Chapter 6
FURTHER CO-OPERATIVE STRUCTURES
Introduction
In this chapter we would like to introduce a few simple or complex co-operative structures, mainly from the viewpoint of the teacher.
Our goal with A handbook for learning together is to introduce readers to the basics of co-operative learning, therefore we emphasise the generative nature of the presented structures here. We will see that the currently used co-operative structures can be deduced from a few basic ones. Readers of the previous two editions have indicated that they would like to read about more methodological examples and co-operative structures in the next edition of our handbook. Therefore we have extended the chapters introducing basic structures and analysing them from the aspect of co-operative principles with some further structures (roundtable, task assignment, round Robin with notes).
In this chapter our main point is not to examine fundamental co-operative principles, since it is certainly clear from the previous chapters that any structure can be regarded as co-operative if the co-operative principles are manifest in them, possibly at the same time. It might be the readers task to examine the structures presented below from the point of co-operative principles, as in the previous chapter. That is, it should be examined whether we rightfully claim that the fundamental co-operative principles are present in the structures presented below.
However, here we attempt to make our readers be able to visualise the whole process during reading, and to understand the methodological aspects of the structures. We did not only have descriptions in mind, but to present different but equally important approaches. Therefore at some points we dwell on the tiniest details, illustrating our subject by examples, while at other points we present complex series of steps. In the appendix attached to the last structure (pair of pairs) we present the short description of 20 co-operative structures, maintaining our point introduced and perhaps proven claim that co-operative structures can be deduced from a few basic structures, upon which an infinite variety of structures can be built following the fundamental co-operative principles. Thus, in introducing co-operative learning it is not our explicit goal to introduce and teach as many actual structures as possible, but to demonstrate the relationship between basic structures and fundamental principles. However, we have collected the short definitions of the structures discussed in the book at the and of our handbook, attaching a sequence of steps to process the collection.
6.1. Paper and scissors
- Sometimes the most simple and trivial exercises can enhance co-operation in the most successful way! Pay attention to the fact that you wish to promote co-operation between different people and personalities begin with simple steps and unchallenging tasks.
Opening up personal spaces
This is one of the most simple co-operative structures that can symbolise constructive and encouraging interdependence.
Give each micro-group regardless of their numbers only one sheet of coloured paper (a different colour for each group) and one pair of scissors. Their task is to cut the sheet into as many pieces as many people there are in the group, but the one who has the scissors cannot touch the sheet. The other members, however, have to move (fold, hold to the scissors, etc.) the paper together, and they cannot let it go. Groups make as many pieces of paper (e.g. for a task of note Round Robin) as the number of their members, and thanks to different colours it also can be seen which group the pieces have been made by.
There is a frequently arising prejudice against co-operative learning, namely whether it is not more than merely playing around. Maybe it has been unravelled from the previous chapters that co-operative learning actually means structuring of learning and not organising games.
However, paper and scissors is a playful structure indeed. The question could arise what kind of developmental effects it may have besides the micro-group cheering at the fact how difficult it is for three people o hold and fold a sheet of paper at the same time.
One function of paper and scissors is exactly to help to get group members together, to draw them closer. The thing the Johnsons describe as face to face, knee to knee interaction as realised in a particularly spectacular way in paper and scissors. Group members fiddle in each others personal space during the task, that is, they get a little closer to each other in comparison to their normal personal spheres. It is an important step, especially in case of groups formed afresh, thus this co-operative structure serves as a very good tool for group-development in addition to the fact that the teacher does not have to make the pieces of paper herself, it is done by the micro-groups.
It is an important aspect especially in case of newly formed micro-groups that we can monitor and improve smooth co-operation within the micro-group before challenging them with more serious tasks. It is expedient to use structures that have no stakes here, i.e. nobody will feel that they have to perform within the micro-group beyond their power. Paper and scissors just a kind of playful task with no stakes, which draws the group together, helps to create the space and informality of personal interactions, without setting a real challenge to anyone. Its goal is that by the time they work on serious learning projects, putting their heads together will be natural, to get them used to the fact the task within the group must be at palpable proximity for everyone.
When we used paper and scissors in a group several times, we felt that the task had become quite mechanic, therefore we came to the conclusion that we would add a question to think about.
The groups after they already have performed the task of paper and scissors successfully get the following task:
The task has to be completed with the least cuttings possible! Groups usually get to twice-cut solutions. The next step is cutting less than twice.
