Class Discussions

In the comments on my last post, H asked, “What have you been doing to get them to this point?” So as requested, here’s some of what I do in my freshmen classes.

Students work in groups. Every day. No matter what.

They start every class period by comparing homework solutions and methods. There is an opener on the board (or screen, if the projector is working) which directs their conversations to specific parts of the assignment. As I walk around checking homework, I listen to the conversations, ask a question or two, and move onto the next group.

At the beginning of the year, when a student would ask me a question, I would reply, “I don’t know. Did you ask your group?” and move on. It was very, very difficult to to that, but I knew if I didn’t start them off working effectively in groups I’d never get them there.

After the small group discussions, we have a whole class discussion. Here is where we clear up any misconceptions I overheard at the start of class (or questions that students asked me in small groups – I’m not ignoring them). The way I do this is by asking questions and having students share their work. I try not to ask yes or no questions. I don’t answer my own questions. I don’t immediately rephrase my question. If no one answers, I wait.

And wait.

And wait.

So far the longest I’ve had to wait is about 4 minutes. They’ve learned they aren’t going to be let off of the hook if they don’t know. I even told one student that he had until the next day to answer the question. You know what? He came back the next day with the answer and was really proud of himself.

Some of my standard questions include:

If we pulled a person in off the street, would they be convinced by your solution?

How does your method compare with his/hers?

How do you know you’re right?

Can you think of another method that would give you the same result?

On what part of the problem are you stuck?

What do you know about the problem?

There are days when it seems like the same three or four students are answering all of the questions. So, when that happens I tell them that they aren’t allowed to answer any questions – they are only allowed to ask questions of other students.

Then there are days in my first period class when no one wants to answer any questions – so I pull out the popsicle sticks.

These techniques are working really well in my freshmen classes. The seniors? Not so much. I’m finding it more difficult to have effective discussions with them for a variety of reasons. I feel like I’m a much better teacher with the freshmen. I don’t know if it is the curriculum, the time of day, or simply that I’m better with the freshmen.

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22 Responses to Class Discussions

  1. Jen says:

    You can have my freshmen…

  2. Jackie says:

    Erh, let me clarify – I think I’m better with my freshmen than I am with my seniors. Your freshmen? Not sure how to respond to that one. No thanks? 🙂

  3. mathmom says:

    That all sounds awesome, except that I would have hated the working in groups every day thing. That’s a personality thing for me, as a pretty strong introvert, and also perhaps a “gifted kid” thing, as the person people would naturally go to for help anyhow. It’s not that I minded helping others informally, but I hated being responsible for a group’s comprehension of a topic, and I hated being “held back” from working at my own pace by having to keep the group up to speed. If I had to do that all the time, it would have made me insane. Just my 2 cents. Your other discussion tactics and questions sound really good. But when I do group work with the kids I work with (middle schoolers) there are one or two who always prefer to work alone, and I usually (but not always) let them.

    I bring this up because I doubt many introverts go into teaching, and thus they may not be aware of or sensitive to the needs of this invisible minority. School is hard for introverts because we need quiet time alone to “recharge”. It is harder if school requires active interactions with other students “all the time”. Being able to work quietly alone in math class for a little while can help an introvert recharge for the other social interactions they want and need to have throughout the day.

  4. Robert says:

    This is a nice post — a good mini-tutorial on effective group learning. I might use some of this myself in calculus next semester, because (1) I hate taking up homework, but (2) I need to know on a daily basis just what the students are having problems with.

    For mathmom- I think it’s certainly possible to adapt some of these techniques for individual learning as well. Give the kids some stuff to do and then give a written answer to some/all of Jackie’s questions, for instance. Most good pedagogical techniques can be adapted equally well to either a group setting or an individual setting. And getting that balance between working in groups and having individual mastery is really important.

  5. Jackie says:

    Mathmom – While they are in groups every day there is also time for individual work (they need to be able to do it on their own too!). When we start a new lesson/assignment I give them time to work privately. Then they move to comparing answers with their groups.

