ORIGINAL ARTICLE
Using video as a tool for promoting inquiry among preschoolteachers and didacticians of mathematics
Dina Tirosh • Pessia Tsamir • Esther Levenson •
Ruthi Barkai • Michal Tabach
Accepted: 26 November 2013 / Published online: 6 December 2013
� FIZ Karlsruhe 2013
Abstract This paper explores the use of video as a tool
for promoting inquiry among preschool teachers and di-
dacticians. In this case, the didacticians are teacher edu-
cators who are also mathematics education researchers.
Preschool teachers recorded themselves with video imple-
menting number and geometry tasks with children and
shared these recordings with other teachers and didacti-
cians. The session where the teachers and didacticians
viewed and discussed these recordings was recorded and
viewed later by a group of didacticians. The multiple uses
of video led to inquiry on several levels. Teachers inquired
into the practice of implementing tasks with children,
evaluating children’s knowledge, and the practice of using
video as a tool. Didacticians inquired into their practice of
research with children, their practice as teacher educators,
the use of video as a tool in professional development, and
the use of video in their inquiry process. Teachers’ and
didacticians’ inquiries led to increased appreciation for the
practice of inquiry, belonging to a community of practice,
and its role in promoting both teachers’ and didacticians’
knowledge for teaching.
1 Introduction
In recent years, there has been increased interest in math-
ematics education at the preschool level and providing
teachers with appropriate professional development (e.g.,
Starkey et al. 2004). This paper focuses on the participants
of one such program, including the teachers and those who
planned, organized, and taught in the program. According
to Jaworski (2004), didacticians of mathematics concep-
tualize and theorize learning and teaching of mathematics,
developing knowledge in these areas. They may also be
teacher educators, preparing future teachers and/or pro-
viding professional development for practicing teachers.
We, the five authors of this paper, are all didacticians who
have worked together for several years conceptualizing the
knowledge preschool teachers need for teaching mathe-
matics (Tsamir et al. 2012). We have also worked together
providing professional development for preschool teachers,
with the aim of promoting both their knowledge and self-
efficacy for teaching mathematics in preschool (Tsamir
et al. 2013). Throughout the years, we have continuously
assessed our knowledge and theories and attempted to
revise and improve the professional development we offer
preschool teachers. Towards this aim, we recently decided
to implement a new way (for us) of using video as a tool in
our professional development course for practicing pre-
school teachers. For the teachers, it was also a first expe-
rience. The central research question we ask is: can video
be used as a tool in forging communities of inquiry and, if
so, how? This paper will present findings related to this
new endeavor.
2 Providing professional development for preschool
teachers: theoretical perspectives and practice
Several theoretical perspectives guide this study. We begin
with theories related to teachers’ knowledge and show how
these theories framed our practice with teachers. We con-
tinue with a review of studies related to the use of video as
a tool in professional development. Finally, we relate to
social perspectives of learning in a community.
D. Tirosh � P. Tsamir � E. Levenson (&) � R. Barkai �M. Tabach
Tel Aviv University, Tel Aviv, Israel
e-mail: [email protected]
123
ZDM Mathematics Education (2014) 46:253–266
DOI 10.1007/s11858-013-0563-x
2.1 Teachers’ knowledge
For the past several years, we have been providing pro-
fessional development for preschool teachers, aiming to
promote their mathematical knowledge and self-efficacy
needed for teaching. Some of our programs extended for
only a few weeks while others extended for as long as
3 years (Tirosh et al. 2011a). In this section, we describe
our theoretical perspectives regarding teachers’ knowledge
and how these perspectives contributed to the organization
of our practice. In later sections, we will refer back to these
perspectives when analyzing our work with the teachers.
Our programs for preschool teachers are guided by the
Cognitive Affective Mathematics Teacher Education
(CAMTE) framework (e.g., Tirosh et al. 2011b; Tsamir
et al. 2013). This framework, presented in Table 1, takes
into consideration the interrelationship between knowledge
and beliefs which can affect teachers’ proficiency
(Schoenfeld and Kilpatrick 2008). In Cells 1–4 and in Cells
5–8, we address teachers’ knowledge and self-efficacy,
respectively. The same framework guides our research
study.
In this paper we focus on the knowledge aspects of the
program. Elsewhere (e.g., Tirosh et al. 2011b) we have
described aspects of our program related to preschool
teachers’ self-efficacy. In framing the mathematical
knowledge preschool teachers need for teaching, we draw
on Shulman (1986), who identified subject matter knowl-
edge (SMK) and pedagogical content knowledge (PCK) as
two major components of teachers’ knowledge necessary
for teaching. In our previous work with teachers, we found
it useful to differentiate between two components of
teachers’ SMK: being able to produce solutions, strategies,
and explanations; and being able to evaluate given solu-
tions, strategies, and explanations (Tabach et al. 2010).
Thus, our framework takes into consideration both of these
aspects of SMK. Regarding PCK, we draw on the works of
Ball and her colleagues (Ball et al. 2008) who refined
Shulman’s theory and differentiated between different
aspects of PCK. We chose to relate to two aspects:
knowledge of content and students (KCS) and knowledge
of content and teaching (KCT). KCS is ‘‘knowledge that
combines knowing about students and knowing about
mathematics’’ whereas KCT ‘‘combines knowing about
teaching and knowing about mathematics’’ (Ball et al.
2008, p. 401). Under this last category, we focus on the
design, evaluation, and implementation of mathematical
tasks. In Israel, there is a new mandatory mathematics
preschool curriculum (INMPC 2008), but few curricular
materials are available. Teachers often find themselves
designing their own tasks and so it is important for them to
appreciate the design process and its implication for cre-
ating learning opportunities.
