Shelley Goldman
email: sgoldman@stanford.edu

Roy Pea
email: roypea@stanford.edu

Heidy Maldonado
email: heidym@cs.stanford.edu

Emerging Social Engineering in the Wireless Classroom

Keywords: wireless handhelds, collaborative learning, algebra, multiple linked representations, teacher support

It! fosters mathematics learning environments where pre-algebra students use handheld technologies to confidently and enjoyably explore and learn about functions. The resources we developed-server-based and handheld software and paper-based student and teacher texts-were packaged as a 20-session unit on code making and breaking and designed to boost students' understanding of mathematical functions and their facility with the multiple representations of tables, graphs and symbols. We field tested the wireless system with two teachers and 120 middle school students during a five week summer school, and conducted studies on the features and function of the technology as a learning and teaching resource. We report on project development and research, focusing on what we learned about the strengths and difficulties of wireless handheld technology in the mathematic classroom, and the emerging social engineering that helped students overcome the technological constraints.

Introduction: Addressing a Need

Global concern to raise lukewarm achievement results on standardized tests and international comparisons across schools, particularly within math and science realms increases the demands upon unprepared and already overburdened teachers. The Code It! Materials --technology and real world based --were designed to address this challenge, capitalizing on developing technology for stimulating high performance while providing a satisfying, successful learning experience on the topic of functions. Code It! features multiple representations of functions to aid learners' development of rigorous algebra skills and is inspired by the curriculum unit, Codes, Inc, developed by the Middle-school Mathematics through Applications Project (MMAP), which teachers found helpful for transitioning to the use of technology and more applications-based curriculum materials [START_REF] Lichtenstein | Final Evaluation Report: Middle-school Mathematics through Applications Project[END_REF].

Technology should be providing tools to support the activities of mathematics classrooms. Data gathering, pattern finding, spatial thinking, working and linking multiple representations, are all possible with computers, yet many problems have accompanied classroom computer use. Even when researchers developed compelling exemplars (Institute for Research on Learning, 1998;[START_REF] Roschelle | Changing how and what children learn in school with collaborative cognitive technologies[END_REF], changes in organizational, social, and pedagogical practices with computers produced high hurdles [START_REF] Goldman | Technology in the Mathematics Classroom: Guidelines from the Field[END_REF]Means, 2001). Recently, the combination of increased access, increasing teacher knowledge, decreasing technology costs, and new portable devices is creating a synergy for new possibilities. With a price tag lower than even the graphing calculators math classes require, greater portability than the slimmest laptops due to their low weight and wireless networking, and computing power comparable to a 1995 desktop or 1997 laptop(1), handhelds thrive across school campuses, often integrated with cellular phones, and with many of the same common productivity applications that appear on desktops. Early studies of handheld technology use are modest yet suggestive of how they might best be applied [START_REF] Soloway | Science in the palm of their hands[END_REF]Curtis, 2002;Luchini, 2002;[START_REF] Vahey | Palm Education Pioneers Program: Final Evaluation Report[END_REF][START_REF] Roschelle | To unlock the learning value of wireless mobile devices, understand coupling[END_REF]Tatar, in press), and the handhelds' beaming ability lets users exchange information easily by direct communication through infrared beaming, and has been used to control audiovisual equipment in the classroom, to share applications, text messages, audio clips, contact information, drawings, and data [START_REF] Batista | Debating the merits of palms in class[END_REF][START_REF] Pownell | Getting a handle on handhelds[END_REF] through a simple physical gesture, even without typing or selecting the receiver's username or identifier.

The combination of versatile modular hardware, integrated with many of the applications of task-specific devices (such as graphing calculators), and full-blown computers (including participatory simulation software, email readers, web browsers, compatible or reduced versions of Microsoft's productivity applications), plus their calendar and organizational functions, make these devices particularly appealing and many thousands of classrooms across the United States are acquiring them. Because of their cost and capabilities, handhelds are perceived as holding the potential for democratizing access to the technology for all students, and of allowing educational researchers unprecedented access to students' records and interactions: from studying social networks at school through the students' beaming logs, to comparisons between the intended curriculum, the taught curriculum, and the learned curriculum, and analysis of the effectiveness of "probeware" applications (where students record real-world data on their handhelds through physical probes for later analysis) and participatory simulations in the classrooms. Instead of four or more students sharing a desktop machine, students can collaborate by fluidly sharing information across devices, or even comparing results by looking at each other's screens.

These are promising trends, and to tap the potential in Code It! we developed representations that can be easily manipulated in an engaging collaborative learning context for deepening understanding of algebraic formalisms (ITEA, 2000;PCAST 1997).

The Setting and Approach

Our research questions are aimed at uncovering the strategies that teachers use to orchestrate the use of handhelds, and identifying the obstacles and affordances they interact with in using Code It! materials and technologies. We partnered with the Stanford Teacher Education Program and the Santa Clara, CA Schools to use Code It! with all of the district middle school students in their summer school program for our 20-session field test with two teachers over a five-week period. Each teacher had 60 students split between two consecutive 100 minute class sessions: one teacher used handheld iPaq computers (PDAs); the other teacher used Compaq Tablet PCs. Approximately 40% of each 110 minute class period was dedicated to encoding and decoding activities with the Code It! materials, with the students separated into four-person groups that remained relatively stable throughout the intervention. The classroom activities and software implemented remained the same throughout both hardware platforms: our present analysis concentrates on only the two PDA classrooms.

We collected several data streams, including observational data, videotapes of teachers and the fourmember student groups used in the classrooms, problem-solving and informational interviews with student dyads, and pre-and post-testing of mathematics knowledge. These methods, of observing and videotaping classroom field tests of materials and feeding back results into the design, enable the development team to define areas for revision based on the use of the materials under real classroom conditions [START_REF] Brown | Design Experiments: Theoretical and Methodological Challenges in Creating Complex Interventions in Classroom Settings[END_REF][START_REF] Cobb | Design Experiments in Educational Research[END_REF]DBRC, 2003). The cycle of development and field test supports our learning about how teachers and students appropriate these materials and how best to iteratively improve the design for achieving the intended teaching and learning goals (and new ones that might emerge).

The project was structured around three strands of activity: materials development, supporting the teachers, and field test research in the classroom. As we address each strand below we emphasize the lessons learned on how social engineering -a term that is often misused in both meaning and purpose by the hacker community -can overcome technological constraints and lead to learning gains for students.

Materials development

We created a technology-integrated 20-session curriculum unit on introduction to functions, with a code making and breaking theme. The unit was developed to bring alive in classroom activity the functionality of the Code It! application with pre-algebra content. The unit places algebra learning in a real-world context-making and breaking secret codes [START_REF] Singh | The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography[END_REF]. Students can challenge others to break their codes to determine message content. The materials are structured so that students must examine properties of functions in general, learn to distinguish among "families" of functions (e.g., linear vs. quadratic) as well as learn properties of each family (such as effects of changes in constants to graph). Connections among symbols, tables and graphs are emphasized in both the software and text materials.

Exploiting the handhelds' wireless connectivity, students can create and exchange codes easily, and records of these transactions can be captured on the server for future analysis, so that the PDA display for any student at any particular time can be recreated. The server also acts as a repository for text and codes created by the teacher and students, providing an easy way to share codes among groups and to distribute practice problems. It is this promise of engaging technology that promotes increased interactions with mathematics and embedded assessment activities that we hope to promote. Code It! software is built to exploit an in-room wireless network allowing students to work on codes together in groups and to share codes between groups. Each PDA is connected wirelessly to a teacher's workstation. The teacher's station, shown in Figure 3, runs administrative software so that the teacher can control and monitor which students are logged into the server, assign them to groups, create and distribute practice problems, and open an observer window to display any group's current state. The observer window is particularly important for teachers because the small display size of the handhelds makes it more difficult to monitor group work in the traditional "over the shoulder" manner. In addition, the server logs each group's activity, allowing a researcher or teacher to reconstruct the precise ways in which students were using the software and solving the math problems. Each student PDA runs Code It! software for creating plaintext, for making and breaking codes, and for uploading and downloading text and codes from the server. Code It! software is written in Java to allow for portability across platforms and for wireless communication. When making or breaking codes, the student's screen displays the encoding function (or current guess) and the graphs and tables that represent the function and the coded text, as Figure 2 illustrates. These representations include the function's expression itself, a graph of the function, a function table, and word and letter frequency tables. Students change the values of the function's coefficient, exponent, constant, and offset by clicking with the handheld's stylus on the small arrows that appear immediately below (to decrease) and above (to increase) each of these terms on the expression. These representations were selected to encourage students' fluency with multiple representations of functions, a central element of secondary math curriculum (NCTM 1989(NCTM , 2000)), as well as to foster collaboration within the student groups, rather than to create an ideal coding tool. Any change made by one student immediately propagates to the other students in his or her group through their server linkage, so the PDAs within a group always display the same function and text. As we discuss in the next section, to foster communication among group members and increase the diversity of information available to the group for the coding or decoding task, students were encouraged through assigned group roles that rotated across days, so that all students took on all roles, to focus on a different representation per teammate. When a group has successfully created or broken a code, they receive a congratulatory message from the teacher's station, which also records their problem and solution with the corresponding time-stamp.

