# Thoughts on ‘Jigsaws’ & Meaningful Group Work

**Some Background:** Wikipedia’s article on Jigsaws, which I skimmed and found the section on Benefits and Steps in Implementation to be similar to what I’ve seen in other literature that I’ve read that is a bit more legitimate than Wikipedia.

**Why I’m Making a Big Deal about Jigsaws:** Fischer & Frey are two authors I was introduced to in preservice pedagogy classes and I’ve applied a lot of their structures/advice in my classroom. I’ve read their books on Improving Literacy and Productive Group Work, both of which are good food-for-thought books and both discuss the Jigsaw strategy. It’s something I hear consistently in relation to Marzano’s research on what increases student achievement especially in the realm of cooperative learning. When I hear teachers-of-teachers (ie: teacher mentors or education professors at universities) give advice to newish teachers (like me) on trying to increase achievement/engagement in their classroom, they always recommend some form of a Jigsaw. In essence, I have in my head that a Jigsaw is the **holy grail** of cooperative learning – there’s engagement, there’s student ownership, there’s synthesis, there’s debate/discussion, there’s group dynamics/social skills at work. Maybe that’s just me and my impression, but because of that, I’ve been trying to see if I could pull it off in my class one of these days and see if it lives up to this pedestal I’ve put it on.

**Thoughts on Jigsaw as an introduction**: I’ve always had a few issues with the traditional Jigsaw that I’ve been trying to overcome. In my mind, a traditional Jigsaw is used to break a broader topic into smaller pieces (ie: overall topic: Abraham Lincoln. Smaller topics: his youth, his presidency, his time in congress, etc). In breaking this topic down, students break off into ‘expert groups’ and create a summary of their particular piece of the puzzle. Then they all come back to their home groups and discuss what each person learned. Thus, each person can come to a conclusion about the bigger piece by synthesizing all the information about the smaller pieces. Then, when the teacher summarizes and clarifies the next day/later that period, each student is already well prepared for what the teacher will say because they’ve already been introduced to many of the ideas from their own research and from listening to their peers. This is a Jigsaw used to introduce a topic.

I’ve been trying for a long time to find a way to incorporate a Jigsaw into my math classroom but I’ve never really been able to find the right spot. One of the biggest roadblocks I’ve come up against is that math is very *procedural – *it doesn’t easily break up into disjoint groups that can be studied independently and then brought back together. Instead, math breaks up into *steps* that can be studied and understood in a sequence – but, trying to understand step #3 without knowing what happens in steps 1 and 2 is useless. Math is also very *hands on* – students learn more from actually doing the problems instead of watching someone else do them. This jigsaw doesn’t really work in either of these situations – but, on further reflection, I don’t really think it’s designed to. Trying to use a jigsaw to introduce something that is mostly procedural is using the wrong tool for the job. Maybe this is why it’s taken me so long to find a good place for it – a lot of first semester was spent working on algebra and arithmetic skills which took a lot of procedural practice. This could also explain why when I did try something jigsaw-esque, it was usually underwhelming.

Even as I think of ways to use a Jigsaw to introduce a topic, there’s still a reciprocal teaching aspect that I’m not completely comfortable with. In an ideal jigsaw, every student returns to their home group and contributes something to the discussion. That something they contribute is **unique** because their expert group is the only group who talked about that particular topic. They have a special piece of the puzzle to contribute and it’s their job to ‘teach’ (at a very very basic level) the rest of their group about this missing piece. **But what if that person can’t contribute?** What if they zoned out in their expert group – didn’t understand – has poor social skills and has trouble communicating. It seems like the whole group suffers in this situation. Actually, in reflecting on some of my early experiments with groupwork first semester, this was the biggest problem I encountered – trying to divide the responsibility and having some students who couldn’t step up the the plate. Several of my students complained about the group structure I was creating and they were right – they were confused about the material because some students weren’t pulling their weight.

