Kellogg, M. & Kersaint, G. (2004). Creating a vision for the standards using online videos in an elementary mathematics methods course. Contemporary Issues in Technology and Teacher Education [Online serial], 4(1). Available: http://www.citejournal.org/vol4/iss1/mathematics/article1.cfm
Creating a Vision for the Standards Using Online Videos in an
Elementary Mathematics Methods Course
Clearwater Christian College
University of South Florida
This paper outlines the efforts of two mathematics teacher
educators in their use of online videos to expose their elementary preservice
teachers to examples of reform teaching, as espoused by the National Council
of Teachers of Mathematics. The online videos provide an excellent source
for reflection, and each author shares their different avenues to encourage
both discussion and reflection about the practices seen on the videos.
Actual student comments about videos they have viewed reveal the motivating
and enlightening nature of this delivery method. While several websites
provide access to online videos, this paper highlights PBS Mathline (http://www.pbs.org/teachersource/mathline/lessonplans/search_k-2.shtm).
The recommendations in the National Council of Teachers of Mathematics (NCTM)
standards documents call for teachers to relinquish their roles as the sole
authority in the mathematics classroom to help students build mathematics knowledge
through the use of problem solving, to orchestrate classroom discourse in ways
that facilitate students' learning, and to use various tools (e.g., manipulatives,
technology) to enhance the learning and teaching of mathematics (NCTM, 1989,
1991, 2000). Although many teachers acknowledge the virtues of the espoused
ideas, they may not be readily able to translate ideas in ways that allow them
to alter their classroom practices (Cohen, 1990; Eisenhart et al., 1993). In
other cases, teachers may take risks but discontinue the use of reform methods
because they lack appropriate feedback or support (Carter & Richardson,
1999; Ensor, 2001; Knapp & Peterson, 1995).
Ultimately, teachers may find meeting and addressing the challenges of the
reform effort difficult if they do not have markers with which to gauge their
level of success after attempting an innovation. Simply stated, the standards
documents encourage teachers to teach mathematics in ways that many of them have
not experienced firsthand. As a result, they have to imagine a classroom they
may have never witnessed. In fact, for many teachers the classroom environments
and interactions encouraged in the standards are a far cry from the kinds of
experiences they had as students. Therefore, it becomes important to engage
teachers in activities requiring them to examine what it means to learn and
teach in environments encouraged by the reform effort (Loucks-Horsley, Hewson,
Love, & Stiles, 1998; Smith, 2001).
As mathematics teacher educators, we have grappled with ways to help elementary
teachers create a vision for a standards-based classroom as they examine their
content knowledge and their beliefs about learning and teaching mathematics.
One major difficulty is that preservice teachers are wary of the innovative
methods introduced in methods courses, especially when they have not seen them
applied in schools. Typically, preservice teachers enter teacher education programs
with pre-existing notions about mathematics classrooms. This may be a result
of what Lortie (1975) referred to as the "apprenticeship of observation."
In other words, they believe that the mathematics instruction they have observed
as students represents how mathematics instruction should be delivered.
Many teacher education programs incorporate the use of field experiences to
help preservice teachers begin to learn what it means to teach. Although the
benefits of these experiences are many, they can also be problematic. For
example, preservice teachers may be in placements that do not support or
encourage the ideas suggested by the reform effort. In fact, although preservice
elementary teachers at our institutions are often involved in field-based
experiences throughout their teacher education program, at the elementary level
there is no guarantee that they are observing teachers as they teach
mathematics. As a result, it has been difficult to help teachers create a vision
for (a) the depth of understanding that can be developed when students are given
opportunities to explore mathematics topics in an active way, and (b) the
implementation of innovative mathematics activities or teaching strategies with
an actual group of students.
In particular, individuals without "profound understanding of fundamental
mathematics" (Ma, 1999) find exploring mathematics from the conceptual
basis difficult. As a result, they believe it would be difficult for pupils
to investigate topics on their own, to reason mathematically, and to present
their ideas to their peers. They, in effect, cannot envision a classroom where
students are encouraged to work together to develop and share multiple strategies
and where authority for mathematical knowledge is shared with the students and
not relegated to the teacher.
