CHAPTER

 
1. INTRODUCTION
2. LITERATURE REVIEW
3. RESEARCH HYPOTHESIS AND RATIONALE
4. RESEARCH DESIGN
5. CONCLUSIONS & FUTURE RESEARCH
6. CITED LITERATURE
7. APPENDICES
    7.1. APPENDIX A
    7.2. APPENDIX B
    7.3. APPENDIX C
 

CMC Computer Mediated Communication

CVE Collaborative Virtual Environment

HMD Head Mounted Display

VR Virtual Reality

1. INTRODUCTION

 

The communication between one party and another over distance has been one of the driving factors in the advance of human civilization and commerce. While face-to-face interaction can be accomplished without the aid of modern technology, distant communication requires some technological assistance. Current communication technologies, such as video teleconferencing, have gained popularity by adding the capability of viewing the party with whom one is speaking, and enable use of visual aids and to interpret reactions. This form of mediated communication has been proven to be very effective in allowing facial expressions to be transmitted (Olson & Olson 1995, Brittan 1992). The widespread use of this form of communication attests to the benefits gained by being able to add visual cues.

 

This is only the beginning in the development of emerging technologies for improving our ability to communicate. As new technologies have emerged, their applications have also changed. The telegraph line, originally used to send coded messages, was then modified to send voice, and modified again to send computer data. As the applications of technology change, the nature of communication changes accordingly (Feenberg, 1989). The introduction of virtual reality in the late 60's and recent advances in networked virtual reality allow researchers to share an electronic space and to be "telepresent" in that space via existing technology such as voice communication or video conferencing as well as a variety of new techniques.

 

One such new technique is the use of an avatar, or virtual representation of the other participants within an environment where multiple users can interact in a collaborative virtual environment (CVE). The development of networked virtual reality and collaborative telepresence has allowed the essence of a person to be conveyed and "interact" in a remote location. In a CVE, the ability to see the person with whom one communicates is augmented by adding three dimensional movement, specialized tools, and a virtual space within which to interact.

 

Communication in a virtual environment not only allows interactants to see and hear remote locations, but also to interact with objects in that distant location. This advance represents a fundamental shift in how we should view human communication (Rogers, 1986). Nevertheless, CVE is new enough that it is not yet fully understood. Few studies have analyzed the ability of avatars to communicate, nor have scholars compared this channel with other, more well established venues, such as video teleconferencing and face-to-face communication. Hence, the importance of avatars and CVE as communication tools of the future need to be examined.

 

An avatar presents a physical presence, even though it is electronic, which has some communication ability. This technique may carry as much information or more than the video representation of a person used in teleconferencing in certain settings. It may even surpass face to face communication in some situations. In this study we will compare communication using face to face, video teleconferencing, and avatars in an educational model. The abilities of the students and instructor to interact will be modified by varying the channels they are able to use to communicate. This research will show that the ability to share space, to have a presence whether real or virtual is more beneficial in task or educational situations than is the ability to see facial expressions.

 

2. LITERATURE REVIEW
 

Technological advancement has brought about a revolution in human communication. Human beings are no longer limited to face-to-face interactions. With the aid of technology, they can engage in communication by phone, by video conferencing, and by avatar. These methods of communication have been found to be effective in transferring information and providing feedback, although the degree to which such communication is successful depends on the channel through which it is enacted and the nature of the message.

 

There are a great number of communication channels, ranging from face-to-face, to various forms of computer-mediated communication (CMC), to CVE's. These channels can be classified into three broad categories: face-to-face, where both participants share the same physical location and are able so see and speak with each other directly, video conferencing, where participants can see each other and can speak through electronic means and avatars where participants share a virtual space and are able to speak through electronic means. Each channel carries unique combination of communication characteristics not present in the others, and, as evident in the literature.

 

As systems become more frequently used, the users' abilities to use the medium and communication over the channel improves. While some channel limitations do apply, the uses of verbal and nonverbal cues are not limited by the medium but by the user. This perception that you can only use certain methods of communication is true until the perception is broken, perhaps by accident, at which point those limitations are gone and new avenues of communication are opened. As Walther and Burgoon (1992) discovered the human need to communicate can overcome technical limitations given time.