Now that some time has passed since some of my failed attempts at groupwork first semester, I realize one reason these students couldn’t contribute is because their math skills were so low – problems with their multiplication tables or integer operations or basic algebra. I suppose an appropriate analogy would be if you designed a Jigsaw that required reading and discussing a portion of a text, then realized that 1/3 of your population was practically illiterate. Another battle I realized I was fighting is that some students have just been trained to shut off in a math class – a type of learned helplessness and lack of confidence that makes it so they will take n0 risks in my class. It’s something I don’t hear about when I read about cooperative learning, so I wonder if this intense of a negative stigma is unique to high school math and therefore not always addressed when talking about ways to implement cooperative learning. I’ve been fighting both of these – low skills and anti-math sentiments – and it’s a battle that has taken me 6 months to overcome with some students. Looking back, I had inadvertently put some students way over their heads without realizing it. To put sole responsibility on them to learn even part of concept was unfair both to them and their group members.

I guess the thing I’m mostly reflecting on is my perception that a Jigsaw is designed to **introduce** a concept and how that perception has led to several failed group activities (well – maybe ‘failed’ is a harsh word. More accurately, the gnawing feeling that I could have achieved the same amount of learning in 1/3 of the time and 1/2 the frustration). I couldn’t figure out how to use a jigsaw to introduce something procedural. I couldn’t figure out how to solve the remedial-student problem. I can’t figure out how to perform that summary/discussion role that is *key* at the end of a jigsaw without it turning into me just reteaching the material and me wondering ‘Why didn’t I just do this in the first place?’.

**Paradigm Shift – Jigsaws at the end of a unit: **I just posted about a group activity I did which I called Expert Groups. It was one of the most successful group activities I’ve done all year, both in popular group metrics (face-to-face interactions, positive interdependence, individual and group accountability) and in actual learning/productivity. As I wrote that last post I was trying to think about what made it so successful and here’s what I came up with:

**It came at the end of a unit**: This solves my struggling-student problem (well, in an ideal world it does). By the end of a unit, most of my students are comfortable enough with the material that they should be able to do it independently and, if I’ve done my job correctly, they should have some confidence in the fact that they’re doing it correctly. This is a polar opposite to what happens with a Jigsaw as an introduction – students are still unsure of themselves from their low skills/low confidence that they don’t want to take any risks. I think my buy-in was much better because of the confidence boost they had been getting throughout the whole unit rather than that unsureness they feel at the beginning of a unit. Also, this is also a statement about the best place for a jigsaw in your whole curriculum – I think it was a mistake to try so many group-heavy activities so early in the year when students were still so unsure and in need of remedial help.

**There were 4 experts instead of 1**: This solves my ‘if one student zones out, the group suffers’ problem. I definitely went around and tried to check in with each group and I’m confident most students understood their own problem, but there were still some students who would have trouble communicating it (sometimes due to legitimate communication issues for which they have an IEP). Having 4 experts let students approach whichever expert they wanted so they weren’t out of luck of one person wasn’t comfortable explaining it.

**Each problem was an extension: **This solves my ‘procedural’ problem. Well, actually, it solves another problem I usually wrestle with regarding group-work:

**Why is this something that should be done as a group instead of something that could be done individually?**I’ve tried some group activities where, when I was done, I realized there wasn’t really any purpose to the group aspect of it – the problems were mostly procedural and could be done by most students individually. The only thing the group aspect provided was forcing some students to ‘tutor’ the other members of their groups, which my smarter students started to resent. With the Expert Group activity, each group had a real-world problem that required a setup before you could actually solve the problem. This setup was different for every problem and was sometimes a little tricky (such as figuring out the similar triangles for surveying a river). Anyway – each problem was an

**application**of the procedural content we’d been learning, and that application is what made each problem unique and worth having an expert for.