Online Video as a Source of Reflection for Preservice Mathematics
This article describes our attempt to combat years of "apprenticeship
of observation" by requiring preservice teachers to observe mathematics
classrooms that are closer in alignment to the recommendations of the standards
than what they may have experienced. No claims are made about the long-term
effects of using online videos nor is our rationale for using them directly
connected to research findings. Instead, this article describes how and why
we have incorporated the use of these videos in our elementary methods courses
and describes the reflections of elementary preservice teachers after viewing
selected videos. Specifically, the ways online videos are used to encourage
preservice teachers to examine their beliefs about how students learn mathematics
and what it means to teach mathematics are discussed. With the help of readily
available online videos, preservice and in-service teachers can be provided
opportunities to examine classrooms that have successfully implemented many
of the ideas espoused in the standards.
First, approaches will be described that were used with preservice elementary
teachers. Then, preservice elementary teachers' reflections after viewing a
particular video are shared. Finally, some of the challenges of incorporating
online videos into an elementary methods classroom are discussed.
Using Online Videos in Elementary Methods Courses
Currently, there exist many sources of videos that can be used to help teachers
examine mathematics teaching and learning (e.g., video tapes, video discs; Friel
& Carboni, 2000). These videos can be used in various ways; however, they
typically require facilitation by an instructor during face-to-face interaction.
For example, in an elementary methods course, instructors can show the Cognitively
Guided Instruction (CGI) classroom videos during a course session and engage
students in a discussion related to teaching and learning (Carpenter, Fennema,
Franke, Levi, & Empson, 1999). However, this structure may require that
(a) the instructor has access to a copy of the commercially available videos,
and (b) the instructor uses class time to show the videos and facilitate the
class discussion. Although important and useful, both of these activities require
the use of in-class time that may limit opportunities to engage in other activities.
Because each of our classes includes many activities we deem important and
do not want to eliminate, we opted to use videos that are accessible on the
Internet. This accessibility allows the incorporation of video in our courses
without consuming limited class time for viewing them. Additionally, preservice
teachers may view these videos at a time convenient for them, and the conversation
is extended beyond established class time. It also provides preservice teachers
an opportunity to reflect upon the material and add to their discussion at their
own pace. To that end, we opted to use PBS Mathline videos, although we acknowledge
that others exist (see the appendix).
We use PBS Mathline videos for the following reasons. PBS Mathline provides searchable
videos of mathematics teaching and learning at each of the grade bands K-2,
(Editor's note: See the Resources
section at the end of this paper for a list of website URLs.) The videos of
mathematics classrooms found at this site address a wide variety of topics,
including numeration, computations, algebra, geometry, measurement, and problem
solving. Furthermore, each broad topic is further categorized according to more
specific mathematics topics. Individuals may view a clip (a small segment of
the lesson), watch the entire lesson, and read the lesson plans for the observed
lesson. In addition to whole class interactions, some of the video segments
include small group or one-to-one interviews with students to reveal their understanding
about particular mathematics topics. Other video segments include teacher reflections
about changes in instruction and goals for the lesson.
Video Assignments in Elementary Methods Courses
The focus of our courses is to offer teachers many opportunities to engage
in and examine the teaching of mathematics using various methods (e.g., discovery
learning, cooperative learning, alternative assessments) and various tools (e.g.,
manipulatives, technology). Class time is spent exploring mathematics conceptually
and discussing the practical implementation of such activities by examining
the roles of the teacher and students in such settings. Overall, the goal is
to familiarize preservice teachers with the recommendations in the NCTM (2000)
Principles and Standards for School Mathematics and provide them opportunities
to experience teaching and learning that adhere to these standards.
Several assignments are given to help prospective teachers reflect on their
potential role as teachers. Viewing and reflecting on online videos represents
one such assignment and accounts for approximately 10% of the course grade.
Preservice teachers are required to view several PBS Mathline videos that highlight
ideas presented in our methods courses (e.g., use of technology, classroom discourse).
