Part A: Concise and effective ways of presenting a Jigsaw design

A1: What is different about Jigsaw?

To repeat: So what distinguishes the Jigsaw learning design?

A1. The teacher is not the subject matter expert.

This aspect has a long history (traditional seminars are supposed to be like this, but seldom are in practice), but also has promising modern reincarnations such as having students write test items for each other. This is sometimes called student generated content (SGC), and/or Contributing-student pedagogy (CSP).

The groups

One kind (the "self-teach", expert groups) are co-experts helping each other prepare material for teaching other students; the other kind (the "cross-teach", home groups) are where students teach each other different parts ("topics") of the overall subject. However in many near-Jigsaw designs, the cross-teach groups are either the whole class, or individuals with different learning goals from each other (example1: as in a traditional seminar, each student constructs something different for the class; example2: each reflecting on their own different, personal professional practice; although helped overall by comments from a group).

(N.B. the terms "collaborative" vs. "cooperative" are not helpful in articulating the contrast between the two group types here. The self-teach groups have the same product goal as each other, and bring their planned presentations up to the best standard that the union of their similar expertise can manage. The cross-teach groups are exchanging an essential service which their fellows cannot provide; a reciprocal service delivery, divided by specialism.)

Aronson's summary of the procedure

• Students are divided into a 5 or 6 person jigsaw group. The group should be diverse (e.g. in terms of prior knowledge and/or level of effort).
• The content is divided into 5-6 segments (one for each member)
• Each student is assigned one segment to learn. Each student should only have direct access to their own segment.
• Students should be given time to read over their segment at least twice to become familiar with it. Students do not need to memorize it.
• Temporary experts' groups should be formed in which one student from each jigsaw group joins other students assigned to the same segment. Students in this expert group should be given time to discuss the main points of their segment and rehearse the presentation they are going to make to their jigsaw group.
• Students come back to their jigsaw group.
• Students present their segment to the group. Other members are encouraged to ask questions for clarification. This is small group, dialogic teaching.
• A test on the material should be given at the end so students realize that the sessions are not just for fun and games, but that they really count.

A2: More visual representations

• Prose e.g. Part A1 above.
• Bullet lists: a mixture of language (often not strictly grammatical) and visual structure.
• Diagrams
• Tables
• Slides

Here are some examples, which are used to express what makes one Jigsaw design for a particular class different from another (given the understanding of essentials expressed in the previous section).

Representation 1: List of bullet points

Aronson's version of Jigsaw for a school class:

• Education Level: US school
• Each learner is a member of not 1 but 2 groups.
• Total number of learners (class size) ≈ 20-30
• Distinct topics learned: ≈ 4
• Cross-teach groups: Group size ≈ 4 (number of groups ≈ 7)
• Self-teach groups: Group size ≈ 7 (number of groups ≈ 4)
• Cross-teach groups: Group size ≈ 4 (number of groups ≈ 15)
• Motivation for learning from peers: regular class assessments, and no other source of knowledge.
• No information / communication technology, nor virtual learning environment used.
• Cycle time: Done every 1-2 class meetings; repeated throughout the term (i.e. about ≈ 10 times). (So not one piece of "groupwork" per semester.)

A case from a CPD workshop:

• Education Level: Professional / CPD.
• Each learner is a member of not 1 but 2 groups.
• Total number of learners (audience size) ≈ 60
• Distinct topics learned: ≈ 4
• Self-teach groups: Group size ≈ 15 but subdivided ad hoc into discussion groups of 3-6 (number of topic groupings 4, but subdivided ad hoc into ≈ 12 discussion groups)
• Cross-teach groups: Group size ≈ 4 (number of groups ≈ 15)
• Motivation for learning from peers: small, it is just a demo.
• No information / communication technology, nor virtual learning environment used.
• Cycle time: done once (within a 2 hour workshop).