While knowledge of mathematical tasks is one of the
aims of our program, engaging teachers with mathematical
tasks is also a means by which other objectives may be
reached. For example, the didacticians in the program often
simulate playing with children with these tasks in order to
promote teachers’ knowledge of mathematical concepts
and pedagogical-mathematical theories such as Gelman
and Gallistel’s (1978) five principles of enumerating, van
Hiele’s model (e.g., van Hiele and van Hiele 1958) for
students’ geometrical thinking, and Tall and Vinner’s
(1981) concept image–concept definition theory. This type
of simulation allows teachers to confront, in a gentle and
respectful manner, their own mathematics knowledge
(Cells 1 and 2 of the CAMTE framework), and serves as a
springboard for a thorough discussion of both common
mathematical errors as well as children’s conceptions (Cell
3 of the CAMTE framework). In time, teachers are invited
to take part in these simulations, promoting their knowl-
edge of tasks and teaching (Cell 4 of the framework). Many
of the tasks we bring to our program are designed by us and
have been implemented in preschools, by us as well as by
preschool teachers who have previously participated in our
programs. Eventually, teachers participating in our pro-
gram are invited to implement some of the tasks with the
children in their preschool classes and share the results of
such activities with the other teachers and didacticians of
the program.
Table 1 The cognitive affective mathematics teacher education framework
Subject matter Pedagogical content
Solving Evaluating Students Tasks
Knowledge Cell 1: Cell 2: Cell 3: Cell 4:
Producing solutions Evaluating solutions Knowledge of students’
conceptions
Designing and evaluating tasks
Self-
efficacy
Cell 5: Cell 6: Cell 7: Cell 8:
Mathematics self-efficacy
related to producing
solutions
Mathematics self-efficacy
related to evaluating
solutions
Pedagogical-mathematics self-
efficacy related to children’s
conceptions
Pedagogical-mathematics self-
efficacy related to designing and
evaluating tasks
254 D. Tirosh et al.
123
2.2 Video as a tool in professional development
The use of video as a tool in professional development was
new for us, but has a wide basis in the literature. When
reviewing these studies, we consider several variables:
What was the purpose of using video? How was the video
used? What were the sources of the video clips shown to
participants? Who were the participants?
The purpose of using videos may differ from program to
program. For example, Star and Strickland (2008) discuss
the need to improve prospective teachers’ ability to notice
important events and details occurring during a classroom
lesson. Towards this aim, participants observed actual
classroom lessons but also viewed several classroom vid-
eos, including ones from the US Public Release TIMSS
video study. Over the course of the program, prospective
teachers’ observation skills improved and they took more
notice of the classroom environment, mathematical content
of a lesson, and the communication between classroom
participants. Ginsburg et al. (2004) also relate to profes-
sional development for prospective teachers. They describe
their program for prospective preschool teachers, during
which participants are required to view and interpret vid-
eotaped examples of young children displaying mathe-
matical behavior during free play and during classroom
teaching episodes. Videos are used to illustrate young
children’s mathematical behaviors and to help prospective
teachers appreciate the role of mathematics during early
childhood. Like the above studies, Santagata and Guarino
(2011) employed the use of prepared video clips during
prospective teacher education but with the specific aim of
developing participants’ appreciation of students’ mathe-
matical thinking. However, unlike the previous studies,
participants were also required to videotape themselves
working with students on problem-based activities. The
aim of this requirement was to focus the participants on the
details of student thinking as well to reflect on the effec-
tiveness of their own teaching. These personal video clips
were not shared with other participants.
Teachers sharing videos made of themselves is the basis
of video clubs, a type of professional development for
practicing teachers, where groups of teachers watch and
discuss videotapes of their classrooms (Sherin and Han
2004). In their study of a series of video club meetings,
Sherin and Han (2004) found that, over time, teachers
became more focused on issues concerning student con-
ceptions, and became more focused on students’ thinking.
The idea of teachers reviewing videos taken of themselves
was also recognized by the UK’s National Council for
Excellence in Teaching Mathematics (NCETM). A report
commissioned by NCETM (Hall and Wright 2007) claimed
that it may be more effective during professional devel-
opment to use video recordings which teachers produce of
themselves than to use standardized video recordings made
for public use. This is echoed by Santagata and Guarino
(2011), who mentioned as an issue the ‘‘distance PSTs
[preservice teachers] might feel between their teaching
abilities and the ability of the teachers portrayed in the
videos’’ (p. 143). Such a distance might also be felt by
practicing teachers if, for example, the videos depict
classrooms from a different culture.
To summarize, the above studies point to the benefits of
using video recordings during professional development,
enhancing participants’ observation skills, increasing their
awareness of students’ mathematical abilities, and pro-
moting participants’ abilities to analyze students’ thinking.
Some of the studies employed the use of publicly available
video recordings while a few encouraged participants to
record themselves. In this study, we are not only interested
in how video was used as a tool for improving teaching
skills. We are also interested in how video was used as a
tool for forging communities of inquiry. According to
Sherin and Han (2004), viewing videos of classroom
interactions with other teachers can ‘‘promote a stance of
inquiry among teachers’’ where teachers ‘‘question, reflect
on, and learn about teaching’’ (p. 165). These reflections
and ideas then become a resource for teachers as they
continue to explore learning and teaching.
2.3 Social perspectives of learning in a community
Our professional development program combines both
cognitive and social perspectives of learning. On the one
hand, we introduce teachers to cognitive theories of
mathematics learning. On the other hand, we view teachers
as members, in this case, of the community of practice of
preschool teachers. Learning may be conceived as
increased participation in the practice of the community
where learners, as opposed to experts, participate in a
limited way with limited responsibilities (Lave and Wenger
1991). In line with Garcia et al. (2006), the theories we
introduce to teachers (e.g., Gelman and Gallistel’s (1978)
five principles of enumerating) become conceptual tools.
‘‘Conceptual tools are understood as those concepts and
theoretical constructs that have been generated from
research … leading to understanding and handling the
situations in which mathematics is taught and learned’’
(Garcia et al. 2006, p. 112). Learning includes identifying
and using these tools in practice. In addition, conceptual
tools enable members of the community to examine and
reflect on their practice and to interact with each other
within the community (Garcia et al. 2006).
Encouraging teachers to examine and reflect on their
practice is one of the goals of professional development.