The first solution is usually no cutting at all: they tear the sheet in three or four pieces, thus they do not need to cut it at all. Then comes the solution of outlines and remnants. Then we start to regard only cutting along a straight line as a valid cut. That is, the task now sounds as: divide the sheet of paper in four equal parts in a way that the one who has the scissors cant touch the paper which has to be moved (folded and held to the scissors) by all other group members.
We have managed to collect 7 or 8 solutions so far in different groups under these conditions, without revealing a single solution to them! When we invented this task we found only one technique which grants solution for groups of 3-6 alike, all the others have been invented by the participating groups.
6.2. Tree of expectations
- Focus on learning instead of teaching! Get acquainted with participants, their personal and social competencies, prior knowledge, existing constructs of knowledge.
- The bulk of students having been socialised in traditional school systems would not admit it to their teachers that they do not know about or are not interested in anything of the teachers topics.
Mapping and following expectations
The following co-operative structure provides an excellent tool for obtaining a deeper understanding of students and for grounding individual development plans. It has low risks in itself, because everyone can reveal as much of their knowledge as they wish, and can ask as much as they want. Their revealed knowledge or their questions will not be graded, that is, there is no risk in admitting their knowing or not knowing honestly. Tree of expectations, as a co-.operative learning structure promotes equal participation by the fact that it does not set great challenges as a condition of participation, but it creates the opportunity of any depth of knowledge and any question for everyone. It is a co-operative learning structure fundamentally determining the activity of learning as a whole, since it is a means of assisting the launching and more accurate planning of the development and learning process.
We connect the structure of the tree of expectations with the structures of window, note Round Robin and KWL chart, since the KWL chart as a starting-point for creating individual development plans can be utilised as well in co-operative learning. It is a tool of individualisation. In the previous chapters we have referred to the fact that co-operative learning starts from individual needs and demands concerning every participant of learning (e.g. all students teacher).
KWL chart consists of four columns; the first one is date-wide, the other three are of the same width and their cells are high and wide enough to write sentences into them.
The first column always has the date of filling the chart; in the second one, with the headline What do you already KNOW? goes what the person knows about the topic in question at the moment (ranging from nothing to technical terms and accurate notions). The next column, entitled What do you WANT to know? has the issues the person would like to learn in connection with the topic or field (they also can range from nothing or naive proposals to concrete and professional questions). Later, at a certain point of co-operative learning, when they already have made some progress in the topic and have some conceptual anchors, students indicate in the column headlined What will you LEARN? what they will have learn in connection with the topic. At a later stage filling in the date again participants write what they already know or have learned, what they would like to learn and wish to learn later concerning the given topic... filling in the whole KWL chart during the development process.
It is important to note that an entry should not exceed 3-5 items (remarks, sentences, notions) to keep the information manageable.
We also can state this as a general rule in co-operative learning; when students take notes for a Round Robin or a window (they collect dates or notions, etc.), let us make it possible to write down only 3-5 items, highlighting the fact that they can write less but not more than that.
It is important to handle information in a structured way in micro-group work as well, especially from the point of equal participation and access. If there is no co-operative structure then there will be no guarantee for some persons not domineering over the group with their questions, or some others, who would not comment on the topic, being able to ask their questions and tell their answers. If one person writes 25 items while another only three, access is not proportionate, since the one writing 25 ones demands much more time of the groups attention than the one with 3 items. It does not mean that those who write 25 should know less, but that they should try to arrange their items in a structure of 4-6 categories.
That is to say, with a simple sequential structure write 3-5 items about the given topic! we enable the realisation of sequencing. Every person elaborates on a single item at the same time, before another group members turn. Structured gathering of information allows for information-sharing to be completed. This way group-work will not get drowned into an infinite series of essayistic monologues. The 3-5 division also corresponds to the nature of our short-term memory that is able to handle structures of 5-7 items efficiently.
The entries on knowledge are always general initially, reflecting naive attitudes or revealing lack of knowledge in any student group, regardless of the fact whether the participants are children or adults, non-professionals or experts. If learning together is successful, entries become more and more accurate, professional, topic-orinted, and the KWL charts are increasingly able to outline individual learning goals, frames of interpretations, knowledge, questions and deficiencies.
The KWL chart is filled in anyway, it is a very rare occasion when someone does not write anything at all, or writes that he or she is not interested in anything at all. And the goal of using co-operative structures is to make participants able to put their doubts, non-understanding, not-knowing, lack of interest in words as honestly as possible concerning the respective topic. Individual development in co-operative learning will be successful when the educator is able to see actual levels of interest and knowledge. Of course, a teacher can see the interests of as students clearly even behind the answers that were just scribbled in the chart, but participants fill in the KWL chart for their own sake; the goal is that the participants should understand where their attitude to the topic arises from, so that they can feel more accepted within the learning process.