Ann Brown:

• Education Level: US middle school grade 6 (11-12 year olds?)
• Class size: ≈30.
• Each learner is a member of not 1 but 2 groups.
• Distinct topics to learn: 5
• Self-teach (expert) groups: 5 groups of size 6
• Cross-teach (jigsaw) groups: 6 groups of size 5
• Motivation for learning from peers: The cross-teach groups give a presentation to outsiders on the whole subject (all topics).
• In this case every learner prepares 1 topic, hears all 4 of the other topics, and gets to teach 4 other students about their own topic.
• Computer technology used for pupils to prepare materials for others.
• Cycle time: The whole design takes 8-10 weeks; and is (ideally) repeated 3 times per year.
• There are other features of her design beyond the basic Jigsaw idea focussed on here (Brown & Campione, 1996).

Honeychurch's first year philosophy tutorials:

• Education Level: University year 1.
• Class size = 14.
• Distinct topics learned: 3
• Self-teach (expert) groups: 3 groups of size 4-5
• Cross-teach (jigsaw) groups: 1 group of size 14 i.e. plenary.
• Motivation for learning from peers: capturing understanding in notes, ready for exam revision.
• Cycle time: Done once per week, repeat throughout semester
• Rotate who within each self-teach groups does the exposition to the whole class.
• In this case every learner hears 3 topics and gets to inform 14 others of their own topic once or twice per semester.

My final year modules?:

Bullet lists: reprise

Representation 2: Diagram emphasising how individuals cross-connect groups

  (Click on the image to see the full size version.)

But this seems to need to be drawn by hand: too much effort for regular use, but perhaps useful in giving talks.

Representation 3: Student allocation tables (in a handout, probably generated in a spreadsheet)

In this first example self-teach groups are emphasised and have their topics listed, while cross-teach groups of 5-6 members (denoted by letters) have to organise meetings which are not specified there. In the second example this is reversed.

A few lines sampled from such a table emphasising self-teach groups		The whole table
Name Author group Topic Cross-teach group Jane 1 False praise A Maria 1 False praise B Ann 1 False praise C Marie-Luise 2 Strengths A Sophie 2 Strengths B Elina 2 Strengths C

A few lines sampled from a table emphasising cross-teach groups		The whole table
Cross-teach group Meeting time/place Name Self-teach group A 10am Room 21 Janet 1 A 10am Room 21 Ursula 3 A 10am Room 21 Maria 6 B 10am Room 232 Ken 1 B 10am Room 232 Adam 4 B 10am Room 232 Lobelia 6

Representation 3B: Multiple allocation tables

Example 2

• Class size = 20.
• Distinct topics to learn: 5
• Self-teach (expert) groups: 5 groups of size 4.
• Cross-teach (jigsaw) groups: 4 groups of size 5.
• In this case every learner hears every topic and gets to inform 4 others of their own topic. And learners can be exactly evenly distributed so that groups of the same kind are of identical size.

Example 3

• Class size = 181.
• Distinct topics to learn: 31
• Self-teach (expert) groups: 31 groups of size 5-6.
• Cross-teach (jigsaw) groups: 31 groups of size 5-6.
• In this case every learner hears 4-5 topics and gets to inform 4-5 others of their own topic. An extra report-back session in self-teach groups could pool all 18 of the 31 topics in principle.
• In this case (with a class size that is a prime number) groups of the same kind must vary in size by at least 1 as the class size isn't exactly divisible.
• This design has abandoned direct teaching of every topic to every student: see part B below.

Representation 4: Slides for showing an audience where to go now

Put up SLH's slides here?

Part B: The underlying and emerging issues in scaling up

B1: The underlying issues in designing a Jigsaw activity

Issue 1: SGC: student authoring

Having basic expository content provided not by the teacher but by students comes in many forms. The content need not necessarily be the main course content: it might be test items, introductions, etc. It has many potential advantages: gives students confidence, trains them in teaching themselves (the most valuable skill they can ever learn in an education system), they are inherently more in tune with their audience (other peers) in explaining things. It is an ancient tradition: that is what seminars are supposed to be.