**Some Final Thoughts**: When I first started writing about this, I was super excited – ‘Yah! I pulled it off! Alright!’ The more I think about it, the more I think all I did was steal Kate Nowak’s Speed Dating structure and just made 4 experts instead of 1. I’m still struggling with thinking up a meaningful group structure to *introduce* something in my geometry classes. The hardest questions to topple are ‘What makes this something that *requires* a group?’ and ‘Is this really the most efficient way to introduce this concept?’. I almost think the two are mutually exclusive – if I make something that requires a group, it’s probably not the most efficient way to introduce a topic; and if it’s an efficient way to introduce a topic, it probably doesn’t require a group. But maybe that’s where math and group work are different from all the Jigsaw examples I read about – If I think about it, the places where group work can really shine is with encouraging habits of mine or standards for mathematical practice, which are *extensions* of things we’ve already been talking about. I guess I’d rather have them struggle together in an exercise that builds their problem-solving skills rather than an exercise that introduces new knowledge and has the potential to create false intuition.

Despite my comment above about group work not being great for introducing a topic, there is evidence in the blogotwittersphere of the opposite here and here. Although, in re-reading these, I’m not sure if the ‘group’ aspect is being utilized as much as I had thought. This isn’t a criticism of the activities – I *love* both of them and I think they’re an amazing way to introduce new concepts – it just reinforces my question about group-necessity and efficiency. They are very efficient and create a deep understanding of the content, but a group is not required to do the heavy-lifting. These last few sentences have been more for me and my own reflections than for anything else.

So, maybe this whole post is just a reaction to my perceptions to cooperative learning as a preservice teacher (which I was a year ago) and how they’ve been challenged and shifted as I’ve tried to implement them in my first year.

Would love lots and lots of thoughts.

**Update**: Read Jason’s comment because it’s amazing: https://mathymcmatherson.wordpress.com/2012/03/19/thoughts-on-jigsaws-meaningful-group-work/#comment-256

I have one quick thought, and I’m sure I’ll have more later as the comments continue… One great introductory thing groups, and jigsaw-y groups in particular, can help with is collecting a lot of data or examples or methods and comparing them.

When investigating triangle congruence shortcuts, different groups can get different partial sets of triangle measurements and try to draw triangles with those measurements. Are all group-members’ triangles the same? Why or why not? Then representatives from each group can meet up and compare: were all your triangles the same? Ours weren’t. Gee, what’s going on here?

Also, when there are concepts that have multiple accessible methods for solving, different groups might solve problems in different ways, and jigsaws can be used to bring those strategies together. For example, representing 3-D things with perspective drawing, nets, and multiple views. Groups could be given objects to represent and a method of representing them to master. Then they could jigsaw and try to determine which drawings represented the same object. Not every kid has to master every way of representing, but they should all recognize them and be able to interpret them, so it’s okay if everyone isn’t an expert in, say, perspective drawing. They can all contribute to saying, “these are both definitely cylinders but that has to be a cone.” I think this can come at the beginning of a unit since it’s not as procedural, and most kids can begin to jump into it as an artistic task (and you can be clever in who gets which method of representing objects).

Max – I’m in total agreement about the idea of a jigsaw being used to create an intuition about a concept by comparing and contrasting similarities/differences/patterns. That sort of structure is one of my default ways to introduce a topic, but I’m never sure if it totally qualifies as a jigsaw or if it’s really something that can be classified as Cooperative Learning. Maybe it is and I’m just being really nitpicky about my terminology. I think the MissCalcul8 examples are a good representation of these types of introductions, but I wonder how much I should balance the group aspect with the individual aspect.

Actually – there it is. That last sentence is what I’ve been trying to say – my biggest struggle with planning group activities is deciding how much to balance the individual aspect with the group aspect. Maybe that’s why I struggle with planning activities at the beginning of a unit – I’m worried that if there isn’t enough individual accountability, then the student won’t have the intuition they need for the rest of the unit. And if they don’t have that intuition, I’m going to have to reteach it to them anyway, which makes me wonder why I just didn’t do that in the first place.

Bell just rang – end of lunch – I’ll think about this some more and come back.

I’ve had success with jigsaw as a end-of-unit review but not otherwise.