Importance of teaching to Code It! success

The teaching component turned out to be as important as the materials and software in ensuring that students get a well structured, engaging and deep mathematical learning experience through Code It! Professional development included three days of training and planning with the teacher partners as well as just in time, in-class support. The workshop included an introduction to the technology and software, as well as discussion and revisions of the curriculum unit and activities. Just-in-time daily consultations ranged from strategic advice on classroom management techniques, to math and technology specific problem solving while implementing the unit, often as a result of the teachers' lack of prior experience with the devices. Teachers were central to the curriculum's success in the classroom. They innovated by creating tasks, activities, and explanations, and by setting into motion social rules for encouraging appropriate forms of mathematical discourse and technology use.

Turning the attentions of students in the Code It! classroom to the mathematics took a great deal of social engineering on the part of the teachers and the development team. The team had to mitigate the effects of the widely heterogeneous groups -in terms of previous mathematics knowledge, English language dominion, socio-economical levels, race, gender, and age -and the constraints of the technology. During the teacher preparation workshop, we decided to introduce rotating social roles within the groups to ensure that all students had a chance to work with each tool and representations during the problem solving process. However, once students learned to code and decode using the PDAs, they forged ahead without clear group structures, leading to heated discussions within the group on recording and changing privileges. We worked with the teaching staff to design social roles that would foster group collaboration, rather than competition.

Linking the process roles of (1) recorder, (2) presenter, (3) publisher and (4) equipment manager to the different code representations in the software, and rotating these roles daily, had several positive effects in addition to resolving much of the inter-group conflict. Role based pedagogy and "group-worthy" tasks have been shown to serve as powerful supports for heterogeneous grouped students [START_REF] Cohen | Working for equality in heterogeneous classrooms: Sociological theory in practice[END_REF], and with Code It! they contributed to increased engagement for more students in code analysis and breaking activities, provided a vehicle for teachers to engage students in content-based conversations, and overcame some of the technological constraints that are discussed in detail below. The student in charge of taking notes (the recorder) one day would also be responsible for monitoring the function graph as the student publisher altered the coefficient, exponent and constant of the function, while the equipment manager and presenter monitored the frequency and function tables, respectively. The next day, roles would rotate so that all students gained experience at interpreting and communicating key indicators for each representation that signaled a closer match between the encoding and decoding functions.

In addition to group roles, another rule was introduced stating that: "all students in a group must be able to explain the strategies and routes to solutions in order to receive credit," which lead to increased team cooperation in heterogeneous groups. Enforcement of these rules, both during in-class presentations and during mathematical activities, often involved the teacher and student teacher querying any student from the group about their strategy and solution, and was facilitated by wall posters reminding students of the rules and rotating assignments. After instituting these social rules new patterns emerged, and we observed multiple instances of the students who took problem-solving approaches talking with those who usually guessed or seemed uninvolved. In addition to this knowledge sharing we recorded an increase in consistency of students' performance over time. This teacher-led social engineering improved group relations and engaged students more deeply with the software and the mathematics under study.

Teachers appropriated the technology into their teaching practices increasingly throughout the summer, as their familiarity and confidence with the tools increased. They assessed students' work and needs, developed activities and code breaking problems to scaffold students' understanding, bridging the gap between simple and complex code breaking problems in the curriculum. Teachers relied on the server screen to keep track at a distance of which students were on-line and which groups were most active. As Figure 3 illustrates, a circle represented each student in a group, and its color changed when the student connected to the server. Teachers monitored group activity through the observer windows, which presented information in exactly the same way group members viewed it, as if the teacher was another teammate, albeit virtual. These multiple views into the groups' activities enabled the teacher to troubleshoot for students who were having log-on issues, as well as to visit groups that were lagging behind in the decoding problems. Furthermore, both teachers used projection equipment with their PDAs, so that they and their students could discuss with visual aids the various strategies for code breaking, as well as demonstrate how the different Code It! tools could be used. These activities illustrate the robustness of the software package, and how teachers made it compatible with their teaching practices.

Technology design and performance

Constraints imposed by the technology in everyday teaching practice were many and ranged from overload delays during whole class log-on, to the lengthy scrolling screen with multiple representations of data, to the fact that the system could log only group work. Specifically, three features of Code It! were shown to need reworking during the classroom test: (1) how mathematical representations and tools are organized; (2) the choice to base the system on group activities and interaction over individual acts; and, (3) the design and usability of record keeping functions-potentially so promising with wireless technology. Given that our developing time for this first version was only twelve weeks, we are looking forward to correcting these three shortcoming in the next software release, but until then let us consider each of these three issues in greater depth:

The Code It! student PDA screen features a vertically lengthy set of representations for the function under consideration, which students scrolled through to focus on their assigned view, as Figure 2 illustrates. These representations are: the encoded and decoded text, the manipulable mathematical function expression, a graph of the function, a function table, and word and letter frequency tables. The word frequency analysis data representation suffered from the system's delay when handling longer codes than three or four sentences, and until student roles were established, the vertical scrolling layout preferenced the graphical representation over others, since it was directly below the manipulable function. The group process and daily rotation of assigned roles for students, attaching each teammate to one of the representations per day, was a compromise between the constraints of the system and the ways students could best benefit from the representations available. Yet although all students gained experience with each representation and the stylus wars for control of the encoding process were resolved in favor of strict, daily roles, some students became alienated, discouraged, and in some instances bored, particularly if they had a less-than-critical role for the day. Through this field test, we were able to deduce that the multiple representation capabilities of the software are a strength and real resource for mathematical work and learning. A question that now remains for investigation is how structured or unstructured students' access to those representations should be.

As we consider the redesign of the system, not only will interface and display constraints -such as buttonlinked screens instead of a longer scrolling window -have to be addressed, but also the underlying system architecture. Although having a portion of the data displayed for interpretation on each student's PDA made for within group collaborative learning, it meant that on any day a student had the opportunity to relate to only one view of the data, and that Code It! activities outside the group were not enabled. That is, students could not practice encoding and code breaking on their own, nor could they draw parallels between representations by comparing them side-by-side. Excitement for exploration of the software turned to frustration -particularly in the first sessions with Code It! -until all teammates had experienced the different roles and representations. Schools also rely on individual accountability, and the Code It! system was unable to account for individual problem solving activity. This field test has proven that we must also support individual activities within Code It!, and we are exploring potential avenues that would maintain support for collaborative learning.

Our design decision was to bias the function of the system to support groups over individual students, and the architecture of the system made the server act as a gatekeeper, transmitting changes from one PDA to all the others within a team, and recording them for later retracing of strategies. However, after this field test we believe that the server can do much more with this information without waiting until class is over. We observed that student groups quickly developed strategies to break codes, which were shared approximately once a week with the whole classroom. Some of these strategies depended excessively on a simplistic approaches, such as curve-fitting functions through the graph that usually got the students within range of a correct code. Many of the students determined the exponent graphically, and often the lead coefficient as well by adjusting the graph. Others consistently sought out single, two, and three-letter words, as well as mappings for the most common letter in the English language ("e") as a path for breaking codes. We are discussing incorporating a prediction capability to the software, which could alert the teacher or team itself when a group is in danger of depending solely on a particular pattern of code breaking. Moreover, as the students presentations of decoding attempts showed, when faced with reconstructing all steps, students needed access to records of their transactions and solutions shortly, before the end of class.

Findings to Date

Preliminary findings include analysis of pre-and post-tests, and analysis of observations, videotapes, and interviews. We report on progress on math test items, and video analysis that indicates increased sharing of mathematics and use of software representations in the groups. Results of the pre-and post-tests in the PDA class (N=45) with our targeted student groups are very promising. The mean increase from pre-to post tests was eight percentage points, with great variability in whether groups functioned well (a fertile area for subsequent studies, as in [START_REF] Barron | When smart groups fail[END_REF]. In four of six focus groups students made significant gains, in some cases raising their scores by 15-30%. The PDA students showed significant gains on test items relating to evaluating exponents and the graphs of functions. On one graphical item, 44% of students answered correctly on the post-test, as compared to only 13% on the pre-test.