Issue 2: Student reciprocal dependence

With reciprocal dependence, student presenters take it much more seriously, and student listeners make questions and comments because they really need to clear up partial understandings. Using others' products need not be by learning from expository material. It might be producing a critique and giving feedback. It might be using test items others have produced. It might be using summaries not directly to learn, but to make an informed choice of which topics to select to learn for the exam.

Issue 3: Social Psychology effect of group bonding FROM joint tasks

Issue 4: Not just exposition; not just 1-group work; but TWO groups

It is learning from personal interaction (e.g. 1:3 teaching ratio) with someone who knows what you need to learn. It is thus essentially dialogic (based on discussion, although not on discussion about opinions on topics no-one really understands). It may be the only way to supply personal dialogic teaching in a mass education system.

Issue 5: Cross-cutting

Ideas of "social integration" (Tinto) suggest this is one factor tending to reduce dropout, and increase student resilience when their education gets tough. It is also essentially Aronson's own motive for developing Jigsaw: to combat race segregation within school classes after US school "desegregation" forced pupils to be in the same room. Ordinary groupwork tends to be segregation into friendship groups, and to do little for or even harm to the integration of the class as a whole.

This issue interacts with whether the Jigsaw process is repeated e.g. weekly in that class, and whether group membership is maintained or remixed each time. For getting growing familiarity and (usually) smooth group functioning, fixing groups is better; but for maximising networking, and integration across the class, remixing might be better.

B2: The numbers

• Except by luck, a class cannot be divided into groups of exactly equal sizes. If the class size is a prime number (e.g. 23, 67, or 181) then it can never be done; but often in any case there are other reasons for fixing group size than divisibility into the class size: see "Issue 6" below.
• The number of topics (sub-parts of the overall subject) to be learned in one Jigsaw activity equals the number of the self-teach groups equals the minimum size of the cross-teach groups. E.g. with class size = 28 and number of topics = 4 = the minimum size of the cross-teach groups = the number of different kinds of self-teach groups; while 7 = the maximum size of the self-teach groups = the number of cross-teach groups.
• The converse isn't true: if you wish, you can subdivide self-teach groups and have more but smaller ones. Often you may not even have to pre-organise this: they'll naturally separate into more useful small groupings.
• Indirect coverage: As the number of topics grows in a big class, personal cross-teaching of all topics isn't possible. However by adding the idea of learners reporting back to their expert groups, after cross-teaching has happened, learners could pool an account of the topics they have heard about; at least in terms of the best they heard. This second-degree relationship allows the number of topics each learner potentially hears about to be calculated, where type1 means self-teach and type2 means cross-teach, as:
  
  • They all learn one topic for themselves: 1
  • They are directly taught by others in their cross-teach group: Type2size - 1
  • and at second hand can hear about: (Type1size - 1) * (Type2size - 1)
  • This adds up (where Type1size is the size of the self-teach/authoring groups) to:
      (Type1size * Type2size) - Type1size + 1  
  • For example with group sizes of 5 or 6, indirect coverage will cover 20 or more topics, while only 14-17 topics would exist for a class of 83 and those sizes.

B3: The three phases

Phase 1: Simple

• Class size = 28.
• Distinct topics learned: 4
• Self-teach (expert) groups: 4 groups of size 7.
          ↔ 8 groups of size 3-4,         2 groups for each topic.
• Cross-teach (jigsaw) groups: 7 groups of size 4.

Issue 6: Uneven group sizes

• Class size = 27.
• Distinct topics learned: 4
• Self-teach (expert) groups: 4 groups of size 6 or 7.
          ↔ 8 groups of size 3-4,         2 groups for each topic.
• Cross-teach (jigsaw) groups: 7 groups of size 3 or 4.

