Multiple learning communities: students, teachers, instructional designers, and researchers

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Multiple learning communities:students, teachers, instructionaldesigners, and researchersALAN H. SCHOENFELDPublished online: 17 Sep 2007.

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DOI: 10.1080/0022027032000145561

J. CURRICULUM STUDIES, 2004, VOL. 36, NO. 2, 237–255

Alan H. Schoenfeld is the Elizabeth and Edward Conner Professor of Education in theGraduate School of Education at the University of California, Berkeley, CA, 94720–1670,USA; e-mail: [email protected]. He is a Past-president of the AmericanEducational Research Association and currently Vice-president of the US National Academyof Education. His research interests include problem-solving, modelling the teaching process,and studies of diversity and equity.

Multiple learning communities: students, teachers,instructional designers, and researchers

ALAN H. SCHOENFELD

Fostering a Community of Learners (FCL) exemplifies a class of pedagogical approachesaimed at having students become reasoners and sense-makers in various content domains.While the pedagogical practices among these approaches vary to some degree, they tend tooverlap in philosophy and general pedagogical style. Hence issues confronted by thoseattempting to implement FCL will be confronted by those hoping to implement similaractivities. The three-level commentary in this paper begins with specific reactions to thepreceding papers, which focused on attempts to implement FCL in different content areas.It continues with a discussion of what counts in FCL: for example, is it a set of participantstructures such as jigsawing, or a set of underlying principles? It concludes with a discussionof systemic issues that will be faced by any pedagogical approach focusing on havingstudents engage in reasoning and sense-making in the classroom.

In broadest terms, the papers in this issue of JCS are about learning to ‘teachfor understanding’ in various subject-matter areas or disciplines—specifi-cally, the ‘amalgamated multi-discipline’ of social studies (Mintrop 2004),science (Rico and Shulman 2004), English language arts (Whitcomb 2004),and mathematics (Sherin et al. 2004). The choice of different disciplines forinvestigation represents both a theoretical commitment and an empiricalstrategy. The commitment is to the idea that disciplines matter in teachingand learning to teach, that the challenges and perhaps even the mechanismsof teaching for understanding in various content domains will be shaped bythe character of the disciplines being taught. The investigative strategy is toexamine the implementation of a reform effort entitled ‘Fostering aCommunity of Learners’ (FCL) (see e.g. Brown and Campione 1996) inthe four domains identified above. This strategy allows for multipledimensions of inquiry.

First, and staying close to the data, there are the challenges ofimplementing FCL itself. FCL includes a carefully delineated set ofclassroom practices, among them decomposing and recombining the topicunder discussion into interlocking subtopics that can be studied bysubgroups of students and then taught to other students. For FCL tosucceed, then, the big ideas of the curriculum need to be identified and

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238 A. H. SCHOENFELD

‘jigsawed’ in ways that are suitable for the intended organization ofclassroom practices. This is a complex design task, to be followed by the yetmore complex task of making the jigsaw come alive in the classroom. In theirintroduction to the papers, Shulman and Sherin (2004) identified fourissues to addressed by all of the researchers exploring the domain-specificimplementations of FCL:

� searching for the ‘big ideas’;� the analytic challenge: When is a disciplinary topic ‘jigsawable’?;� curricular habits and their impact on pedagogical changes; and� the challenges of implementation in a community of learners.

The papers here provide useful evidence regarding what it takes to make thiskind of programme ‘work’.

Second, the organization of the study, with parallel inquiries in differentdisciplines, facilitates exploration at the epistemological level. In what waysdo the answers to these questions (and others) depend on the disciplinebeing studied? For example, is mathematics ‘a discipline apart’, as Sherin etal.’s (2004) title suggests? What are the commonalities across disciplines?What are the unique features that may shape (successful) FCL implementa-tion in particular ways?

Third, the specific implementations of FCL discussed in the four papersraise several general issues related to teaching for understanding. FCL is anotable exemplar of a family of approaches to pedagogical reform that haveat their core the following sets of ideas:

� The disciplines themselves are ways of making sense ofphenomena;

� Learning a discipline involves learning prototypical or paradigmaticways of sense-making in that discipline as well as coming to gripswith a substantial body of domain-specific knowledge;

� Classroom activities must foster active engagement with thecontent and processes of the discipline, with students developingand testing ideas in ways consistent with the paradigms of thedisciplines they study. Learning involves membership in intellectualcommunities, where ideas are developed and shared collaboratively.Relevant activities include investigations of various sorts (some-times individual, sometimes collaborative), codification of andreflection on what has been investigated, and the active commu-nication and critique, both orally and in writing, of what has beenlearned.

That is, FCL is an exemplar of a class of pedagogical approaches aimed athaving students become reasoners and sense-makers in various contentdomains. While pedagogical practices vary to some degree from oneapproach to another (e.g. the ‘jigsaw classroom’, which is a design feature ofFCL, is not a typical feature of other reforms), these approaches topedagogy share much in philosophy and general pedagogical style. Forexample, the four FCL principles of learning are ‘activity, reflection,collaboration, and community’. Hence, to a significant degree, the issuesconfronted by those attempting to implement FCL will be confronted by

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MULTIPLE LEARNING COMMUNITIES 239

those hoping to implement other reform activities. The reports in the fourpapers in this JCS issue thus raise some general issues for consideration.

This commentary will touch upon all three of the dimensionshighlighted above: the implementation of FCL, epistemological issues, andgeneral issues of implementing ‘reform’. I shall first canter through the fourpapers in order, highlighting points relevant to the three dimensions.