These trends are particularly exciting because these results were for students in grades 6 through 8 who were placed in heterogeneous groups regardless of their previous school math course achievement. Many students in the class had done poorly in sixth or seventh grade math, and were required to attend the summer academy to advance to the next grade, while some students had completed the first year of algebra. The teacher's recommendation and innovative social structures encouraged the more skilled algebra students to help others, and the pre-and post-test results showed that these interactions may have had an impact on achievement. Currently, we are analyzing the activities and progress of four groups of students in the two handheld classrooms, which we captured through 120 hours of classroom interaction video, the server's records, and code-breaking strategy interviews with twelve pairs (N=24) of students in these chosen groups at the conclusion of the program.

Future plans for the project include a significant redesign of the software for version 2, such that no representation is privileged over others, as the graph view was preferred in this version over the function table, letter frequency and word frequency table representation. Depending on the more familiar graph led some observed groups to follow simplistic decoding strategies that comparatively did not improve their dominion of functions as much as their peers', such as predicting the range and domain of the encoding function by methodically changing values in the function until the axis labels came within the range of the traditional alphabet.

We seek to address the ideal balance between scaffolding for collaboration and individual exploration of the encoded functions, within the Code It! software environment, so as to lessen opportunities for disruptive styluswars. Our upcoming iteration will incorporate a flexible grouping mechanism, while maintaining both the appeal of collaboration and software robustness that made this first experience with Code It! successful. We are also considering ways to decouple the individual PDAs from the system. This would allow for students to explore and problem-solve individually as well as in groups, and as well as provide opportunities for "anytime, anywhere computing", home and family connections.

Endnote

(1) The comparison is based on the reported clock speeds of the Toshiba Libretto (70CT : Pentium MMX 120 MHz), a PC laptop introduced in 1997; the Apple Macintosh 7200, a desktop computer introduced in 1995, which could go 120 MHz, and the latest Palm Tungsten T handheld introduced in 2003, which on average can reach 120Mhz as well. Information for this comparison was obtained from: http://www.priceminister.com/offer/buy/1192850/PR030, http://www.applehistory.com/7200.html, http://www.palm.com/products/handhelds/tungsten-t/specs.html, March 2003.

Figure 1 :

 1 Figure 1: Student groups working on Code It!

Figure 2 :

 2 Figure 2: Three Code It! representations on a student's PDA: The expression and graphical screen view of a code solution, the frequency tables' view and the function table's view.

Figure 3 :

 3 Figure 3: Teacher's view on the server, with observing windows for every group in the classroom

Acknowledgments

The WILD Team @ Stanford members contributed to the Code It! work reported herein. Thanks to Toby White, Lee Martin, Sarah Walter, Gloria Miller, Mike Mills, John Murray, from Stanford University, and to Nicolai Scheele and Wolfgang Effelsberg, from University of Mannheim (Germany). Special thanks to our partnering teachers and their students, the Stanford Teacher Education Program and the Stanford student teachers, and the Santa Clara School District. This project was supported by Stanford Center for Innovation in Learning (SCIL) and the Wallenberg Global Learning Network. We hankfully acknowledge an HP mobile wireless computing equipment grant to SCIL.


V Lazarus

F.-G Buchholz
email: fus.buchholz@t-online.de

M Fulland
email: fulland@fam.upb.de

J Wiebesiek

Comparison of predictions by mode II or mode III criteria on crack front twisting in three or four point bending experiments

Keywords: and mathematical subject classification numbers as needed Brittle fracture, mode II, mode III, Maximum tangential stress criterion, 3D crack path, 3D fracture criteria

Comparison of predictions by mode II or mode III criteria on crack front twisting in three or four point bending experiments

Veronique Lazarus, F.

Introduction

In homogeneous isotropic elastic media, except in some special conditions, it is well known that whatever the external loading, the crack front bifurcates in order to reach a situation of pure mode I as the crack propagates [START_REF] Hull | Fractography. Press syndicate of the university of Cambridge[END_REF]. A literature survey of mixed mode crack growth can be found in [START_REF] Qian | Mixed mode fatigue crack growth: a literature survey[END_REF]. Under mode (I+II) conditions, the crack kinks to annihilate mode II, as depicted in figure 5(c). The value of the corresponding kink angle can be obtained, for instance, by the Principle of local Symmetry (PLS) of [START_REF] Goldstein | Brittle fracture of solids with arbitrary cracks[END_REF] or by the maximum tangential stress criterion (MTS) [START_REF] Erdogan | On the crack extension in plates under plane loading and transverse shear[END_REF]. In presence of mode III, to reach a situation of mode I, the crack front twists around the direction of propagation. The way this twisting occurs is case dependant : in some cases, it occurs gradually (fig. 1(a) and 1(c)), in some other cases abruptly (fig. 1(b) and 1(d)); sometimes the whole front twists in one-piece (see fig. 1(a) and 1(b)) and in some other cases, the front twists piecewise leading to a factory roof pattern (see fig. 1(c) and 1(d)). The conditions of transition between these several crack patterns remain an open question. For instance, gradually piecewise rotation has been observed by [START_REF] Sommer | Formation of fracture 'lances' in glass[END_REF], [START_REF] Hourlier | Fissuration par fatigue sous sollicitations polymodales (mode I ondulé + mode III permanent) d'un acier pour rotors 26 NCDV 14[END_REF]; abruptly piecewise rotation by [START_REF] Palaniswamy | Crack extension in brittle solids[END_REF]. In [START_REF] Makabe | The formation mechanism of the factory-roof pattern in a torsional fatigue specimen with circumferential notch[END_REF], depending on the loading conditions, both progressive and abrupt rotation have been observed. Abrupt piecewise twisting at a small length-scale III ϕ m and progressive rotation of the whole crack front at a macroscopic length-scale, has been observed in three or four points bending (3PB or 4PB) experiments. Such experiments and observations have been made by [START_REF] Yates | Crack propagation under mixed mode (I+III) loading[END_REF] on steel specimens in fatigue, by [START_REF] Cooke | Fracture propagation paths under mixed mode loading within rectangular blocks of polymethyl methacrylate[END_REF], [START_REF] Buchholz | 3d fracture analyses and experimental results on three-point bend specimens with slant cracks[END_REF][START_REF] Buchholz | Comparison of computational 3d crack path simulations with experimental findings for 3pb-specimens with inclined crack planes[END_REF]on PMMA blocks in fatigue, by [START_REF] Lazarus | Crack paths under mixed mode (I+III) or (I+II+III) loadings[END_REF], Lazarus et al (2001b) on PMMA specimens under monotonic increasing loading. These patterns can also be recognized on geological materials [START_REF] Pollard | Formation and interpretation of dilatant echelon cracks[END_REF][START_REF] Aydin | Progress in understanding jointing over the past century[END_REF] at different length-scales.

The qualitative way of crack propagation is well explained by its tendency to reach mode I conditions [START_REF] Hull | Tilting cracks: the evolution of fracture surface topology in brittle solids[END_REF][START_REF] Pook | On fatigue crack paths[END_REF]. But it is not sufficient to predict the propagation path quantitatively and a few fracture criteria have been proposed so far. Concerning the abrupt rotation of the crack front, several criteria have been proposed. But the only paper we are aware of, that compares the results with experimental findings is [START_REF] Cooke | Fracture propagation paths under mixed mode loading within rectangular blocks of polymethyl methacrylate[END_REF], who showed that all the criteria overestimate the real value. Lazarus et al (2001b) proposed the following fit:

ψ = 1 4 arctan 2K III (1 -2ν)K I (1)
by interpolation of their experimental data. In the special case of 3 or 4 PB experiments, the gradually rotation of the front, has been predicted, on the one hand, by [START_REF] Gravouil | Non-planar 3d crack growth by the extended finite element and level sets. II. Level set update[END_REF] and [START_REF] Buchholz | Fracture analyses and experimental results of crack growth under general mixed mode loading conditions[END_REF] using MTS-criteria and by [START_REF] Lazarus | Crack paths under mixed mode (I+III) or (I+II+III) loadings[END_REF]Lazarus et al. ( , 2001b) using a criterion predicting the twisting rate of the whole crack front. Whereas the kink angles given by MTS criteria lead to the annihilation of mode II, the twisting rate of [START_REF] Lazarus | Crack paths under mixed mode (I+III) or (I+II+III) loadings[END_REF]Lazarus et al. ( , 2001b) ) leads to the annihilation of mode III. Hence it may be surprising that both criteria manage to find the experimental propagation path. Also the aim of this paper is to discriminate these two kind of criteria by comparing the predictions of the MTS criterion [START_REF] Erdogan | On the crack extension in plates under plane loading and transverse shear[END_REF] or its 3D extension [START_REF] Schollmann | A new criterion for the prediction of crack development in multiaxially loaded structures[END_REF] and those of the criterion proposed by [START_REF] Lazarus | Crack paths under mixed mode (I+III) or (I+II+III) loadings[END_REF]2001b) to 3PB fatigue experiments performed on PMMA. These experiments are presented in section 2. Both modes II and III are present in the experiments. By symmetry, mode II Stress Intensity Factor (SIF) takes opposite signs at each side of the front, hence MTS criterion (or equivalent 3D ones, see section 3.2) predicts an opposite sign of the kink angle. Mode III yields a uniform twisting of the whole front by Lazarus et al. criterion (section 3.3). Hence, at least qualitatively, the same kind of twisting propagation path is expected and the quantitative comparison (section 4) with the experiments shows that both criteria allow to recover quite well the experimental values. Nevertheless, two facts shall limit the extensive use of MTS criterion (or equivalent ones such as PSL or 3D-MTS generalisation) in presence of mode III although MTS criteria seem to be sufficient for any practical engineering purposes. The first fact is that increasing mode III over mode II rate, gives advantage to Lazarus et al. criterion toward the MTS one, and the second that MTS criterion predicts well the kink angle near the free surfaces but too low ones near center of the front. For γ = 90 0 , the initial notch is located in the middle (x, z) plane of the specimen. Due to symmetry reasons, the crack is then loaded in mode I only and crack propagates straight and breaks the specimen in two equivalent pieces. For γ less than 90 0 the initial notch is loaded in both tension and out-of-plane shear, and the crack bifurcates during propagation. Pictures of the propagation path (fig. 3) show that the crack front gradually twists around the direction of propagation to finally reach the middle mode I plane (x, z) of the specimen. Hence, crack propagates to annihilate shear loading. One can notice in figure 3(b), that the rotation becomes more important with decreasing value of γ. By observing progressive crack growth during the experiments, one can also notice that the intersection between the crack surface and a plane (y, z) is always straight. This will be of importance for the geometric description of the crack surface. . Our principal aim in this paper is not to determine the angle ψ locally for positions along the crack front (although it will be needed in one of the crite-ria) but the geometry of the macroscopic smoothly twisting crack extension.

Propagation criteria

Preliminaries

Figure 5(a) schematically shows the whole extension of the crack obtained experimentally, and figures 5(b), 5(c), 5(d) this same extension but restricted to a distance of propagation δ from the initial slit, δ being supposed small enough so that crack extension in each plane x 3 = Cst. coincide with its tangent (fig. 5(c)). Let us denote d the half-length of the initial front, ϕ(x 3 ) the kink angle (rotation angle of the crack extension around Ox 3 ) at the point of coordinate x 3 of the front, ϕ m the kink angle for x 3 = d. The intersection of the crack and a plane x 1 = δ being observed to be a straight line, one easily shows (see figure 5) that ϕ(x 3 ) is of the following form:

ϕ(x 3 ) = arctan x 3 d tan ϕ m . (2)
Since some experimenters give values of the rotation rate dγ/dδ rather than the kink angle, we give also the following relation between ϕ m and dγ/dδ, which can easily be derived from figure 5(d):

dγ dδ = tan ϕ m d (3)
Nevertheless in the sequel we will focus our attention on the determination of the kink angle. The value of the rotation rate can then be deduced from equation (3).

For the determination of this kink angle, two types of criteria are proposed in the sequel. The first type predicts independently the kink angle at each point x 3 of the crack front by using the values of the SIFs at the same point x 3 , hence will be called local type criteria in the sequel. These criteria are the PLS [START_REF] Goldstein | Brittle fracture of solids with arbitrary cracks[END_REF], the MTS [START_REF] Erdogan | On the crack extension in plates under plane loading and transverse shear[END_REF] and its 3D extension [START_REF] Schollmann | A new criterion for the prediction of crack development in multiaxially loaded structures[END_REF]. The second type of criteria supposes that the kink angle is of the form of equation ( 2) and predicts the maximum kink angle ϕ m or equivalently the rotation rate dγ/dδ considering the mean value of the SIFs along the whole crack front. They will be called global type criteria in the sequel. These criteria consist in maximizing the mean value of K I (mode I SIF) or the mean value of G (total energy release rate). All these criteria are described in the following sections.

Local type criteria

Consider a point of the crack front and denote K I , K II , K III the SIFs at this point. After propagation the crack has kinked

O x 1 x 2 x 3 x y z (a) Whole surface O 2d δ ϕm x 1 x 2 x 3 (b) 3D view of the local kink- ing x 1 x 2 ϕ(x 3 ) (c) In a plane x 3 = Cst.
x 1

x 2

x 3 The Principle of Local Symmetry states that after propagation the mode II SIF shall become zero. This yields [START_REF] Amestoy | Crack Paths in Plane Situations -II. Detailed Form of the Expansion of the Stress Intensity Factors[END_REF]:

x 3 z -d d δ tan ϕ(x 3 ) δ tan ϕm γ(δ) γ(δ = 0) (
K I F II,I (ϕ) + K II F II,II (ϕ) = 0 (4)
where functions F i,j have been derived in [START_REF] Amestoy | Crack Paths in Plane Situations -II. Detailed Form of the Expansion of the Stress Intensity Factors[END_REF].

The Maximum Tangential Stress criterion states that the crack propagates in the direction where the circumferential tensile stress σ θθ is maximum. This yields:

K I sin ϕ + K II (3 cos ϕ -1) = 0 (5)
The 3D extension of the MTS developed by [START_REF] Schollmann | A new criterion for the prediction of crack development in multiaxially loaded structures[END_REF] states that the crack will grow radially from the crack front into the direction which is perpendicular to maximum principal stress σ ′ 1 . This direction corresponds to an abrupt twist angle ψ of the front around the direction of propagation and a kink angle ϕ which are linked to the SIFs by:

6 K I tan ϕ 2 + K II 6 -12 tan 2 ϕ 2 (6) + 24 K I -3 K II tan ϕ 2 • K I tan ϕ 2 + K II 1 -2 tan 2 ϕ 2 + 32 K 2 III tan ϕ 2 • 1 + tan 2 ϕ 2 2 • 4 K I -12 K II tan ϕ 2 2 + 64 K 2 III 1 + tan 2 ϕ 2 2 -1/2 = 0
Since PLS and MTS criterion give nearly the same value of the kink angle 2 , we will only consider in the sequel the MTS and 3DMTS criterion.

Global type criterion of Lazarus and Leblond

Starting from the idea that the twisting of the crack front is due to the presence of mode III, a criterion linked to the disappearance of mode III has to be derived. This criterion is necessary of global type (that is involving all the points of 1 Other criteria exist, see [START_REF] Qian | Mixed mode fatigue crack growth: a literature survey[END_REF], but the aim here is not to make a systematic review of these local criteria but to compare two types (local and global) of criteria.

2 Indeed Amestoy and [START_REF] Amestoy | Crack Paths in Plane Situations -II. Detailed Form of the Expansion of the Stress Intensity Factors[END_REF] have shown that the difference is of order m 6 with m = ϕ/π the front) since this twisting around the direction of propagation can only be achieved if all the points twists together. [START_REF] Lazarus | Crack paths under mixed mode (I+III) or (I+II+III) loadings[END_REF]2001b) proposed two such criteria: MVG: maximize the Mean Value of G(x 3 , δ) along the front with respect to ϕ m MVK: maximize the Mean Value of K I (x 3 , δ) along the front with respect to ϕ m where G(x 3 , δ) denotes the total energy release rate and K I (x 3 , δ) the mode I SIF, both after a propagation over a distance δ and at the point of coordinate x 3 of the front. One has:

G(x 3 , δ) = 1 -ν 2 E K 2 I + K 2 II (x 3 , δ)+ 1 + ν E K 2 III (x 3 , δ) (7)
Applying these criteria for a vanishing δ, that is, a vanishing crack extension length, one gets a zero value for ϕ m .

This implies that the criteria must be applied after a nonzero propagation length. On figure 4(b), one observes the presence of little facets at the beginning of the propagation. During the formation of the facets, the points of the crack front propagate in an "individual" manner. Afterwards, as soon as the facets have disappeared and the entire front twists as a whole, their behaviour becomes "collective". From there derives the idea to fix δ in the criteria to the experimentally measured length δ c of these little facets.

