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Introduction

Many times teachers obtain resources and have not had exposure to their applications. This approach minimizes the potential benefits of the application and typically creates a frustrated teacher who avoids the resource and possibly others like it in the future. This is not a new scenario and certainly not specific to the influx of technology in the classrooms. However, computers, the Internet, software and the host of other technology peripherals have exacerbated a system in which teachers are inundated with new and potentially useful tools. Suddenly, teachers have computers in their classrooms, and others even have access to the World Wide Web; however, very few instructors are provided training or experience on how to incorporate technology into their daily teaching. Occasionally, teachers are trained on basic word processing and spreadsheet applications, but authentic integration into specific content areas is still lacking.

If we look into the future and identify resources that have a high probability of being used, we can "get a jump on" our own professional development and our own designing of instructional strategies so that we’re ready for the resources when they arrive. "Play is a vital ingredient to learning" (Kaplan, 2000). Let’s play now so that we can exploit the benefits that the new tools offer us soon after they are available in our schools. Currently, there are numerous possibilities for teachers to use effective technology in their lessons, but which ones are feasible, which are cost-prohibitive, and which ones simply do not work?

One resource whose application can currently be used on a small scale is an Internet communication vehicle called a whiteboard. Today, there are many of these applications available and free to everyone, and although they are seldom used in education today, they will be widely used in two or three years. We encourage early adopters to venture out and review the potential of this device, so they can take advantage of this technology when it is widely available.

What is an electronic whiteboard?

An electronic whiteboard is an online tool, which allows teachers and students (and even parents/guardians or administrators) to communicate synchronously via text, graphics, and/or other visually descriptive means. It allows participants to use drawing and/or annotation tools to develop collaborative images or to annotate documents that can be viewed by all participants simultaneously. A whiteboard is defined for these purposes as a large two-dimensional space in which users can post objects for all users to see. This definition has some specific implications; for example, the word "users." The idea is that multiple users who can post and/or see objects displayed can access whiteboards.

There are many makes and models of whiteboards, such as Microsoft Netmeeting, Groupboard.com, Wintronixinc.com, Teachers-shoponlin.com and one embedded in Blackboard.com. It is not our intention to discuss the advantages of the products of these companies, but to inform the readers that whiteboards are available from a variety of vendors.

Whiteboard experiences

One experience I had using a whiteboard was to design a lesson for future teachers so they could experience the power and usefulness of this tool. Since meaningful two-way communication about academically oriented problems was the goal, I asked a university colleague to assist in designing a lesson for students to explore in pairs. During the design, we enunciated the objectives to one another and then positioned ourselves at computers next to each other in order to troubleshoot potential problems with our whiteboard activity. Using as little verbal communication as possible, we implemented a "dry-run" of the lesson and made the necessary modifications so it would properly demonstrate the desired lesson. The modifications were extensive; in fact, the rehearsal was extremely useful in that it made us realize what it would take for students to have a successful and meaningful first whiteboard experience. Effective, focused written communication skills are essential and much more vital than the minimal technical skills required to operate the whiteboard system. With our logistical data, we redesigned the exercise so that the future teachers would be able to navigate through the activity.

Actual student whiteboard data

Data was collected from an actual mathematics methods online classroom exercise, which involved one-on-one tutoring using the whiteboard. By having this experience, the future teachers will be familiar with one more method of instruction that hopefully will be available to all in a few years. The academic content for the lesson was based on the Competencies and Skills Required for Teacher Certification in Florida. The problems came from the Study Guide for the Florida Teacher Certification Examination for Mathematics 6-12 published by the Florida Department of Education. A reproduction of one of the graphics from the booklet was drawn on the whiteboard (Figure 1, next page). Each methods student met one-on-one with the instructor. Meeting times were prearranged based on appointment times given to the instructor by each individual in the class.

A "Play with Purpose" session

White board screen shot

Figure 1. Sample graphic created in whiteboard

Depending on the features of the whiteboard being used, transcripts can be kept. Below are excerpts from a transcript of a "dry-run" session between the two authors. (The diagram in Figure 1 above was drawn during this session. The question relates to drawing.)

Dry-run transcript

Jh So, tab what is the relationship between line EH and line BF?
tab The line BF is perpendicular to the line EH, jh.
Jh tab, can you identify two lines which are parallel?
tab Line AE is parallel to line BF.
Jh Super, tab!
Jh tab, if you drew a line from E to B, what is the relationship to newly formed triangle?
Jh Well let’s draw it, tab?
tab What do you mean by your question?
Jh Let me diagram it.
Jh So, now what is the relationship of line EB to triangle EBF?
Jh Now tab what is the length of our newly formed hypotenuse?
Jh So, tab if the lengths of the segments are: FB = 1 and EF=1,what is the length of EB?
Jh tab, if the length of FB is 1 cm and the length of EF is 1, what is the length of the hyp?
tab the length of the hypotenuse would be the square root of (1^2 + 1^2)
tab That’s the square root of 2…for the length of the hypotenuse
Jh Super, tab!
tab Thanks for the help, jh.
tab bye
Jh bye

Below is the written transcript from an actual whiteboard experience. Drawings were not preserved, because the whiteboard being used did not have the electronic capability of saving drawings. The discussion relates to a multiple-choice item in the study guide for the mathematics certification examination. The stem of the item is presented in Figure 2. The reader will notice that, although the item was presented using a multiple-choice format, the instructor asked a number of probing questions about lengths of sides of different triangles. Only when the instructor had established that the student grasped the patterns for 3-4-5 right triangles, did she address the question the student posed at the onset of the session.