The papers

Social studies

Mintrop (2004) leads with a discussion of epistemological issues, notingthat social studies is not a discipline itself, but an ‘amalgamated multi-discipline’ that draws from numerous disciplinary traditions (history,sociology, and anthropology, for example) and social concerns (e.g. a wishto teach ‘citizenship’). Moreover, there is little consensus on content. Thefield’s multi-disciplinary foundations might provide a vehicle for ‘jigsaw-ing’, with different perspectives on an issue being represented by tools andtechniques of different disciplines. However, designing and scaffoldingsuch layers of analysis call for deep knowledge of the different disciplinesand the ways they work. Deep knowledge of one domain is a fair amountto expect of a teacher or instructional designer; deep knowledge of manyis likely to be rare. Beyond that, Mintrop notes, ‘what are provisionalproducts of ongoing scholarly dialogue within the research community areoften received by schools as truths or facts, reified in textbooks’. It may,he suggests, be difficult to transcend a truth/fact orientation via con-structivist pedagogy.

Mintrop’s empirical study describes the sequence of conceptual hurdlesencountered by four teachers as they planned and developed an FCL unit.In summary, he notes that ‘the search for discipline-based big ideas is anarduous task in social studies’. To foreshadow much of my discussion, let menote that the last three words of the quotation are unnecessary. The searchfor discipline-based big ideas is an arduous task—period! One should not besurprised that the four teachers involved had a hard time. Similarly, it shouldnot come as a surprise that the teachers encountered an ‘activity block’ intrying to design instruction. Under the best of circumstances, trainedinstructional designers labour mightily to craft lessons that ‘work’. The taskis that much more difficult when one tries to design new activity structuresto fit into a novel instructional format. The natural temptation for anyteacher, not just these four, is to rely on a form of bricolage: ‘What do Iknow that’s close, and how do I modify it so that it works in this context?’What teachers often know and feel comfortable with are activities—forexample, having a vote or debate as a means of having students engage inaspects of participatory democracy. These ‘work’ in that they are engagingand that students seem to learn something from them. Why not start withthese? Given the context, it makes perfect sense. Likewise, Mintrop’sobservation that in student–teacher interactions the teacher’s voice tendedto dominate also makes sense. Anyone who thinks it’s easy to adopt

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pedagogical practices that are at significant variance with one’s old practiceshasn’t tried it. Simply put, old habits die hard!

The comments in the preceding paragraph are meant to be general,establishing a theme to be pursued later in this commentary. I do, however,want to make one comment particular to this paper. What one seesthroughout Mintrop’s analysis is the facilitator’s perspective. (This is notsurprising, given that the facilitator was the author of the paper.) As a result,what occurred in reality is measured against the template of the author’sexpectations—a rather high ideal. What is lacking from the paper is not simplythe teacher’s voice, but the teacher’s perspective. While it may be that the ‘bigideas’ were obscured because of changes in the activity structure initiated byteachers, it may be that there were some gains in compensation. It would begood to hear about the trade-offs from the teachers’ perspective—notsimply to give them voice, but perhaps to understand important dimensionsof classroom activities that are absent from the current analysis.

Science

Rico and Shulman (2004) begin by contrasting science with social studieson epistemological grounds. I must start my response by noting thatcoherence is in the eye of the beholder: What appears coherent from oneperspective may seem fractionated or incoherent from another perspective.It may well be that at some level, ‘science’ is much more coherent than socialstudies. However, references to ‘the discipline of science’ and ‘a sharedscientific process that permeates all the [scientific] disciplines’ may overstatethe case. Physicists and biologists are most likely further apart in theory andmethod than are anthropologists and sociologists. Indeed, even if one stayswithin the life sciences, microbiologists and taxonomists may be furtherapart in theory and method than are anthropologists and sociologists. Oneof the more interesting things to watch over the past decade has been thedebate in the USA over national science standards, both in the NationalResearch Council (NRC) and in the scientific community at large. In theNRC, it was difficult to achieve consensus because of differing paradigms indifferent scientific fields: while there is general agreement on whatconstitutes a solid argument, there is enough divergence with regard tomethod that agreement on unifying principles and methods was hard toachieve. (There is, as Rico and Shulman report, a ‘unifying concepts andprocesses standard’, which represents broad but somewhat vague con-sensus.) In the scientific community at large, the ‘science wars’ mirrored the‘math wars’: some argued for ‘process’, and some argued for ‘content’.There were Nobel Prize winners on both sides. In science as in socialstudies, there is a good deal of controversy. There is in English language artsand mathematics as well.

Rico and Shulman’s work overlaps with Mintrop’s in approach andresults. Their first two research questions, focusing on unit design, concern‘big ideas’ and their decomposition into jigsawable pieces. It was easier forthe biology teachers with whom they worked to identify big ideas than it wasfor the social studies teachers—the teachers had the advantage that some of

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the extant biology curriculum, and the science standards, are organized thatway. Yet these teachers discovered, like their social studies colleagues,jigsawing is not that easy. They, too, found that it is all too easy to lose thefocus on big ideas amidst the myriad details of curriculum design andimplementation.

Rico and Shulman go beyond Mintrop in problematizing the teachers’engagement with the curriculum. Their questions

� What do these teachers value as ‘knowledge’ and ‘learning’ for theirstudents?