According to Jaworski (2006), inquiry can be used as a tool
to enable members of a community to ‘‘engage critically
Using video as a tool for promoting inquiry 255
123
with key questions and issues in practice’’ (p. 187). When a
community’s way of being is to reflect on, research, and
critique its current practice, it may be said to be a com-
munity of inquiry. In this paper, we describe a session of a
professional development program where preschool
teachers and didacticians inquired into the practice of
teaching mathematics in preschool. This form of collabo-
ration between teachers and researchers through inquiry
was called co-learning by Jaworksi (2003). Our community
included new as well as experienced teachers, and teacher
educators who, in our case, were also university-based
mathematics education researchers. The practices of our
community included teaching, inquiry, and teacher edu-
cation. It could be said that the aim of inquiring and
reflecting into our mutually supportive practices was to
contribute to the development of these practices. In addi-
tion, we, the didacticians, engaged in reflecting on our dual
practices as teacher educators and mathematics education
researchers. While all of us were involved in the planning
and organization of the program, not all of us attended
sessions of the program. Thus, it may be said that our
community of inquiry included insiders, those that actively
participated as teacher educators, as well as outsiders who
did not participate as teacher educators in the program but
joined in the inquiry of the practice (Jaworski 2003). In the
next section we describe in more detail the setting of our
study.
3 Setting
Sixteen preschool teachers, with a Bachelor’s degree in
education, participated in the particular program described
here. All were teaching 4–6-year-old children in municipal
preschools. The program consisted of ten 3-h sessions at a
professional development center, and focused on teaching
number and geometry concepts in preschool. In Israel,
teachers are encouraged to participate in professional
development courses. The authors of this paper collabo-
rated on the design of the program, including the mathe-
matical tasks that would be implemented with the teachers
and children and the video task which would be assigned to
the teachers. There was one main teacher educator, Ruthi,
who taught and directed all the program sessions and two
other didacticians, Dina and Esther, who attended several
sessions. During the program, the preschool teachers, along
with Ruthi, chose several mathematical tasks to implement
with individual children in their preschool classes. Those
tasks were designed by us and had been implemented in
preschools by us, as well as by preschool teachers who had
previously participated in our programs. The teachers
agreed to implement the same tasks in order to be able to
compare results of their efforts. The teachers then
videotaped the task implementations, chose segments for
sharing, and viewed and discussed those segments collec-
tively with the teachers and didacticians. Questions
regarding task design, task analysis, task implementation,
children’s learning, and the use of video were raised and
explored, leading to an inquiry norm (Jaworski 2006) for
these sessions. The community attending the sessions
where video segments were discussed included all of the
participating teachers and Ruthi. Dina and Esther also
participated in two of these viewing-videos sessions, each
one at a different session. These sessions were videotaped
and transcribed.
After the program was over, Ruthi sat with Esther,
present at one session, and Pessia, who was not present at
any of the sessions with the teachers. Together, the three
didacticians watched the recordings of two sessions where
teachers’ videos were viewed and shared. The discussion
between the three didacticians was recorded and tran-
scribed. This transcription was reviewed by Dina, present
at one of the viewing sessions, and Michal. Thus, addi-
tional viewpoints were added. To summarize, video
recordings were used in several ways by both teachers and
didacticians. Teachers recorded their mathematical activi-
ties with children and together with didacticians ques-
tioned, explored, and discussed their practice, including the
practice of using video as a tool. Didacticians recorded
their activities with teachers and then questioned, explored,
and discussed their practice. Offering and receiving critical
comments by didactician colleagues is a form of mentoring
which can support the professional growth of didacticians
(Jaworski 2008). It is our collective inquiry into this new,
for us, practice of using video as a tool in professional
development which is the focus of this paper.
4 Methodology
This paper presents a case study of one group of didacti-
cians and one group of preschool teachers, inquiring into
their practices. The central research question of this study
is: can video be used as a tool in forging communities of
inquiry and, if so, how? When choosing data samples to
analyze, we focused on Cells 3 and 4 of the CAMTE
framework (see Table 1) and searched for segments where
teachers and didacticians questioned elements of their
practice related to implementing tasks and segments where
they reflected on students’ learning. We were also inter-
ested in segments where teachers and didacticians reflected
on the practice of using video as a tool in their own
learning. Finally, regarding the didacticians, we also sear-
ched for segments that would illustrate their dual roles of
teacher educators and mathematics education researchers.
Examples which best illustrated the effect of using video
256 D. Tirosh et al.
123
on forging communities of inquiry were chosen for pre-
sentation in this study.
Analysis of data was conducted in line with the CAMTE
framework and theories of learning related above. Thus, we
analyzed what aspects of tasks and teaching (Cell 3) and
students’ conceptions (Cell 4) came to light as participants
inquired into their practice. We also attempted to unravel
the episodes in terms of the ways in which the teachers and
didacticians interacted with each other within the com-
munity, not only who said what and who learned what, but
the different roles played by participants.
5 Findings
Two main strands of data resulted from this project, the
first stemming from preschool teachers’ inquiry into their
practice and the second from the didacticians’ inquiry into
their practice. This section is organized in the following
way. Excerpts from one session in which teachers viewed
themselves are presented, beginning with a short intro-
duction to those excerpts. Those excerpts are then followed
by corresponding segments from the discussion didacti-
cians had when viewing those particular excerpts. The
CAMTE framework, which helped organize the profes-
sional development program, organizes these sections as
well, as we focus first on knowledge of tasks (Cell 4 of the
CAMTE framework) and then on knowledge of students
(Cell 3 of the CAMTE framework). When analyzing this
session we relate to social perspectives of learning as a
community.
5.1 Learning about tasks through inquiry
Analyzing mathematical tasks, their design, affordances
and constraints, and their implementation, was central to
our program with preschool teachers. This section begins
by presenting a segment of the lesson where teachers dis-
cussed video clips brought by three teachers. Each clip
shows the teacher engaging one child with a task designed
to evaluate the child’s ability to enumerate 30 items. The
original task, which had been chosen during previous
program sessions, was to consist of the teacher requesting
the child to count 30 objects. The videos could then pro-
vide an opportunity to view and discuss various ways and
strategies children may use to deal with this problem.
