Volume 6. November 2006. Article ID 1344
Our purpose in this descriptive, exploratory study is to report on our efforts in conducting a cyber tutoring project that combined two curricular domains ---- mathematics education and engineering education. Although we had carried out 6 prior cyber mentoring projects involving aspects of scientific literacy (Boxie & Maring, 2001; Maring, Levy, & Schmid, 2002), the project reported here was the first time we designed one in the areas of mathematics education and quantitative literacy.
Since 1999 we have carried out over 35 cyber tutorials [often referred to as "cybermentoring projects"]involving preservice teachers and tutees in elementary, middle, and secondary schools dispersed across Washington state. Our cyber tutorials employed video conferencing as a system and tool, utilizing both "desk top video conferencing" [e.g., iVisit, CU-SeeMe, NetMeeting] and, since 2002, high end video conferencing (Johnson, Maring, Doty, & Fickle, 2006). But, the project we are reporting on here involves the first time we have carefully explored cyber tutoring in mathematics. Our overarching research question [and, actually, the point of our paper] had two parts: does cyber tutoring in mathematics provide opportunities for worthy practical experiences for preservice teachers and does it also provide robust opportunities for further research into questions and topics related to mathematics education. In this report, we offer details about two engineering mathematics application/engineering assignments ---- a pop bottle activity and a plastic straw bridge building exercise. The focus of our paper is more largely about mathematics, engineering design, and tutor/tutee interaction than it is about technical considerations related to the video conferencing.
In this report, our primary purpose is to explore tutor/tutee interactions (carried on through video conferencing) in the context of a bridge building simulation, using plastic straws and masking tape. The project used cyber connectivity to engage preservice teachers and pupils with each other as tutors and tutees in an alternative high school 110 miles from our campus. The school was located in a small city in an agriculturally based rural community. Since the school district is committed to mathematics education for all students and since administrators perceived the project as innovative and motivational, permission was quickly granted to conduct the project. When we asked the teacher of the tutees to describe their alternative school context, she said that it resembled many American alternative high schools in that at-risk students, teen parents, working teens, former drop outs, non-traditional learners, and self-directed learners comprised the school population. Some of the students viewed as at risk were often described as discouraged, disinterested, or hard to serve learners when they were in traditional classrooms. Many of the students had records of failing grades, behavioral problems, and chronic absences. As for the mathematics background of the cyber tutees, they were enrolled in "Basic Mathematics," a "practical" mathematics course for less advanced students and for whom the geometry and algebra courses offered at the alternative high school would not be appropriate. Although the cyber tutees were high school sophomores and juniors, the teacher recommended that the cyber tutoring focus on reviewing or reteaching mathematics related to concepts and procedures taught in earlier grades [e.g., fractions, ratios, perimeters and how these had relationships to geometric shapes].
Since this was a new subject matter area for us to apply cyber mentoring/tutoring to, we were more interested in investigating pedagogical aspects than in delving deeply into learning theories, the ins and outs of problem solving, or how the project might result, causally, in a positive impact on pupil learning. However, by the time we completed our analyses of this cyber tutorial in mathematics and engineering applications, we could see that its cyber context had potential for examining some of the current issues and trends in research in mathematics education. For example, investigations of video conferencing tutorials could be used to analyze levels and components of "mathematics talk" (Hufferd-Ackles, Fuson, & Sherin, 2004) on the parts of cyber tutors and cyber tutees. The dialog below provides a sample of one of the discussions that took place between a student and her cyber tutor. The [negative] attitudes towards mathematics revealed in the dialog, because they were a major part of the cyber tutor/tutee interactions during the project, are presented and discussed in subsequent sections of this of this report.
Kim: I am just a designing person. That's why we did so well on the [design the pop bottle] candle [project] because I designed it and decorated it.
Cyber tutor: Yeah, but we are going to learn a lot about math and angles and ...
Kim: I don't like angles.
Cyber tutor: [Is that] right?
Kim: Hmm, hmm, hmm. this [building a straw bridge project] is more of a guy thing and I...
Cyber tutor: You know, it doesn't have to be a guy thing, though. I enjoy this kind of stuff, Sara enjoys this kind of stuff.
