# How To Help a Quiet Class

This term I am teaching a very quiet precalculus class. I am having trouble getting students to answer questions or respond to verbal prompts, even questions I know they can answer. What I initially chalked up to first-day shyness has persisted into the 3rd week of class, so I'm reaching out. This is unusual for me, and all of my usual tricks are failing.

The Symptoms:

• Students will not answer basic questions from me.
• Students will not work with or talk to each other (they sit at tables of four), even when I give very clear instructions on that point.

Why This Matters to Me:

1. Creating dialogue is, at least, an educational habit I've long had. When I show an example, I am always asking questions of the class so they can take part in the work, laboring to understand why certain steps are taken and how to avoid common pitfalls. At their most basic level, these questions can involve recall of basic, level-appropriate facts ("what is the period of sin(x)?" or "which side of the triangle is the hypotenuse?"). On the other end of the spectrum, I will ask concept or open-ended questions, or try to play devil's advocate. I have now nearly ceased asking questions as I can anticipate a full 15 seconds without an answer from my class (I generally will not wait longer than this before giving the answer to a basic-fact question or just asking a different question). If my question was too hard, I will ask a simpler one to the same effect. I have relied on this verbal feedback from students so that:

• I can tell that someone is following the argument I'm making.
• Hearing fellow students answer basic questions sets an expectation for the class about what things they should know or be learning.
• I can get the students' consent to make an aside comment or touch on tangential information.
• I can give students the opportunity to give their own ideas or pose their own questions about a problem.
• (maybe more important than I'd like to admit) I don't feel like I'm just engaging in mathematical performance art in front of an audience.
2. I want my students to learn to talk to each other, as appropriate, when they solve a problem. I also want them to take a basic direction from their instructor. I think my students (these are mostly engineering or science majors) should be discussing the work with each other, able to ask and/or answer questions about a solving process. When I pose an involved problem for them to solve, often my first direction (after I read the problem statement or ask them to read it for themselves) is for them to just talk together for 1-2 minutes about ideas for how to approach the problem. I want everyone on the same page so that nobody just sits there without any idea of what to do. I'll be very specific about what I want them to do. Example:

"Don't take out your calculator yet. First just try to correctly draw the situation from the problem, and label what what numbers you know. I will give you 1 minute to draw. Then share your drawing with your group and see if you can improve it in any way before we jump in and do any algebra."

After a minute, I'll say:

"OK -- that was a full minute. Now everyone take a minute to share your drawing with the group. See if you have all the important details or if you forgot something. Ready...go."

[Absolute silence. No sharing of papers. Maybe one person glances at the person's paper next to them without saying anything.]

What I want:

In a math class where you receive almost no verbal feedback from your students, how do you encourage it? I want to address this as pertains to a math classroom, so I'm looking for your experience -- that is why I'm asking this here (not at the general education stack exchange). I want to help foster communication in my class while still teaching the topic at hand.

Do you have any math-specific activities/strategies that encourage student/instructor and student/student communication? Have they helped you with a particularly quiet class?

Finally, this class is generally doing fine on individual assessments. Am I just asking or expecting too much from this group?

• One other point -- At the start of class, I often ask students to write solutions to homework problems on the chalk boards around the room. At least half of them will do this, and they will verbally answer a few questions about what they wrote. So, they are in it when we're discussing something they wrote (and also, perhaps just as importantly, when it's a problem they've had some time to think about). – Nick C Aug 16 '18 at 21:27
• Are you teaching using the first language of the students? – Joel Reyes Noche Aug 16 '18 at 23:40
• @JoelReyesNoche Yes, I meant Academia, and I am using the first language of the students. – Nick C Aug 17 '18 at 2:54
• There are some writings about "Talk Moves" and "Intentional Talk" that may be of interest to you; especially the former. If I had to offer one suggestion, it would be: When you ask questions, begin with a turn and talk - students speak to their neighbor for 1 minute (this often ends up being longer in practice) about the question at hand. Then, ask whether anyone would like to share something that came up in their discussion - either what they said, or what their partner said. – Benjamin Dickman Aug 17 '18 at 21:43
• When I read the title of this question I switched "Quiet" and "a" which made it a really different question. – James S. Cook Aug 18 '18 at 14:18

I've had a remarkable (remarkable to me) success in a different environment on a different topic, so I am not sure this will translate. But I'll mention in anyway.