� What are their curricular habits and tendencies, and how do thesehabits, which may differ substantially from the habits of thediscipline of science, affect the implementation of a reform such asFCL?

open up an arena for inquiry, and they provide interesting and importantdetail about the implementation of the two science projects. For example,we find that:

Jerry . . . provided students with the list of questions they had generated afterwatching the video Hemo the Magnificent, but he had not screened thesequestions to determine which would lead to successful research. As a result,many students were confused by what they were to do as research. Moreover,although Jerry believed that once he had students researching their ownquestions they would be internally motivated, this was often not the case.Rather, several students would forget which topic or question they were to beresearching. To further compound the difficulty, Jerry gave his students a listof questions . . . to answer each week. These questions were fact-based and, inmost cases, unrelated to a particular research question. Answering themcompeted for class time with students’ own research questions. As one studentsaid to Jerry in frustration, ‘What do you want me to do—my research or thesequestions?’

The bottom line is that building a research culture is hard. There aremultiple dimensions to this. Building a research culture includes teachingstudents to frame questions that are meaningful and answerable, helpingthem learn to find useful sources of information and then to unearth therelevant information from it. It involves developing skills of collaborationand communication. Each of these skills is a major endeavour in itself;trying to do them all at the same time is extraordinarily difficult. It shouldcome as no surprise that ‘for Marvin and Jerry, the notion of science asinquiry and research was abandoned for the more familiar (and moreaccessible) “school” notion of science as a body of facts to be gatheredand memorized’. It is to Rico and Shulman’s credit that they help usunderstand why.

English language arts

To ‘what is social studies?’ and ‘what is science?’ we now add ‘what isEnglish?’ Whitcomb (2004) begins her paper by pointing out that there aredivergent approaches to conceptualizing and teaching English language arts,

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and the same ‘traditional’ versus ‘reform’ tensions found in the otherdisciplines discussed in this JCS issue. In this arena, like the others, it is notso easy to identify and jigsaw big ideas.

Each of Whitcomb’s three cases echoes themes from the previouslydiscussed studies. Debbie’s ‘crisis’ occurred when she realized that fleshingout the FCL lesson she had crafted in broad outline would demand moretime, knowledge, and skills than she had: ‘I don’t have time to get theresource materials; I have to prepare the students for high school; I’m not ahistory teacher’. Debbie’s statement recognizes at least two classes ofdifficulty: first, that instructional design of any kind is quite time-consuming; and second, that her planned approach would call forknowledge of both the historical and the English language arts traditions.She, like the social studies teachers who might hypothetically haveapproached a topic from various disciplinary perspectives, finds that shelacks the disciplinary knowledge to do so.

[Sidebar comment: while the teacher’s perspective is heard in thissegment, the researcher’s perspective dominates, as it did in Mintrop’s.Like Whitcomb, I have sympathy for the idea of grappling with ‘the actualhuman experience depicted in the literature’ and would certainly hope thatstudents come to feel what they read. At the same time, it appears thatDebbie’s students made more sense of the concept of metaphor than hadher previous students, in a way that made the class come alive for them.That’s a decidedly non-trivial achievement, and one to build on. Todismiss it as reification of language-as-artefact is to negate theachievement.]

Allie’s story is interesting for a number of reasons. First, perhaps justby omission, there is minimal mention of jigsawing. If jigsawing eitherplayed a minimal role or was interpreted by Allie in a way significantlydifferent from that prescribed in FCL, then her design of a unit thatfocused on knowledge-in-action tells a story of the development of a‘reform’ unit, not specifically of an FCL unit. Second, I suspect that it isno accident that Allie had ‘an impressive professional developmentresume’. As noted above, instructional design is quite difficult. Whileextensive experience with professional development is no guarantee ofsuccess, it may well enhance the likelihood of it. Third, Allie’s develop-ment of the FCL unit provides a nice indication of constructivism inaction: she starts with what she knows and self-consciously moves towardwhere she wants to be.

Patrick’s story indicates many things: the difficulty of instructionaldesign, the modification of FCL as he made it his own (‘Patrick, likeDebbie, felt overwhelmed by a full FCL unit. He also simplified FCL tomake implementation manageable. However, Patrick’s strategy of simplifi-cation focused on working with one participant-structure until he was ableto foster authentic dialogue. Listening to his students’ conversations helpedhim understand how the students read a challenging text. His goal wasfostering discourse, not implementing a participant-structure.’), and on thefact that he went through various ‘stages’ on the way to developing a unitthat worked for him. I shall return to all of these issues in the discussion thatfollows.

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Mathematics

The paper by Sherin et al. (2004) raises a number of important themes.It tells a dual story, of instructional design/implementation and of teacherchange. That’s the way it should be. The two live in dialectic: Sherin etal. show how the teacher, David, changes in response to his attempts toimplement FCL, which changes as he does. The paper also highlights therole of participant-structures such as jigsawing as a means to an end,rather than an end in themselves. In Sherin et al.’s analysis, jigsawing isseen as one, but certainly not the only way to foster productive discourse,enhance communication skills, and develop understanding. The authorsargue that other participation structures that result in the creation of aproductive discourse can be true to the spirit (or principles) of FCL, ifnot the letter. These themes are central to two of the three issues Ioutlined in the introduction to this review: what it means to implementFCL (and with what success), and general issues of implementing‘reform’.

Let me begin by pointing out the commonalities between this paper andthe others, partly to show that mathematics is not, as its title suggests, ‘adiscipline apart’, and partly because the conclusions of Sherin et al. apply toand inform the other papers.