Kim: Hmm. (smiling but still not convinced)
Using video conferencing in preservice teacher education is a relatively recent innovation (Phillion, Johnson, & Lehman, 2003; Anderson & Rourke, 2005). Nichol and Watson, (2000), in England, described their uses of video conferencing and video tutoring with preservice teachers. Their analyses of the archived tapes focused on verbal and nonverbal communication in the tutorial process. They concluded that video tutoring can potentially be a more effective form of tutoring than face-to-face interaction. Edens (2003) conducted formative and summative evaluations of a video conferencing project involving preservice teachers and noted that benefits for preservice teachers included contact with students in real classrooms, use of technology in teacher preparation coursework, and collaboration between schools and universities.
We designed a pop bottle activity and plastic straw bridge building exercise in such a way that they had clear foci on mathematics applications (e.g., use of fractions, ratios, and perimeters and their relationships to geometric shapes). The video below provides a brief introduction to the project along with a sample clip of instructional interaction. Notice that the cyber tutor mentions both the process and the answer. She values the tutee’s use of correct thinking and procedures more than getting the correct answer. Although the tutor/tutee dialog in the video clip might be depicted as a valuing, on the part of the tutor, of correctness over thinking about procedures, the tutor indicated in a subsequent conversation with the teacher and a supervising professor that she intended her words to be an encouragement for procedural thinking.
Video Overview. (Click on image above to launch)
We also designed and guided the tutorial and mathematics activities so that they aligned with the construct of "quantitative literacy" (National Research Council, 1993; Madison and Steen, 2003) and empirically verified social learning theories pertaining to tutor/tutee interactions (Lepper, Drake, & O’Donnell, 1997).
In order to facilitate team building in the context of socialized learning, the initial phase of our unit involved asking tutors and tutees to experience a unified vision of what is meant by "engineering design competencies." To accomplish this, we urged them to be creative as they constructed some object as a team from a two-liter pop bottle. As a result, in this team-building exercise, tutor-tutee teams created a terrarium, a candle holder, a race car, and a flower pot. After completing the design and construction of these "creations," team members took physical measures and made calculations. Their mathematics applications complied with the participating teacher’s earlier specifications of the germane state mathematics standards [referred to in our state as Essential Academic Learning Requirements].
After the pop-bottle project’s team-building and design activities, we began the bridge-building "adventure." The aim of this stage of the project was to enable the pupils to continue their mathematics learning in designing, constructing and analyzing a prototypic engineering-type model. The assignment for the teams called for a bridge made of plastic straws to span a 14 inch space between two movable tables. Connector options included masking tape, straight pins, small finishing nails and gumdrops. A test of the bridge’s strength would be determined by wrapping a string around its center and suspending gradually increasing weights, up to ten pounds, from the string. Key mathematics concepts included the Pythagorean Theorem, perimeters and areas of triangles, and ratios pertaining to weight-of-bridge-to-load-supported.
An initial step of our mathematics/engineering applications project was to create a collaborative relationship between the preservice teachers, classroom teacher, and faculty. Hence, in our early video conference planning meetings, we identified the educational goals of everyone involved. The primary stakeholders were engineering and education faculty who wanted to design and carry out a project as one of the initiating events that would lead to the formation of a engineering and education partnership and center. Quantitative analysis along with engineering applications in mathematics, both in K-12 and postsecondary educational contexts, were envisioned as a major emphasis of the future center. Since the bridge-building/mathematics activity and project was viewed by many on our campus as worthy and interesting, it actually did play a part in establishing the "Engineering Education Research Center" on our campus. The classroom teacher participated in the project because she felt it would help some of her students stay engaged in mathematics learning and because she felt it would be a helpful practicum experience for preservice teachers. The preservice teachers volunteered for the project because the cutting edge technology intrigued them and because they valued having an additional practicum/hands on opportunity to become better prepared for careers as teachers. The tutees liked the project and looked forward to the weekly sessions, too. They enjoined the attention and assistance of college students and felt that the video conferencing was "cool".