With one change, the same quiet "labs" turned into such lively conversations that I now have to raise my voice above the din to interrupt them with instructions. The change was from allowing students to work in pairs of their choice, to working with randomly assigned partners. At the start of each class, I run a program (projected for all to see) that randomizes the pairings, then they get up, move around the room, introduce themselves, and start working on the "lab" exercises. This with about $30 \pm 5$ students. Somehow the random mixing and the weekly surprise partners totally changes the atmosphere.

Of course I'm not addressing the content of the exercises, reporting out, creating a non-threatening environment, etc., etc. I recognize those considerations may dominate.

• I should have listed some of the other things I have tried with this group. I always do something along the lines of your suggestion. In my case, I shuffle a deck of cards and randomize students into new groups, and this usually gets them working together (particularly if it is a graded assignment or partner quiz). This also did not do much to encourage them to discuss the material. It's been a go-to method to to make class more lively. – Nick C Aug 17 '18 at 3:00
• @NickC You can edit that information into the question. – Tommi Brander Aug 17 '18 at 6:36
• @NickC: I must admit I don't understand their resistance "to discuss the material." That's exactly what my students want to do. Might there be some fear of exposing their ignorance, in a fixed-mindset context...? Quite a conundrum. I appreciate your sharing. – Joseph O'Rourke Aug 17 '18 at 22:49
• @JosephO'Rourke: Note that on attempted replication, "growth mindset" theory has turned out not to work so well (in fact, opposite the theory): medicalxpress.com/news/… – Daniel R. Collins Aug 18 '18 at 6:13
• @DanielR.Collins: I don't think that paper will be the last word on growth mindset. – Joseph O'Rourke Aug 18 '18 at 12:26

Start calling on students individually without waiting for any one to raise their hand. For a long time I never did this since I am conflict avoidant and since I didn’t want to put students on the spot, but then I witnessed another instructor masterfully call on every student throughout the course of one class period. The key point to add is that when a student you call on doesn’t know the answer or gives an incorrect answer or gives no suggestion, start a dialogue with them - asking easier and easier questions until they get something right.

• Interesting. What size of class is being considered? – Daniel R. Collins Aug 18 '18 at 6:11
• 20 to 30 students. Also class period length is 90 min. I don’t end up calling on every student. – usr0192 Aug 18 '18 at 13:40
• I would advise against that. It can embarrass students who are not as active in the course or as fast in answering questions. Whether we like it or not, students can feel competed against. There are better forums for encouraging conversation such as the course's online forums (eg. Piazza is a famous one). – OOESCoupling Jul 2 at 19:06

Here are some ideas:

1. Try using shared vertical surfaces for doing problems. For example use whiteboards/windows. According to Peter Liljedahl http://www.peterliljedahl.com/publications/building-thinking-classrooms, having to share the writing space can encourage discussion. He suggests vertical non-permanent surfaces, but any shared space is better than individual spaces.

2. Perhaps put the discussion on paper: students write comment/question and pass it between the table group. Alternatively, they all write down the idea they found most interesting/useful and you collect them all. I would shy away from asking them what they struggled with here. I don't have a reference for this being a good idea.

3. Use the principles outlined in "Five Practices for Orchestrating Productive Mathematical Discussions" (NCTM in the USA link). The idea is to look at student work as they are working and ask particular students if you can share their work. Then you present their work/ask them to present it, and you lead class discussion about different approaches to the work.

Am I just asking or expecting too much from this group?

I empathize with your goals completely, and they are honorable. Bear in mind that sometimes, due to a conflation of factors, a particular class climate may be such that this just never gels no matter what you do.

In my master teaching folder I have a half-dozen post-it notes for (hopefully very rare) emergency or worst-case scenario events. One of them reads as follows:

If class is uniformly dumb (all blank stares to questions), just fire out answers to verbal questions! (else class gets slowed down & runs out of time)

I haven't had to implement that for about the last year, I think. Hopefully you find some better solution in your current case, but do keep that in your toolbox as a last-gasp response.