[B] Why not have an odds and ends group much different in size?
In dividing a class into uneven groups, you can either have some the preferred size and the rest just one learner more (or less) than the preferred number; or else you can have all groups except one the best size, plus a single group with the remainder (often with several fewer, or more, than the rest). In the rest of this page, I've assumed that staying within one of the preferred group size is best. However this really depends on what the reasons behind the chosen preferred group size is (see next "Issue7"). And there can sometimes be a good reason for one group being different in size. For example, the "odd" group might be given the task of creating and maintaining an index to the others groups' work, or a glossary to complement it, or ...

[C] What to do if students join late or drop out?
Especially in large university classes, it is usual for real participation to change after group allocations have been made, both through dropouts and late arrivals. It is best to be ready for this. Obviously if you're lucky new arrivals will happen just after a dropout has emerged, and can replace them. With uneven group numbers, it is obvious you should add a student to one of the groups with a smaller number. If you are unlucky, then new arrivals fill up the slots and trigger the need for a new group, and the need to redeploy some existing students into it. For example, if the number of topics is 4, then cross-teach groups will have 4 ideally, and some will have 5 if numbers are uneven. When all groups have 5 you must, and when 4 groups have 5 it is desirable, that you create an extra group and move 4 students (the new one plus 3 redeployed) into it.

Issue 7: Validation by staff members

Ann Brown talks about this in terms of multiple sources of expertise: peers, older students/mentors, teaching staff, visiting (or remote consultations with) experts. However another angle is to identify this need as "validation" rather than authoritative subject knowledge. Students want to be sure not just that they got some fact right, but that they are giving reasons of the right kind (arguing like a philosopher in a philosophy class, citing evidence of the kind that a psychologist accepts in a psychology class, like a mathematician in a maths class), presenting at the right level (not too formal or too informal), discussing in the right way in the groups, doing what is required in this class. These things could possibly be said to be part of being a subject expert, but only in the cultural sense of having the right implicit skills: not in the sense that they are facts and ideas written in the textbook.

It is likely that they don't need much validation of this kind at all: but that they may need some. For instance Jim Baxter gave feedback to a class of 550 by selecting the best two bits of submitted groupwork each week and circulating them to the whole class along with comments on what made them the best. Students can do a remarkable amount of self-judgement but they do need some point of comparison.

This can be done in small classes by staff are circulating and listening in on groups, and occasionally commenting. This was probably done by Aronson and Ann Brown, judging by the descriptions, but this issue was not brought out. However it is an issue or constraint to bear in mind as class sizes rise; and also, has to be thought about in versions of Jigsaw mediated by software where the teacher isn't visibly circulating.

Another method, described by Ann Brown, is occasional benchmark lectures.

Issue 8: What size is best for groups?

Experts, and teachers, often have firm opinions on the best size for groups; but they do not agree with each other. There are a number of reasons for this, including that better individual skills makes for better group functioning (so optimal size can depend on learner's skills), larger groups take longer to settle down to optimum functioning, age etc. However the most important reason is that the best size for a group depends on what the group is doing. In deciding on your preferred size for each type of group, this is what to consider first.

Some constraints or issues (partly conflicting) on optimal group size.

1. In Jigsaw designs, each cross-teach group must have one learner for each different topic as a minimum. (And that could vary from week to week with how the teacher thinks the overall topic can sensibly be divided.) If there is an extra learner in the group, some topic will have not one but two "experts" on it. This potentially diminishes the responsibility, and so pride after success, of the learners. This is an argument for preferring the minimum size for cross-teach groups (one person per topic).

2. On the other hand, having two (or even more) people per topic in each cross-teach group means that the presenter will be much less anxious because their fellow expert can remedy any omissions they make. Thus larger self-teach groups can be less stressful for cross-teaching. Furthermore, if groups remain stable over multiple cycles (e.g. repeating once a week, with different subjects) then they can take turns to take the lead in presenting, and to support the other; and so each will have a turn at presenting. This is an argument for larger cross-teach groups.

3. In practice we must expect some absences on any given day, so having two experts per topic in each group can also usually cover for that. Otherwise, other members of that cross-teach group would never learn about that topic. This is another argument for larger cross-teach groups.