The cyber tutors met via video conferencing with the classroom teacher and, on campus, with faculty from engineering and education to plan the project. As a part of these planning discussions, state "essential academic learning requirements/EALR’s" in mathematics were considered as a framework to identify areas for tutorial focus. Based on these deliberations, the lessons took place in two stages. The first involved a pop-bottle activity. Adapted from Transferable Integrated Design Engineering Education/TIDEE (Davis, 2004), the pop bottle lesson was developed to enhance team-building and design experiences. The lesson plan chosen for the more extensive mathematics/bridge-building simulation was also adapted from TIDEE (Davis, 2004).
Written directions for the pop bottle exercise are given in the image below, along with a link to a PDF document describing additional details. This exercise set the stage for the tutees early in the tutorials, preparing them for the mathematics focus of the overall project by including such mathematics vocabulary as measurements, units, inches, centimeters, circumference, and fraction.
Written Directions for Pop Bottle Exercise and Contest. (
Download complete PDF version for class use)
Our cyber tutors were "trained" when we discussed with them guidelines for expert, effective tutoring (Lepper, Drake, & O’Donnell-Johnson, 1997). We had selected Lepper’s recommendations and analyses to provide a research-based, yet concrete list of "expert" tutorial practices for the cyber tutors. To bring this research down to a practical level, we constructed an "INSPIRE" hand out, shown below, to guide tutor behavior and related reflections, discussions, and analyses of archived or transcribed interactions.
reliance on, and commitment to, a fundamentally Socratic style of tutoring.
make increasing demands on the students in each tutoring sessionand
use progressive strategies when debugging and incorrect response.
convey their high expectations in a very indirect and unprepossessing manner.
are likely to ask students to explain their strategies or to summarize their problem-solving process.
devote a great deal of effort to encouraging or motivating students, not just to work hard, but to enjoy their work and to feel challenged, empowered, and curious about the domain of study.
After we discussed Lepper’s ideas with the cyber tutors, we provided assistance regarding tutoring in the context of high end video conferencing. The guidelines below contain this additional tutoring advice (adapted from Roller, 1998).
Tutoring is more effective than group instruction for many reasons. These include more time spent reading, immediate feedback, more tailored teaching, more extended interaction between tutor and student, and strong positive emotional relationships.
The classroom teacher chose students to participate in the cyber tutoring based on their expressed interest in the project. Each of the students was enrolled in an Applied mathematics course at the school. In this article, we are focusing descriptions and analyses primarily on tutor/tutee interactions involving a female graduate student cyber tutor who recently completed her student teaching and a female alternative high school senior who strongly disliked mathematics.
In addition to the
training offered when we gave them and discussed the INSPIRE and Guidelines handouts, we also provided the cyber tutors with hands-on pre-tutoring introduction to the operation of the Polycom video conferencing unit. This technological training included such technological skills as using the document camera, the zoom and pan features of the remote controller, and integrating the uses of a pc or of a tablet pc as part of the cyber tutorials. As noted in the introduction, we also provided a written overview to the plastic straw bridge building exercise.
Most of the 12 cyber tutoring sessions took place during one semester once a week for an hour. However, during one of the sessions, the distant tutees became so interested and engaged that they asked their teacher and were given permission to video conference for a second hour. In order to provide our cyber tutors with an overview and the proposed schedule of the project they had volunteered for, we wrote up a Bridge-building Simulation summary document in PDF format and emailed it to them.
The transcribed dialog below took place after the pop bottle experience, described previously. It illustrates talk on the parts of a cyber tutor and two tutees related to length of a diagonal, the use of a
new tablet pc, and
missing pieces in the measurements of triangles.
Kevin: [laughing to signify his answer of
Cyber tutor: Hold on... let me show you. (Pauses) I'm using our new
tablet pc computer, so I'm all excited. I'm drawing on the computer screen. OK? so we have two inches here. Hey, I can make it black too. Oops. And you want tot tall part of our triangle there to be four inches, Kevin?
Kevin: Two times four divided by two. (as he is calculating area)
Cyber tutor: OK. well, this is going to be our c squared, or our c actually. This is just going to be our c. So this will be our a, our b, and our c. To find the length of c, right here [using a pen on the worksheet under the document camera]... the formula is a squared plus b squared equals c squared. So hey, Kim, why don't you do this on a piece of paper...