5.1.1 Teachers inquiry into tasks
As the teachers began to share their videos with each other
and with Ruthi, the main teacher educator, and Dina, it
became clear that here (and with the implementation of
other tasks as well) teachers implemented the task in
different ways. One teacher, Ellen, piled 30 objects on the
table and requested the child to say how many objects there
were. A second teacher, Bettina, placed more than 30
objects in a basket and asked the child to take out 30
objects. The following discussion resulted from viewing
those videos. The names of all teachers are pseudonyms.
Segment T1a:
Ruthi: Ok. What would you like to say?
Bettina: About the enumeration evaluation task. I didn’t
(pause). Was I supposed to do it like Ellen did,
putting the 30 on the table? Or tell the child to
take out 30?
Ruthi: Ok. First, we see two differences in the task.
Right? Bettina had a basket with more than 30
disks, and the child had to take out 30, as
opposed to Ellen, where all of the 30 were
placed on the table and the girl had to count.
First, these are two different tasks… Also, if she
would have placed in the basket exactly 30
objects, would that be the same task?
In the above segment we see how the teachers, along
with Ruthi, deal with the fact that not all of the teachers
implemented the tasks in the same way. This could have
caused dissonance and criticism among the group. Indeed,
we see from Bettina’s initial comment that she is con-
cerned about the fact that she implemented the task dif-
ferently from Ellen; she wants to know what she was
‘‘supposed’’ to do. Ruthi, however, turns the discussion
away from this type of criticism and uses it as an
opportunity for growth, to discuss with the teachers the
differences between the tasks, even adding an additional
version of the task to the two previously viewed. Adding
another possible version of the task validates Bettina’s
contribution as one which can extend the teachers’
appreciation of task variety. In the following segment, the
teachers discuss the level of difficulty of the tasks. The
discussion arose spontaneously.
Segment T1b:
Lori: If the 30 are in a basket, one on top
of another, the child has to take out
(the objects) and that would force
him to make some order. It’s more
difficult.
Ruthi: The way Ellen did the task, the
difficulty is thinking of a strategy to
separate the objects that were
counted from those not counted.
Using video as a tool for promoting inquiry 257
123
Dina (Didactician): I would like to ask something.
Which task is the most difficult?
We are talking about three tasks.
Write them down. The first task, we
saw by Ellen, is when there are 30
disks piled on the table and you have
to enumerate them. The second task,
Bettina’s, is that there are lots of
disks in a basket, more than 30, and
the child has to take out 30 disks.
The third task, suggested by Ruthi is
to have a basket with exactly 30
disks and the child has to say how
many there are.
(Teachers start commenting all at
once what they think).
Dina: In the end everyone will get a chance
to vote. But now, everyone thinks to
themselves … Take for yourselves a
minute, each one quietly, to
themselves, and write down the
tasks in order of their difficulty.
Matana: Wait. In the first task, can the
children organize the disks in some
way?
Dina: They can do as they please.
Tina: The third task is the easiest and the
first is the most difficult.
Nina: The first is easiest, then the third,
then the second.
Lori: I agree with Nina.
Shiela: I think the first is most difficult and
the second and third are the same
level.
(More teachers say what they think).
Dina: Before deciding on the order of
difficulty, try yourselves to do the
tasks. For each task, what do you
need to do? Try to analyze the
complexity. Then try to see the task
through the eyes of the children. And
then, try out the tasks with children
in your class.
In segment T1b, we see contingent action (Rowland
et al. 2005) on the part of the didacticians as they build on
Lori’s spontaneous inquiry into the difficulty of tasks and
demonstrate to the teachers how to think about tasks,
including the teachers in the practice of analyzing tasks.
Behaving like a community does not mean that everyone
must agree or that there is no time for individual thoughts.
On the contrary. Dina specifically makes time for each
teacher to think for herself. Being able to come to indi-
vidual conclusions is part of the practice of preschool
teachers and should be recognized as such. In addition,
Dina invites the teachers to try out all three tasks in their
preschool class, thus encouraging them to continue the
inquiry process, seeking evidence for what is more or less
difficult.
5.1.2 Didacticians’ inquiry into tasks
The recording of the above session was viewed by Ruthi,
present at the session, and Esther and Pessia, not present
during that session. Watching the video of the program
session triggered the didacticians to continue inquiring into
what makes a task more or less difficult for children while
developing a meaningful vocabulary.
Segment D1a:
Pessia: So, Ruthi, which of the tasks do you think is the
easiest? (Pessia is referring to the three
enumerating tasks discussed during the viewed
lesson).
Ruthi: I think the question should be something like, if
the child succeeded in the first task, will he
succeed in the second task and if he succeeded in
the second task, will he succeed in the first task?
Pessia: First of all, you are coming up with a definition,
which is very nice. You are, in essence, asking
yourself, what is an easy task? And you’re trying
to build a definition (for an easy task).
Ruthi: Right.
Pessia: In essence, we go back and forth between popular
common language and more exact language.
There isn’t only one thing which makes a task
difficult. It was the teachers who brought up the
question of which task was easy and which was
difficult for children. But from a research
perspective, we have evidence (from studies
with children), and so I define easy and difficult
as the likelihood that a child will succeed in
correctly completing the task.
Pessia opens up the discussion among didacticians by
turning to Ruthi and asking her what she thinks regarding
the difficulty of the tasks. Ruthi rewords Pessia’s original
question. Pessia recognizes this rewording of the question
as an attempt to define, or perhaps set standards, by which
we can classify a task as being easy or difficult. Pessia also
points out that notions such as ‘easy’ and ‘difficult’ have
popular meanings as well as scientific meanings. As
258 D. Tirosh et al.
123
teacher educators, we recognize that knowing what makes
a task more or less difficult is an important aspect of
teachers’ knowledge for teaching mathematics. As a
research community, we may look at our own practice as
researchers, and come up with evidence-based definitions.