4. The self-teach / experts groups can be any size on the face of it. In practice, it depends on what exactly they do in the groups. If they are all well-prepared, then they might practise their presentations in turn, getting others to critique them. Probably group sizes of 3 would be best, to maximise the time each has to present, while still getting at least 2 sets of comments.

5. If they are well-prepared in the sense of having read the material but are not confident in their understanding, then discussing the meaning is the central task. Good results are often had with pairs for this, though larger numbers guards against getting stuck with others who have the same problem, or the same (unfounded) agreement on the meaning. Here optimal outcomes will depend less on having some optimum number in the group than on having a mix of opinions in every group or pair.

6. If they are very varied in how well prepared they are, then these self-teach groups are remedial in nature, and in effect we will have a two tier cross-teach design, where in the "self-teach" groups a well prepared student teaches the unprepared (and gets better at this by practice in the light of the questions they ask). In this case, they need to sort themselves out into groups with at least one well prepared student in each.

   Thus this solves the problem of large variations in effort (motivation) between students, where it exists (often in first year); but tends to require larger self-teach groups (six rather than three, say).

7. In variants of Jigsaw where self-teach groups are authoring large materials (rather than short oral presentations), then each such group is likely to split itself up and each produce separate sections. In this case small group sizes could be better, so that the joint product doesn't lose overall coherence. It is natural for joint product groups to make a division of labour, but to be less good at combining the parts. Furthermore, in all joint product tasks, the bigger the group the more effort has to go into inter-communication rather than into direct production.

8. Another issue is validation of student (group) activity by staff ("Issue 7"). This may favour having larger groups so that staff can listen in on them, occasionally commenting (and correcting or validating). However as class sizes rise, this cannot be a sustainable approach, and some other way of addressing validation will have to be used.

   What size audience is best?

SLH, Jaye's classes.

Phase 2: Fragmenting self-teach groups (Issue 9)

• Class size = 60.
• Distinct topics learned: 4
• Self-teach (expert) groups: 4 groups of size 15
          ↔ 12 groups of size 5,         3 groups for each topic.
          ↔ 20 groups of size 3,         5 groups for each topic.
• Cross-teach (jigsaw) groups: 15 groups of size 4.
• In this case every learner prepares 1 topic, hears all 3 of the other topics, and gets to teach 3 other students about their own topic.

If it is all taking place in one big hall, then it may be enough to tell learners to congregate in 4 areas for self-teach, as in the diagram which can be projected as a slide, then fission into 3 subgroups within each area.

Alternatively, you could calculate the split on the spreadsheet and allocate 12 self-teach groups, which would probably be best if they have to arrange their own time and place to meet.

This has already introduced the feature of duplicate authoring, where rival self-teach groups may produce materials or presentations addressing identical topics, but do so independently. This is implicit in all jigsaw self-teach groups, but will remain unreconciled (i.e. the best understanding and presentation ideas will not now be merged) as numbers grow and self-teach groupings fission.

Phase 3: Prioritising real, interactive cross-tutoring and learning by students (Issue 10)

In this approach as class numbers rise, true face to face interactive cross-teaching is maintained, with all students exchanging their understanding in small groups (e.g. of 4). This could be the only way to get real interactive (discussion based) learning and teaching in mass classes: use Jigsaw.

Self-teach or expert groups become huge, and are subdivided as discussed above. A way of modifying the procedure so as to take advantage of the large numbers and get some cross-fertilisation between subgroups who are authoring the same topic might be to have not two main steps as in basic Jigsaw (time with the self-teach group, then time with the cross-teach group) but:

1. Own (small) author i.e. self-teach group, creating a presentation or written materials in collaboration.
2. Cross-critique other author groups doing the same topic: each from the original group split up and visit, say, four others; exchanging comments or perhaps giving a trial talk and getting feedback from this knowledgeable audience.
3. Cross-teaching.

• Example table
  • Class size = 83.
  • Distinct topics learned: 6
  • Self-teach (expert) groups: 6 groups of size 13-14
            ↔ 18 groups of size 4-5,         3 groups for each topic.
  • Cross-teach (jigsaw) groups: 14 groups of size 6-7.