The claim is oft made that all teaching methods are applicable for all subjects — usually by folks running super-broad training lessons for kindergarten and 12th grade teachers simultaneously — but that isn’t always the case.

I’ve used expert groups at the end of a unit as test prep (ugh) and have been looking for better ways to use this activity. I like your idea of making each problem an extension. I was thinking about another possible answer to your question “What makes this something that requires a group?” What if, instead of focusing on four different topics/procedures as I have done in the past, students were given problems each of which allowed for a variety of different strategies/representations? I’m thinking of something like Jo Boaler’s pattern piles. Or, maybe each problem could steer students towards a certain strategy. For example, if I were introducing unit rates in Math 8 (best deal? type problem), I could have one problem that could be easily solved using proportions and scale factors, another using unit rates, another using common multiples, and another using ratio tables.

Jason’s comment pretty much sums up much of my experience as a student teacher. Cooperative learning activities were shared in a humanities context. Then, someone waves their hands and says “and this, of course, can be done in secondary math”. I guess that’s why I’ve stuck with expert groups – each student is expected to learn the concept/procedure in much the same way. I don’t think the activities where students are given different roles (researcher, writer, illustrator, etc.) work in math… but I’m willing to be proved wrong.

Chris – I agree with your thinking about better ways to use the jigsaw structure to create a more meaningful group experience – I think it’s similar to the suggestion Max made above about using the jigsaw to encourage students to solve problems in different ways and then bring all of those methods back together. That’s essentially your suggestion with the rates problems and using different strategies to solve them.

My thoughts on jigsaws and group work have started to turn towards if it’s possible to use a disjoint group structure (ie: all students work on something slightly different) to efficiently _introduce_ a concept in a math class and what that would look like. Everyone who’s commented so far has confirmed my suspicion – that it’s easier to use the group structure to review something rather than introduce it. The suggestions above also reinforce this idea that a group structure can be a powerful way to reinforce these difficult-to-teach problem-solving strategies and habits of mind. There is something powerful about having students discuss the different methods they used to solve a problem and a jigsaw could be good for that.

I guess I’m realizing that a Jigsaw is a good tool to extend knowledge and encourage habits of mind/problem solving, but I’ve never seen it discussed in this way. And it’s made me second-guess a lot of the ways I was trying to use groups when I first started teaching. Or maybe I’m just not good enough at it yet. I still use the social aspect of my classroom to help introduce a concept and encourage thought, but I can’t always answer the question ‘Why do I need three other people to do this?’

/shrug. I’ll keep thinking.

You’re right. My suggestion was the same as Max’s. Maybe this conversation is suggesting a different question – a different jigsaw justification. Instead of asking ‘Why do I need three other people to do this?’ we should be asking ‘How does working with three other people add to my understanding?’ Thanks again for sharing this. Your post and Max’s comments have me now thinking of new ways to use groups. For some reason, I was stuck on the four expert groups having to learn/teach four different procedures.

Like you guys are saying, I think it comes down to purpose.

The Complex Instruction crowd would say that you need to be in groups because the richness of the task is such that it would be impossible (or at least less fully realized) to complete on your own and that the use of mathematical discourse is crucial to understanding.

The Kagans of the world use it to force interactions and ensure equal participation and accountability.

Kapur’s productive failure model uses groups in the opening invention (failure) stage. My understanding of his argument is that the initial invention stage prepares students for the direct instruction that follows. That is, he doesn’t expect students to learn a specific skill, but that by productively failing at the problem, you are better prepared to mentally frame the DI.

IIRC the original Jigsaw classroom was originally created to ease racial tensions in newly integrated schools by forcing interactions and giving students superordinate goals.

I will consistently argue that if you want a student to learn a specific skill in a specific way, you have to direct teach it at some point. My personal feelings are that it should come after students have had a chance to play and argue but you can find plenty of folks who will tell you to teach it first.

So….if you were to ask me, I’d say what’s your purpose for the group work? After you’ve decided that, then figure out what structures to use.