The first commonality is that mathematics shares with the otherdisciplines (or multi-disciplines) the property that there are controversieswith regard to its epistemological foundations—or to be more precise, whatconstitutes ‘thinking mathematically’, which is presumably the goal ofmathematics instruction. A major shift has been from ‘content’ to ‘contentand process’: the US National Council of Teachers of Mathematics’(NCTM) (2000) Principles and Standards for School Mathematics outlines fivecontent standards and five process standards (i.e. problem-solving, reason-ing, connections, communication, representation) as goals for learningschool mathematics. The term ‘math wars’ is evidence of the controversialnature of these goals.

The second is that in this domain, like the others, big ideas are not veryeasily identified and defined. Given the topic of probability as the focus ofinstruction, would a group of teachers, or mathematicians, independentlyidentify the same big ideas in probability? It is likely that a randomly selectedprobabilist, or another teacher, could come up with something quitedifferent than David did. (In fact, while David’s choices are quitereasonable, they bear only passing resemblance to the standards andexpectations for probability found in NCTM’s Principles and Standards(2000).)

Third, jigsawing is hard. Having chosen the big ideas of probability thathe did, David faced the formidable challenge of jigsawing them for researchgroups—a challenge he ultimately decided to foreswear. (N.B. I disagreewith the conjecture of Sherin et al. that mathematics, because of itshierarchical nature, offers unique difficulties for jigsawing. More about thisbelow.)

Fourth, the transition from ideas to a detailed instructional plan isdecidedly non-trivial.

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And fifth, developing a ‘discourse community’ or ‘culture of inquiry’requires a set of pedagogical skills that are quite subtle and difficult tomaster.

Finally, David, like so many of the other teachers described in this issueof JCS, found the combination of all these things—even with the support ofthe ‘Fostering Communities of Teachers as Learners’ team—far too muchto do all at once. He, like all the teachers, faced a choice: try to do it all, withthe inevitable results, or try to accomplish a more focused subset of theactivities, transforming oneself (and FCL) thereby. One of David’s majorgoals shifted from implementing FCL via jigsawing to supporting a richdiscourse community and having his students ‘engage in meaningfuldiscussions’. Although those are not the precise words Whitcomb used todescribe Peter’s changes in the English language arts study, they could havebeen.

In short, the story in mathematics echoes the story in the other fields.Equally important, the conclusions that Sherin et al. draw from their studyalso apply to those fields. I turn to those in the next section.

Discussion

Let me now return to the three themes highlighted in the introduction:issues pertaining to FCL; what is domain-specific and what is not; and thelarger issues around building capacity for ‘reform’ given the current contextin the USA.

Issues pertaining directly to FCL

My comments in the preceding section on mathematics regarding theuniformity of findings across the four studies by Mintrop (2004), Rico andShulman (2004), Sherin et al. (2004), and Whitcomb (2004) serve as atemplate for this discussion. Let me follow the progression of ideas fromgeneration of a unit through its implementation.

First, there is the choice of big ideas. This was a challenge in all of thedomains, and for good reason(s). Because my area is mathematics, let meillustrate the issues in that domain. Historically speaking, one consequenceof the ‘cognitive revolution’ starting in the 1970s is that there was a seachange in the field’s understanding of the dimensions of mathematicalthinking and learning. This change was the backdrop for the NCTM’s(1989) first volume of ‘Standards’, the Curriculum and Evaluation Standardsfor School Mathematics. After a decade of curriculum experimentation andfurther research (and some controversy), NCTM embarked on therefinement of the message in the original Standards document. Theproduction of the Principles and Standards document (NCTM 2000)involved a team of 25 writers over a period of three years, in heavyconsultation with more than a dozen mathematical societies. As one of thegroup leaders in the writing of this document, I can attest to the greatdifficulty this hand-picked team of writers had in defining a coherent ‘road

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map’ through the big ideas of pre-K-12 mathematics. Such conceptual workis excruciatingly difficult even for accomplished professionals.

Moreover, there are issues of grain-size that must be addressed incurriculum development. These receive scant discussion in these papers(and, to the best of my knowledge, in other papers on FCL). FCL units aretypically short in duration. One must therefore ask how the ‘big idea’ of aunit matches up with the big ideas of the domain. David’s choice ofprobability as a unit for FCL development hits one of the big topics inmathematics: ‘Data analysis and probability’ is one of NCTM’s five focalcontent arenas for school mathematics. But it is a huge topic. Within it,NCTM identifies four standards: formulating questions; selecting and usingappropriate methods for data analysis; developing and evaluating inferences;and understanding and applying basic probabilistic concepts. Each of thesestandards is further elaborated into content-related ‘expectations’ forspecific grade bands, and each of those would be further refined for units ofinstruction. A fully integrated unit on probability would tap into all of thesebig ideas at some level—but only at some level. Over time, students’experience would build into a coherent whole, with some small ‘big ideas’dealt with at the unit level, other larger themes visited repeatedly over theyear(s). In short, there is not a one-to-one correspondence between unit sizeand the size of big ideas. It does makes sense, as a design heuristic, to ask‘What are the fundamental ideas I want students to grapple with in this unit?What do I want them to grapple with over the whole year? How can they fittogether?’ A central design issue is to fit things together so that students seeboth the trees and the forest.