 

Even with the adaptation of channels to be more communicative, some channels, by design, carry more information. Galbraith (1973) (1977) proposed that the characteristics and structure of communication would vary with relation to the information that was required. Daft and Lengel (1981) discuss this idea of media richness, that the more information that a channel can support the richer and more communicative the channel is. Variations of the use of richness of communication was studied by Short (1974) advancing the work of Morley and Stephenson (1969). Short varied channels of communication between tele-conference, "loud-speaking" audio and face to face and found similarities in the tele-conferencing and face to face in the ability to successfully negotiate. Shorts findings suggest that media richness has a significant effect on the outcome of the negotiations. It could further be implied that the use of "richer" media had a better ability to present the case of the negotiator, or the transfer of knowledge, or at least point of view.

 

Culnan and Markus (1989) put forth the theory that the abilities of a channel to convey cues had a direct effect on the channel's ability to transmit broader communication especially intrapersonal and personal variables. This "cues filtered out theory" supports the idea that nonverbal cues can not be communicated in environments that do not support face-to-face style communication. This filtering of cues biases channels to less interpersonal, more task oriented communication situations.

 

In more recent studies it has been found that over time, mediated forms of communication are not necessarily biased toward unsocialized, task based, lack of interpersonal forms of communication, or the cues-filtered-out theory (Walther & Burgoon 1992). Indicating that channel use over time can expand communication that is limited in short channel interactions, such as experimental settings. The significance of communication, intent and meaning are modified as users and society become more accustom to the systems and more comfortable using them.

 

Variations of a communication medium for research purposes are usually based on a scenario for the communication such as a task or educational setting. The measures of the communication dependent variable can then be observed or measured in the qualities of the task or education. Olson and Olson (1995) used a comparison of video versus face-to-face in task oriented encounters and "results showed that with video, work was as good in quality as that [of] face-to face. (p. 362)" While there is not a claim of better communication there is the perception by the users that " video makes them feel more able to communicate. (p. 362)" In human communication, face-to-face or mediated, this perception plays a critical role in the ability to use the medium. The perception that communication is not possible will limit the channel regardless of the real capabilities of the channel.

 

 

The ideas of a virtual shared workspace and related tools have been examined (Dourish & Bellotti 1992; Fish, Kraut., Root, & Rice, 1993; Tang & Isaacs, 1993). In most systems the conditions are generally similar, users are able to see one another and there is two way audio. They also are able to share a common workspaces, usually a text field and a "white board" or drawing area. These methods of communication have been found to be effective in the transfer of information and the ability to have feedback. Use of shared workspaces have been found to be effective especially in task oriented situations. The abilities to communicate using a number of different methods, computer mediated, telephone and face-to-face combined with the ability to respond with varying levels of information support and at various times appear to be the strengths of these forms of communication.

 

In a very interesting study, Isaacs, Morris, Rodriguez and Tang (1995) compared the use of live presentations to that of computer supported video conferencing systems. Participants were able to view the presenter and ask questions. Transfer of information, and level of interactively were compared between face-to-face and computer mediated communication conditions. Questions in the mediated version were asked in a written format using text windows. Isaac's found that using video based systems, individuals asked questions at a rate equal to those in a live setting, however follow up questions were less likely. Users also preferred the post and pre meeting discussions, available only to the face to face users, which allowed them to expand on ideas.

 

Salzman (1995) studied the use of "Newton World," an environment to teach Newtonian physics, as an educational medium. Users wear a head mounted display (HMD), data gloves and in some cases a haptic feedback vest. They are then immersed in a virtual environment in which they can interact and observe the principles of Newtonian physics, such as being able to drop a ball from different heights and then observe it hitting the floor from multiple view points, including that of the ball. The results did not show significance in improved understanding of Newtonian physics when comparing responses from pre to post. The reason for this lack of significance was thought to be short exposure to the VR world. Users were too interested in the environment to pay close attention to the subject matter.

 

Salzman’s tests did however, show correlation's between feedback devices, menu configurations and increases in certain testing areas. Users who received certain cues, such as the haptic feedback, tested better in areas where those cues were uniquely descriptive, such as collision. Suggesting that what cues and channels are effective is dependent on the environment and on the application. Certain technology better lends itself to the communication of ideas or concepts.