Hungarian pedagogical culture often lacks acceptance of not knowing or lack of interest. However, is it not the task of teachers working in public education not to refuse those who do not want to learn, but to enable them to learn autonomously? If I cannot see and understand that the participants are not addressed, not moved by the topic, they are not interested and cannot make connections to their lives, it will be hard to motivate them to learn, and teachers can easily turn to games of power. The goal, for both of us, is to be aware of real attitudes and interests, so that we can structure our further activities on their basis. In my group I have mentioned several times, overtly admitting lack of interest was the fact that led to the solution; while if I had stuck to the well-planned syllabus, this sincere relationship would have been corrupted very soon. Our syllabus arising from lack of interest, however, became very successful as i already have referred to that since three months later the children, who never had read before and had flouted literature, were editing their own literary journal.
KWL chart in itself, of course, is not a co-operative tool, it can be used in any forms of traditional class-work as well, the question is what happens to the information revealed in the chart subsequently. However, joining it with the tree of expectations, we can use KWL charts for co-operative learning purposes as well.
Below we present a version of the tree of expectations, step by step:
- Everybody receives a size A/3 sheet of paper on which they make their own KWL chart in one particular colour.
- Everyone writes 3-5 items in the first two columns individually.
- They collect the items in a window by means of Round Robin. The items in the columns I KNOW are written by the Recorder with his own colour marker in a window, while the Taskmaster writes the items under I WANT to know in another window, in another colour. In both cases, Round Robin is controlled by the Encourager, while the Timekeeper makes sure that they finish within the time limit.
- After collecting them, the group chooses the four most important items they know, and the four most important things they want to know. (They always choose as many items as the number of group members.) These are underlined by the Timekeeper in a third colour (four important things from I KNOW) and by the Encourager in a fourth colour (four important things from I WANT to know). Then they write the name of the group in the centre of the window (Recorder) and the letters KWL (Taskmaster). The teacher puts up a tree of expectations drawn on a big sheet of paper on the board.
- Each group is given a sheet of paper in different colours. Micro-group members pair up (at their will, or e.g. in pairs of Recorder-Encourager and Taskmaster-Timekeeper).
- They cut the sheet in half by means of Paper and scissors.
- Pairs grab a piece of colour paper and a pair of scissors.
- One pair looks at the underlined KNOW items, while the other at the WANT to know items, either as they divide them between themselves, or as the teacher assigns them.
- One of the pairs (e.g. Recorder-Encourager) cuts out 4 flowers of the coloured sheet by way of Paper and scissors, big ones, so that they even can write sentences on them.
- The other pair (Taskmaster-Timekeeper) cuts out 4 pieces of fruit in the same way.
- They write the four items from I KNOW on the pieces of fruit individually in a pair, and the other pair writes the four underlined items from I WANT TO KNOW on the flowers.
- When they are ready, everyone gets a flower and a fruit with an item on it.
- They present the flowers and fruits by means of Note Round Robin, then they use Blu-tack to put them on the expectation tree of the class. If there is a group that wishes to put further flowers of fruits on the tree, of course, we must allow that, although it is important to emphasise that the tree only should include the items regarded as most important, since all of these have been recorded in the windows mad by the micro-groups.
- After each learning session the class returns to the tree of expectations: the representatives of each micro-group (e.g. the Taskmaster) take off their previously stuck flowers.
- They deal them out in the micro-groups, and by means of Round Robin they discuss if they already have got an answer for the question on the flower. If yes, they put the answer in words and write it on the back of the flower, and then cut the flower to the shape of fruit perhaps with Paper and scissors and discard the cut-off parts (the question and the answer must be on the fruit!). If they see that they have not found an answer to their earlier question, they do not write anything on the flower.
- By way of Note Round Robin, we collect the flowers having ripened into fruit in a basket drawn under the tree, then we put the flowers back on the branches.
- To take our tree of expectations further, we can get children to write new items in their KWL charts, thus creating more flowers and fruit for the tree.
When, concluding a learning session, we get back to the tree of expectations, our aim is not to make every flower unreasonably yield fruit, but to get an accurate picture of the progress of the group, their still existing questions and attained knowledge. The remaining flowers more and more accurately indicate the questions left from processing, and the issues to be focussed on during structuring learning.
The fruits of knowledge and question-flowers on the tree of expectations outline the information connected to the topic which the participants think to know, and the lines of interest that may help in planning further learning processes, to the whole class. When the flowers, or at least some of them have yielded fruit, micro-groups can write new flowers which hopefully will be more accurate and/or professional.