Second, there is the issue of jigsawing. All four papers testify to itsdifficulty, for one of two reasons: (a) not all big ideas lend themselveseasily to the process of decomposing and recombining that lies at the heartof the jigsaw method, and (b) some of the ‘natural’ methods of construct-ing jigsaws may demand competencies that extend far beyond that of mostteachers (or designers or researchers). Regarding (a), it is certainly thecase that each discipline has some topics or big ideas that are nicelyjigsawable. The life sciences offer many, in that living systems can beexamined at multiple levels; it is no accident that FCL got its start there.Literature offers many in that there are the stories told, the meanings theyhave, the tools used to create the stories, etc. Social studies is, as Mintrop(2004) discusses, inherently multi-disciplinary, and thus inherently jigsaw-able. Much of mathematics is as well. For example, a central concept inmathematics is that of multiple representations: a problem situation mightbe represented verbally, in drawings, via symbols, in tables, etc. Each ofthese representational modes makes it easier to see some things, harder tosee others. Part of knowing mathematics involves knowing which repre-sentations provide what kinds of information, and being able to translatefrom one representation to another in the service of solving problems.Situations that can be analysed in multiple ways are ‘naturals’ forjigsawing. I suspect that in every domain, there are some topics/ideas thatcan be jigsawed, some not. But even if many can, the experiences reportedin this set of papers suggest that the task is daunting in general—and noneof the designers truly succeeded at it.

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Turning to (b), I note that three of the papers provided examples of‘natural’ decompositions that demanded skills beyond those possessed bythe teachers doing the designing. In social studies and English language arts,there was the possibility of looking at (historical or literary) events thoughmultiple disciplinary lenses. But that required deep knowledge of multipledisciplines, which is rather rare in individuals. That is not to say that teamsmight not manage to design multiple-discipline jigsaws—but then one facesthe structural issues of teaching multidisciplinary offerings in schools nottypically organized to support them. In short, to demand ‘jigsawability’ of atopic/idea is to apply a huge constraint on the design of instruction.

Third, there are the complexities of moving from an outline of a unit (sayat the jigsaw level) to the level of detail that actually supports instructionalpractice. These are easy to underestimate, and one pays the price for doingso. The typical figure used in classical instructional design is that it takesprofessionals between 50 and 100 hours to develop one hour of polishedinstructional materials. Mind you, that’s for people who are trained at thatjob, and who are working in a familiar tradition. In the papers reported here,teachers and facilitators who did not necessarily have design experiencewere asked to craft complex units that were decidedly non-traditional. Is itany surprise that they found the task overwhelming? In some cases, theforest got lost for the trees. For example, big ideas regarding electoralpolitics were lost in the details of the social studies unit, where students’election campaigns were aimed at their fellow students rather than at thehypothetical constituencies their fellows represented. In science, the issue of‘why have invertebrates survived’ got lost in Marvin’s classroom, and theinterconnectedness of body systems got lost in Jerry’s. In other cases, theteachers (wisely) abandoned the task of designing whole units in favour ofsmaller, more manageable tasks.

Fourth, there are at least two levels of difficulty to confront in movingfrom detailed design (even if the design is good) to making things come alivein the classroom. One level of difficulty can be invoked by a name: ‘Mrs.Oublier’ (Cohen 1990). As Cohen’s study showed, it is a lot easier to adoptthe rhetoric of reform than to adopt the practices of reform. Indeed, one canthink one is engaging in reform while in fact implementing practices that areat best hybrids of the traditional practices from which one is trying tochange. In case after case in the papers here, we read of the teachersconfronting their own well-established habits—and, more often than not,succumbing to them.

The second level of difficulty is the challenge of creating cultures ofinquiry. Consider the fact that those who have managed to do so arejustifiably famous, e.g. Ball and Lampert (Ball and Lampert 1999, Lampert2001) in mathematics, Minstrell (2001) in physics. Likewise, you won’tneed your toes to count the number of theorists and designers of suchcommunities (e.g. Brown 1992, Collins 1992, Brown and Campione 1996,Cognition and Technology Group at Vanderbilt 1997 [led by Bransford],Cobb 2001, Scardamalia and Bereiter 2003); your fingers will suffice.

This is an arena in which I can speak from personal experience: I spentmany years developing and teaching my problem-solving courses as‘microcosms of selected aspects of mathematical practice’ (also known as

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‘cultures of inquiry’). Building an intellectual community is hard, even whenit’s a full-time job. Doing it as an ‘add-on’ to ongoing responsibilities is thatmuch harder.

Put these four sets of difficulties—finding big ideas, finding a plausibledecomposition for purposes of jigsawing, designing non-standard instruc-tion based on the jigsaw, and teaching in ways that foster the developmentof intellectual communities—together and you have a monumental chal-lenge. This would be a major challenge for a seasoned design team andteachers who are well accustomed to ‘reform’. To ask teachers withoutmuch design experience and relatively unseasoned facilitators to take onthis challenge is to ask a great deal. The efforts of the four teams discussedhere were little short of heroic, and their limited accomplishments shouldbe judged accordingly. It should be understood that pioneering attemptsdemand heroic efforts, and that prototypes (both of process and ofproduct) necessarily have lots of rough edges. What has been presented inthis set of papers is a collective design experiment, where the goal was tocreate something important in order to examine and improve it. As hasbeen seen, the outcomes fell short of expectations (for all of the reasonsidentified above). However, they can be considered improvements in bothprocess and product over much traditional instruction, and catalysts forprofessional growth as well. On their own terms, those are non-trivialachievements.