 

This ability to be part of an environment, virtually, has added to the abilities in educational environments to examine things not reachable in the physical world. VR's three dimensional abilities and the lack of physical limitations such as size, distance, time, forms a powerful educational and communication tool. (Biocca, 1992; Bricken, & Byrne, 1993; Dede, 1995; Erickson 1993; Salzman, Dede, & Loftin 1995)

 

3. RESEARCH HYPOTHESIS AND RATIONALE

 

As discussed earlier, the channels of face-to-face interaction, video-conferencing, and CVE, have different degrees of effectiveness in communication given the unique characteristics of each channel and their application. In face-to-face communication, the communicator has relative position, tehe ability to point and gesture, and to use facial expression to convey meaning. In the video teleconferencing model, the ability to use facial expression is still available, however there is no shared space, nor is the ability to gesture in that shared space. In an avatar model, the ability to use facial expression is no longer available but there is a shared space and the ability to use gestures (Leigh, Johnson, Vasilakis, & DeFanti 1995).

 

As Nilan (1992; see also Krueger, 1991) points out, since avatars are not bound by physical laws, their potential to convey meaning beyond human capacity seems possible, although how meaning is processed remains to be explored. Understanding the differences between face-to-face communication and avatars will provide information about the features they share, such as position, relative distance, gross-gesturing ability, and pointing. Comparisons of face-to-face and video will allow identification of the communication qualities the two channels share; that is, facial expression and the ability to identify human form and face. The comparison of avatar and video will allow comparison of projected images and the effects of position and gesture versus facial expression. In the comparison of avatars and face to face will allow identification of the importance of sharing a space, either virtually or physically.

 

Given the assumption that the ability to share a space and to gesture with relation to that space is important, the amount and quality of information conveyed using an avatar should be similar to or greater than that of the face to face interaction. The use of video teleconferencing, where the space shared is not a common space, will show a lower ability to convey information given the same topic. This variation of the media richness will point to the importance of shared space in educational settings. The abilities of a user appearing as an avatar can be greater than that of a person appearing in a face to face, giving the potential for the avatar channel to be richer than that of face to face. That is however, not the intent of this study.

 

The role of nonverbal, while not a focus of this research, is a significant factor and demands some discussion. It is almost impossible to define what might or might not be used nonverbally in a communication situation, especially given advances in not only technology but the users' modifications of application of that technology. A prime example is the use of emoticons, character symbols to denote non-verbal cues, such as a wink, ;^). It is not the intention to describe how the cue was interpreted or formed, what is important in this research, is to show the effects of the communication, without quantifying the unique cause (Steuer, 1992).

 

Identifying the underlying and/or overriding principles can improve the development of these technologies and the situations in which they can be best used. Although the technology of VR is a modification of other communication models, the evaluation of the medium can be cast from existing techniques. New codes and techniques will have to evolve to evaluate the full medium and it’s unique abilities (Biocca, 1992).

 

In order to have a full appreciation of the significance of avatars versus teleconferencing some indication of the difference in transporting these different channels over wired or fiber optic networks is needed. Video used in this study requires a network connection with the capabilities of transporting at least 209 Megabit’s per second constantly, any variations in this bandwidth will result in visible errors in the image. (See "Video over ATM and Existing Networks" for more information on other capabilities.) By comparison the avatars used in this study transmit only their position in the virtual world, a mere 80 bit’s of information, and a constant bit stream is not necessary.

 

If avatar’s can provide a better tool for communicating in some circumstances, then the requirements for that communication is minimized, with out sacrificing the quality of the content. Given the dramatically smaller data volume that avatars use compared to video, larger numbers of users can exist in the same networked space. One of the challenges faced by the computer communications industry is bandwidth, how much information can be transported at a given time. Anyone who has downloaded images on the Internet has experienced the implications of low bandwidth. There is no doubt that the ability to download images is valuable. Successful application of techniques such as avatars offer a new communication paradigm only if their communication abilities can rival or exceed that of existing mediums.

 

Therefore the use of a multivariate study to examine the ability of avatars to convey communication versus teleconferencing and versus face-to-face in a task or educational setting will provide a structure and differentiation for this type of model. The face-to-face model is used as a basis of comparison.

 

Hence, this research will compare all three channels with respect to their ability to communicate information. Specifically, the hypothesis stipulates that the use of avatars is closer to face-to-face in its ability to communicate, for the following reasons. First, avatars allow participants to interact with one another directly in a virtual environment, much as face-to-face interaction does. Second, avatars allow participants the ability to communicate nonverbally through position and gesture, which, again, makes it similar to face-to-face interaction. In video conferencing, interaction is possible only through the two dimensional screen, and nonverbal cues can only be observed from the image that is on the screen, the area of interaction is not shared. Thirdly, this sharing of space, or presence, is more important in educational settings than is the ability to see and interpret facial expression.