    Robert – I like the immediate input I get as to what they’re understanding (and what they aren’t). Of course I still collect and grade some assignments, but being able to check in with each student and look at their work on a daily basis helps me to decide where to direct the rest of the class period. Having them up at the board working helps too.

    There is the occasional day when a student isn’t working well in his/her group (they are only 14). They get “voted off the island” for the day. Works like a charm.

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  7. H. says:

    My students are mostly in groups too, but I haven’t been as consistent as you have in insisting that they rely on each other, and this sounds much better. How often do you rearrange the groups?

    Maybe the reason why the seniors aren’t doing as well with this approach is precisely that they haven’t been trained this way from the start, and the expectation that the answer should just be given by the teacher is that hard to change after a certain point.

  8. Jackie says:

    We change groups about every three weeks (except for the current unit). I use mostly random groupings. I say mostly as there are times when the random method puts too many kids together that just shouldn’t be. Also, I have a two students who are deaf and the interpreter prefers they are in the same group.

    I think you’re right on with your assessment of the seniors. Any advice?

  9. bk2nocal says:

    I really like this idea for going over homework. I’m going to try it in my critical thinking class in college. Much of the time in that class, the students are not forced to CONSIDER and DEFEND their responses, and this seems like a good non-defensive method of doing that (with specific questions to guide their discussion). I am also teaching a small group class in college and I THANK YOU for introducing group work techniques so early on. Although I agree that there are introverts and there must be a balance, it is imperative that students learn to function as cohorts, both for their academic and professional careers.

  10. Jackie says:

    I’m interested in hearing how this goes in your class. Good luck and thanks for supporting the early use of group work.

  11. Sarah Cannon says:

    This is one of those posts that makes so much sense, I leave feeling inadequate. “Of course that’s what I did wrong.” I need to make them rely on their groups more than I have. They sit in them, but I don’t have them use them as much as I’d intended. Thanks for the reminder of what I wanted it to look like. Now to see if I can get there this year.

    Because I’ve got the older students, what is working with your seniors?

  12. Jackie says:

    That’s a great question Sarah. I do have the seniors sitting in groups. Getting them to understand effective group work has been more of a challenge. I need to do a better job of structuring group activities for them (different curriculum). I’m also not sure how much change I can affect at this point – but I’m still trying.

    Your comment made me think of using a jig-saw. Thanks!

  13. mathmom says:

    I’m going to play the Grinch here and say that I think most group work in high school(and often beyond) is not “effective group work” and probably cannot be due to the nature of the groups.

    For group work to be effective, in my opinion, everyone in the group must contribute something that no one else could contribute as well as they, and everyone in the group must benefit from the interaction.

    If you have some students in the group who are always getting help and never able to contribute, and others who are always giving help and never getting any help or new inspirations, then the group is not, in my opinion, effective. It may be effective in relieving the teacher of having to answer everyone’s questions in an overcrowded classroom. And students who end up being the tutors in this manner do gain real skills by doing this. But I’d really call this delegation, or peer tutoring, and not “real” group work. If some students are always “giving” and never “receiving”, as seems likely in a group of kids forced together by the teacher in a math class, then it’s not a true collaboration.

    I never experienced effective group work in high school. I did (sometimes) in college, and I do (more often than not) in my work life.

    In college, there were often times when I worked on problem sets with a group that more or less came down to me tutoring other, or others tutoring me! Neither of those are what I would call effective group work, though they were nice in a social sense in many cases. But I had one friend who I worked on some classes with whose strengths really complemented my own. I was great at brainstorming solutions, and he was quick at recognizing when something I’d thrown out was going to work. We both contributed, and we both benefited. That was my first experience with an effective collaboration. That’s what group work should look like, in my opinion.

    Now in my professional life, I work with people who have lots of different areas of expertise; different experiences, etc. When we need to complete a project that draws on a number of areas of expertise, we get together the relevant people. Everyone has something to contribute, and the project benefits from everyone’s contributions.