My final comments in this section are for the most part abstractions ofthe comments made in the paper by Sherin et al. In the introductory sectionof their paper, they note that initial attempts to employ the techniques ofreciprocal teaching directly in mathematics were unsuccessful. Looking backon that work, they comment as follows:

[W]hat we find compelling is the route they took to adapt this structure formathematics. They did not simply transfer the activities that had been provensuccessful in one domain to another. Rather, they went back to the principleson which the structure was developed, and then looked for strategies thatwould be appropriate for mathematics. This suggests two underlyingassumptions: it is important to consider whether a participant structure isappropriate for a given domain, and it is the application of the principles ofFCL that should remain intact, and not necessarily the participantstructures.

This, I think, is precisely the point! As has been seen, jigsawing turns outto be easy in some cases, near-impossible in others: to require it—eventhough it gives a distinct ‘signature’ to FCL lessons—is to over-constraininstructional design. Rather, the goal should be to operate in a spiritconsistent with the goals and principles that underlie jigsawing. It is worthnoting that Whitcomb’s (2004) paper on FCL in the English language artsprovides explicit support for this notion: Whitcomb’s concluding section,‘tinkering with participant structures’, shows that teachers managed tomake progress by adapting the techniques of FCL to the local context.

The only friendly amendment I would make to Sherin et al.’s commentsis to substitute the words ‘for a given topic or unit’ for ‘for a given domain’in the quotation above. As I have stressed, some topics or units in almost anyintellectual domain will be suitable for jigsawing; and many will not. It just

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doesn’t make sense to demand the same participation structure for alltopics.

What is domain-specific and what is not?

The concept of domain-specificity was a core assumption built into thisstudy. By examining attempts to develop FCL units in four different contentareas, the researchers could look for both commonalities and differences.What they found is a mixed bag.

This is, I think, what should be expected. On the one hand, it is clearthat there are fundamental differences in content, processes, and epistemol-ogy between different fields. In consequence there will be differences inpedagogical goals, pedagogy, and the knowledge that underlies it (includingpedagogical content knowledge).

For example, let me contrast two quantitative domains, mathematicsand physics. I am a mathematician by training, and not a physicist. This isnot because both disciplines were equally accessible to me and I chose one.It is because I had an affinity for the modes of thinking prevalent inmathematics. (In fact, much of the way physicists think was mysterious tome.) When I began exploring mathematical problem-solving, I foundfundamental differences between the organization of mathematics andphysics at the content level. In a sense, the principles of physics drive theorganization of content. Within content domains (e.g. kinematics orelectricity and magnetism) physics is taught according to principles, and theproblem-solving in each domain is largely aligned with the application of therelevant principles. In mathematics, life isn’t so simple. Content is arrangedaccording to subject-matter domains (algebra, geometry, probability,calculus, etc.). However, problem-solving strategies (for example, draw adiagram; consider easier related problems; prove uniqueness arguments bycontradiction) typically cut across content areas and are almost neverderived from principles. And, of course, the pedagogical content knowledgeof these two subject-matter domains differs as well. There is plenty of reasonto think that some effective practices for teaching mathematics might bemuch less effective for teaching physics, and vice versa. And that’s justmathematics and physics. Along some dimensions, at least, one mightexpect differences at least as large as these when one throws social studies,English language arts, and the life sciences into the mix. In short, disciplinesmatter! This was made clear when Debbie, confronting the restructuring ofher lesson, said ‘I’m not a history teacher’ (Whitcomb 2004).

On the other hand, there are ways in which the differences betweendisciplines matter less than one might think. For the past decade myresearch group (the ‘Teacher Model Group’ at Berkeley) and I have beenworking on the construction of a theory and an associated analytic model ofthe teaching process (Schoenfeld 1998, 2002). The goal of the model is tobe able to explain how and why teachers make ‘on-line’ decisions as theyteach. The fundamental idea behind the model is that a teacher’s choices aregrounded in the teacher’s knowledge (of the students, of the subject matter,etc.), goals (short- and long-term, content and social), and beliefs (about the

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domain, about learning, about teaching, about the students). The workinghypothesis is that if one has compiled enough information about a teacher—what the teacher’s goals and priorities are, what the teacher knows, and whatthe teacher believes—then one ought to be able to model the teacher’sdecision-making. The model is constructed in a principled rather than adhoc way: the same ‘architecture’ (the way in which knowledge, goals, andbeliefs interact) should, in principle, enable one to model teachers who havevery different knowledge and styles.

The empirical programme for testing the theory included systematicchoices of teaching that varied along specific dimensions: for example, theteacher’s experience, the nature of the lessons (e.g. traditional or reform),and the nature of the classroom community (teacher-directed, teacher-shaped, co-constructed). The first case, on which we cut our analytic teeth,was of a traditional high school mathematics lesson taught by a beginningteacher. The second was of a non-traditional physics/mathematics lessonwith explicit social and epistemological goals, taught by an experiencedinnovator. Modelling it turned out to be straightforward. The third case wasa third-grade lesson taught by Deborah Ball (Ball and Lampert 1999).Modelling that lesson turned out to be an extraordinary challenge, for anumber of reasons. The agenda didn’t go in the directions the teacher hadplanned; much of what took place was shaped by student contributions; thestudents were much younger and the classroom community radicallydifferent than in the other cases; and a good part of the conversation wasabout reflecting on what the students knew and had learned, so that theepistemological grounding for the lesson differed from the others. We tookon the challenge of modelling this lesson because of its complexity andinterest, and because it stretched our analyses in multiple ways: if we failedto model it, it would point to the boundaries of our theory and models; if wesucceeded, it would document their scope. A year into our third analysis,when we published a paper (Schoenfeld 1998) describing the first twoanalyses (which, as the theory dictates, used the same architecture formodelling instruction), we noted that we were having difficulty with thethird. In response to this article, some colleagues (see, e.g., Borko andPeressini 1998, Leinhardt 1998) claimed that we were doomed to fail onepistemological grounds. They argued that the kind of analytic model weproposed was indeed suitable for modelling highly-structured interactions instructured analytic domains such as high school or university mathematicsor physics, but that modelling significantly different kinds of classroomdiscourse or subject matter would turn out to be beyond the scope of themodel.