Watching the video of the program session also led the
three didacticians to discuss the pedagogical task given to
the teachers, that is, the task of investigating the levels of
difficulty inherent in solving each task.
Segment D1b:
Pessia: What is the aim of this activity?
Esther: Wait a minute. Which activity?
Pessia: What could be the aim of doing this type of
activity with the teachers?
Esther: You mean the activity of sorting tasks according
to their level of difficulty (see Segment T1b). Ok.
Ruthi: I think, first of all, the aim is to show the teachers
that there isn’t one answer, one way of knowing
which task is more or less difficult. It is to show
them that each task has its own element of
difficulty. Also, to expose them to the different
variants of tasks and what differences might
make a task more or less difficult. Also, that you
need to go to the field and check it, to try each
one with children, before deciding which of the
tasks is more or less difficult.
Segments D1a and D1b, taken from the didacticians’
discussion, illustrate how watching our own practice led to
different directions of inquiry. Esther’s comments illustrate
this complexity; she is unsure of which activity Pessia is
relating to, the enumerating tasks implemented with the
children, or the sorting activity given to the teachers. An
additional complexity and strength of the didactician’s
inquiry session stemmed from the didacticians’ dual roles as
mathematics education researchers and teacher educators.
As mathematics education researchers, we asked ourselves
how we would define the level of difficulty of a task. We
then switched roles and, as teacher educators, we asked
ourselves why it is important to discuss this with teachers.
We learned that this type of activity with teachers promotes
their knowledge of task variation, task analysis, the
importance of evidence-based assertions, and adaptability.
While the above segments revolved around knowledge
of tasks (Cell 4 of the CAMTE framework, Table 1), in the
next section we present segments which revolve around
knowledge of students. As above, we first bring segments
from the session where teachers viewed videos of them-
selves. This is followed by segments taken from the dis-
cussion didacticians had when viewing those segments.
5.2 Learning about students through inquiry
In addition to promoting preschool teachers’ knowledge for
teaching number concepts, such as how varying a task may
promote different counting strategies, the program aimed to
promote knowledge for teaching geometry concepts. Dur-
ing the program, the teachers, along with Ruthi, chose to
implement a task for evaluating children’s ability to iden-
tify examples and nonexamples of triangles. The task
consisted of showing children cards with drawings of
intuitive and non-intuitive examples and nonexamples of
triangles produced by the didacticians (Tsamir, et al. 2008),
one drawing to a card, and asking the child if the drawing is
or is not a triangle and why. The teachers agreed on the set
of examples and nonexamples to use as well as the order in
which the figures would be presented to the child.
5.2.1 Teachers’ inquiry into their students’ knowledge
As before, teachers videotaped themselves implementing
this task with children. In the segments below we illustrate
how viewing video recordings stimulated inquiry into
children’s reasoning related to triangles. The segment
begins with an introduction by Ruthi and continues with
the teachers’ and didacticians’ discussion which followed
the viewing of clips presented by three teachers.
Segment T2a:
Ruthi: So, first of all, it’s important to listen and that is
how all of us learn. We designed very specific
questions and on the one hand we wanted to be
very exact in the questions but on the other
hand, we have dilemmas which arise when
sitting with the child. Ok. So, we’re not here to
say if what you did was ok or not ok. We’re here
to see what we can learn. So, let’s watch the
video about the triangles.
(The teachers, along with Ruthi and Dina, watch
three recordings of different teachers each
implementing the triangle task with a child in
their kindergarten class).
Ruthi: What can we say about the children?
Ann: The first child, all of his answers had to do with
vertices…Dalia: Even when there was an open figure ( ),
he said it was missing a vertex.
Ruthi: Also the second child said it was missing a
vertex. The first (child), said it (the figure) had
two vertices. Still they referred to vertices and
not to the critical attribute of being closed.
Using video as a tool for promoting inquiry 259
123
Miriam: But when the triangle-like figure had a round
edge ( ), he did relate to it. In other words, he
knows that a triangle has to have straight lines.
He knows that having three vertices is not
enough. The lines have to be straight.
Ann: The third child said it was a triangle because it
was closed. But that’s not enough because a
circle is also closed. I would have expected the
child to say also that it has vertices and straight
lines.
In the above segment, Ruthi begins the viewing session
by reminding the teachers of the purpose of watching each
other’s videos. As the expert practitioner, she enjoins them
to focus on the child in the video, and not on the teacher.
After viewing the video clips, the teachers point out that
two children seem to be focused on the vertices of the
figures and that they barely mention other critical attri-
butes. In other words, their inquiry is focused on what can
be learned about the children’s geometric reasoning from
viewing the clips. While they acknowledge that the chil-
dren correctly identified all of the figures, they are not
satisfied. Dissatisfaction leads to further inquiry.
Segment T2b:
Ruthi: He (the first child) did say it (the open figure
) was not a triangle.
Pat: Maybe he knows more than vertices but has
difficulties retrieving knowledge.
Dorit: We could have asked him.
Sari: It’s like he understood the topic but … we could
have asked him what else. The same for the third
child.
Ruthi: First of all, they were able to identify the
prototypical triangle ( ) and they explained
why it was a triangle using critical attributes.
They didn’t say it was a triangle because it looks
like the roof of a house. But they didn’t use all of
the critical attributes, just vertices.
Ruthi begins by focusing on what the children did know.
As the expert practitioner, she sets the tone of inquiry. The
first child may have focused only on vertices but he did not
say a figure was a triangle when it was not a triangle. This
perhaps leads the teachers into acknowledging that
although the first child seemed to focus on vertices, it does
not mean that he is not aware of other critical attributes. In
other words, their inquiry into children’s knowledge is
guided by the question of what the children know, and not
only by the question of what mistakes they are making.
Taking together the two segments, we see that the teachers
begin to realize that it is not simple to evaluate children’s
knowledge and that further inquiry is necessary. Both Dorit
and Sari mention the need for further questions. Ruthi ends
this part of the discussion by pointing out another positive
aspect of the children’s geometric knowledge, the chil-
dren’s use of critical attributes and mathematical language
when judging the figures.