 

My research hypothesis is:

 

H: Use of avatars in educational based collaborative virtual environments have a stronger correlation to face-to-face communication than video conferencing does to face-to-face in the ability to convey information and understanding.

 

Since no attempt is being made here to expand on the face-to-face channel (Durlak, 1987), the face-to-face model is used as a basis of comparison. Using multivariate analysis to examine the ability of avatars to convey nonverbal communication versus teleconferencing, and versus face-to-face, in a task or educational setting will provide the structure and differentiation for this type of model. The type of communication channel, video conferencing, face-to-face and avatar will be varied in an educational setting and the ability of the students to understand and reproduce the information covered will be examined as a dependent variable.

 

Some definitions are necessary of the technical terms and how they are to be used in this research:

 

Collaborative Virtual Environment (CVE): a stereoscopic projected environment in which images are drawn for the position of the user. Other users or other presence's are located in the environment and share the virtual space.

 

Avatar: an incarnation of a user in a virtual environment or other place. In this experiment, all avatars will have the same abilities: the ability to point, and to show relative position and the direction in which they are looking. Each case will see the same instructor avatar, and for the instructor the student avatar will be the same.

 

Video teleconferencing: the use of two way video, where the instructor can see the student and the student can see the instructor. The cameras will be in one position so that an upper torso or head-and-shoulders shot will be transmitted.

 

* Audio in Avatar and video sections will be exactly the same, eliminating it as a contaminating variable.

 

Face-to-face: dyadic communication using the same VR environment as other tests.

 

4. RESEARCH DESIGN

 

Research will be conducted using college students from the University of Illinois system. In order to classify subjects each case will fill out a short questionnaire. The questionnaire will gather information for tracking each case based on the last 5 digits of their social security number. It will also gather demographic information, such as sex, race and age as well as consent to participate in the research. In addition to demographic information, several questions will probe the cases past computer usage, interests in mathematics and interests in science fiction. While no matching is planned using these factors, they do present potentially contaminating variables, with the possibility of scoring differently do to increased interest.

 

Another potential for contaminating variable is the "gee whiz" effect that VR, especially the projected VR style used in this experiment, can cause. Often participants in demonstrations can not concentrate on the content of the demonstration, not because of the quality of the demonstration or the effectiveness of the medium but because of the fascination with and newness of the environment. In order to minimize this all cases will go through a short training course prior to the beginning of the educational program. All participants receive the same training.

 

The cases will then be randomly assigned to one of the three conditions. Each case will be sent individually to an instructor to receive instruction in an abstract topic, such as four-dimensional objects. One of the groups will see only the instructor as an avatar, one only the video image of the instructor, and the third the instructor will join them in face-to-face interaction. The instructor will have the same visual cues as the students; students seeing the instructor as Avatar will also appear as an Avatar to the instructor. They will receive timed instruction (about twenty-five minutes) on the subject. The educational package used, the course of instruction outline, and the instructor will be the same for all condition. An brief outline of part of the educational plan is in Appendix A.

 

Because of the unique nature of the instruction the testing instrument will test method will also be somewhat unique and will test a number of levels of knowledge. It has been found that testing using common testing methods, written questions answered with multiple choice, fill in the blanks or essay, show lower results, not from a lack of understanding of the material, but from trouble translating the experience to a new medium. The test will be devised independently of the instructor, and will consist of multiple choice questions, fill in the blank and essay questions based on information given in the instruction. Many of the questions will be shown on video tape or with the use of a computer monitor, so that the technique used to explain the information will also be used to test the information. Questions will be devised to test three levels of knowledge as a measure of the dependent variable.

 

Questions will be devised to test the case's ability to recite information given in the instruction, some questions will be based on principles related to information applied in the instruction and some of the questions will be new applications of the information given in the instruction. Questions will form one of three basic formats, either true or false, multiple choice and explanation or essay. Scoring for the multiple choice and true false sections will utilize right or wrong answers. Scoring for the essay section will be done by a group of experts on the subject using a 5-point Likert type scale for level of correctness and the level of understanding, two scales for each question. Comparisons will then be drawn from the communication conditions versus scoring results in the sections of the testing instrument.

 

5. CONCLUSIONS & FUTURE RESEARCH

 

The use of communication technology has an effect on communication. Studies have been conducted that show these effects vary by transmission channel and by the nature of the communication. The communication strengths and weaknesses of a technology can only be assessed in a given setting or context. Education has been an outstanding model for testing communication theory, since the roles and purpose of the participants are clear and testing is an integral component of the process. How techniques of communication in a channel are used is not easy to qualify but the effects can be measured. The results of this study will shed light on the qualities and effects of different communication conditions of channels in a collaborative virtual environment design.