There are cases when the tree of expectations stops at the level of elaboration outlined in the above example. However, we can take it even further: we give the fruits back to the groups that have made them, with the task to make detailed notes on the topics they think they know and they find important, then to present these to the other groups by means of e.g. written group Round Robin or expert jigsaw. Meanwhile the teacher takes on raising the answering of emerging questions to the focus of structuring learning, using them as a kind of guideline.
The windows made during the above steps contain all knowledge and question items, therefore it is expedient to make these windows made by the micro-groups public and accessible, for example, to tape them on the group-desks. Or to solve the detailed elaboration of the knowledge-fruits which are not on the tree but are included in the window within the micro-group, individually.
It is useful to choose the detailing of knowledge items when the teacher concludes from the fruits containing a sentence or a term that there is something to work on indeed, because the revealed knowledge is not thorough enough.
It is also worth to dedicate some time to elaborate on general or inadequate answers, since it gives a more accurate picture to the teacher in terms of what kind of misunderstandings, attitudes and deficiencies he has to face in the process of mutual learning.
In case of the questions which are not on the tree but are there in the window, we can assign volunteering individuals to try to find answers continuously. The aspects emerging in them can be continuously articulated both during micro-group work in the publicity of the whole class.
During the production of the expectation tree, at the section when they perform collection on pieces of paper, i.e. when they put the flowers and fruits on the tree, the teacher basically only has to ask interpretive questions. The purpose of the tree of expectations is not checking and assessment, but recording the actual status of their knowledge and to collect the items and questions thought to be important by the micro-groups for the publicity of the large group.
6.3. Guided collage jigsaw
- Playful forms of guided group-formation provide us with an excellent opportunity for mapping the group! Do not only guide the games, but observe happenings and behaviours. Get acquainted with the participants!
Observing the groups at group-formation
This structure has been described in the section about group-formation, however, let us examine now how we can observe important elements of behaviour with the help of a simple and playful task. We plan the micro-groups in advance for this structure, we design their make-up based on sociometry and heterogeneity on the account of existing and developable skills.
As preparation, take as many blank sheets of colour paper (or pictures connected to our topic, or short, printed texts) as the number of micro-groups you intend to form. Write the names of the children belonging to the same micro-group in the four corners of the sheet, then cut up the sheet in a way that each name goes into a different piece.
Participants draw randomly and simultaneously from the pieces (collage pieces) with the names turned down. When everybody has drawn one, they check whose name is on the paper, and they give it to that person. If they find their own name, they keep it. When they have given it to the person with the name, they are waiting for someone to come up to them with their piece. When everybody has their own names, you can assign the next task: everyone finds the people whose pieces complete theirs perfectly along the sides, putting the colour pieces (pictures, texts) together like a collage.
The groups that have found each other choose a group-desk and sit down.
When each group has sat down, they glue their pieces to the big size A/3 sheet in a way that the pieces together form some/any kind of shape. Everyone can move and glue only their own pieces!
Later you can tell the groups that have completed their other tasks before the others to complete their composition with different colour markers, but everyone can use only one randomly chosen colour.
In terms of methodology, guided collage jigsaw is one of the most simple ways of guided group-formation. In 3-4 minutes we have exactly those sitting at the same desk we want to, and we do not have to interfere in group-formation for a second. Moreover, it is done in a playful and active form.
When either children or adults receive their collage piece, the large group usually can be characterised by two kinds of behaviour: there are people who instantly start and go to find the owner of the piece, while others do not move, they just watch what the others do, then finally lumber over to the group they belong to. When we analysed this sequence of steps with teachers, and drew their attention to these two types of behaviour, they usually judged that the first type of behaviour (which is described as proactive) is the right one, while the other (reactive) rather refers to laziness, incapability, inhibitions. That is, initiative and activity are represented as positive values for them, while strategies based on reaction and observation is hidden by overemphasising proactive behaviour. However, if we think about it, when we need to cross a busy road, reactive strategy may be the better one...
Maybe it would not been so lucky if everyone ran around proactively to find one another, since if there are some people staying where they are, pairs or groups will find each other more easily! The point here is to observe behaviour patterns.