5.2.2 Didacticians’ inquiry into students’ knowledge
As the didacticians viewed the above segments of the
program session, they also inquired into the practice of
evaluating children’s knowledge.
Segment D2a:
Pessia: The movie made me think of, and somehow we
never discussed this together, when a child
answers a certain way, how do we continue?
What questions do we want to ask the child when
we want to evaluate his knowledge and also when
we want to teach? As teacher educators, we
should think about this some more. Then we can
build a tool. If the child lists one critical attribute,
ask this. If the child lists two critical attributes,
ask this.
Ruthi: Ok. But we have to test it. Because, even if I see
that the concept of vertices is very dominant and
I ask the child, what else does the triangle have,
and then I do this a few times, then the child will
start responding automatically, with a list each
time. I don’t know.
Pessia: No. I don’t mean it like that. Yes, of course I
want to know if the child is aware of all of the
critical attributes of a triangle. But I also want the
child to feel the need to respond with more than
one critical attribute. Like, to explain why an
orange (the fruit) is an orange, it isn’t enough to
say because it’s (the color) orange.
Ruthi: But, by not asking the children additional
questions, we may see (in the videos) two
children for whom vertices are very dominant
but for one, this leads to correct identification,
while for the other it doesn’t.
Pessia: Who and what are we focusing on – the teachers,
or our understanding of the children?
In the above discussion, we see that the didacticians are
also interested in inquiring into children’s knowledge.
However, for them, the inquiry takes on different levels.
First, there is the level of the researcher interested in
260 D. Tirosh et al.
123
learning more about children’s knowledge. How can we
assess children’s knowledge? What tools do we have?
What questions should we ask? What is it that we want to
evaluate—children’s use of critical attributes when rea-
soning about triangles or their need to express more than
one critical attribute when affirming that some figure is a
triangle? Ruthi then brings the inquiry to another level, the
level of the teacher educator. What can the teachers learn
from the videos of the children and what might be learned
about children’s knowledge by not asking further ques-
tions? As before, we see the complexity involved in the
didacticians’ inquiry.
Viewing the segments from the program session also led
the didacticians to inquire into their students’ knowledge,
their students being the preschool teachers participating in
the program.
Segment D2b:
Ruthi: As the teacher of the course, what struck me most
when I watched the video (of the program
session), was the opportunity to see what they
(the preschool teachers) learned. How they
talked, the language they used to analyze the
(videos).
Pessia: What I hear (in the teachers’ discussion) are
mathematical comments or actually, mathematical
and pedagogical-mathematical points because
they are talking about the child but they are
using very precise mathematical terms … and the
language is fluent, it’s communicative … which
allows them (the teachers) to talk about the
mathematics and what the children know. And
you (Ruthi) stressed the point of what the child
knows, what he expressed, and that we can’t
assume that he doesn’t know. We have to make an
effort to introduce a culture (among teachers) of
seeking out what the child does know and not only
pointing out what the child does not know.
Through inquiry approaches, knowledge in the com-
munity of practice has developed. While Ruthi pointed out
her satisfaction in the teachers’ ability to evaluate their
young students’ knowledge, Pessia points out that their
language has developed; it is mathematical, precise, and
fluent, allowing them to participate more fully in the
community of inquiry. Pessia further points out the need to
continuously develop the norm of inquiry for this com-
munity, the norm of seeking out what a child knows in the
midst of apparent gaps in knowledge.
Ruthi pointed out that it was the act of watching the
videos of the program session that afforded her the
opportunity to evaluate her students’ knowledge. In the
next sections we bring excerpts where the teachers and
didacticians inquire into the use of video during the pro-
fessional development program and as a tool for reflection.
5.3 Reflecting on the use of video as a tool
The use of video as a tool in professional development was
new for the teachers as well as for the didacticians. As
such, it was an object of inquiry during the program,
reflected upon by the teachers together with the didacti-
cians as well as separately afterward by the didacticians.
As above, we first present excerpts from the teachers’
comments related to the use of video. However, unlike the
previous section, the excerpts we present from the didac-
ticians’ discussion are not necessarily related to the specific
excerpts from the teachers’ discussion.
5.3.1 Teachers inquire into the use of video
At times, as will be seen later, the didacticians specifically
brought up the issue of using video during professional
development with the teachers. However, during the first
session in which teachers viewed video recordings, spon-
taneous comments arose, mostly having to do with tech-
nical issues revolving around this tool. One of these issues
revolved around the challenge of simultaneously videoing
oneself while sitting and implementing a task with a child,
and trying to keep an eye on everything else happening in
the class.
Segment T3a:
Bettina: I didn’t have anyone to help me so I also had to
record (myself working with the child).
Ruthi: So, you interviewed the child and also recorded
the interview … It’s not easy.
Bettina: The hardest part is that the child does not have
eye contact with you.
Ruthi: I saw that you placed the camera on the table.
That was good. Because what we really want to
see is the table, what the child is doing.
Bettina: I tried putting it (the camera) on a chair.
Ruthi: The recording came out fine.
The above example illustrates that inquiry into the
practice of using video means trying to understand the
different aspects of its use, including what makes the
practice difficult for teachers. In other words, the teacher
was not merely complaining, or venting her frustration, in
order to gain sympathy from the other practitioners. She
was acting as a member of a community of inquiry,
Using video as a tool for promoting inquiry 261
123
questioning her difficulty and analyzing what caused that
difficulty. The difficulty did not stem from having to do
two things at once but from the loss of eye contact with the
child. Her innovative solution, placing the camera on the
table, was then analyzed by evaluating the resulting video
clips. Two teachers solved the problem in a different way.
Segment T3b:
Nan: I went to a different kindergarten class where the
children didn’t know me and videoed children in
that class. That can influence if the child is
cooperative. And even if he cooperates with me, it
may affect what the child does, even if he really
knows the ideas.
Pat: Why didn’t you video children in your own class?
Nan: Because I wanted to record more than one child
and so it was easier to go to another class.
Sari: You can see in the recording that at first the child
is very quiet and is constantly looking at the
camera and not really cooperating. But then, she
opens up and goes with the flow and talks more.