That turned out not to be the case. Ultimately, we managed not only tomodel the third piece of instruction, but discovered that, at a particularstructural level, it had significant commonalities with one of the otherlessons. The teacher in the high school physics lesson, which focused onunderstanding classroom-gathered data, and the teacher of the elementarylesson, which focused on reflecting on how and what the student knew, usedthe same kind of iterative routine for soliciting student comments andframing classroom discourse around them. In short, the lessons werefundamentally different in some ways and fundamentally similar in others.

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The same can be said of problem-solving. I have already noted thatproblem-solving in mathematics and physics can be very different because ofthe nature of the domains. Yet, I will argue that there are powerfulsimilarities in not only mathematics and physics, but in any problem-solvingdomains—among which I include social studies and English language arts.For some years, my analytic work focused on what it means to thinkmathematically. The argument made in Mathematical Problem Solving (1985)is that to understand someone’s success or failure in a mathematicalproblem-solving context, one has to examine the following aspects of theindividual’s understanding:

� knowledge� problem-solving strategies� metacognition� beliefs

The claim was that failure to attend to any one of these might cause one tomiss the cause of success or failure—that is, there might be a problem in theknowledge base; the individual might or might not have access to relevantproblem-solving strategies; he or she might make efficient use of resourcesor squander them; he or she might have a set of beliefs (or practices) thateither provided or precluded access to useful information. In MathematicalProblem Solving the details of the argument were worked out in mathematics.Needless to say, the way they play out in mathematics is very mathematics-specific. The knowledge base is mathematical, and strategies are largelymathematics-specific. An exception, metacognitive issues are relativelycontent-independent. But then, beliefs are developed through experience,and mathematical beliefs are developed through one’s experience withmathematics. Hence Mathematical Problem Solving is very mathematics-specific. But the framework described in the book is not.

Consider writing, for example. There is a knowledge base for writing,which includes tacit and explicit knowledge of grammar. There are strategiesfor writing, e.g. ‘free writing’, outlining, the use of topic sentences, etc.Metacognition is a big issue: ineffective writers lose track of their audience,their line of thought, etc. And beliefs play a major role: one will approach thetask of writing a paper very differently if one believes that ‘writing is puttingdown what’s in your head’ or ‘writing is an arduous process of organizing andreorganizing what you know until it is expressed in a way that makes sense tothe target audience’. In short, the details of problem-solving in mathematicsand writing appear totally different, but the framework for examining successor lack thereof in the two domains is the same. The same can be said of history:Wineburg (1991a, b) has made the case that the details of historical analysesare specific to the paradigms of sense-making in history, but the dimensions ofsense-making in history are very much like those bulleted above.

To make matters even more complex, I should note that there may benearly as much within-discipline variation in some disciplines as there isacross some disciplines. For example, the original FCL work was done inthe life sciences, which makes good sense: systems which operate at multiplelevels offer significant potential for jigsawing. But what about work inmicrogenetics, or recombinant DNA? Is that kind of work similarly

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decomposable? In mathematics, some topics are not, at least not easily. Yetone of the main themes in mathematics (and one of NCTM’s five processstandards) is ‘connections’. This is based on the idea that there are oftendifferent mathematical ways of looking at the same phenomenon, and thatconnecting them is a powerful idea. The idea of multiple mathematicalperspectives or representations seems eminently jigsawable. Within physics,some arenas may be easily decomposable (if you know enough) and othernot. And so on.

Now, where does this leave us with regard to FCL? It seems to me thatthere is a unifying theme, and that is the theme of sense-making. Perhaps themost powerful thing that disciplines have to offer is that they providefundamental ways of viewing the world; of enriching our understandings.Mathematics has some particular ways of doing this; social studies(including constituent disciplines of history, anthropology, sociology, etc.)has others; the sciences in general and the life sciences in particular haveothers; and English language arts more still. From my perspective, the mostpowerful reason for studying any of these fields is to develop the set ofunderstandings—knowledge, methods, and perspective—that give one agreater capacity for experiencing and making sense of things one encoun-ters. For me, that’s the big big idea; there are many more bite-size big ideaswithin and across disciplines. The question with regard to instruction is howto have students engage with the content so that they develop under-standings of those big ideas. As discussed above, some big ideas in almostany domain are likely to be jigsawable. To the degree that jigsawing promotesstudent engagement with and understanding of those ideas, it seems a greattool to use. For any big idea, the real question is, what kind(s) of classroominteractions will foster engagement with and understanding? It seems clearthat the notion of ‘community of learners’ is essential. To function as realcommunity, the people involved must develop powerful modes of inter-action over matters of substance. Indeed, this is, in essence, the top-leveldescription that Brown and Campione (1996: 293) give for ‘the basicsystem’ underlying a community of learners (see figure 1).