They are asked to view the entire lesson and contribute to a discussion about
what they observed. The goal of this assignment is to have preservice teachers
view various mathematics classrooms so they can identify the characteristics
that make them effective, to examine the reasoning of students, and to begin
to consider and examine those behaviors they may emulate; thus, the videos provide
alternatives to traditional mathematics classrooms they have experienced or
The expectation is that, while viewing the video lessons, preservice teachers
reexamine their deeply held beliefs regarding what it means to learn and teach
mathematics. A secondary purpose for requiring preservice teachers to view these
videos is to make them aware of a resource they can use for ongoing professional
development once they complete the teacher preparation program.
The PBS Mathline site contains many videos that address precise aspects of
both NCTM content and process standards for grades K-12. For our viewing assignments,
we each select specific videos to support ideas addressed during the course.
For example, while the topic of problem solving is being covered, a video depicting
the use of problem solving in the classroom would be assigned.
Although we share a common view regarding the use of online videos, the implementation
at our respective institutions differs. Kellogg teaches at a private liberal
arts college that has a network designed to facilitate creating websites to
accompany courses (see Figure 1). His methods classes
usually average from 10 to 16 preservice teachers each semester, providing opportunities
for all to participate in class discussions. Typically, six online videos are
assigned for viewing throughout the semester to complement course content and
address specific NCTM (2000) standards, including such topics as assessment,
technology, number and operations, algebra, geometry, measurement, data analysis,
and problem solving.
For example, while discussing alternative assessment, the preservice teachers
are asked to complete Web Video Assignment #2 by viewing the online video Bead-Dazzling
(click on "Watch Entire Lesson"). This video shows a teacher interviewing
students in real time. To accomplish this assignment, the students log into
the course website, and proceed to click on the "Web Video 2" link
in the "New Announcement" portion of the web page. After clicking
on that link, a page opens with general instructions about viewing the video
and what mathematical content will be addressed (for example, see Figure
2). The preservice teacher then simply clicks on the appropriate link found
in the "Manage Links" portion of the same Course Website.
After viewing the online videos outside of class, preservice teachers are asked
to complete a form to help initiate class discussion and promote personal reflection.
They are asked to list ways in which the teacher's actions and the activities
offer students opportunities to experience standards-based instruction. Additionally,
preservice teachers are asked to provide evidence of student behaviors indicating
that the goals of the standards are being realized. During the next class session,
the preservice teachers are engaged in a discussion of the video assignment.
In contrast, Kersaint teaches at a large public research institution where
Blackboard, a web-based tool to help the instructor make instructional material
available to course participants, is provided to facilitate online discussion.
Thus, she has the infrastructure to post information online, allowing preservice
teachers to link to videos directly from the course and to respond to an online
discussion about the viewed lesson. The class size for an elementary methods
course is typically 35 preservice teachers, which impacts the amount of class
time that can be devoted to extended discussion about the videos. As a result,
the discussions of the videos are relegated to ongoing conversations using the
discussion board outside of class time.
In her course, preservice teachers are asked to view videos that address the
following content areas: problem solving, numbers and number sense, fraction
concepts, and proportions. (The preservice teachers in this case are taking
the first course in a two-part elementary mathematics methods course sequence.
The first course focuses on number concepts and operations. The second course
deals with geometry, probability, and data analysis. Algebra is addressed to
some extent in both courses.) However, the discussions typically address the
process standards observed. In most cases, preservice teachers are presented
with options they can view at each of the levels—K-2 and 3-5. For each of the
lessons viewed, preservice teachers are required to (a) identify the lesson
that was viewed and indicate how (and what) NCTM standards are being implemented;
(b) describe how the viewed lessons differ from the mathematics lessons they
have participated in or have observed; and (c) describe what they have learned
about becoming a mathematics teacher from viewing the videos.
Additionally, preservice teachers are given the option to discuss other
important issues that were not addressed in the three categories identified. For
example, they often discuss how the class was organized (e.g., classroom
management). To encourage dialogue, they are required to respond to comments
provided by at least two of their peers. This requirement has resulted in
ongoing discussion, as preservice teachers reply to comments provided about
their particular reflections.
Preservice Elementary Teachers' Reflections
After viewing these online videos, preservice teachers in each of our courses
have commented that it is helpful to view the ways teachers apply the reform
recommendations that they studied in the methods class. The videos help validate
the instructional approaches presented in the course, as well as present
mathematics in an intriguing manner. In fact, preservice teachers often report
that they learn mathematics while viewing the videos. For many, the online
videos provide their first exposure to standards-based mathematics instruction,
and their responses have been positive.