Ruthi: The camera is a factor which needs to be
considered.
Sari: I think we should have brought the video camera
to class before this assignment and maybe use it
during other activities.
(Other teachers comment that in their class,
recording classroom events is a common
occurrence and thus they did not feel the same
hesitancy on the part of the children as other
teachers felt).
While Nan claims that technical issues caused her to go to
another class to take the video, it could be that she was
uncomfortable videotaping children in her own class. Ruthi
is less involved in this inquiry than she was during previous
segments presented above. On the other hand, there seems to
be a genuine inquiry into the different ways teachers can
video children and how to use this tool so that it will not
interfere with the main goal of evaluating children’s
knowledge. As the teachers ask each other questions and
exchange ideas, they are developing a community of inquiry.
At the end of the session, Dina initiated an inquiry into
the use of video as a tool during professional development.
Segment T3c:
Dina: What do you think? Is there a point to videoing
yourselves? We could have brought you ready-
made video clips. What do you think?
Sari: It teaches me about myself. It’s feedback.
Pat: We can’t always remember the details. When
you can go over something again and again you
see the details and learn from it.
Dorit: It raises questions because here you see things
differently from there.
Nan: I was anxious, what would others say about the
video, about me?
Ruthi: What about watching the videos that other
teachers made?
Bettina: I think that there are two dimensions to the
video recordings: about us and how we carried
out our roles as teachers and also how the
children behaved. It’s a very important tool.
After I watched the recording three, four times, I
saw things that I hadn’t seen before and I
thought about how I could improve, improve my
teaching and also improve how I see the child.
Lori: What I really liked, is thinking together with
others about the same thing. One (teacher) pays
attention to this and one pays attention to that. I
believe that when several minds think together
you see more clearly.
Dina: I also enjoyed watching the videos together, that
suddenly someone sees something, and someone
else sees something else.
Dina’s question at the beginning of the discussion
directs the teachers to reflect on the fact that they watched
videos of themselves and not of some anonymous teacher.
The first three teachers only relate to their personal expe-
rience, what they learned from watching themselves, how it
made them feel, and the advantages of being able to watch
a clip over and over and focus on details. They do not relate
to the communal experience. It could be that the newness
of the experience caused them to be more introspective and
reflect on their personal experience. The fourth teacher
brings up the community, noting that it made her anxious
to think that others would watch her. It is Ruthi who directs
the teachers to also inquire into the experience of watching
together each other’s video clips. She is reminding them
that watching the videos is not only a personal practice but
a community practice.
5.3.2 Didacticians inquire into the use of video
Perhaps it is natural that, on their own, the teachers focused
on the technical issues involved with videoing themselves.
However, for the didacticians, the main focus of inquiry
was the way in which video was used during the program,
if its use was warranted, and if the way in which it was
used was beneficial. Inquiry into the way in which video
262 D. Tirosh et al.
123
was used began with the teachers, but was initiated by the
didacticians, as shown above. This line of inquiry was
continued by the didacticians when they watched the video
of the program session.
In segment D2b, we presented part of a discussion the
didacticians’ had regarding the teachers’ fluent use of
mathematical language when evaluating children’s geo-
metric knowledge. Below, we bring another part of that
discussion where the didacticians inquire into the practice
of watching video clips during professional development.
Segment D3a:
Ruthi: I’m watching it (the video of the program
session) and I have to ask if the video which
we saw (the video clips that teachers viewed
during the session), if that is what helped (in
developing teachers’ fluent use of mathematical
language), and I think yes, because it’s authentic.
Pessia: It makes it authentic and it triggers discussion.
Esther: What do you mean by authentic?
Pessia: There are two levels. First, what you see with
your eyes is worth a thousand words. And then
there’s the level that the child is someone you
know, it touches the group in a very intimate
way. We could have brought stories of
anonymous children, or said that so and so
from my friend’s class did or said such and such,
or you could have said, this happened in my
class. We’re talking about different levels of
involvement and this adds another perspective,
the affective perspective.
Ruthi raises the question of how watching video clips
of the children might have contributed to the fluency with
which the teachers used mathematical language. Her use
of the word ‘authentic’ is repeated by Pessia but ques-
tioned by Esther. It is not so much that Esther does not
know the plain meaning of the term ‘authentic’ but rather
that she is pressing for a deeper inquiry into the practice
of watching videos, questioning what makes it authentic.
To this, Pessia responds by raising the possibility of
alternative practices, and inquiring more deeply into the
specific practice of viewing videos taken in one’s own
classroom.
Lastly, we present a segment which illustrates some of
the major questions and dilemmas we had (and still have)
regarding the use of video during professional
development.
Segment D3b:
Ruthi: During the first session I was thrilled to see how
many teachers brought clips. I didn’t really
believe that they would all do it.
Esther: I remember that we worried about that.
Ruthi: But look how much time was wasted with
technical problems. Also, some of the clips
they brought were of poor quality, there is so
much background noise or you can’t really see
what the child is doing. So, it’s harder to learn
from those video clips.
Esther: Which raises the dilemma of letting everyone
show their clips or if you should watch them first
by yourself and then only show a few of them.
Pessia: Just as we feel responsible for promoting their
mathematical knowledge and their knowledge of
students, maybe we should be more responsible
for preparing them to use video as a tool,
including the technological aspect. Sometimes,
because of what happens on the sidelines,
everything can collapse. If you ask someone to
use a tool when that person doesn’t have the
proper skills, it can damage the effectiveness and
benefit which may be reaped from its use.
Ruthi: What is our aim (in using video)? For me, as the
teacher, I see the video clips as a source of
material for promoting the mathematical
development of the preschool teachers but
maybe also I want to take advantage of the
situation in order to help them see the video as a
tool and assist them in using the tool.
Esther: Maybe we need to plan more time for them to
practice this skill during the program or
demonstrate how we use a video camera in our
research. Especially if we want them to continue
using video as a tool for themselves, even after
the program is finished, so that they will continue
to reflect on their practice.