White board screen shot

Figure 2. Mathematics item discussed in tutoring session

Archive for Secondary Math Methods MAE6336_036 on Mar 1, 2001

tab has entered. 08:52:13 PM
Student B has entered. 08:53:41 PM
Student B has left. 08:53:47 PM
tab Hi Student B
tab Oops you must have been "kicked" off because you’re not here now.
Student B has entered. 08:55:14 PM
Student B I’m in now
Student B Sorry about that
tab Great
tab guess what…i can’t find the booklet
Student B Oh, no!
tab so you’ll just have to tell me what the problem is that we’ll work on
Student B I"m realizing that I need to bone up on my formulas
tab let’s try one…which formula?
Student B My trig skills are rusty.
tab ok can you draw or describe one of the problems
Student B One question was : Given Tri ABC and the measures as indicated, find the measure of segment AB
Student B I’ll draw the triangle.
tab go ahead
Student B oops
tab like that?
Student B I haven’t figured out how to get the lines to remain.
tab double click
tab erase and start over now
tab good
tab nice
tab ok…i can’t erase A?
Student B A is correct.
tab ok
tab Let’s go to a different triangle first and we’ll eventually get back to this question
Student B ok
tab what’s the length of the hypotenuse?
Student B This is a right triangle.
Student B The length would be 5
tab good
tab your turn
Student B length = 10
tab scroll down and i’ll draw some more
Student B length = 15
tab super
tab kinda bad…but
tab can you get this length?
tab 3, 4, 5 … 6, 8, 10 … 9, 12, 15 … 2, 1.5, ???
Student B length = 5/2
tab do you think you can give me a similar one?
Student B I can try.
tab go ahead
tab what are the lengths of the legs?
tab 20
Student B correct
tab what if the length of hypotenuse is 5 million and the length of one leg is 4 million for a right triangle.
tab what’s the length of the third leg?
Student B The other length is 3 million
tab super…ready to erase all of this and go to your question now?
Student B yes.
tab go ahead and erase all of it Student B
tab ok i’ll show you some triangles
Student B ok
tab what is other angle, Student B
Student B 60
tab good
tab length of hypotenuse?
Student B has left. 09:17:09 PM
Student B has entered. 09:18:41 PM
tab hi again do you have aol?
Student B Sorry, my ISP kicked me off. No, I have msn.
Student B 4
tab ok…we’re almost done…can you still see the triangles
tab oh good
tab can you get this one?
Student B 4*square root of 3
tab excellent…now you erase and redraw the problem
tab what is the question?
Student B find the length of seg. AB
Student B Length would be 3* square root of 3
Student B AC would be 6?
tab Nice job…we’re done unless you have anything else … yes 6
tab thanks for doing this, Student B
Student B Thank you, Dr. Bratina.
Student B I appreciate all of your help.
tab have a nice evening, Student B!
Student B You too. Thank you.
tab bye
tab has left. 09:24:30 PM
Student B has left. 09:24:30 PM

Student perspectives on the whiteboard experience

Many students enjoyed their whiteboard experience and its potential use for their students in the future. Methods students had positive comments concerning the potential uses and the application for this type of tool in the classroom. The following are actual excerpts from whiteboard sessions:

Excerpt #1

tab you did a really nice job picking up on this
Student C this is kind of neat
tab do you see the potential two or three years from now?
Student C yes

Excerpt #2

Student D Have a good night. I enjoyed working with you on this project. I LIKE this white board. I think it’s going to be a very helpful tool in the future.
Student E It can be useful. This is definitely a case where practice makes perfect. See you in class.

Excerpt #3

Student C hey its been fun
Student A Guess I’ll see you later
Student C this thing is cool
Student A I’ve really learned alot THANKS!

"Off task"

Some students will find themselves off-task on the whiteboard. Students will also find themselves off-task in the classroom. Regardless of the environment, students will sometimes find themselves off-task. The remedy for this challenge will be the same whether online or offline — well-planned, organized, worthwhile lessons.

Whiteboard potential for education

Today, this very minute, whiteboards are not universally used in the classroom, although it was not long ago when classrooms did not contain overheads, video tape recorders, and a host of other tools that are now commonplace. Will the whiteboard become the next globally accepted educational tool? Maybe not, but many believe it will become a useful component of engagement and learning. So our prediction is that whiteboards will be one of many tools that teachers will be using with their students and students using with one another as they do their homework.

A final word

Like other technologies, however, using a whiteboard does not guarantee effective learning. These tools are intended to promote two-way communication as a springboard for discussions in which students justify the procedures they used to arrive at their answers, listen critically to the arguments of others, and refute them or offer other reasoning strategies. They also can receive assistance on topics on which their understanding is weak. But the technology could be used in ways that have nothing to do with such goals. So the effective use of technology involves many teacher decisions and direct forms of teacher involvement (Bransford, Brown, & Cocking, 1999). In other words, technology does not replace the teacher. "The teacher plays several important roles in a technology-rich classroom, making decisions that affect students’ learning in important ways…The teacher must decide if, when, and how technology will be used" (NCTM, 2000, p. 26).

Before you have your own students go ahead to use a tool, you’ll want to practice using it yourself. Why should we restrict ourselves to structuring creative children’s lessons that center around playfulness? How about playing while we’re creating those lessons! We hope you’ll "Play with Purpose" on a whiteboard, so you can "get a jump on" your own professional development and be ready to incorporate whiteboards into your instructional repertoire when the tool becomes available on a large-scale.

References

Bransford, J. D., Brown, A. L., & Cocking, R. R. (Eds.). (1999). How people learn: brain, mind, experience, and school. Washington DC: National Academy Press.

Gallagher, T. (2000). Florida teacher certification examination for mathematics 6-12 (3rd ed.). Florida Department of Education, Third Edition.

Kaplan, J. S. (2000). Are we teaching our children to play? Florida educational leadership 1(1), 33-35.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.