To view the video prior to reading the reflections of preservice teachers,
go to To
Half or Half Not and click on "Watch entire lesson." This
particular video was assigned toward the latter part of Kersaint's course after
the preservice teachers had opportunities to discuss pertinent mathematics content
and pedagogical issues related to developing students' conceptual understanding
of rational numbers. The preservice teachers reacted to the lesson and described
how the NCTM standards were reflected in the lesson. For this particular assignment,
preservice teachers were given great flexibility regarding the nature of their
Individual teachers focused on different aspects of the mathematics classroom
as they viewed the lesson. (All names used are pseudonyms.) Some reacted to
the global features of the lesson:
This video shows just how much fun you can have with math and that you don't
need to just place a worksheet full of fractions in front of your students.
The children seemed to feel confident and enjoyed the activity a lot. This
activity provided students with a very neat way to understand fractions and
it stimulated interest in the topic. (Kelly)
Other preservice teachers discussed particular components of the lesson, such
as the use of multiple representations, the use of writing in the mathematics
classroom, or the use of real-world applications.
By seeing the different ways that one slice can be made into two equal parts or
by using the...geoboards they [the students] are able to notice that a shape is
not required to stay in one aspect of view. When you ask them to cut a square
in half they most likely have one line of symmetry in mind but by demonstrating
the different possible ways he [the teacher] opened their thinking the next time
they face a similar task. (Kelly)
Writing in the mathematics classroom:
I also liked the way that he asked the students to write a letter to the
customers about the problems with the ribbons. This gave the students a chance
to practice their writing skills as well as an opportunity to practice
communicating their mathematics understanding. (Ken)
Real-life applications: "I liked how this teacher incorporated
a real life situation into a math problem" (Tristen).
Still other preservice teachers focused on the teacher's behavior and commented
on his rationale for teaching the way that he did and the students' engagement
in the process of learning.
Allowing students to explore mathematics:
It also caught my attention when the teacher said that he rarely gives the students
answers. That he just lets them figure it out on their own. I think this is
something that I really need to work on. When I am working with a student I
am so tempted to tell them that they have the answer right or that it is wrong,
etc. I want to cut in and finish their sentence or complete their thought and
show them how to do the problem. I know that I really need to work on being
patient and hold my tongue and let the student figure things out on his own.
The students were asking questions among themselves and not relying on the teacher
to give the answers. They were actively engaged in the learning process. (Stan)
The children were very creative in figuring out how to make halves without duplicating
the work of other children. (Bob)
By having students reason and justify their answers they were really required
to think about what they were doing. (Karen)
Student presentations and communication:
The students had to orally explain their ideas to the class and the reasons
for what makes something half. They eventually discovered that the two parts
had to be equal, without being told by the teacher. Then a student reasoned
that the line dividing the halves did not have to be straight, as long as the
pieces were the same size. (Nicole)
It was a creative way to get the children to see how many different ways they
could show 1/2. It got the children to communicate their understanding about
fractions. It was fun for the students and it can help the teacher assess which
students understand the concepts. (Kamara)
Questioning: "I like the idea that he asks a lot of questions
to get the students engaged in the lesson" (Freda).
Use of manipulatives:
I had no idea what geoboards were when we began this class. Learning about manipulatives
and what a powerful tool they can be in reaching students and enabling them
to understand and explain math concepts has really made me think about other
day-to-day objects that could also be used as manipulatives. It was also exciting
for me to see a young teacher in a position using creative and exciting ways
to teach math. (Danielle)
Others reflected on their own experiences as learners of mathematics:
When I learned fractions, I had thought to myself, "When will I have to
use these?" But the teacher did a marvelous job showing the students and
having them act out various situations that do use fractions. I liked how the
teacher cut out the bread into the halves. The students explained also. I was
getting stumped for a bit after he asked are there any other ways to cut the
bread in half because I had never thought to cut a zigzag in the bread. But
as long as both parts of the bread were equal it worked. (Daria)
This type of classroom setting was very different than when I learned
fractions. We did not play any games. We just worked from the textbook. I
learned from this video to be creative when teaching mathematics. This makes it
more fun for the students to learn math and they are more interested in
The comments provided by the preservice teachers reveal how they began to
examine key aspects of mathematics teaching and learning. In fact, they were
commenting on methods that many initially thought were impossible to do with
students. Moreover, several preservice teachers reported that they viewed other
videos that were not assigned and looked forward to viewing more.