• • Class size = 83.
  • Distinct topics learned: 4
  • Self-teach (expert) groups: 4 groups of size 20-21
            ↔ 20 groups of size 4-5,         5 groups for each topic.
  • Cross-teach (jigsaw) groups: 20 groups of size 4-5.

• • Class size = 181.
  • Distinct topics learned: 3
  • Self-teach (expert) groups: 3 groups of size 60-61
            ↔ 45 groups of size 4-5,         15 groups for each topic.
  • Cross-teach (jigsaw) groups: 60 groups of size 3-4.

• • Class size = 660.
  • Distinct topics learned: 3
  • Self-teach (expert) groups: 3 groups of size 220
            ↔ 165 groups of size 4,         55 groups for each topic.
  • Cross-teach (jigsaw) groups: 220 groups of size 3.
• • Class size = 5,000 e.g. MOOCs.
  • Distinct topics learned: 3
  • Self-teach (expert) groups: 3 groups of size 1666-1667
            ↔ 1221 groups of size 4-5,         407 groups for each topic.
  • Cross-teach (jigsaw) groups: 1666 groups of size 3-4.

You may think it better to have, in cross-teach groups, two rather than one expert for each topic as this reduces anxiety in the presenters. If the Jigsaw is repeated more than once (for different subjects) then each pair can alternate as to who leads. However this doesn't change the pattern as class size rises e.g.:

• Class size = 181.
• Distinct topics learned: 3
• Self-teach (expert) groups: 3 groups of size 60-61
          ↔ 45 groups of size 4-5,         15 groups for each topic.
• Cross-teach (jigsaw) groups: 30 groups of size 6-7.

What is the value of direct cross-teaching?

• They should have practice giving talks, not only at writing.
• They should have practice at teaching in a dialogue: not just delivering a monologue from a stage. It is just as bad to miss this out from training, as it is to miss out giving talks; and the poor quality of some Graduate Teaching Assistants shows the consequences of doing so. If lectures should be avoided in favour of discussion (and having learners read the basic material in advance), then shouldn't this argument be applied equally to peer teaching in Jigsaw designs?
• Such dialogues tend to increase the "presenter's" understanding as well as the hearers'. Trying to teach something for the first time is one of the most learning-promoting activities any student can do.

One question is what the right size for such a cross-teach group is. The smaller the more likely it is that each learner is able to ask any questions they need to ask. On the other hand, it may be true that having more than one "expert" for each topic makes it flow better, by having them support each other. Having more than one expert per topic in each cross-teach group also makes the design much more robust against student absences. In that case, the minimum cross-teach group size will be twice (or thrice) the number of topics, rather than only once.

Phase 4: Prioritising original authoring: student generated content (Issue 11)

Another reason for this approach is that there are some kinds of material that do subdivide in this way into huge numbers of items that constitute a useful whole. E.g.

• Having students author test questions (MCQs). < ref>
• Vocabulary items for learning a foreign language. Easy to get them to create entries for words (or a dozen words per group) not in the core vocabulary of the textbook.
• Constructing a really big resource, using a large class. E.g. collaboratively to create a Dictionary of Psychology / Geology etc.: one entry per team. An encyclopedia of Positive Psychology.
• Combinatorial exercises. Having students create exercises (for their own class) in cases where a really thorough set of exercises would deal with all combinations of elements (not just the one new element being taught, or all elements so far jumbled together). For example in maths, you might want learners to be able to add, subtract, multiply, divide, and calculate exponents (e.g. two cubed), perhaps for complex numbers rather than integers; and to do this in any combination. That is 5 elements. Each separate group task is defined by which of these elements is and is not to be included. With 5 elements, there are 2^5 = 32 combinations, so 32 "topics" for groups. With 10 elements, there are over a thousand distinct combinations (topics for groups). The group that gets in,out,in,in,out has to create exercises using addition, multiplication and division (but not subtraction or exponents). If, for instance, the exercises involve both adding and multiplying then they will involve questions of association i.e. does 'a + b * c' mean '(a+b) * c' or 'a + (b * c)'? So more elements is likely to mean more complex issues, but examples with only a few terms (2 or 3 terms like a,b,c in the example); while fewer elements allows more terms (e.g. adding a thousand numbers, or bigger numbers). Pedagogically, it is easier to learn one element at a time; but learning to combine them is also important: but requires different exercises.

