BOOK OF PROBLEMS

 

 

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INTRODUCTION

 

In re mathematica ars proponendi quaestionem pluris facienda est quam solvendi.

The above motto, on the front page of Georg Cantor's thesis, is cited in Stanislav Ulam's (1991) autobiography "Adventures of a Mathematician." Cantor's affirmation that "in mathematics the art of asking questions is more commonly applied than that of solving problems" is more than a statement of fact. For someone who, like Cantor, the creator of Set Theory and discoverer of transfinite numbers, could look at mathematics as a tremendous accomplishment of the human mind, the same statement also becomes an article of faith. To advance in any science, the most important thing is to be able to ask questions: to ask the right questions and to ask them the right way. In other words, knowing to formulate what one does not know is a fundamental step in the advancement of knowledge.

Despite appearances to the contrary, we still know very little about human learning. Many respected educational researchers will not agree with this statement and claim that, thanks to their work and that of their colleagues, we have a good handle on the issue of learning, particularly, that we are pretty well able to create in a deliberate fashion the conditions necessary for desired learning outcomes. They are right, to an extent, as long as one defines learning as the consequence of instruction; they are entirely wrong if one is willing to look at learning as something more broadly defined. The description below aims at providing further insight into the problem and makes suggestions for addressing it through the creation of a Web-based "Book of Problems." It is the text of a proposal for an alternative interactive discussion session at the Annual Meeting of the American Educational Research Association (AERA), to be held in New Orleans, Louisiana, April 1-5, 2002. Unfortunately, though acceptance of the proposal was recommended by all three reviewers (mean overall recommendation rating 4 on a scale of 5), the session could not be accommodated at the AERA meeting in question, due to the exceptionally high number of symposia submitted for 2002.

In view of the high level of support and enthusiasm for the idea from the community of scholars interested in developing it (see below), the Book of Problems initiative remains under active development and alternative ways are being explored for its implementation. Interested scholars and practitioners who believe they can make a significant contribution to the effort are invited to make themselves known by writing to [email protected], specifying the nature of their interest and indicating the kind of contribution they expect to be able to make.

Meanwhile, AERA Division C, Section 5, reviewer comments concerning the proposed session have been added at the bottom of this page, considering that they give an indication of how an initiative of this nature is being received by a body like AERA. They may be seen as a first instance of the dialogue we are trying to create around this issue in addition to actually operationalizing the Book of Problems.

 

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ABSTRACT

THE BOOK OF PROBLEMS (or what we don't know about learning)

 

An Alternative Interactive Discussion Session Proposal for the
Annual Meeting of the American Educational Research Association
New Orleans, April 1-5, 2002
 

Rationale

The problem addressed in the proposed alternative session is our state of knowledge about human learning. The underlying rationale is that we know very little about human learning and that, by clarifying what we do not know, carefully recording and annotating unsolved problems, it should be possible to inspire entirely new areas and new kinds of research into human learning.

The above assertion concerning the state of knowledge about human learning must be qualified with reference to how learning is defined. Most people don't define learning explicitly. However, even if they don't define it explicitly, it can easily be derived from their writings that their implicit definitions of learning are limited to what happens in a purposefully structured learning environment in which desired attitudinal or competence goals are to be achieved along the lines of well-designed processes. Such settings are the ones in which most of the existing research practice is rooted. Basically, therefore, what we learn from educational research is that "well-designed instruction works," each specific study adding to our knowledge of what "well-designed" means and the term "instruction" referring to processes ranging from highly directive ones that make people learn in prescribed ways to the more imaginatively designed environments that allow people to find their own ways to specifically defined learning goals. There is very little research about learning that takes place beyond the instructional context, such as incidental learning, or about how attention to the conditions of learning in multiple settings (instructional as well as non-instructional ones) may mutually reinforce the depth of our learning. We avoid messy situations.