 

The development of networked virtual reality and collaborative telepresence has allowed the essence of a person to be conveyed and interact in a remote location. Multiple users can interact in a CVE. This electronic shared workspace and related channels of communication offer the ability to effect variables such as time, space, size and location. With variations in these areas that do not vary in the physical world, there is a shift in the communicative nature of this medium. The ability to not only see and hear remote locations but to also interact with objects, tools and other users is still a new enough concept that it is not fully understood. The change in these abilities presents a fundamental shift in how we should view human communication (Rogers, 1986).

 

The adoption of new tools of communication such as CVE have broadened horizons and potential, bringing education into a new era (Hutchison, 1995). The introduction of these technologies has minimized obstacles such as distance, time and space. In many instances, this will no doubt improve education. Nevertheless, how these benefits will be applied and how they will effect educators and students have yet to be fully understood. Testing has been one of the major problems in the area of educational virtual reality, as you change the manner in which you teach a subject, you must also change the manner in which you test the subject. Hopefully these teaching and testing methods allow for better application and retention of the information. Testing in this area should be conducted and will no doubt provide interesting results.

 

There are numerous methods of displaying virtual reality, from fish bowl or monitor based technology, to head mounted displays, to projection based systems such as that used in this research. All of these technologies have similar goals and different methods of reaching those goals. It would be very interesting to see this research replicated using other technology.

 

 

6. CITED LITERATURE

 

Biocca, F. (1992). Communication within virtual reality: Creating a space for research. Journal of Communication 42(4), 5-22.

 

Bricken, M., & Byrne, C. M. (1993). Summer students in virtual reality. In Wexelblat, A. (Ed), Virtual reality applications and exploration (pp. 199-218). New York: Academic Press, Inc.

 

Brittan, D. (1992). Being there: The promise of multimedia communications. Technology Review 95(4), 42-51.

 

Cullan, M. J., & Markus, M. L. (1987). Information technologies. In F. M. Jablin, L. L. Putnam, K. H. Roberts, & L. W. Porter (Eds.) , Handbook of organizational communication: An interdisciplinary perspective (pp. 420-443). Newbury Park, CA:Sage.

 

Daft, R. L., & Lengel, R. H.(1986). Origanizational information requirements, media richness and structural design. Managment Science 32(5), 554-571.

 

Dede, C. (1995). The evolution of constructivist learning environments: Immersion in distributed, virtual worlds. Educational Technology, 35(5), 46-52.

 

Dourish, P., & Bellotti, V. (1992). Awareness and coordination in shared workspaces. Proceedings of the Conference on Computer Supported Cooperative Work. New York: ACM.

 

Durlak, J. T. (1987). A typology for interactive media. In M. L. McLaughlin (Ed.), Communication Yearbook 10 (pp. 743-757). Newbury Park, CA: Sage.

 

Erickson, T. (1993) Artificial realities as data visualization environments. In Wexelblat, A. (Ed), Virtual reality applications and exploration (pp.199-218). New York: Academic Press, Inc.

 

Feenberg, A. (1989). The written world. In R. Mason & A. Kaye (Eds), Mindweave: Communication, computers and distance education (pp. 22-39). Oxford: Pergamon Press.

 

Fish, R. S., Kraut, R. E., Root, R. W., & Rice, R. (1993) Video as a technology for informal communication. Communications of the ACM, 36, 48-61.

 

Galbraith J., (1973). Designing Complex Organizations. Reading, MA: Addison-Wesley.

 

Galbraith J., (1977). Organizational Design. Reading, MA: Addison-Wesley.

 

Hutchison, C. (1995) The ÔIPC OnLineÕ: Juex sans fronti res on the cybercampus. Journal of Computer Mediated Communication [Online]1(1), 45 paragraphs. [1996, September 15].

 

Isaacs, E. A., Morris, T., Rodriguez, T. K., & Tang, J. C. (1995). A comparison of face-to-face and distributed presentations. CHI '95 Moasic of Creativity (pp. 354-361). Conference Proceedings of CHI '95. Denver: ACM.

 

Krueger, M. (1991). Artificial Reality II. Reading, MA: Addison-Wesley.

 

Leigh, J., Johnson, A. E., Vasilakis, C. A., & DeFanti, T. A. (1995). Multi-perspective collaborative design in persistent networked virtual environments. Paper presented at the VRAIS convention, Washington, DC.