Prior to using these videos, the instructors agreed that they faced a higher
level of resistance regarding the use of reform methods than presently occurs.
Although the preservice teachers typically engaged in activities that were part
of the course, the level of reflection regarding such activities was lacking.
Preservice teachers often assert that many of the discovery approaches used
would be difficult for students, particularly when they themselves found the
pertinent mathematics challenging. This often meant that they rejected the
possibility of using such approaches. However, after viewing the videos of
students doing mathematics, talking mathematically, and presenting their
findings, preservice teachers are more able to understand alternative approaches
and consider their use.
Class discussions about course activities, as well as possible students' responses
to those activities, have always been incorporated into our elementary mathematics
methods courses. However, we find that preservice teachers respond differently
when they are able to make personal connections to the content presented in
the online videos. Rather than making claims about what may or may not be possible
in the classroom, the conversation has shifted to include what needs to occur
to help facilitate reform recommendations.
Although preservice teachers' reflection improved in both courses, there was
a marked difference in the level of reflection provided by the preservice teachers
in the two courses. One possible explanation for differences in teachers' reflections
could be the method used to facilitate the discussions: in class vs. online
format. During in-class discussions, preservice teachers may be reluctant to
share their perspectives regarding a topic or occurrence because of immediate
reactions by peers with opposing views. Some may find their peers' emotional
or passionate responses stifling. Additionally, reticent individuals may not
contribute to the class discussion because other more vocal individuals may
dominate the discussion.
In contrast, using the online discussion board gives every preservice teacher
an opportunity to reflect and share his or her point of view. Kersaint finds
that preservice teachers who are reluctant to participate during in-class
discussions often provide insightful comments during the out-of-class, online
discussion. Using an online discussion board enables individuals to share
thoughts and comments that they may generate long after a particular discussion
or in reaction to something someone had written but they had not originally
considered (see McDuffie and Slavit, 2003, for an extended discussion about the
potential that discussion boards provide). No matter the format, discussions are
an important aspect of incorporating online videos into elementary methods
Thus far, this article has focused primarily on sharing the potential
benefits of using online videos. However, as we refine the implementation of
online videos in elementary methods courses, we have had to address several
challenges. For example, the availability of appropriate technology is often an
issue. In early implementation, preservice teachers with only dial-up Internet
service attempted to view the videos at home. However, a high-speed Internet
connection is necessary to view the streaming video contained in the video
clips. Consequently, preservice teachers have been encouraged to view the videos
on campus. Additionally, problems with campus networks can wreak havoc with
individuals trying to access the video assignments, especially when deadlines
Other issues extend beyond the technology or format used for discussion. As
an example, should teacher educators establish the context for viewing a video
prior to asking preservice teachers to view it or should preservice teachers be
asked to view the videos without such contextual information? The former may
lead preservice teachers to respond in ways they perceive are expected by the
instructor. In contrast, in the latter approach preservice teachers may not make
anticipated links. A related issue is the placement of videos in the sequence of
course activities. Should the video be used to introduce specific concepts that
will be addressed or should the video be a culmination of previous interactions?
Which approach might result in improved reflection? With each question we pose,
we find that there are other related questions to be addressed.
Although we do not claim to have all the answers to these questions, we do
feel strongly about the use of such videos in our courses. We find that preservice
teachers are attentive and reflective in class because they see the application
of course topics taking place in classroom settings. Although instructors may
identify videos that suit their own particular purposes, the use of online videos
seems most appropriate when the videos are selected to support specific teacher
development activities and reflection is facilitated in some way.
Embedding these videos as part of elementary teachers' preservice mathematics
education has helped them appreciate alternatives to traditional methods for
learning and presenting mathematics ideas. The intent is not for preservice
teachers to blindly emulate the behaviors of the teachers they observe, but
instead to examine the type of learning possible when students are asked to
engage in mathematics, to reason mathematically, and to communicate their ideas
to their peers. The online videos offer an accessible and affordable learning
experience, which lends itself to discussion and reflection.