The past decade has seen an emerging interest in broadening the way we look at learning to beyond the instructional context per se. According to De Vaney and Butler (1996), past definitions of learning have long remained under the spell of Hilgard's (1948) definition, which states that "learning is the process by which activity originates or is changed through training procedures…as distinguished from changes by factors not attributable to training" (p. 4). Only quite recently, this close linkage between instruction and learning has started to disappear. Driscoll (2000), for instance, analyzes the definitional assumptions shared by current learning theories. She notes that, in order "to be considered learning, a change in performance or performance potential must come about as a result of the learner's experience and interaction with the world" (p. 11; emphasis added). Tessmer and Richey (1997) argue for broadening the instructional design concerns to beyond the instructional context as such and to recognize "context" as an important factor in the design of instruction. Shotter (e.g. 1997) emphasizes the dialogic nature of learning, as do Savery and Duffy (1995) with particular reference to constructivist learning environments. John-Steiner (2000) elevates the idea of dialogue to the level of creative collaboration. Visser (2001), building on these different definitional developments, while attempting to bring the various pieces together, proposes a definition that looks at learning as a "disposition to dialogue" rather than as the collection of mental processes that result from such a disposition; that furthermore recognizes the ecological integration of diverse levels of organizational complexity at which the dialogue takes place, involving, in addition to individuals, social entities of varying size; and that finally sees as the purpose of the dialogue our ability to "interact constructively with change," rather than the mere acquisition of particular behaviors necessary for such interaction.

Looking at human learning from the perspective of these emerging definitional assumptions gives a clear sense of how much more complex the world of learning is than we ever thought. Consequently, it also heightens our awareness of how little we actually know about that complex phenomenon. Confronted by this enhanced awareness of the limitations of our knowledge, it is worth looking back at the history of science and ask ourselves if anything can be learned from the ways in which human knowledge developed, going from crisis to crisis.

Progress in several fields of intellectual endeavor has greatly benefited from open dialogue among scientists who were concerned with what they did not know, rather than with what they already knew. A clear example can be found in the history of how our understanding of the fundamental structure of matter and energy advanced throughout the twentieth century, particularly during the first half of it, thanks to the willingness and audacity of the scientists involved to keep challenging each other at the frontier of what was known, i.e. looking out over the vast unknown (e.g. Pais, 1991).

Another interesting example, which inspires the current proposal, can be drawn from the history of mathematics in the first half of the 20th century. The Polish school of mathematicians, who used to gather in the cafés and tearooms in such places as Lwów, developed a book in which they inscribed - and annotated - the great unsolved problems of their discipline. The book was kept in the Scottish Café in Lwów (whence its name: The Scottish Book) and handed by a waiter to the mathematicians in attendance when they so wanted. Miraculously, this fascinating notebook, the collaborative conscience of the mathematicians of the time regarding what they did not know, escaped the devastation of World War II and its aftermath and eventually got published. While it was kept, it used to help challenge those who wanted to be challenged to try and solve these problems. (The story of the Scottish Book can be found in Ulam [1991]. The print edition of the Book is hard to come by. A version of it, which was edited and translated by Ulam, was published in 1957 in Los Alamos, NM, by the Los Alamos Scientific Laboratory. An excerpt of the Book can be found at http://www.icm.edu.pl/home/delta/delta2/dlt0209.html.)

It is contended that in the science of learning we have reached a breakthrough stage that calls for a similar honest reflection among scientists on what they do not know as a means to move forward. Consequently, it is appropriate for those scientists who have an interest in broadening and deepening the meaning of learning to do what the earlier referred Polish mathematicians did: keep a book of what they don't yet know - not the nitty-gritty of it, but the really important problems - and use it as an inspiration for them and others to advance. While it would be attractive to use coffee and tea houses as gathering places for the discussion of such matters, it is now more appropriate to make this a Web-enabled effort as far as recording and annotating of the problems is concerned. The actual gatherings that contribute to filling the book progressively may well be linked to events such as the annual meetings of AERA where many of them come together anyway in a more or less frequent fashion. Such gatherings can be complemented by various modes of electronic interaction in between of face-to-face events. The current proposal thus aims at starting the effort off on the occasion of the AERA 2002 Annual Meeting. The overall theme of that meeting, "Validity and Value in Educational Research," provides a most appropriate framework for the launch of a Web-based "Book of Problems," focusing on what we do not know about learning.

Nature of the proposed session

The proposed alternative session will bring together selectively invited prominent researchers to discuss ways of broadening research agendas in the area of research on human learning. In addition to the scientists invited prior to the meeting, the session will be open to attendees of the AERA 2002 Annual Meeting who, based on the program information, decide to attend. There will be no paper presentations. Rather, in the running up to the session, a concept paper will be prepared by the chair and circulated among the group of seven additional scientists mentioned in the section on "Panelists" with the aim of enhancing the document. The enhanced version of the concept paper will be distributed to other selectively invited colleagues who will be asked to attend the proposed session and to partake in its preparation and follow-up. The concept paper will also be given to conference attendees who decide to join the session at their own initiative. They will have equal status in the discussion with those researchers who have been previously invited. In addition, the concept paper will be made available via the World Wide Web.