    I think the key is forming groups based on complementary strengths and needs. I don’t do groupwork at my job based on whose office is near mine. My boss doesn’t pre-assign me to a group without a particular project in mind. I am invited to join groups, or invite others to join with me, when there is a set of needs to meet.

    I’m not saying that there’s anything necessarily wrong with setting up peer tutoring or delegation situations in a high school classroom. I think they may be great strategies in many classes. I have often argued in favor of “making” more talented math students act as tutors, *sometimes*, because of the skills they gain by doing that. But I would caution you to make sure that the “tutors” don’t resent the situation, and to keep in mind that not every great math student is naturally a great teacher. If you want students to be doing teaching, I think you need to teach them how to teach effectively (lest both they and their “students” grow frustrated). And I would put forth my Grinchly claim that this has little to do with “effective group work” in the real world.

    Of course, I don’t know Jackie’s classes, and maybe she really does have effective groups of kids whose strengths complement one another’s, and really are able to do effective group work in a high school math class.

    But… I don’t think that happens often. And, given that, I’m not really sure what the point/benefit of supposed “group work” in high school is, in a situation where groups are pre-assigned, and the odds of a great serendipitous meeting of complementary talents seems unlikely. I think it models “real life” group work much less than people would like to believe.

    Sorry for the long ramble!

  14. Andy says:


    I agree with your assessment of the way groups tend to work in college, business, or, for the most part, high school. However, I’m not sure I quite agree with your definition of “effective group work” for schools.

    [Just to clarify, I’ll note here that I think Jackie is talking about having groups work together on figuring out small problems they may have in understanding material or short questions that can be done in a few minutes, not large projects, which may be more applicable to what you’re discussing.]

    (I’ll focus on high school courses at the moment, so assume anything I mention relates to those.) In nearly all cases, the purpose of a group discussion/project is not necessarily to get something done in the shortest time or with the least effort. (While I’d say these are important skills, they are more important later, while it is, in my opinion, more important to learn concepts in high school than how to sprint to the end of a project.) With that in mind, I’d have to say that “effective group work” in schools is significantly different than what it might be in the college or business world.

    What, then, is the goal for group work in high schools? That’s clearly up to personal definition, as many things are. I’d say it’s to help people better understand the content they’re working on, be it math, history, science, or literature. How does that happen? Well, the idea is that at least one person understands what is going on, and can help explain it to the rest. Or, between the three or four people in a group, they might be able to scrounge up a book and figure out what they don’t understand.

    Odds are that one of those two methods in a group can help all the members figure out most of their content-related problems. But there will certainly be things for which groups don’t work, which is where the teacher comes in. This might be the case more often when students have similar strengths (and weaknesses), but hopefully a good teacher can shift groups around so this is less of a problem. So, groups certainly aren’t the “alpha and omega” of making students understand, and a good teacher is still necessary, but they can help solve many problems.

    In terms of unbalanced groups, you mention that the “more talented” students may not appreciate always helping others in the class. This may, in fact, be true for some students. In some ways, that’s just the way things work, and they’ll probably end up explaining many things to others even after school. But also, any student who doesn’t ever have any questions about any of the class content is either kidding themselves, or should be in a different class. If they need to stay in the class they’re in, then group work may not end up being too productive for them, but hopefully they can help it be productive for others.

    Overall, I’m not really sure that high school group work is supposed to model “real life” group work, and I agree that it doesn’t really do that. But I think it offers good opportunities for learning from peers, lets students learn from someone other than the teacher (which can be really helpful if the students don’t learn well from how the teacher teaches, or otherwise can’t learn from the teacher), and helps them interact with people with different abilities in a somewhat structured setting.

    I may have completely missed something important you were saying, or possibly the entire point. I’m pretty sure my comment rambles more than a little, as well. Hopefully you can at least make sense of what I’m saying, and determine if it applies to what you were saying.