In order to apply the criteria, let us suppose the length δ c of the extension to be small enough for the expansion of the stress intensity factors K I (x 3 , δ), K II (x 3 , δ), K III (x 3 , δ) in powers of the crack extension length δ obtained by [START_REF] Leblond | Crack Paths in Plane Situations -I. General Form of the Expansion of the Stress Intensity Factors[END_REF] and Lazarus et al (2001a) to be applicable. These expressions give the SIFs after propagation K p (x 3 , δ) in function of the initial SIFs K p (x 3 ), p = I, II, III. Denote k p the mean value of these quantities:

k p = 1 2d d -d K p (x 3 )dx 3 (8) If |k III /k I | ≪ 1 and |k II /k I | ≪ 1
, the criteria MVK and MVG then give respectively the following formulas for ϕ m :

ϕ m = 8 1 + 16 √ 2 3π δ c a - 5 12
δ c a + 6 π 2 -3ν 2 -ν δ c d δ c d k III k I (9) ϕ m = 4 (2 -ν) 1 3 + 4 √ 2 3π δ c a - 16 3π 2 δ c a + 2 π 2 -3ν 2 -ν δ c d δ c d k III k I (10)
These theoretical expressions of ϕ m were obtained analytically for |k III /k I | ≪ 1 and |k II /k I | ≪ 1. However, ϕ m can be computed numerically for arbitrary values of K III (x 3 )/K I (x 3 ) and K II (x 3 )/K I (x 3 ). The results show that the analytic formulae are valid even for k III /k I and k II /k I of order unity.

It is logical to assume that the initial facets, which are deduced from the initial slit by a rotation of an angle ψ about the Ox 1 axis, disappear when they merge into the global crack surface which gradually rotates about the same axis with the rotation rate dγ dδ . Hence, the length δ c is linked to the rotation rate by the following formula:

dγ dδ δ c = ψ (11)
In this expression, ψ may be evaluated through Eq. ( 1) and dγ dδ through Eqs.

(3) and, ( 9) or ( 10). Since ϕ m itself depends on δ c , Eq. ( 11) in fact yields an equation on this quantity which must be solved numerically to obtain δ c as a function of K III /K I . Associated with Eqs. ( 9) or ( 10) the criterion gives finally ϕ m as a function of K III /K I , a, d, and ν.

Comparison with the experiments

Determination of the SIF

The Stress Intensity Factors are computed using the program ADAPCRACK3D developed at the Institute of Applied Mechanics at University of Paderborn [START_REF] Fulland | Adapcrack3d-development of the program for the simulation of three-dimensional crack propagation processes[END_REF][START_REF] Schollmann | Development of a new software for adaptive crack growth simulations in 3d structures[END_REF]. It is a Finite-Element based tool for simulation of crack propagation processes in threedimensional structures. The program delegates the determination of the mechanical fields to the commercial FE-Solver ABAQUS. Using these fields, the SIFs for all three fracture modes are then determined by the module NETCRACK3D by the use of the MVCCI-method [START_REF] Rybicki | A finite element calculation of stress intensity factors by a modified crack closure integral[END_REF][START_REF] Buchholz | Improved formulae for the finite element calculation of the strain energy release rate by the modified crack closure integral method[END_REF]. They are given in figure 6 for one half of the front (the other part can be deduced from the fact that due to symmetry considerations, K II /K I is an odd function of x 3 and K III /K I is an even one). Results for the points located at points x 3 = ±d shall be disregarded since the classical SIFs cannot be defined at these free surface points [START_REF] Bazant | Surface singularity and crack propagation[END_REF] due to the corner singularity, which differs from -1/2. One observes that K III predominates over K II , that K III /K I is nearly uniform and increases while γ decreases (more inclined notch). and 3DMTS criteria and on the other hand, MVK and MVG criteria (again only the values for one half of the front is plotted thanks to symmetry and external points shall be disregarded since SIF are not defined at these points). Experimental kink angles are obtained by measuring the kink angle ϕ m at the free surfaces x 3 = ±d and using equation ( 2) to obtain them for the interior points of the front.

The following observations become apparent:

1. Despite the two concepts rely on totally different aspects of the loading situation of the crack front both predictions of the kinking angle are quite satisfactory. 2. For the MTS and 3DMTS criteria, an excellent agreement is found near the free surfaces. But the kink angles are notably underestimated in the middle of the front. This is not surprising, since the small initial facets, which could be observed in the experiments, suggest that the twisting linked to mode III, is of relevance in those cases. Due to its omission, the twisting of the whole crack front is underestimated. Even if global type criteria give better prediction for the initial kink angle, application of the local type ones iteratively during propagation gives a crack surface very similar to the experiments (see fig. 9 compared to 3(a)). This demonstrates the ability of ADAPCRACK3D to perform simulations of 3D crack propagation paths, even if the initial kink angle is slightly underestimated. The mesh and the deformation of the specimen during computation is depicted in figure 10.

Conclusion

By comparison of the criteria with the experiments, one can notice that: It can finally be concluded, that obviously the crack front rotation, which is observed under notable mode III influence in 3PB specimens, can be described by both local and global type criteria. Hence, it is not possible to definitely conclude whether the twisting observed in 3PB or 4PB is a mode II or a mode III effect. But since the global type criterion gives better results, one shall conclude that it is rather a mode III one. Now, a more extensive experimental study of crack propagation paths in presence of mode III shall be done. The conditions of transition between these several crack patterns (abrupt or progressive, one-piece or piecewise twisting, see fig. 1) shall be lightened. The size effects, loading conditions on the spacing and rotation angle of the factory-roof patterns shall be studied. Extensive comparison of the twisting angle ψ of 3DMTS criterion or the empiric formula (1) with the twisting of the facets are envisaged in a near future.

Fig. 1

 1 Fig. 1 Several basic propagation possibilities in presence of mode III

Fig. 2

 2 Fig. 2 3PB-specimen with an inclined initial notch

Fig. 3

 3 Fig. 3 Gradual one-piece crack twisting

Fig. 4

 4 Fig. 4 Different stages of the crack propagation path

Fig. 5

 5 Fig. 5 Schematic view of the crack surface and local kinking

4. 2 Fig. 6

 26 Figures 7 and 8 compare the experimental kink angle along the front with the ones obtained by, on the one hand, MTS

Fig. 7 Fig. 8

 78 Fig. 7 Comparison of MTS, 3DMTS and MVK, MVG

Fig. 9

 9 Fig. 9 Computed crack paths

  Fig. 10 Deformed FE-model of the 3PB-specimens (γ = 45 0 , displacement magnification factor DMF=50)


Carmen Zahn
email: c.zahn@iwm-kmrc.def.hesse@iwm-kmrc.dem.finke@zgdv.de

Friedrich Hesse

Matthias Finke

Roy D Pea
email: roypea@stanford.edu

Michael Mills
email: mmills@stanford.edu

Joseph Rosen

Joseph Rosen

D Suthers

T Koschmann

Joe Rosen

Kenneth Dauber

Robb Lindgren

Paula Wellings

Sarah Lewis

Lori Takeuchi

Advanced video technologies to support collaborative learning in school education and beyond

Keywords: Cognitive tools, advanced video technologies in school education, teacher education, collaborative knowledge construction

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INTRODUCTION

In school-based education, video is often used to enrich regular lessons and as supplement to teacher lectures and explanations in front of a class. In this case, video is a presentation medium used to display information to illustrate and dynamically visualize knowledge to foster a better understanding. Although the results concerning the effectiveness of using videos as presentations are inconsistent, empirical findings on learning with video media consistently show that audiovisual presentation formats facilitate the comprehension and transfer of knowledge, especially in those domains where dynamic processes and concrete objects or complex systems need to be observable for a proper understanding of the topic (for overview, see [START_REF] Wetzel | Instructional effectiveness of video media[END_REF][START_REF] Park | Instructional conditions for using dynamic visual displays: A review[END_REF].