The didacticians raised several questions including the
various aims of using video during professional develop-
ment and the responsibilities of teacher educators when
introducing this tool during professional development.
Esther’s comment at the end reminds the didacticians that
video is not only a tool for use during professional devel-
opment but has the potential to become a tool used by the
preschool teachers as they continue to inquire into their
own practice.
Using video as a tool for promoting inquiry 263
123
6 Discussion
Two communities of practice need to be considered when
summing up this paper. The first community consisted of
the preschool teachers, Ruthi, and Dina. The second
community consisted of the five authors of this paper.
The main practice of the first community was to inquire
into mathematics teaching and learning in preschool,
focusing on implementing tasks and evaluating children’s
conceptions. The one session presented in this study was
typical of later sessions as well. What did they learn from
viewing the video recordings? If we view learning as
increased participation in the practice of the community
(Lave and Wenger 1991), then we should ask if the teachers
increased their inquiry into their teaching of mathematics.
The answer is yes. Teachers increasingly engaged with
critical questions of their practice (Jaworski 2006), such as,
what makes a task more or less difficult for a child and how
to evaluate children’s knowledge. Another aspect of
learning is identifying and using conceptual tools in practice
(Garcia et al. 2006). Although the teachers did not relate by
name to theories such as Tall and Vinner’s (1981) concept
image–concept definition theory, teachers did relate to
critical attributes and prototypical images, illustrating how
theories and concepts became tools for analyzing children’s
conceptions. It could also be that watching the videos,
seeing the shapes as the children saw them, enhanced the
teachers’ inquiry related to geometrical concepts.
The second community was the group of didacticians.
This community essentially inquired into two practices.
Like the first community, they inquired into the practice of
implementing tasks with children and evaluating children’s
knowledge, but from the perspective of practicing mathe-
matics education researchers. In addition, the second
community inquired into the practice of teacher education,
of promoting preschool teachers’ knowledge for teaching
mathematics as well as developing preschool teachers’
practice of inquiry.
How can we describe or relate to learning in the second
community? Because we are describing our own learning,
the reader should keep in mind that the answer to this
question is very personal. As a community of inquiry, we
see evidence of our learning in the new directions our
inquiry moved. For example, our research group has
experience studying preschool children’s counting strate-
gies and their ability to identify two-dimensional shapes
(e.g., Tsamir et al. 2008; Tsamir et al. 2010) as well as
experience studying preschool teachers’ knowledge for
teaching equivalence and their knowledge and self-efficacy
for teaching two- and three-dimensional shape identifica-
tion (e.g., Tirosh et al. 2011a, b). Yet, watching and dis-
cussing the video of the program session led us to new
research questions and to question our own definitions, for
example of what makes a task more or less difficult, or
what is the aim of engaging teachers in some task. Thus, it
may be said that video was a tool which promoted our
inquiry. It was also the object of our inquiry. While most
previous studies used prepared video clips in their pro-
grams (Santagato and Guarino 2011), we chose to use
videos prepared by the teachers themselves. While video
clubs (Sherin and Han 2004) do make use of videos taken
in the classrooms of the participants, in those studies it is
usually an outsider who does the recording and the pro-
gram facilitator who chooses segments to view. In our
study, it was the teachers who recorded themselves and
chose the clips to share with others. This led to many
questions, such as what may be the advantages and dis-
advantages of having an outsider film the videos in the
kindergarten class.
As mentioned earlier, this was not the first time we had
offered programs for preschool teachers. What was new
was the element of using video to forge among the teachers
a community of inquiry and to move forward our own
inquiry community. Developing an inquiry community
involves developing both an inquiry stance as well as
developing a community. Regarding the practice of
inquiry, this study showed that when a discussion revolves
around a video segment, details, which perhaps get for-
gotten or may not seem important to one person, become
an issue to be discussed by others. Regarding the com-
munity, when a discussion revolves around a video seg-
ment, it becomes real and vivid. It allows all of the viewers
to experience, together, what was seen by one. In addition,
we believe that letting the teachers choose which segments
to show allowed them to play an active role in the com-
munity, inviting them to take a lead. Simply put, there was
more involvement.
To conclude, although this paper presented a case study,
we believe that results may be generalizable if additional
circumstances are taken into consideration. The didacti-
cians’ inquiry community experience guided them as they
introduced a new tool into their own inquiry community
and as they sought to use video as a tool when developing
an inquiry community among the teachers. In addition, the
didacticians practiced using video to further their own
inquiry community, allowing them to experience, to a
certain degree, what the teachers were experiencing.
Finally, while the CAMTE framework was used originally
to organize dimensions of knowledge the didacticians
wished to support, it also guided both the teachers’ and
didacticians’ inquiry into practice, showing that the
framework applies for didacticians as well as teachers. To
sum up, like other tools, a certain amount of experience
might be needed, along with a guiding framework, for
video to become a successful tool in developing an inquiry
community.
264 D. Tirosh et al.
123
7 Epilogue
Four months after Ruthi, Pessia, and Esther sat and viewed
the program session described above, Ruthi sat again with
Esther, but this time Dina and Michal joined. The aim of
the discussion was to review again what we had seen and
discussed and to see if we had any new questions and
insights which might influence the professional develop-
ment program currently underway with a different group of
preschool teachers. This session among the four didacti-
cians was also recorded. We noted that due to advances in
video technology, many of the issues which arose during
that first session did not arise during the current program
and that the teachers were able to focus more on learning
from the videos. Ruthi noted that she felt more confident in
her role as the expert practitioner when using video as a
tool during professional development. New questions and
directions for inquiry arose, mostly focusing on the math-
ematical tasks implemented with children. Finally, 2 weeks
before submitting this paper, the five of us sat together to
prepare the last session of the current program. It took only
2 minutes for someone to say, where is the video, why
aren’t we recording this discussion? Of course, we went to
get the video camera. In other words, inquiry has become a
way of being for our group and video a tool which can
facilitate this practice.
Acknowledgments This research was supported by The Israel
Science Foundation (Grant No. 654/10).
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