  Similarly in an introductory course on computer programming: variable declarations, initialisations, while loops, subroutines, expressions etc. need soon to be exercised together, not separately. Even in History you could consider this, where the elements might be a set of theoretical perspectives (e.g. Marxist, Feminist, military technological determinism, social history) and a set of time periods (the 1830s, the 1940s). Exercises with a single theory would require a deeper analysis, while those with several will be "compare and contrast interpretations" exercises. Exercises are time-consuming for teachers to construct; but a big class can generate a large bank of them for learners to select from.

Issue 12: Indirect topic coverage

1. Own (small) author i.e. self-teach group, creating a presentation or written materials on collaboration.
2. Cross-teaching.
3. Report back in author groups: what is best out of the other topics each of you has heard about?

Given this procedure, then the number of topics each student may hear about is given by the formula for indirect topic coverage given in section "B2: The numbers" above. However as the examples below show, this only helps for a bit, and as class size grows even further it eventually becomes entirely ineffective.

Examples of this line of development

• • Class size = 83.
  • Distinct topics learned: 18
  • Self-teach (author) groups: 18 groups of size 4-5.
  • Cross-teach (jigsaw) groups: 14 groups of size 5-6.
  • Coverage with report-back: ≈ 17 of 18 topics.

• • Class size = 181.
  • Distinct topics learned: 60
  • Self-teach (author) groups: 60 groups of size 3-4.
  • Cross-teach (jigsaw) groups: 36 groups of size 5-6.
  • Coverage with report-back: ≈ 13 of 60 topics.

• • Class size = 660.
  • Distinct topics learned: 165
  • Self-teach (author) groups: 165 groups of size 4.
  • Cross-teach (jigsaw) groups: 132 groups of size 5.
  • Coverage with report-back: ≈ 17 of 165 topics.

• • Class size = 5,000 e.g. MOOCs.
  • Distinct topics learned: 1666
  • Self-teach (author) groups: 1666 groups of size 3-4.
  • Cross-teach (jigsaw) groups: 1,000 groups of size 5.
  • Coverage with report-back: 13 of 1666 topics.

Conclusion

Ths will affect the motivation for learners using each others' products. With a small number of topics, which all learners are taught, you can arrange that all learners really need to understand this material e.g. by testing it in exams without a choice of topic. When there is more material (topics) than a student can learn (or the Jigsaw can teach to all), which is quite common in university courses, then you have to consider the motivation for using it even more carefully than normally. On the other hand, if all the material on the whole course comes from one student or another, then this is not a particular problem.

The next design issue (12) in developing this line is whether or not to subdivide the class into subsets with good cross-cutting interaction (only) within each of these subsets; or whether to take care to inter-connect the whole class in one huge network.

Phase 5: Degenerate group sizes. Can it make sense to have either group of size 1?

Reciprocal Peer Critiquing
Crossteach group size = 5-20 (say); self-teach size = 1, topics = ?.

Patchwork text
Crossteach group size = 6 (say); self-teach size = 1, topics = 6.

Each student has a personal topic (e.g. their own essay title; or reflecting on their own past professional practice). By presenting to each other, they get personal feedback on a topic that is generally similar to each other, but completely different in the specifics, and in the personal significance.

These two cases involve students who are learning different things in terms of concrete cases, but the same things at an abstract level (e.g. how to write that kind of essay).

