Using video as a tool for promoting inquiry among preschool teachers and didacticians of mathematics

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.

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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

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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


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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.


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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


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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.


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


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,


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


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.


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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.


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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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Documents

Using video as a tool for promoting inquiry among preschool teachers and didacticians of mathematics