It stands to reason that there are lots of ways to implement this generalkind of structure—indeed, many of the most influential reform designexperiments implement it in some way or other. Needless to say, the devil isin the details. What I am suggesting here is that there are multiple ways ofengaging in research and sharing information over consequential tasks, andthat no one participant structure will be the optimal (or even a good) choicefor all consequential tasks. The task of the implementation and design teamis to match the match the participation structures with the tasks. If thissuggestion moves us from FCL in particular to reform at large, so be it.

Building capacity for reform given the current context in the USA

In this concluding section I would like to take a step back from theimmediate analysis of the four discipline-specific attempts to teach via FCLdiscussed in this set of papers and place them in the context of current USeducational practices.

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In many ways, the trajectory of FCL exemplifies the trajectory ofeducational innovations (in particular, design experiments) in the USA. Theprocess begins with a small team of innovators developing a pilot project(the ‘alpha’ version). If the project seems promising—that is, it attractsother adherents who can attract funding for the experiment—the next phaseis to move to beta-testing. The project is still close to its originators in termsof inspiration, but the goal is to see if it can live in the hands of others, whoreceive guidance and support. If it does, then the hope is for either larger-scale implementation—possibly through commercial or federal funding if amajor component of the project is materials development, perhaps throughvarious districts picking up on a ‘good thing’ and making it their own.

The four studies described in this set of papers can be seen as beta-testing. FCL had been pioneered by its developers. Now the idea was to seehow it worked in new contexts, still close to the nest. This fits the classicalpattern of US entrepreneurism. The inventor tries to build a bettermousetrap, sees if it works, and then tries to sell it. With all due respect, myview is that that process may work for some mousetraps, but it is close toinsane for potentially large-scale educational innovations.

As suggested in my previous comments, the ‘basic system’ of FCL asdescribed in figure 1 captures the intended substance of many content-richdesign experiments in contemporary education research. Such designs

Figure 1. The ‘basic system’ of a community of learners (from Brown andCampione 1996: 293).

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typically involve identifying big ideas; outlining new curriculum units;designing the units in detail; and teaching the new units. Recall mydiscussion of the specifics of FCL implementation. Identifying big ideas ishard: accomplished researchers (and teams of researchers) often differ aboutwhat is important. Instructional design, especially of non-standard curricu-lum units, is extremely challenging. Carrying out the design to the level ofimplementable curriculum is at best a major time-consuming effort. Andthen, carrying out instruction that fosters the growth of an intellectualcommunity requires a set of pedagogical skills that few possess. In short,every one of the steps described here calls for significant expertise—insubject matter, in design, in teaching. Yet, the ‘mousetrap’ system of fundingalmost guarantees that, even if such expertise is assembled for the alphaversion of implementation, it will not be available for the beta version. Theresult is that the new design-and-implementation teams face monumentalchallenges. Those challenges undoubtedly result in significant professionaldevelopment for the participants, some of which has been documented inthis set of papers. They result in research-related information about ‘whatworks’ and what needs to be changed in the beta versions. But, the need forsimultaneous work on all fronts (big ideas, overall and fine-grained design,and teaching) makes it extremely difficult to make real progress on any ofthose levels—it’s sort of like learning to juggle while learning to ride aunicycle! As a result, the odds of developing materials that will ‘travel’further are decreased.

The difficulties here are systemic, and they point to issues in the USeducational system. One aspect of teaching in the USA is that teachers areoften de-professionalized. After a year of post-baccalaureate training (if theyhave a separate year!) most teachers are certified and then go off to teach inwhat Lortie (1975) calls the ‘egg-crate’ organization of schools—they teachin their own self-contained classrooms and have little opportunity forinteraction with their colleagues. Increasingly, under the assumption thatteachers are not well enough prepared to be given discretion in theclassroom, school districts are adopting highly scripted curricula andteachers are being held accountable for following the scripts. The flipside ofthat coin is that when states or districts revise or update their instructionalframeworks and standards, teachers are often asked to develop newcurriculum units from scratch! There is a serious mismatch between thepreparation teachers are provided with for various aspects of their work andsome of the tasks they are asked to undertake. In some other nations,teachers are treated more like professionals. In Japan, for example, ‘lessonstudy’ provides a mechanism by which, as a defined part of their job,teachers interact with their colleagues over matters of lesson design andstudent learning; as part of the process they observe and discuss each other’slessons (Stigler and Hiebert 1999). Over time, they broaden theirpedagogical content knowledge and deepen their design skills. Even so,Japanese teachers are not expected to design lessons from scratch. Workingin the context of a stable nationally defined curriculum, their job is typicallyto take well-designed lessons and work to make them come alive in theclassroom. On the one hand, this is much more constraining than the UStradition; teachers have less freedom to explore and innovate. On the other

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hand, it is far more professional: teachers have ongoing professionaldevelopment in the context of their work, and are asked to do meaningfultasks that fall within the sphere of what they have been prepared for! In thiscontext, the notion of highly scripted lessons would be an insult.

I do not make these comments to suggest that the USA adopt othernations’ practices, but rather to point out the extraordinary difficulties thatthose who hope to develop educational innovations have to confront. FCLis an exemplar, a powerful innovation that would profit from a richerresearch-and-development context and a set of mechanisms that enabledevelopers to move through beta-testing to more large-scale implementa-tion. In the absence of such mechanisms, progress will be much slower thanit should be.

Acknowledgement

Permission to reprint the figure in this paper has been kindly granted byJoseph C. Campione.

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Documents

Multiple learning communities: students, teachers, instructional designers, and researchers