Cyber tutor: Kim, do you have the paper that we did the original problem on last week? Or any piece of paper?
Kim: I got a piece of paper...
Cyber tutor: OK, the formula, have you guys done that before to find missing pieces of measurements of triangles?
Cody: Most people [in this class] are basic math, not too much algebra, so they may have...
Kim: Yean I'd say so [meaning
I've done this kind of math before.]
After this interaction, one of the project directors, who was monitoring the session, reminded the cyber tutor to be mindful of how expert tutors avoid "telling" too much or too often, in keeping with the tutor training guidelines for being Socratic and for using scaffolding. He also talked with the cyber tutor about how the use of inductive questioning can often be a more effective pedagogical approach than direct telling.
Subsequent dialogs between the cyber tutor and tutees showed how the cyber tutor encouraged the tutees to stick with the project in the transition to the straw bridge building exercise [note the last scaffolding technique in the Guidelines, above]. We want to point out that most of the interaction, when it revealed "mathematics phobia", involved "Kim", the tutee of focus in our study. Later on, in our "Impact on Student Learning" section, we will discuss how she did not let her distaste for mathematics prevent her from earning her GED.
Tutee "Kim" struggled with her lack of knowledge of how to do the calculation of the area, exhibiting yet again her pervasive dislike of another aspect of mathematics. The "calculation of the area" dialog also revealed that the cyber tutor employs Lepper’s "Encouraging" guideline yet again in order to get "Kim" to stick with the challenge and mathematics task at hand.
As we noted in our Introduction, our study was descriptive and not an experiment. Thus, to measure impact, we rely on anecdotal information buttressed by some quantitative data.
In phone conversations with the teacher, we learned her professional judgment that "Kim’s" attitude towards mathematics and doing her daily mathematics assignments greatly improved during and after the cyber tutoring. The teacher noted that she felt the pop bottle and bridge building simulation definitely contributed to "Kim’s" staying in school, doing her mathematics assignments, and earning her GED. In the same phone conversation, the teacher said that she felt the video conferencing tutorial was a "very powerful motivation and tool" for her students and especially for "Kim" to "stick with and keep doing mathematics." Both common sense and the fact that our study is descriptive prevent us from even wanting to infer that the cyber project "caused" "Kim" to succeed in these ways. But we do think that her involvement in the 14 video conferencing sessions helped improve her attitude, which in turn contributed to her larger success. In terms of objective data, the teacher provided the following information about "Kim's" growth in mathematics:
We designed this project to meet the interests of various stakeholders: engineering and education faculty, a classroom teacher, preservice teachers, and students who were tutored.
One of our major purposes was to determine if an engineering problem could be utilized to shed light on tutor/tutee interactions in cyber contexts. We also wanted to see if the use of high end video conferencing as a tool for educational partnerships would be feasible when the curriculum dealt with mathematics and engineering-related applications.
In carrying out the project with alternative high school students, we saw that both the cyber tutor and the tutees were quite engaged in the activities. One tutee, about to graduate from the alternative high school, exhibited impressive academic gains that the teacher felt helped her move from being "on the verge of dropping out" to showing clear improvements in her test scores, number of assignments completed, and grades in mathematics. The preservice teachers who served as cyber tutors spread the word to their classmates that cyber tutoring is "fun" and innovative, that it provides them with helpful experiences and confidence before they begin their capstone student teaching, and that it is a worthy addition to their resume when they begin their searches for teaching positions.
Our experiences in this project indicate to us that cyber tutoring in mathematics and engineering applications has potential in terms of providing more "field-based" experiences for preservice teachers and for reaching high need and under challenged students who might not have access to other support.
In our upcoming work, we are taking steps to address the following questions:
Many of the foregoing directions and considerations for future research arose not only out of our successes, but also out of the problems and shortfalls we encountered. In closing we should acknowledge briefly that all of our cyber tutors would have benefited from additional tutor training experiences, that some of them would have tutored more effectively if they had more regularly utilized "peripherals" such as the document camera and integrated laptops into the tutorial sessions, and that all of the cyber tutors would have done a more effective job if they had been provided more coaching and reflection opportunities by professors and graduate students who are specialists in mathematics education. In our ongoing and upcoming research, we are attending to these matters.