Purpose of the session

The session, both through the process of its preparation and implementation, has the following objectives:

Panelists

As will be clear from the above description, none of the alternative session formats listed for the AERA 2002 Annual Meeting matches exactly the needs of the above-referred discussion. However, that of the "Panel Discussion" comes closest, followed by the formats of "Interactive Symposium" and "Symposium." To comply with the given session formats, the chief actors in the proposed session are referred to here as chair/organizer and panelists.

Chair/organizer of the session is Jan Visser, President, Learning Development Institute (LDI) and Principal Investigator of LDI's Meaning of Learning (MOL) project. For the purpose of organizing the session and its follow-up, he will be assisted by Yusra Laila Visser, Researcher at Florida State University and co-investigator of LDI's MOL project.

The following scientists, listed alphabetically, have agreed to join the panel: Carl Bereiter (University of Toronto), Marcy Driscoll (Florida State University), Vera John-Steiner (University of New Mexico), David Jonassen (University of Missouri), Rita Richey (Wayne State University), Gavriel Salomon (University of Haifa), and Marlene Scardamalia (University of Toronto).

Session procedures

As mentioned, there will be no paper presentations during the proposed session. An expectedly large proportion of the participants will come well prepared for the debate. They include researchers identified by the organizers and the team of, currently seven, scientists who have already joined the initiative. In addition, other interested researchers will themselves take the initiative to contact the organizers ([email protected]) on the basis of information available in the program of the AERA 2002 Annual Meeting or on the Web site of the Learning Development Institute. Participants who "discover" the session only while in New Orleans will be somewhat less prepared, but everything possible will be done to make their participation as effective as possible for the stated purposes of the session and as beneficial as possible for themselves. This may require a very brief summary of issues at the outset of the session.

The value of the session lies in the energetic participation of all its participants in the debate. The chair will apply his considerable experience in conducting such sessions in ways that create maximum involvement of the participants. Depending on the size of the audience, part of the debate during the proposed two-hour session may be conducted in small groups so as to raise the level of creative engagement. In line with the set purpose for panel discussions, emphasis will be on the ad hoc interchange, recognizing the value of both divergence and convergence of positions in clarifying the issues concerned. To allow this ad hoc interchange to develop effectively, a fair level of improvisation will characterize the procedures of this session.

Long-term issue

It is expected that the community of scientists whose establishment is aimed at through the proposed session, while begun in the AERA context, will grow beyond that same context. The science of learning is a truly transdisciplinary field. The Learning Development Institute (http://www.learndev.org) and its partner, the International Center for Transdisciplinary Studies and Research (CIRET; http://perso.club-internet.fr/nicol/ciret/) will work together to achieve that aim.

Division/Section/SIG sponsorship

The broadness of theme of the discussion makes it difficult to place it within the purview of a particular division/section or SIG. Division C as a whole is the one whose overall interest is most comprehensively related to the area covered by the proposed session. However, sections of other divisions and particularly a number of SIGs may also have a keen interest in it. The proposal is submitted, in accordance with set procedures, to one section (Section 5) of Division C only. It is proposed, though, that sponsorship by the Division as a whole be considered and that co-sponsorship by sections of other divisions and SIGs be sought as appropriate.

References

De Vaney, A. & Butler, R. P. (1996). Voices of the founders: Early discourses in educational technology. In D. H. Jonassen (Ed.), Handbook of research for educational communications and technology. New York, NY: Simon and Schuster Macmillan (pp3-45).

Driscoll, M. P. (2000). Psychology of learning for instruction. Needham Heights, MA: Allyn & Bacon.

Hilgard, E. R. (1948). Unconscious processes and man's rationality. Urbana, IL (as quoted in De Vaney & Butler, 1996).

John-Steiner, V. (2000). Creative collaboration. Oxford, UK: Oxford University Press.

Pais, A. (1991). Niels Bohr's times: in physics, philosophy, and polity. New York, NY: Oxford University Press.

Savery, J. R., and Duffy, T. M. (1995). Problem based learning: An instructional model and its constructivist framework. Educational Technology, 35(5), 31-38.

Shotter, J. (1997). The social construction of our 'inner' lives. Journal of Constructivist Psychology, 10, 7-24.