At a demonstration class where we learned together with a group unknown for me, when they had to glue the collage pieces together, a girl, following proactive strategy, glued her own piece own instantly, not leaving enough room for another girls piece; it stuck out of the paper. The members were discussing what they should do now. The others group have finished, and the visiting teachers were smirking: now, this group has not even sat down and they got stuck, unable to solve a simple problem. Perceiving the increasing tension, I stepped up to the group and suggested them to solve the problem later; by that time the glued piece will be dry at least. I worked for one and a half hours with the groups, and like all of them, this particular group took part in each task and always managed to finish in time. At the end of the lesson they lifted up their collage made of the pieces and completed with markers. They stepped out of the size A/3 rectangle, and glued the stuck out piece in cubist style extending over the frame and while they all took an active part in the lesson, all four of them were colouring the sheet until they got a constructivist piece of art that combined the two geometrical shapes with really artful devices. All the other groups glued their pieces in the middle of the sheet. When I showed them the constructivist work, the teachers opinion was that alas,, they could not complete their task properly, because a piece was sticking out... Is that really the point we should think of in this example?
The above example clearly shows that a constructive reactive solution reacting to a problem that slips into group-work easily, became invisible for educators preferring their own concepts and behavioural patterns.
While for me it was rather disappointing that all the other groups glued their parts in the middle, behaving as model students, with zero creativity, the teachers assessed any deviance from it as a mistake, regardless of the fact that the task was worded as any composition, and also of how much creative the solution of our group was in order to correct their mistake. Actually, seeing the work of the faulty group in progress, the other groups started decorating, too; one of them even copied our groups graphic and colouring ideas. What was seen as faulty and mistaken by the teachers, became a model to follow for the groups.
It is clear that the point of our example is not the mistake but the fact that the faulty group stayed on their task in a very serious, persistent and hard-working manner (since they were working on their picture parallel to their other task, and could even complete it, while the other groups could not, although that was not even in the task).
Earlier the teachers general complaint was that those children were unable to focus on their task, they were not even interested in their own performance. However, observing co-operative structures, for me it was apparent that they were success-oriented: they do not go on until they complete a task. I found it to be task-oriented behaviour that while all the other groups have sat down, they still were standing at a corner of their desk standing closely , discussing the solution, gesturing and fiddling over the A/3 sheet.
In this group we could give the role of the Encourager to the girl throwing herself into the task fervently, and we could teach her Rally Robin to grant equal participation. She could start a Round Robin before each task (building on her proactivity), and when all the others have told their words, she can add her own thoughts (developing reactivity). The Encourager also has to make sure that Round Robin always need to be started by someone else. Thus there always be occasions when she can start it (gratifying, experiencing her proactivity) by presenting her own opinion.
Perhaps it is apparent from the above example that by observing individual and interpersonal behaviour, and with the help of scientifically proved behaviour models (e.g. proactive/reactive) our own development plans and ideas can be suited to steps of the chosen co-operative structures. In addition, due to the publicity of co-operative structures we can receive immediate feedback on whether what we have planned works indeed, and we will have a collective model the role of the Encourager returning to which from time to time, we can adjust the development of adequate application of proactive and reactive strategies.
6.4. Pair of pairs
- Co-operative structures enable the processing of a large amount of subject materials in class with the participation of each student.
Ingraining a large amount of wide-ranging subject materials
This structure is a variation on jigsaw within the micro-group; not unlike Kagans pairs-check. It works primarily in groups of four; the version for three-strong groups can be read below.
We form pairs within the micro-group (e.g. on account of roles, like Encourager-Taskmaster and Timekeeper-Recorder). Pairs are given either one task each, or individual tasks. (Thus one or two topics can be present per pair, and 2-4 topics within the micro-group, which means that in case of n micro-groups 2 or 4xn topics can be there.)
If they have a joint task, they start working on it together, assuming some role (e.g. the Encourager puts things into words, and the Taskmaster takes notes, then they swap); in case of individual tasks, they work on their own and then check and learn both topics in pairs. In any case, the concluding step is to present their topic (or topics, if they had different ones) to each other in order to check if they will be able to explain it to their peers as well.
The next step is changing pairs (e.g. Encourager-Timekeeper, Recorder-Taskmaster), thus creating mixed pairs in which at least one of them will have knowledge about each topic in the micro-group. The pairs tech each other on their topics, providing each other with the previously made notes or presentation tools by means of note Round Robin in pairs.
When all two or four topics have gone round, they change pairs again; now those work together who have not so far (Encourager-Recorder, Timekeeper-Taskmaster). The task is simple: each person questions the other one now without notes on their own topic, and if necessary, they clarify and reword some points.
The two or four topics have gone round the in the micro-group between the pairs, thus it can be assumed that all group members know each topic.