Carter, R., & Richardson J. (1999). Dilemmas of constructivist mathematics
teaching: Instances from classroom practice. In B. Jaworski, T. Wood, &
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perspectives (pp. 69-77). Philadelphia, PA: Falmer Press.
Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B.
(1999). Children's mathematics: Cognitively guided instruction. Portsmouth,
Cohen, D. K. (1990). A revolution in one classroom. The case of Mrs. Oublier.
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Eisenhart, M., Borko, H., Underhill, R., Brown, C. Jones, D., & Agard,
P. (1993). Conceptual knowledge falls through the cracks: Complexities of learning
to teach for understanding. Journal for Research in Mathematics Education,
Ensor, P. (2001). From preservice mathematics teacher education to beginning
teaching: A study in recontexualization. Journal for Research in Mathematics
Education, 32, 296-320.
Friel, S. N., & Carboni, L. W. (2000). Using video-based pedagogy in an
elementary mathematics methods course. School Science and Mathematics, 100,
Knapp, N. F., & Peterson, P.L. (1995). Teachers' interpretation of "CGI"
after four years: Meaning and practices. Journal for Research in Mathematics
Education, 26, 40-65.
Lortie, D. C. (1975). Schoolteacher. Chicago: The University of Chicago
Loucks-Horsley, S, Hewson, P.W., Love, N., & Stiles. (1998). Designing
professional development for teachers of science and mathematics. Thousand
Oaks, CA: Corwin Press.
Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah,
NJ: Lawrence Erlbaum.
McDuffie, A. R., & Slavit, D. (2003). Utilizing online discussion to support
reflection and challenge beliefs in elementary mathematics methods classrooms.
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National Council of Teachers of Mathematics. (1989). Curriculum and evaluation
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for teaching mathematics. Reston, VA: Author.
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Other Sources & Online Videos
-- The Modeling Middle School Mathematics
"Modeling Middle School Mathematics is a professional development program
using video lessons and Web-based Internet materials to examine each of the
five NSF-funded middle school math initiatives: Connected Mathematics, MathThematics,
MathScape, Math in Context, and Pathways" (MMM, 2003; http://www.mmmproject.org/video_matrix.htm).
In addition to other information, this site contains video clip examples from
each of the curricula. The clips address a variety of ideas, including student/teacher
discussion, student activity, student dialogue, student work, student presentations,
group work, group discussion, interviews with teachers using the materials and
FCAT Staff Development Tools
This staff development tool is a program that was developed to help teachers
prepare students for Florida¡¯s high stakes assessment, the Florida
Comprehensive Assessment Test. Regarding mathematics, two sites were developed,
one at the 5th grade level and one at the 8th grade level. Each of these sites
includes video of Florida teachers teaching mathematics.
FCAT 5th Grade Math
FCAT 8th Grade Math
Bead-Dazzling - http://pbs-mathline.virage.com/cgi-bin/visearch?user=pbs_mathline&template=template_3-5.html&query=VideoAsset:atmp_bd%2BAND%2BClipAccess:Public&grade=3
PBS Mathline - http://www.pbs.org/teachersource/math.htm
Grades K-2 - http://www.pbs.org/teachersource/mathline/lessonplans/search_k-2.shtm
3-5 ¨C http://www.pbs.org/teachersource/mathline/lessonplans/search_3-5.shtm
6-8 ¨C http://www.pbs.org/teachersource/mathline/lessonplans/search_6-8.shtm
9-12 - http://www.pbs.org/teachersource/mathline/lessonplans/search_9-12.shtm
To Half or Half Not - http://pbs-mathline.virage.com/cgi-bin/visearch?user=pbs_mathline&template=template_3-5.html&query=%2BVideoLessonName:To%2BVideoLessonName:Half%2BVideoLessonName:%22or%22%2BVideoLessonName:Half%2BVideoLessonName:%22Not%22&grade=3&MathCategory=0&Me
Clearwater Christian College
|Figure 1. Screenshot of Kellogg's website.
|Figure 2. Screenshot of Kellogg's assignment to watch
the Bead-Dazzling video.