Tessmer, M. & Richey, R. C. (1997). The role of context in learning and instructional design. Educational Technology Research and Development 45(2), 85-115.

Ulam, S. M. (1991). Adventures of a mathematician. Berkeley, CA: University of California Press.

Visser (2001). Integrity, completeness and comprehensiveness of the learning environment: Meeting the basic learning needs of all throughout life. In D. N. Aspin, J. D. Chapman, M. J. Hatton and Y. Sawano (Eds), International Handbook of Lifelong Learning. Dordrecht, The Netherlands: Kluwer Academic Publishers.

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THE "BOOK OF PROBLEMS" COMMUNITY OF SCHOLARS

The initiative to create the Book of Problems originates from:

The names of the following scholars were included in the above session proposal to AERA:

The following scholars have added their name to the initiative at a later stage:

 

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AERA Division C, Section 5, reviewer comments

From: [email protected] [mailto:[email protected]]
Sent: Friday, October 26, 2001 1:06 PM
To: [email protected]
Cc: [email protected]
Subject: AERA: Division C:Section5: Cognitive, Social, and Motivational processes: Proposal # 5191

===================================================
Username: jvisser
Proposal #: 5191
Title: The Book of Problems (or what we don't know about learning)
===================================================

Dear Dr.Jan Visser:

It is with sincere regrets that I must inform you that your submission to the Division C:Section5: Cognitive, Social, and Motivational processes (above title) was not accepted for the (sic). We typically have a 50% acceptance rate and we again had a large number of exceptionally high quality submissions this year competing for 10% fewer program slots than we had last year. Therefore some paper and symposia that might have been accepted in prior years did not make it into the program this year. I encourage you to seek outlets for the work you submitted and cintinue to submit to Division C:Section5: Cognitive, Social, and Motivational processes in the future.The rating sheets from the reviewers who reviewed your submission are enclosed for your information. I hope you will find the comments helpful.

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Reviewer Comments:

Reviewer 1
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Choice of problem/topic4
Theoretical Framework4
Methods
Data source(s)
Conclusions/Interpretations4
Quality of writing/organization4
Contribution to field4
Membership appeal5
Would you attend this session4
Overall Recommendation4
Comments While I take issue with the proposer's premise that educational researchers avoid "messy situations" in their attempts to understand human learning and development, and while I would not equate incidental learning with controlled or "neat" experimentation, the premises do serve as interesting points for debate and dialogue. Certainly, the strongest selling point here is the list of players, whose insights and perspectives on human learning and development would be worth hearing for many people. Therefore, I would recommend alloting space to this particular session.

Reviewer 2
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Choice of problem/topic4
Theoretical Framework5
Methods
Data source(s)
Conclusions/Interpretations
Quality of writing/organization5
Contribution to field5
Membership appeal4
Would you attend this session5
Overall Recommendation5
Comments Definitely accept this. This presents a new idea on how to establish working learning communities and promotes scholarly endeavors to the highest level. This is the type of thing a graduate student just preparing to enter the world of academia needs to see. This shows what true scholarly discourse looks like and illustrates the far reaching benefits of the activity. Audience appeal may not be as high as one would hope because I think many people want a take home intellectual product that they can look to for inspiration, ideas, etc. in their own research. That purpose may be seen as more difficult in this new arena.

Reviewer 3
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Choice of problem/topic3
Theoretical Framework3
Methods
Data source(s)
Conclusions/Interpretations3
Quality of writing/organization3
Contribution to field2
Membership appeal2
Would you attend this session3
Overall Recommendation3
Comments This proposal is a little indefinite. I find it difficult to see where it goes beyond what we already know. Although some sources are cited for supporting the discussion, Hilgard is suggested as the primary past influence, with the more recent notions represented by Driscoll. This is debatable. One should not neglect any of the more recent contributors within the realm of "cognitive psychology" or of those who advocate a constructivist approach. One who has made a major impact on this field and who has been neglected is Donald Norman, whose work is NOT based on the earlier definitions. Further, I see no effort in this paper -- even though it is within the instructional technology area -- to employ empirical support for the issues addressed. In a sense, it appears to be an attempt to build a "straw person" and then to demolish it. However, I have great respect for the potential contributors and therefore find it possible to recommend it for the program, even though not wholeheartedly.
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Sincerely,
Dr. Eric M Anderman
[email protected]


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