It is apparent that in this structure equal participation and access, constructive and encouraging interdependence, and even parallel interaction are evidently manifest. Pair-work is checked in another pairing, by learning, and this learning activity is checked once again in the third pairing. They receive continuous help: in the first pairing they have a pair to work with (if they cannot succeed in pairs, they can turn to another pair of another micro-group for help, given that there is another pair with the same topic). Then, when teaching their next pair, the previous one is still there although working with someone else, but still accessible, still can be addressed and asked, since they are sitting at the same desk. The same is true for the third arrangement. So the opportunity for learning together is given at each step.
The only question is how the topics processed by the micro-groups would reach the other micro-groups. If we observe the situation after pair of pairs, we can see that we have thematic micro-groups in which each member knows about every topic within the group, however, the micro-groups have got acquainted with different topics within the large group, in other words, they have become experts in different topics. That is, they can be regarded as expert groups for a jigsaw activity, so there is nothing left but to restructure the class and create mixed expert groups in which each micro-group is represented by an expert!
When we restructure the large group into a jigsaw after pair of pairs, we must make sure that the new, mixed expert groups should not include more than 4-5 people.
For example, Encouragers of each group, Recorders of each group, etc. make up an expert group, and if there are 6 or 7 of them, it is more expedient to divide them into trios or quartets working parallel with each other, and I would ask for cross-checking by sending envoys. The notes taken by the pairs and micro-groups, which they used for preparation during pair of pairs, can be forwarded by the written form of group Round Robin.
It is important to highlight that in each of these new small groups there is only one representative of a micro-group, who has to know all the notes taken in the original group; even if it was made by another pair, he or she has had the opportunity to get acquainted with it during pair of pairs.
In case of written group Round Robin, we must draw attention to the fact that they need to check the conveying of new information in Round Robin. That is, when someone teaches their topic in the mixed expert group, with the help of the notes on the desk and their own notes, then they also will need to ask the others in Round Robin, with the purpose of making sure together whether everyone has understood the topic (or can solve the mathematical problem, or can summarise the historical event, relation, etc.).
If each Round robin has been completed concerning the notes, only then they can pass their notes and receive another ones. Written group Round Robin is finished when all written notes have gone around.
In case of written group Round Robin it is quite frequent that groups process and learn the materials at different paces (a group might do it more deliberately and thoroughly, while another rather focuses on the notes both strategies are supportable, regardless of the fact that one demands more time). Therefore it is expedient to pass notes on to the desks in batches of two or four, thus some notes are omitted, which can be solved by temporal differentiation. We put in front and behind the faster group a chair, and we put an extra package on the receiving chair from which they take the notes from the other group. Thus the faster group can take and pass notes at their own pace. It is important, however, that different groups should not be delayed by more than one step, otherwise it means that the time dedicated to the structure is not in correspondence with the competencies of the groups.
Kagans inside-outside circle can contribute to jigsaw work and further ingraining especially if we have initiated a topic by means of pair of pairs, the ingraining of which is there among our learning goals.
We link inside-outside circle and pair of pairs through jigsaw. Students in micro-groups learned 2-4 topics during the pair of pairs activity, then taught these to the others in jigsaw, and they learned the topics of the other micro-groups as well, so everyone knows each pairs topic or topics.
For the inside-outside circle we ask the original pairs to get hold of their shared note together from two sides, and then line up behind each other this way. Then we bend this double line pairs still holding their notes and form two concentric circles in a way that one person from the pairs is outside, while the other one is inside. We turn the pairs to face each other and adjust the circles, with the pairs still holding their notes! Then the paper is taken by the inside one, and the outside circle takes one step aside, while the insiders does not move, but questions their peers stepping up to them on their own topics. If their peers is successful, the insiders congratulate; if not, they give help and then check if their peers have come any closer to the topic now with their help.
We provide only a short time for this presentation and feedback; subsequently the outer circle takes another step aside, then gives another presentation with the help of the inner circle. They keep progressing this way until everybody faces their original pairs again.
Now the pairs swap; insiders become outsiders and vice versa. Now the new outsiders go around and present the topics with the help of the new insiders, and they go around until they face their original pairs again.
By the time they have completed the circle, every topic has been covered, and it also provides an excellent opportunity for developing communication and empathy.
The question might arise that if the teacher leads the large group through this triple structure (pair of pairs, jigsaw, inside-outside circle), how he or she can see into the processed topics, how he or she can interfere the processes if someone happens to take a topic afar. The key of the whole process is the structure of pair of pairs; here is the point at which such sources must be provided for participants which are able to grant successful achievements to a higher degree. The teacher can observe pair of pairs without disturbing the participants, it is enough to step beside the pairs and watch their work quietly. If she finds that they are struggling, she asks about it, and if she was right she can suggest that the group ask another pair with the same topic, or if there is no such other pair, she can draw their attention to the textbook, earlier notes, etc.