SLH tutorials
Class: 14; topics = 3; Self-teach: 3 groups of 4-5; Cross-teach: = 1 group of 14.
But could have been:
Class: 14; topics = 3; Self-teach: 3 groups of 4-5; Cross-teach: = 2 groups of 7.

Presentation practice
Self-teach size = 3; topics = 1; cross-teach size = 3. [concrete view]
Self-teach size = 3; topics = 1; cross-teach size = 0. [abstract view]

Here the exercise is for each group member to prepare the same topic, and in turn present to the others; for critiquing on presentation technique. They steal methods from each other; and practise critiquing as well as generation (authoring). It relies on the knowledge being already in their heads (more or less), and improves method. This is also a good revision technique, in contrast to a common technique of dividing the knowledge work amongst a group (as in a conventional Jigsaw).

My year 4 courses
Self-teach size = 6; topics = 18; cross-teach size = plenary.

Problem is: making students really use each others' products.

Collected summaries of group allocations in Jigsaw designs

Sorted by class size		Sorted by number of topics

B4: Rough list of design decisions

Group allocation design decisions

0. (Given the class size is fixed, known.)
1. Decide whether the Jigsaw process is done once in that course / semester, or is repeated weekly or daily.
2. If repeated, then will you maintain group membership throughout the course, or "remix" groups each time?

3. The number of topics (that the overall subject is to be divided into) e.g. 3 or 4.
4. Preferred number to have in cross-teach groups (i.e. the preferred number of experts / topic in each cross-teach group e.g. 1 or 2).
5. How to achieve usage by learners of their peers' products. I.e. why would students need to learn in the cross-teach groups? (See below for more.)
6. If the class is large, decide which to give priority to: personal teaching, or original authoring by each learner.
7. Build in report-back step? yes/no
8. Build in expert cross-critiquing step within expert pools? yes/no
9. Student knowledge delivered by a) exposition, or b) exposition with dialogue; or c) reading / JustInTime style interactive session which assumes reading.

10. Self-teach: minimum, maximum size of groups, number of groups (decide one of these three numbers and the others are more or less decided too).
11. Cross-teach: minimum, maximum size of groups, number of groups (decide one of these three numbers and the others are more or less decided too).

Wider course design issues

1. Is the subject for the whole Jigsaw suitable? One that will benefit from discussion?
2. Are the subtopics suitable? both self-contained enough to study, but inter-dependent enough to make the cross-teaching matter.
3. Consider giving the students a voice in creating and/or selecting the subtopics.
4. Why would students need to learn in the cross-teach groups? Three general alternative answers to this:
   • An exam covering all the topics. (This might become visible as notes taken for future revision.)
   • Because you have arranged for Cross-Teach groups to themselves give a talk / write materials for an outside audience on how the topics combine into an overall idea.
   • Some other project they are required to do where they have to combine the topics.
5. What concrete deliverables will you formally require from each student (other than group participation)? E.g.
   • Written material (web or paper) from the self-teach groups?
   • Oral presentations from the self-teach groups to the class or to a cross-teach group?
   • Written material (web or paper) from the cross-teach groups?

Part C: problems, design issues

(if , when) Students don't like Jigsaw

Late comers to the class / dropouts

Learning on the spot

• Class size = 25.
• 3 groups of 8 or 9 for expert/ self-teach groups.
• 8 groups of 3 or 4 for jigsaw / cross-teach groups.

In practice, although there will only be 3 kinds of self-teach group, one per topic, it may be better to subdivide these into groups of 3 or 4 (no exact plan is necessary).

Thus in a CPD presentation about Jigsaw, you can use this kind of plan for a demo so that the audience can experience it. Again 3 (say) topics (perhaps presented on briefing sheets). Any number in the "class" i.e. audience. Organise / impose jigsaw groups of 3 each, 4 to take care of odd numbers. For instance:

• Audience size = 100.
• 3 groups of 33 or 34 for expert/ self-teach groups; naturally will fragment into smaller subgroups e.g. of 3 or 4.
• 33 groups of 3 (or 4) for jigsaw / cross-teach groups.

With some advance homework