A second way of utilizing video in school education consists of depicting concrete real-world problems or cases that then are related to more abstract knowledge and problem solving skills. This is illustrated, for example, by the famous "Jasper Woodbury Series", a set of interactive videos developed by the Cognition and Technology Group at Vanderbilt University in the late 1980's and 1990's for complex mathematics problem solving (Cognition and Technology Group at Vanderbilt University, 1997). In this case, video is an interactive medium both presenting data and situating knowledge for the purpose of "anchored instruction" [START_REF] Barron | Doing with understanding: Lessons from research on problem and project-based learning[END_REF]CTGV, 1997). Here, students are not only supposed to watch and listen to the stories of the protagonist (Jasper Woodbury), but also to work actively and collaboratively with the interactive videos in class. Interestingly, it could be shown in an experiment that those groups of students who were asked by their teacher a) to pose their own subordinate questions while working with the video and b) to self-dependently find the relevant information to answer these questions in a video episode outperformed other groups of students who just viewed the video episode and received general text-based information on problem solving (unrelated to the video). Thus, if a teacher's guidance related directly to the Jasper story and included active cognitive processing of the information displayed in the videos, students learned better to solve mathematical problems than when they just viewed a video episode and received general training in problem solving in parallel (Van Haneghan, [START_REF] Van Haneghan | The Jasper series: An experiment with new ways to enhance mathematical thinking[END_REF]. To conclude, students guided to actively explore video information can build dynamic mental models of situations (associated with their individual prior knowledge) and relate these to the higher order cognitive skills of collaborative complex problem solving [START_REF] Kozma | Will Media Influence Learning? Reframing the debate[END_REF].

A third well-established way of introducing video into school education is performing "video projects" as a specific kind of media project [START_REF] Baake | Projekte als Formen der Medienarbeit[END_REF]. Such video projects rely on an idea sometimes described as "learning by design" (LBD, [START_REF] Reimann | Design, Diskurs und Reflexion als zentrale Elemente virtueller Seminare[END_REF] or "project-based learning" [START_REF] Baake | Projekte als Formen der Medienarbeit[END_REF][START_REF] Bereiter | Emergent versus presentational hypertext[END_REF]. In this paradigm, video is used as a design medium whereby students engage in active video production as a motivating and authentic collaborative task. In other words: video is not only used to present information or situate a problem to be solved (like in the "Jasper Woodbury Series"), but creating video artefacts is the problem to be solved.

As an example, students are sometimes asked by their teacher to shoot a video clip as their homework. When the lessons are about "advertisement," students may produce a video showing a TV-ad. To accomplish this, students have to structure their knowledge and present their understanding of TV-ads, and they need certain cognitive and social skills to accomplish this activity successfully. In particular, they have to learn a) how TVads are produced and how they are persuasive (understanding of lesson content), b) how to use a video camera and how to edit videos (technical routines), c) how to visualize a theme or certain emotions, how to use film techniques in order to persuade people (rhetorical skills), and d) how to negotiate different ideas within a team, and how to collaborate and coordinate the process of video production (social skills). More generally speaking, video production might not only be considered valuable for its own sake (and in design areas or the arts), but as engaging important mental and social processes (in those who accomplish the tasks) that eventually help to develop both the acquisition of interdisciplinary (meta-) cognitive and social skills and a deep elaboration of the topic at hand (Carver, Lehrer, Connell & Erickson, 1993;Scardamalia, in press). We elaborate on this idea below. Research literature in this area consistently emphasizes these potentials of design projects as an instructional method promising to serve several important educational goals at once: the goal of training skills, the goal of building dynamic social relations and of building knowledge (see Oser & Patry's 1990, 1994 taxonomy). The goals of training skills, building dynamic social relations and collaboratively building knowledge become increasingly important in our modern society where more and more individuals have to cope with complex topics, teamwork and large amounts of information every day [START_REF] Roschelle | Changing how and what children learn in school with computer-based technologies[END_REF]-and where media competencies and digital literacy can almost be regarded as "survival skills" [START_REF] Baake | Projekte als Formen der Medienarbeit[END_REF][START_REF] Eshet-Alkalai | Digital literacy: A conceptual framework for survival skills in the digital era[END_REF]. Accordingly, collaborative multimedia design projects using the services of emerging computer technologies have become particularly popular in school education -despite the fact they might be rather costly and require new forms of professional development for teachers to support such student work. Examples include contextualized multimedia editing (e.g. [START_REF] Beichner | Multimedia editing to promote science learning[END_REF][START_REF] Pea | Learning through multimedia[END_REF]Scardamalia, in press), interactive game design (e.g., [START_REF] Kafai | Affordances of collaborative software design planning for elementary students' science talk[END_REF][START_REF] Rieber | Children as designers of educational computer games[END_REF] and hypermedia design (e.g., [START_REF] Bereiter | Emergent versus presentational hypertext[END_REF]Carver et al., 1993;[START_REF] Erickson | The evolution of critical standards as students design hypermedia documents[END_REF][START_REF] Stahl | Hyper-Text-Schreiben -Die Auswirkungen verschiedener Instruktionen auf Lernprozesse beim Schreiben von Hypertext [Hyper-Text-Writing -The effects of different instructions on learning by writing hypertext[END_REF]. These examples all have in common that they intentionally involve additional creative activities for structuring information in non-linear ways and integrating dynamic visual media with texts. It is expected that here, the potential benefits for student designers are augmented by the specific cognitive skills of "meta-representational" and "meta-relational" thinking [START_REF] Carver | Learning by Hypermedia design: Issues of assessment and implementation[END_REF]. This leads us to a fourth way of using video in school education that we have been investigating and that we conjecture will be important for both formal and informal learning activities: the use of advanced digital video technology in support of collaborative knowledge building processes.

DIGITAL VIDEO TECHNOLOGY AND GROUP KNOWLEDGE PROCESSES

Introducing video into school education in the future could consist of introducing advanced digital video technologies that will broaden the spectrum of use paradigms described above. Our two groups-in Germany and the United States-have been working in parallel on exemplars of a paradigm that is already a part of our everyday lives, but which has been minimally appropriated yet in K-12 education. Advanced digital video has brought about new conventions of filmic expression in many areas-whether in the arts, at home or in the workplace. For example, in entertainment we use DVD movies that are partitioned into chapters or scenes (including extra scenes that were not shown in the original movie) and which can be randomly accessed by the viewer. Moreover, in workplaces, advanced digital video technology is not only a means of communication via video conference. It is also used for video analyses (e.g., in the area of professional sports, or teacher education). And it is used for collaborative work in life sciences as was illustrated by [START_REF] Sutter | Instructional Artefacts[END_REF] describing the case of two groups of medicine experts from two distant hospitals in Sweden: Here, surgeons, radiologists and cardiologists from two networked groups discussed coronary diagnoses of patients (who had been examined only in one of the hospitals) by means of special X-ray videotapes of patients' coronary and a video display pointer allowing participants to point to visual details and to add comments to the video information either verbally or by direct pointing.

To conclude, the use of video today might well include the selection of single scenes or objects from existing video information and even the direct integration of video scenes with e-communication tools. The number of workplaces that are making use of advanced video being used in different ways is steadily increasing. Thus, we are confronted with a situation where we need to establish new components of visual literacy (Messaris, 1994) and digital literacy that relate to such work scenarios. Literacy concepts cannot be restricted to static and text-based media anymore, but have to integrate the understanding, analysis and active use of nonlinear and audiovisual media as well including the use of digital video technology [START_REF] Pea | Learning through multimedia[END_REF][START_REF] Pea | Distributed multimedia learning environments: Why and how? Interactive Learning Environments[END_REF]Stahl, Zahn, Schwan & Finke, submitted). To this end, advanced digital video technologies may become part of our educational systems. The question is then: How can such technologies be implemented in schools and in educational and learning processes broadly? To approach these questions, we will consider existing advanced educational digital video systems that were developed on the basis of cognitive and socio-cognitive psychological and pedagogical considerations.

Learning to observe -Learning to analyze.

The DIVER system was developed by the Stanford Center for Innovations in Learning. DIVER is based on the notion of a user "diving" into videos, i.e., creating new points of view onto a source video and commenting on these by writing short text passages or codes [START_REF] Pea | The DIVER™ Project: Interactive Digital Video Repurposing[END_REF]. DIVER makes it possible to readily create an infinite variety of new digital video clips from any video record. A user of DIVER software "dives" into a video record by controlling-with a mouse, joystick, or other input device-a virtual camera that can zoom and pan through space and time within an overview window of the source video. The virtual camera can take a snapshot of a still image clip, or dynamically record a video "path" through the video to create a dive™ (which we also call a DIVER worksheet, see figure 1 below). A dive is made up of a collection of re-orderable "panels", each of which contains a small key video frame that represents a clip, and a text field that can contain an annotation, code, or other interpretation. Diving on video performs an important action for establishing common ground that is characterized as "guided noticing" (Pea, in press). The use of the virtual camera for the framing of a focus within a complex and dynamic visual array directs the viewer's attention to notice what it is that is thus circumscribed, and the point-of-view authoring thus guides the viewer to that noticing act. In this way, DIVER can be used as a tool to promote the development of "professional vision" in learning within disciplinary domains [START_REF] Goodwin | Professional vision[END_REF].

