stupid questions.

Conversely, the other possible reason for silence is that your students **already know everything you've been telling them**, e.g. because you're (intentionally or not) repeating something that was covered in an earlier course. They *could* answer your questions (at least with "yes, I know all this"), but they won't, because they assume that the questions are really meant for some other students who *don't* know the subject already, or that you're only asking to make sure you can safely move to the next topic (and that you'll do so if nobody speaks up).

In your case, I do suspect that the first explanation is more likely, but you should keep in mind that both are, in fact, possible. It's also quite possible for *both* reasons to occur simultaneously in the same class: some of your students could be silent because they have no idea what you're talking about, while some others might be silent because they already know all of it and don't want to interfere while you explain it to the rest.

This can also be highly cultural. Here in Finland, for example, I've heard several lecturers coming from abroad (especially from the U.S.) complain about getting "nothing but blank stares" from the class, because Finnish culture is traditionally a *lot* less outspoken than, say, in the U.S., and people coming from other cultures may not immediately recognize the subtle body language cues that can, sometimes, signal the difference between "I'm not asking questions because I want you to move on" and "I'm not asking questions because I have no idea what to ask".

OK, so what to do about it?

First of all, the situation you describe seems like a perfect opportunity to **take a few minutes to explain** that you *really do* rely on feedback from your students to know whether you're going way too slow or way too fast (or both), and that you really want them to speak up even if (or *especially* if) they have nothing to say but "I don't get any of this" or "I already know all of this". Try to create a friendly and relaxed atmosphere, let your students know that it's *always* OK to ask question or speak up, and, when they do, make sure to respond positively.

Second, if you're still getting no response by asking the entire class, don't be afraid to **pick a random student** and address your questions to them personally. As uncomfortable as it might, initially, feel to the student who ends up in the "hot seat", it at least ensures that they can't just "let someone else answer", and so gives you a single direct data point about that student's level of understanding.

Also, since you say that you feel more comfortable teaching in a one-to-one setting, you can always just pick one student out and **work it out with that student until they get it**. The odds are that, by doing this, you're also helping all the *other* students who may have the same or similar difficulties. Besides, by taking time during class to specifically engage one student in dialogue, you're showing the other students that they can also ask specific questions without worrying about "wasting time" or disrupting your lesson plan.

Jsor's suggestion of **picking a "stooge"** to sit in class and speak up when the other students won't is also excellent, and something I would've suggested myself. If you're a professor, it can be a TA who sits in class; if you're the TA yourself, it can be any student you trust to do the job. If necessary, ask a friend who's done the same class recently to join in and ask basic questions if your students won't. I've *been* that stooge before, and I can testify that it really does work.

Finally, and somewhat tangentially, it occurs to me that you might need to simply **lower your expectations** a bit. You're TA-ing a course on "math for chemists", presumably aimed at undergrad chemistry majors with no prior math background since high school. I don't know about your chemistry students, but back when I did my minor in chemistry, even using the quadratic formula to solve second-order equations was considered "advanced math" — i.e. something that the students would not be generally required or assumed to know — in first or second year chemistry courses.

Yes, courses like "math for chemists" exist precisely to provide some of those missing math skills needed for certain topics in chemistry, but the point is that you *really* can't assume in such a course that the students know anything past the minimum high school math curriculum — and they may have forgotten much of that. It *probably* doesn't include differential equations, and I'm pretty sure that it won't include Taylor series. You're going to have to start from the basics — equations, variables, constants, basic algebra — and work up from there, brutally distilling each concept down to the bare minimum necessary to work up to the more advanced topics you're really supposed to be teaching.

Or course, as a TA, that's *primarily* your professor's responsibility, but *your* job is to fill in the missing gaps for each student on an individual level. If you've got a good textbook (or a good set of lecture notes) for the course that presents all the preliminary material in a clear and concise form, I'd suggest reading it until you know most of it by heart.

If you *don't* have one, try to *find* one; even if it's not official material for the course, having a good introductory textbook aimed at students like yours to fall back on is worth its weight in gold. It means that, when a student asks you "what's a differential equation?", you can just paraphrase what the book says about them, instead of having to make up your own five-minute explanation of differential calculus on the spot.

(Of course, it should go without saying, but you should not follow any book slavishly. Rather, use the book as a "cheat sheet" for your own teaching, as and when needed.)

Are all your examples thinks that chemists students will care about? Or are you trying to force maths on them that they don't yet know is of value? – Ian – 2014-05-06T11:34:10.123

1No one is going to fully understand something after an explanation. Even if each piece is acknowledged in isolation, it takes time for a true understanding to take root. – Tac-Tics – 2014-05-08T20:10:38.467

To clarify: replacing another TA for two weeks, so I knew neither the students, the other TA (which was not the one I was replacing) or the math handled in the course very well. The course was 'mathematics for chemists', and we divided some topics between the three of us. This all made it very hard to judge if the students didn't understand and were too shy to ask, or did understand and were too shy to let me know (or they just didn't care). So Ian, no, and no. Tac-Tics: the explanation was meant to be a recap of something they should have seen before. – Ruben – 2014-09-07T19:49:34.363