    (As an aside, I’m not [quite] out of high school yet, but I wish I’d gotten more chances to discuss things in groups like this. Social interaction + problem solving = good, at least in my book.)

  15. mathmom says:

    Andy, I think you’re right about the value in high school group work in terms of freeing up the teacher more, and empowering students more. And I think that having students explain something they understand helps them cement their knowledge. Hearing it in a different way, from a peer, may help someone understand better.

    But… I think it’s important to keep in mind that not everyone is a “natural” at teaching. Expecting students to “teach” one another without giving them any training in how to be effective at this can be an iffy proposition. I can imagine frustrating situations where the student who understands the math can’t think of any other way to explain it than they way Jackie used, and may be frustrated with her group mates for not understanding despite her repeated attempts to explain. Meanwhile the group mates may be getting frustrated that they aren’t being given the help they need to understand the topic. I suspect that Jackie is on top of this, though, and that being freed up from answering all the questions that the groups are able to answer allows her to concentrate on those kids. My main suggestion would be: if you’re expecting students to teach one another, then don’t just help the student who didn’t get the math, but also support the student who couldn’t figure out how to teach it.

    My rant about HS group work not being like “real life” group work came out of the fact that a lot of people advocate lots of (artificial) group work in high school (and college) to prepare students for the fact that they will have to be able to “work with others” later in life. I think it’s a false assumption that the group work in school does anything to prepare students for genuine group work in a job situation.

    If you can make an argument that it’s pedagogically advantageous for students to learn from other students rather than directly from a trained teacher, then use group work for that. I’m not sure that it’s really pedagogically “ideal” but then, what in the real world is ideal?

  16. Jackie says:

    mathmom – You said, “… everyone in the group must contribute something that no one else could contribute as well as they, and everyone in the group must benefit from the interaction.” Well, that would be wonderful if I could choose the students in my classes. Needless to say, that isn’t the case.

    Of course some students contribute more to their groups than others. However, the recent letters included in portfolios have indicated those who have been taking more than giving are aware they need to step up their contributions. We’re working on it. This also reminds me of something that happened in class two years ago, which deserves a post of its own.

    Is it “ideal” for the students to be working in groups? I don’t know. On most days, I think it is. Do I have evidence to back it up? Only anecdotal.

    Andy was correct when he said that the students are not working on large projects. Nor are they working for a group grade. Each student is assessed based upon his/her own work.

    I agree that an understanding of the math does not guarantee a knowledge of teaching (I’ve had a few professors that prove that one). We do work on effectively explaining the mathematical concepts. I think this not only helps the students who are having difficulty, but as I tell the cherubs, “If you can’t clearly explain it, I’m not sure that you fully understand it.”

    Of course I wish I had unlimited time to spend individually with each student. I don’t. By having them work in small groups, I think I can better monitor what’s going on. I follow the “Rule of Three” that I picked up while observing at I.M.S.A. a few years back. If three students have the same misconception or question, it is time to bring it to the attention of the whole class and clear it up.

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  18. mathmom says:

    Jackie said “Well, that would be wonderful if I could choose the students in my classes. Needless to say, that isn’t the case.”

    …which is why I said that (what I consider) “effective group work” can’t really happen in a high school math class.

    I admit I have a personal bias going here, because I hate working in forced groups like this. I have no problem working in genuine group situations in my job, in my volunteer work, etc.

    bk2nocal’s assertion that “it is imperative that students learn to function as cohorts, both for their academic and professional careers” is one that I don’t buy into since I see the “group work” done in a class like this as so utterly unlike the kind of group work that is important in a professional career.

    If certain students are consistently giving more than they are taking from this type of group work, they may be resentful of having to always work in this way. I say they “may” because this will be highly dependend on their personality, their enjoyment of teaching, etc.