Figure 1: DIVER worksheet

Originally, DIVER's primary focus was for supporting research activities in the learning sciences (such as interaction analysis: [START_REF] Jordan | Interaction analysis: Foundations and practice[END_REF], and in teacher education, where video analyses play a major role for understanding one's own behavior and reflecting on it in relation to the behavior of others. DIVER has also been designed to enable the active exploration of panoramic video data-where one or more digital video cameras and associated mirrors are used to capture 360-degree horizontal imagery. In this case as well, the user may select visual information by virtually 'pointing to it' in the much larger spatio-temporal data structure of the video, for the purposes of collaborative reflection and analysis. The final product then is a collection of separate short video segments with annotations that represent the user's point of view on the video.

There are two different ways users work with video using the DIVER approach. In the first, after creating a dive using the desktop DIVER application, the user can upload it onto WebDIVER, a website for interactive browsing, searching, and display of video clips and collaborative commentary on dives. In an alternative version of the WebDIVER system, one can dive on streaming video files that are made accessible through a web server over the Internet, without either requiring the downloading of a DIVER desktop application or the media files upon which the user dives. Using WebDIVER in either of these ways, a dive can be shared over the Internet among teachers, student-to-student, teacher-to-students, or in other scenarios with colleagues and become the focus of knowledge building, argumentative, tutorial, assessment or general communicative exchanges.

On a more generic level, however, the system might be described as providing a cognitive tool that enables "pointing to video" and thus helping to develop skills of observation and noticing details and enhancing the probability that in the collaborative processes, the focus of attention and negotiating of meaning between participants in a conversation will build upon a common ground. With DIVER it becomes obvious that advanced technology may not only amplify existing kinds of activities and communication, but that it might augment our spectrum of activities and initiate entirely new forms of learning [START_REF] Pea | Beyond amplification: Using the computer to reorganize mental functioning[END_REF][START_REF] Beichner | Multimedia editing to promote science learning[END_REF].

The DIVER system distinctively enables what its creators call "point of view" authoring of tours of existing video materials in a way that supports sharing, collaboration, and knowledge building around a common ground of reference (Pea, in press; also see Goldman-Segal, 1998 andStevens et al., 2002 for related prior work). This form of communication with video is important for tapping the powerful potentials of video-enhanced learning.

Learning to integrate text and video -Learning to design non-linear information structures.

The web-based HyperVideo system for collaborative learning was developed at the Computer Graphics Center/Darmstadt in cooperation with the Knowledge Media Research Center/Tübingen. It is based on the idea of "annotating movies," i.e. selecting video segments from a source video and having spatio-temporal hyperlinks added to video by multiple users. The overall design approach encompasses several steps: (1) information is mainly presented by video, (2) knowledge can be collaboratively expanded by means of both dynamic links and written e-communication, and (3) the process of knowledge building is reflected in a resulting hypervideo structure we denote as a 'dynamic information space' of a collaborating group (DIS, [START_REF] Zahn | Collaborative knowledge building based on hyperlinked video[END_REF][START_REF] Chambel | Hypervideo design and support for contextualised learning[END_REF]. Users of the HyperVideo system can create their own dynamic sensitive regions ("hotspots") within video materials and add multiple links to these sensitive regions. Links can consist of data files uploaded from a local computer, as well as URLs. The links (or the associated information elements, respectively) can then be discussed by means of an integrated e-communication tool. Thus, both randomly accessing information provided by others and adding one's own new information and knowledge becomes possible with the HyperVideo system.

The system is based on client/server architecture. The DIS containing the content of the hypervideo is stored entirely at the server side preventing the users for any form of data inconsistence. The web-based graphical user interface (see figure 2 below) allows the adaptation due to different GUI layouts and consists basically of a special video player that visually displays the spatio-temporal hyperlinks within the video frame and offers functionalities in order to create new video annotations. The cross platform video player itself is written in JAVA using the Java Media Framework for the purpose of manipulative video rendering. New created video annotations are immediately transferred from the client to the server in order to be instantly shareable by the community. The system concept On a generic level, the HyperVideo system can be described as a cognitive tool enabling the linking of video information thus helping to learn to establish non-linear information structures and to focus attention and discussion in collaborative learning on associated concepts or related external representations of knowledge (e.g., a visible object and a text, or visible object and a formula). The system was first developed for unspecified situations of CSCL. The basic idea was that structuring hypervideos by dynamic links can serve to promote both learning to integrate different information elements and to develop non-linear knowledge structures by collaboratively designing information and discussing links.

Figure 2:Graphical user interface of HyperVideo

Hypervideo authoring has been discussed repeatedly as an opportunity for performing collaborative hypervideo design projects in educational contexts [START_REF] Chambel | Hypervideo design and support for contextualised learning[END_REF][START_REF] Zahn | Authoring hypervideos: Design for learning and learning by design[END_REF]. Additionally, the new technology was evaluated and further developed during three psychology courses at the University of Muenster/Germany. These courses were planned according to an instructional program based on courses of hypertext writing, developed by [START_REF] Stahl | Learning by writing hypertext: A research based design of university courses in writing hypertext[END_REF] on the basis of models on text writing (e.g., [START_REF] Bereiter | The psychology of written composition[END_REF]. The course concept aims at utilizing central features of hypervideo design as constraints that foster knowledge transformation in learners (Stahl, Zahn, Schwan & Finke, submitted; Stahl, Zahn & Finke, submitted). The concept also aims at controlling basic influencing factors that were identified earlier by [START_REF] Stahl | Hyper-Text-Schreiben -Die Auswirkungen verschiedener Instruktionen auf Lernprozesse beim Schreiben von Hypertext [Hyper-Text-Writing -The effects of different instructions on learning by writing hypertext[END_REF] in the context of hypertext design tasks at school. These factors are of essential importance for our present purposes, as will be described in the following section.

ADVANCED DIGITAL VIDEO SYSTEMS AS 'RHETORICAL PROBLEM SPACES' IN COLLABORATIVE SITUATIONS

Applying the Bereiter & Scardamalias (1987) model of knowledge transformation to the process of learning by hypertext design, [START_REF] Stahl | Learning by writing hypertext: A research based design of university courses in writing hypertext[END_REF] assume that the peculiarities of hypertext may influence the process of learning in very specific ways: 1) Hypertexts are non-linear media, so hypertext design processes do not only include linear writing processes, but also the selection and creation of small "nodes" and the representation of concept relations by links and an overall structure (integration). Also multiple ways of "reading" the hypertext must be considered (e.g., multiple audience perspectives). This should lead learners to a very deep elaboration of content. 2) Hypertext design problems (due to their complex nature) are solved in cooperation and collaboration with others, so the production process has to be coordinated in a group. This should lead to collaborative knowledge building and knowledge exchange. 3) Hypertext design has just begun to emerge, so that even among professionals different 'metaphors' (= genre knowledge and mental models of the medium) can be applied. To be able to work and learn, students have to consciously develop and negotiate upon a joint idea of 'what a hypertext is' as a first step of their coordinated work. Finding an appropriate metaphor should lead to developing discourse knowledge, on the one hand, and further joint elaborations of the content, on the other hand. These assumptions are also substantiated by empirical results: The reflection of different audience perspectives has been found superior to not doing so. The thorough evaluation of links representing semantic relations between nodes has been found to lead to a deeper elaboration than not using such activities. And finally, a space metaphor showed to guide knowledge transformation processes better than a book metaphor of hypertext [START_REF] Stahl | Learning by writing hypertext: A research based design of university courses in writing hypertext[END_REF]. Similar assumptions might be made for hypervideo design processes, too, as was suggested by Stahl, Zahn & Finke (submitted).

As was described in the previous section, we view advanced digital video technologies as cognitive tools according to a perspective of distributed intelligence (Pea 1993[START_REF] Pea | The social and technological dimensions of "scaffolding" and related theoretical concepts for learning, education and human activity[END_REF]. Merging this view with the works on hypertext design fostering knowledge transformation processes [START_REF] Stahl | Learning by writing hypertext: A research based design of university courses in writing hypertext[END_REF], we might generally perceive advanced digital video technologies as establishing new rhetorical problem spaces with their own rhetorical rules. These rhetorical problem spaces can well be understood in the sense of [START_REF] Bereiter | The psychology of written composition[END_REF] who assumed two problem spaces as important for text writing: the content problem space and the rhetoric problem space. However, because in the present context we have to deal with digital video, rhetoric problem spaces are understood as (audio-)visual ones instead of being merely based on text. Consequently, the rhetorical rules of our new rhetorical problem spaces can be extended by visual codes and the editing styles of different film genres (filmic codes of mise en scène and montage, see [START_REF] Metz | Film Language: a Semiotics of the Cinema[END_REF]Salomon, 1979). In sum, the rhetorical rules relating to hypervideo -as to our opinion -include rules relating to different text genres, to the visual codes and styles of static pictures/graphical displays, as well as to the dynamic visual codes of film and animations.