In the second step of pair of pairs she can hear the topics being taught, so she can observe not merely joint note-taking, but transferring knowledge, the results of learning and comprehension; and she can provide resources again if she finds that the topic could be elaborated further on.
During the third step when they check learning in the third variation of pairs it is almost enough to listen to the rhythm of the dialogues, because it becomes salient instantly when checking gets stuck somewhere, and this is another chance for providing resources.
Going on to jigsaw, at the stage of Round Robins when members of the mixed expert groups pass on what they have learned from their peers the teacher also has the chance to monitor how the knowledge the micro-groups have elaborated on and understood is conveyed to the other groups.
During inside-outside circle, it is also worth to listen to the rhythm of the dialogues, and there is a great opportunity to observe individual students as well. If the teacher follows the activity of a few participants in the inside-outside circle, she can see, if nothing else, by their meta-communication, how many per cents of the covered topics they have an explicit knowledge assessed as acceptable by their peers, and in how many cases the insider had to speak about the topic.
How thoroughly the students engage in learning and how correctly they teach their peers, it is the responsibility of participants. When the teacher interrupts the above steps the aim is not to give speeches and presentations, but to make participants increasingly able to process and convey information together.
For the sake of learning, group assessment also can be made about pair of pairs. Let us see an example!
Make a large placard with as many columns as the number of topics covered by the pairs within the whole large group. It contains three rows: write the topics in the top one divided by columns and make the cells of the second and third rows as wide and high that you can stick named notes in it; seven or eight ones in a cell. Have the groups make as many nametags so that each member has 6-8 of them.
Now ask every participant to list 3-5 topics which they can present very well, and 3-5 others that they should still work on in their notebooks or on a separate sheet of paper.
When this is done, ask them to recall when they were standing in the inner circle during inside-outside circle, and questioned the others about their topics. Now they have to write the names of 3-5 people on their tags (only one on each tag) who could present the topic well, and 3-5 ones to whom they had to help, who they think need some more learning in that topic (of course, they can write less names, but not more).
When the nametags are ready, they all bring them out and stick them to the respective cells under their own topics.
Now they take their notebooks or sheet and check how many places their names have been written under well-known and still deficient topics, and they indicate these on their sheet of paper. Everyone can find experts of their weak topics in the chart, so we also can ask them to add a name to the topics to be strengthened, so that they can ask for their advice.
It also can be interesting to see how many weak areas have been found in case of a certain individual; whether it is more or less than his or her own list, etc.
This evaluation reveals, among other things, if there are topics where there are more names to work on; or, if we have done our job well, there are no such names under most topics.
It also can be seen how exhausting inside-outside was for example, if participants write much more deficiencies individually than their peers questioning them in the circle, it is a different situation from the one in which the list of individually recognised deficiencies is much shorter than in the feedback given by the peers. The assessment also can reveal where the learning process got stuck: as early as at pair of pairs, or later in jigsaw, since we know exactly who taught whom what and when.
Of course, we can check the effectiveness of the process in more simple ways, like testing. The purpose and role of the above self-assessment primarily is that participants can publicise their experiences arising from teaching each other, and utilise them for the sake of their own development.
6. 5. Parallel expert jigsaw
- Do not think that a large class can obstruct co-operative learning. The best way we can grant active participation in learning in case of these class is using co-operative structures.
Jigsaw in large classes
In the last few decades in education governance one hand did not know hat the other was doing. While financing bodies have been encouraged or compelled to create large classes by way of financing, teachers have been expected to provide increasingly inclusive, personalised and individualising service, based on individual development plans. Conclusively, we often teach in large groups, since it is a typical symptom of Hungarian public education from nursery school to university. Expert jigsaw is easy to realise in classes or groups of 16-20. 4 or topics, one per group; then 4-5 expert groups in the class, and at the end everybody gores back to their original groups to learn and to teach. However, in a class of 25-32 further questions arise. Let us imagine a large group of 27. That means we will have 6 groups of four and one group of three. That is, seven groups in total!
There are mostly four people in a group, which means four topics. But if we put them together, there will be seven students in an expert group (plus we will have a group of six). These are not micro-groups any longer, and the chance of equal participation decreases due to the size of the group. And if we still can provide this opportunity by means of fundamental co-operative principles, then the time will double up in comparison with a group of for! That is, it would be better to put the experts together in the form of micro-groups (rather to have 3-4 people than 5-6)!