  19. Andy says:

    mathmom’s earlier comment today (4:13) mentioned that “not everyone is a “natural” at teaching.” I’d have to agree. And certainly there are people who can explain things reasonably well, but for whatever reason don’t wish to. I’d have to say that while this may mean that a group may not work the best in some situations, that also doesn’t disqualify it from being useful experience other times. I don’t really think we disagree on this point – she (appears to be) pointing out why group work is not necessarily the best way for all students to learn, or for preparing students for “real world” work, while I’m simply trying to show that they can be useful in many cases, but not all.

    She also says, “If you can make an argument that it’s pedagogically advantageous for students to learn from other students rather than directly from a trained teacher, then use group work for that.” I have absolutely no data to support this, nor any articles to cite, but rather anecdotal experience that says that some people, who have been raised in “traditional” teacher-centered classrooms, initially have a hard time learning things from their peers. I’m guessing this is at least partially because the teachers always provided the correct answers, their peers didn’t, and so they learned to trust the trained teacher and mistrust their peers (for learned content, anyway, not that they no longer trusted their peers in general). Certainly, then, an argument can be made that learning in groups (at times, but certainly not for the entire class) is indeed advantageous to students: Knowing how to learn from peers is extremely important in “the real world,” as there will basically never be a trained teacher waiting to give them the correct answer.

    I’ll agree with mathmom’s idea that (her definition of) “effective group work” is pretty unlikely to actually happen in school groups, just because of the nature of the people that must work together and the fact that they will rarely have skills that mesh perfectly.

    However, I will wonder a bit about mathmom’s idea that all school group work is unlike what will be done in the “real world.” I think bk2nocal’s idea is pretty much correct: everyone will, at one time or another, need to be able to work with people they may prefer not to work with. And in reality, it’s likely to be somewhat often. While mathmom may work in an environment where it’s always possible to form a group with cohesive participants, there are many times when group members are chosen not for their ability to communicate with each other, but for other merits. And if that’s the case, students will need to be able to handle situations when they’re up at 10 at night, trying to explain to the team in India (that just woke up) over the phone exactly what problems were found in the last day and some suggestions for how to fix them. (This is a bit of an extreme example, but it illustrates the point.) In short, if students can’t communicate effectively with others, they will have a very hard time in most jobs. Now, I would say many people don’t think that should lie within the bounds of a class theoretically entirely devoted to math, but I would argue that math is absolutely no good if you are unable to communicate and use math to actually solve problems.

    That last paragraph got a bit long and rough around the edges, but I’ll leave it there. I suppose the overall idea is that group work hopefully helps students understand material from their peers, and should at least give students experience working with others who have different (and possibly not complimentary) skills. However, it is not what the entire time should be spent on, nor is it a replacement for actual teaching. (I’d argue it needs a very good teacher to be done well.) And while it may model some interactions in “real life,” it does not effectively give a good representation of what more “effective” group work will be like after school.


  20. mathmom says:

    You’re right, Andy, learning good communication skills is important for later in life. (And you’re also right that not all groups are ideal, of course.) But is just being put in a group and being “expected” to communicate what you know an effective way of learning such skills? I feel that the skills probably need to be explicitly taught (as if you have time, on top of the math curriculum, I know…) and that just throwing students into a group and expecting them to communicate doesn’t really teach communication much better than throwing someone in a pool and expecting them to swim teaches swimming. (Some may figure it out; others will drown.)

  21. e says:

    I have used similar methods in my math for elementary teachers course. Specifically, not answering questions while they are doing group work but rather directing them to each other. I had a huge rebellion on my hands and the most common comment was that they felt I wasn’t teaching them because I wouldn’t answer their questions 🙂 I think most changed their perspective by the end of the semester. I did still have a few who thought that they needed to do less group work and more listening to my lecturing!

  22. Jackie says:

    e – More lectures huh? (making note to hear one of e’s lectures). I’m glad to hear most of them “got it”. Hopefully this means they’ll be using similar techniques in their own teaching. I’m curious – what are the math for el ed requirements in your part of the country? (I hope I’m not opening a can of worms here).

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