COLLABORATIVE ACTIVITIES INVOLVING ADVANCED VIDEO TECHNOLOGIES

We are now exploring in pilot studies a variety of ways that collaboration can be advanced in learning using advanced video technologies such as the two systems we have described. In WebDIVER, learners can collaboratively analyze video records from archival sources (e.g., science videos, social studies content), or from video they have themselves collected (e.g., of fieldtrips, art museums, classrooms, or playground activities). Using the HyperVideo system, learners as well as teachers can collaboratively create hypervideo documents (e.g. in university courses, as mentioned above) on the basis of existing or of self-shot videos. Learners can generate links connecting related information, they can add information of any kind to a source video (e.g. an instructional video) and they can discuss their contributions with others. In both the German and Stanford software systems, collaborative video work can take place either face to face in a computer-intensive school setting or after-school club, or over computer networks, involving distant locations, either synchronously or asynchronously. In both systems, learning scientists can also collaboratively engage with video, to interpret and analyze educational interactions or other behaviors of interest to their studies.

In preliminary work with the WebDIVER collaborative video analysis framework, we have found utility in the following scenarios: (1) pre-service secondary teachers in Stanford's school of education, creating dives of ten-minute unedited videorecordings of their own teaching, which they analyze with respect to the rubrics which their faculty mentors use to evaluate their work; (2) learning science doctoral students collaboratively analyzing teaching videorecords according to different disciplinary perspectives (anthropology, linguistics, sociology, developmental psychology, educational psychology, cognitive science) and then working to combine them to deepen the quality of interaction analyses; (3) distributed researchers working to analyze video data from user studies, in this case, of preschool children interacting with a touch-screen video-based storytelling system we call KiddieDIVER, and providing a collective set of recommendations via a dive on these data that was shared with the software engineer over the web for review and implementations of software improvements based on insights from the collaborative video analysis activity; (4) faculty use in preparing dives on videos of secondary educational practices that are used in lectures to exemplify and explore theoretical concepts from the research literature used in their courses (e.g., cognitive apprenticeship, scaffolding, academic language); and (5) a film studies professor working with his students to compare several different film versions of the Shakespeare Play Henry V. We make several points on the last scenario to exemplify the transformative nature of such activities with respect to common pedagogical methods. In each of these scenarios, as in the German hypervideo experiences, we are finding that collaborative diving requires working in new rhetorical spaces, in cooperation and coordination with others. For example, WebDIVER users creating collaborative analyses wish to sustain a private-public boundary even for synchronously-developed collaborative dives, and to have control over when their respective contributions are made reviewable by their collaborators in the common web space in which they are working.

Film students spend considerable time studying major filmmakers, film genres such as film noir or new wave cinema, the grammar of cinematography [START_REF] Metz | Film Language: a Semiotics of the Cinema[END_REF] including shot segmentation, camera movements such as panning and tilting, and transition effects such as cut and fade, as well as narrative techniques such as montage and flashbacks, and the animated special effects that have defined recent film developments. DIVER provides a new tool for the faculty member and film student to develop the web of perceptive knowledge that ties together the history of films, filmmakers, film methods and techniques and film criticism. In a film studies course now underway using DIVER at Stanford, graduate students in film are studying the relationship between the actor and the written work: How is the medium used to tell the story? For example, students are looking at two clips, the 1989 film adaptation of Henry V directed and played by Kenneth Branagh, and the 1944 film version of the same Shakespeare play directed and played by Laurence Olivier. The same scene and words will be analyzed: Henry V's "Crispin's Day" speech. Previously the film studies professor provided a related assignment to students-describing in an essay what was different about each actor's interpretation-but by having them write about the movie scenes from memory. With WebDIVER, film students are able to point to specific space-time regions of the film in real-time examples from each movie, and to justify their analysis with video-based argumentation using the scenes from the movies being compared. This exercise will take place outside of the classroom, as a homework assignment. Each student is given their own protected workspace, and they access the films and the WebDIVER analysis tool on-line via a web browser. Students will then present their analysis in class, also using WebDIVER. The students will have a chance to comment on each other's work, both orally in class and again later on-line by adding messages and comments to the web-based Dive worksheets. Although this same assignment has been used in film class before, this will be the first time a) students will be able to point directly to the scenes they're analyzing and referencing; and b) an informal learning discussion (via web page collaborative commentary) will continue outside of the classroom presentations. In WebDIVER, students can also literally navigate the movie by way of the actor's/script's utterances (i.e. click on an utterance and go directly to the corresponding scene in the movie). The utterances also scroll along with the movie. The professor anticipates a nuance and depth to analysis that he has not experienced using his previous approach to instruction and assessment.

Pilot studies involving the HyperVideo system include an experimental comparison of how (and where) authors with different prior knowledge would suggest placing hyperlinks in biology videos [START_REF] Zahn | Authoring hypervideos: Design for learning and learning by design[END_REF]. The results of this study revealed that authors of different knowledge backgrounds (contentexperts, media-experts) developed similar ideas of a hypervideo structure, which were mainly based on formal features of the source video (such as, for example, terms included in the audio track). Results also showed -and this is more interesting in our context -that the linking decisions of expert-authors were quite congruent with those of novice users, indicating that even users with low prior knowledge were capable to make meaningful linking decisions. This provides a minimum basis for applying hypervideo design tasks at school. Field studies extending this basis also conducted as already mentioned above: in three courses at the psychology department of the University of Muenster/Germany students designed hypervideos on topics such as 'techniques of presentation and moderation' in the first course [n = 16] and 'the study of psychology in the University of Muenster' in the second course [n = 10]. These courses were evaluated extremely positive by the students (Stahl, Zahn & Finke, submitted).

Our current work includes a school project, where hypervideo design will be applied in German secondary schools to support media education in German native language lessons ("Deutschunterricht"). The topic will be TV-advertising. We plan to study the collaborative analysis of TV-ads based on the DIVER system and the collaborative hyperlinking of TV-ads based on the HyperVideo system. Altogether, we will conduct two large experiments in a learning lab. Our interest is to investigate the interactions of DIVER and HyperVideo as two generic types of digital video technology with a) individual cognition (i.e. mental models of "hypervideo" in learners) and b) teacher's instructions (i.e. the support of group discussion by teachers) and the influences of these interactions on group knowledge processes. This future-orientation leads us to the last section of this paper.

CONCLUSION AND FUTURE WORK

In writing about modern music, writing, art and science, Umberto [START_REF] Eco | The Open Work[END_REF] notes that "'open' works, insofar as they are in movement, are characterized by the invitation to make the work together with the author and that (2) on a wider level (as a subgenus in the species 'work in movement') there exist works, which though organically completed, are 'open' to a continuous generation of internal relations that the addressee must uncover and select in his act of perceiving the totality of incoming stimuli."

To the extent that DIVER and HyperVideo use can make video and movies and other rich media 'open' to HyperVideo linking and to Diving-interpretation and extensible use with guided noticing, DIVER path moviemaking making and annotation-there is without question an active role for the reader, who becomes an author in bringing the work of the video or other medium to a more completed state in his or her interpretations of it. DIVER also provides a tool for evidence-based argumentation, in which one uses what one notices in the medium to make a case around it, and thus extends the work in significant ways with the act of authoring the dive.

For the constructivist educator or more generally for those who want a more active voice in media uses for communication and knowledge production, these two systems exemplify a video use paradigm for education that moves away from today's broadcast-centric and asymmetric uses of video to the communicative empowerment of the video user, who can easily craft point-of-view movies within movies with commentaries and hyperlinks to share with others. We view this fundamental shift from consumption to authorship of video points-of-view as a vital transformation in the use of the video medium for advancing learning and education.

The HyperVideo system was developed at the Computer Graphics Center in Darmstadt, Germany in cooperation with the Knowledge Media Reasearch Center in Tuebingen, Germany.

DIVER software and affiliated services with patents pending. The DIVER project work has been supported by grants from the National Science Foundation (#0216334, #0234456, #0326497) and the Hewlett Foundation. The DIVER team contributing to these efforts includes Roy Pea (Director),