In such cases we divide the large group into two, more or less equal parts (in our example, four plus three groups belong together). It is useful to take care of heterogeneity here as well, that is, the available human resource must be distributed evenly, for the sake of equal access. It is expedient to divide the two parts physically as well, i.e. to create row A and row B in the classroom. It is important to make everyone aware of the fact which row they belong to, since although they sit down in micro-groups, they will have to go around individually during expert jigsaw, but within their own rows.
The four topics can be run parallel, in two times two groups. There are four people in a group; that is how we can structure the topics and the expert groups e.g. on account of the roles (the Encouragers of rows A and B work on the same topic, the Recorders of rows A and B also work on another one, different from that of the Encouragers.. etc.) Here the question is how the information between the two rows will be available for everyone in the large group (both row A and B). it is expedient to ensure discussion at the level of expert groups. That means that when the experts reach 50% progress, they can send envoys to each other! The goal is that concerning a topic, every important piece of information needs to be present in the project products of both expert groups (it can be, for example, a jointly made note in each expert groups). The experts sit back to their original groups (the Encouragers of row A into their original micro-groups in row A, etc.) in possession of their notes. Now they teach their topics to their peers in the micro-group, one by one (e.g. by way of Round Robin), on the basis of their notes made with their expert partners. There is only one note at any one desk at the same time, so it is always the expert of the given topic who teaches the others. These notes can be passed on to other micro-groups within a row in the form of a written groups Round Robin, thus there always will be an expert of the actual topic in any micro-group.
In our example, there is an expert missing in the only three-strong group, here the teacher can join them (which means a single, not too long direct task in the given topic), but it is better if the experts put together such notes that can be used on their own.
It is useful to allow sending envoys at this point as well, if an expert is in trouble, or an expert note is difficult to read or comprehend. These times it is better allow co-operation between the rows, because someone goes to their expert peer in another micro-group, he will interfere them in learning another topic. In contrast, in the other row it is enough to check with the help of the placards spread on the desks which group is discussing his topic, and there the whole micro-group will be interested in his question, since they are learning the same topic. The question from the other row serves as direct feedback on their own activity: are they able to answer the question?
When all topics have gone around (within the two rows, with the help of the their respective four notes), we can link the two rows together again, e.g. by assigning checking tasks. That is, the expert groups sit together again in the rows, and put together exercises for the others. In the next step the two rows work together in the original micro-groups, but each has a worksheet made by the expert group of the other row. The two groups can be joined even by a lying game, in which the original micro-groups make up true-or-false statements, and the whole class (i.e. the six other micro-groups) take part in the game, taking turns in guessing the false ones among a micro-groups statements.
The experience of sending envoys shows that groups working separately accept ideas and opinions from other groups depending on their openness, even when the topic is the same. Therefore it is advisable to make groups working on the same topic work with different methods learning and recording. This way sending envoys will include a task reinforcing interdependence: translation. For example, one group writes down the most important key sentences of a topic in the form of roundtable, while the other one has to make a visual summary of the same topic, which cannot contain any texts or numbers. When sending envoys, they turn the visually encoded message into text, while the text is presented visually that is what we mean by translation here. As the second step, they prepare both the visual and the text-based summary of the topic (i.e. those who wrote a text earlier now draw, and those who drew, now write a text). In our experience translating textual-notional messages to visual ones and vice versa contributes to understanding each other significantly by opening up a variety of dimensions of articulation, thus translators can join the process of comprehension at several points, information is available through several filters (auditory and visual, obviously, but also kinaesthetic e.g. when interpreting visual structures, dynamic pictures).
About class sizes, again. Since in one row there are only three groups, but four expert notes move around between groups, one note always have to be omitted and placed on an empty desk or chair so that the groups can pick new ones from there and put old one there back again.
With 28 people we will not have a deficiency in the previously 3-strong group, that is, a problem is eliminated although there are more people. With 29, we can set up a group of five members, in which the most difficult topic will have two experts! This time extra care needs to be taken of equal participation between them. That is, initially they need special, step-by-step attention (e.g. when teaching their original micro-group, one of them presents and the other questions the group.) With 30 people two 3-strong groups are advisable instead of one with 6 members; now we have eight groups, which makes expert jigsaw easier. With increasing sizes (31-32) 3-strong groups disappear, and a beautiful co-operative structure based on a 2X4X4 parallel expert jigsaw develops.