 

Morley, I.E. & Stephenson, G.M. (1969) Interpersonal and interparty exchange, a laboratory simulation of an industrial negotiation at the plant level. Journal of Psychology 60, 543-545.

 

Nilan, M. S. (1992). Cognitive space: Using virtual reality for large information resource management problems. Journal of Communication, 42(4), 115-149.

 

Olson, J. S., & Olson, G. M. (1995). What mix of video and audio is useful for small groups doing remote real-time design work. CHI '95 Mosaic of Creativity (pp. 362-368). Conference Proceedings of CHI '95. Denver:ACM.

 

Rogers, E. (1986). Communication technology. New York: The Free Press.

 

Salzman, M.C., Dede, C., Loftin, R. B. (1995). Usability and learning in educational virtual realities. In Proceedings of the Human Factors and Ergonomics Society 39th Annual Meeting. (pp. 486-490).Santa Monica,CA: The Society.

 

Short, J.A., (1974). Effects of medium of communication on Experimental negotiation. Human Relations, 27(3), 255-234.

 

Steuer, J., (1992). Defining virtual reality: Dimensions determining telepresence. Journal of Communication, 42(4), 73-93.

 

Tang, J. C., & Isaacs, E. (1993). Why do users like video? Studies in multi-media supported collaboration. Computer Supported Cooperative Work 1, 163-196.

 

Walther, J. B., & Burgoon, J. K. (1992). Relational communication in computer-mediated interaction. Human Communication Research, 19 (1), 50-88.

7. APPENDICES
1. APPENDIX A

 

The use of the educational model provides the opportunity for contamination due to improvement of the instructors during the course of teaching the material a number of times. In order to minimize this the initial instruction is given to three graduate students in mathematics by a professor with an interest in 4 dimensional objects. These three students will receive the instruction in all of the three formats varying which one they star with, so that all will receive instruction initial instruction in a different communication condition. This will help to evaluate possible bias caused by the initial instruction. They will be tested at the end of their first session and at the end of all sessions to show comparisons of continued learning given a longer exposure to the material. This may also point to a correlation between condition and depth of knowledge, although the testing size will too small for valid results. These graduate students will then be the instructors for the actual study.

 

Each graduate student will teach two students in each communication condition, as an avatar, face to face and using video conferencing. The sequence of each instruction will be recorded to provide evaluation of improvement of the instructor and eliminated of that as a variable. The use of a number of instructors will also allow the quality of the instructor to be eliminated as a contaminating variable.

 

2. APPENDIX B

1. The idea of dimensions is discussed and a general concept of what level of understanding the student subject has. A dimension is a way of describing space.
2. Discussion of a point being a position in a coordinate system and not actually occupying any space. A point is a zero dimensional object.
3. If you move a point in a point in a direction, say across, you will make a line. A line is a one dimensional object. In this example it does not have thickness or height. In our VR example we use a line segment to visualize a line.
4. If you take a line and extend it in a direction that is perpendicular to itself, say up wards, you create a plane, a plane is a two dimensional object. In our VR example we use a square to visualize the plane.
5. If we take all of the points in a plane and move them in a direction that is perpendicular to itself, say back, we create a three dimensional object, in our case a cube.
6. A cube is a three dimensional object, but we are able to represent it in two space, by drawing a projection or shadow of the object. The drawing is a two dimensional representation of a three dimensional object.
7. The analogy of dimensions has progress the same way from a point to a line, to a plane, to a cube and now we will take the same analogy one more dimension. If we take all of the pints on a cube and we extend them in a direction that is perpendicular to cube we get a hypercube.
8. In the same manner that we could project a cube onto a two dimensional surface, we are able to project a hypercube into three dimensional space. The ideas of dimensionality do not have to stop at four, the mathematical models can continue through multiple dimensions.
9. The student can then move the hypercube in four space and ask questions. The student then destructs the cube, and reconstructs it explaining what they know about the properties of dimensions in general and the hypercube model in particular.

1. APPENDIX C

Sample Test questions:

1.If a 2 dimensional object has 4 one dimensional sides and a three dimensional object has 6 two dimensional sides, how many three dimensional sides does a 4 dimensional object have:

A. 8

B. 10

C. 12

D. It is not possible to know

Can you explain your answers?

2.A hypercube is a 4-dimensional object which can be unfolded into ____ dimensional objects.

3.What new properties would a point possess if a new dimension is added?