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Journal of Pedagogical Research
Volume 6 , Issue 4, 2022
https://doi.org/10.33902/JPR.202213433
Research Article
An investigation on self-regulation activities of
novice middle school mathematics teachers
Ramazan Gürel 1, Erhan Bozkurt 2, Pınar Yıldız 3 and İ. Elif Yetkin Özdemir 4
1
1Burdur Mehmet Akif Ersoy University, Faculty of Education, Burdur, Turkey (ORCID: 0000-0003-1710-2743)
2Uşak University, Faculty of Education, Uşak, Turkey (ORCID: 0000-0002-5524-6994)
3Çanakkale Onsekiz Mart University, Faculty of Education, Çanakkale, Turkey (ORCID: 0000-0002-6729-7721)
4Hacettepe University, Faculty of Education, Ankara, Turkey (ORCID: 0000-0001-8784-0317)
This study employed a qualitative research design to describe and analyze self-regulation processes
(monitoring and control) of the novice middle school mathematics teachers in terms of teaching activities.
The participants consisted of six mathematics teachers with five or less years of teaching experience. The
data of the study were mainly collected through the observations of the lessons taught by the teachers and
semi-structured interviews conducted with the teachers. The results revealed that the teachers' monitoring
and control behaviors were affected by the goals they set. With regard to student-oriented monitoring,
they generally focused on the cognitive development of the students. Compared to student-oriented
monitoring, teaching-oriented monitoring was rarely observed. The most obvious control behaviors of the
teachers were emphasizing the rules and algorithms, and taking responsibility for completing the task in
challenging situations. It was also revealed that the teachers did not monitor carefully and systematically,
and as a result, the mistakes they made during the teaching process were not noticed. These results
highlight the need for pre- and in-service training programs that will aid in the development of
monitoring and control skills in novice middle school mathematics teachers.
Keywords: Middle school mathematics; Novice teachers; Self-regulation; Monitoring; Control
Article History: Submitted 2 October 2021; Revised 30 January 2022; Published online 17 September 2022
1. Introduction
Professional vision is described as a competency that can be acquired over time and involves
actions that are unique to teachers' professions, such as observing potential classroom situations
and expanding effective teaching environments by drawing insightful inferences from these
situations (Goodwin 1994; Sherin 2014). Novice teachers need to consider and observe the potential
effects of each situation that arises in the classroom because they are unfamiliar with the features
of effective learning environments (Boshuizen & Schmidt 2008). As a result of such evaluations
and observations, novice teachers will create concepts, strategies, and practices that will shape
their professional lives.
Address of Corresponding Author
Ramazan Gürel, PhD, Burdur Mehmet Akif Ersoy University, Faculty of Education, Department of Mathematics and Science Education,
15030, Burdur, Turkey.
gurelr@gmail.com
How to cite: Gürel, R., Bozkurt, E., Yıldız, P., & Yetkin Özdemir, İ. E. (2022). An investigation on self-regulation activities of novice
middle school mathematics teachers. Journal of Pedagogical Research, 6(4), 168-189. https://doi.org/10.33902/JPR.202213433
R. Gürel et al. / Journal of Pedagogical Research, 6(4), 168-189 169
Research indicates that novice teachers struggle to complete some educational tasks compared
to experienced teachers (Borko & Livingston, 1989; Reynolds, 1992; Wolff et al. 2016). For instance,
it has been noted that novice teachers rigidly adhere to the lesson plan while lecturing (Borko &
Livingston, 1989; Westerman, 1991). These teachers' top concerns during instruction are to get
students' full focus on the tasks at hand and finish the lecture as planned, therefore they could act
hurriedly (Berliner, 2001; Housner & Griffey, 1985). Additionally, it is argued that novice teachers
do not focus on making sense of the student ideas in the teaching process (Jacobs et al., 2010) and
have problems in noticing the pedagogical effects of the events in classrooms (Sherin & van Es,
2005). For instance, these teachers struggle with their ability to identify crucial mathematical
situations that could enhance student learning, to monitor students, and to provide appropriate
feedback in a classroom setting environment (Berliner, 2001; Peterson & Leatham 2009).
Furthermore, it has been reported that novice teachers have difficulty in producing appropriate
responses and explanations to student questions and comments, rarely make a relationship
between concepts in the explanations they made, and have struggle to modify their lesson plans in
line considering student needs (Borko & Livingston, 1989; Westerman, 1991). Briefly, it is claimed
that novice teachers struggle to put the comprehensive lesson plans they developed into action
(Borko & Livingston, 1989) and that they are prone to straying from the educational objectives
(Borko & Livingston, 1989; Westerman, 1991).
1.1. Theoretical Framework
In order to successfully control their cognition, motivation, and behaviour to deal with the
challenges they face when teaching, novice teachers should regulate themselves. The self-
regulation of students and teachers with regard to learning activities is typically explained using
Zimmerman's (2000) cycle self-regulation model. The model, which consists of a three-phase
cyclical process, views self-regulation as being made up of the following components: Forethought,
includes people's beliefs and preparation for the task; Performance, includes people's self-control
and self-observation; and Self-reflection, refers self-judgement and self-reaction. In this study, the
performance component of the Zimmerman’s (2000) self-regulation model and the components of
monitoring and control of the Yetkin Özdemir et. al.’s (2020) self-regulated teaching model are
used. The latter model relies on the assumption that monitoring is focused on the variables
influencing teachers' performance during the teaching process and how their performance affects
this process. To get a sense of their own teaching performance, teachers should pay close attention
to their own explanations, questions, tips, and directions during the teaching process (Yetkin
Özdemir et. al., 2020). By observing their students, teachers can determine whether a newly
implemented teaching method serves its purpose and the impact this has on student engagement
in the course. By building a connection between the monitoring activities with various objectives,
teachers who self-regulate can notice problematic situations related to the teaching process and
decide on appropriate adjustments. As well as checking whether the lessons are presented in
accordance with the scheduled content and whether different sorts of questions are solved in the
classroom, teachers can make revisions as they see necessary.
Zimmerman (2002) refers to two strategies which make it possible to carry out self-monitoring:
self-recording and self-experimentation. In order for the monitoring process to be effective,
teachers can determine the situations that increase or decrease the effectiveness of different
teaching processes by trying different teaching techniques and strategies and by keeping
systematic and regular records (Yetkin-Özdemir et. al., 2020). According to Zimmerman (2002), the
methods used in the self-control process (imagery, self-instruction, attention focusing, and task
strategies) assist individuals in maintaining their attention and completing their activities. The self-
regulated teaching model makes the assumption that the control process comprises adhering to the
planned teaching process. Teachers can follow the lesson plan from different sources, develop
certain routines, and organize the sequence of the lesson by dividing its content into subareas.
According to this model, the monitoring and control activities are interrelated processes. Teachers
R. Gürel et al. / Journal of Pedagogical Research, 6(4), 168-189 170
can make some adjustments, such as making the content easier or harder, depending on the results
of monitoring the teaching process (Yetkin-Özdemir et. al., 2020). Self-regulated teachers may
relate these two processes and develop effective teaching strategies to solve the problems that they
detect during the monitoring activities (Yetkin-Özdemir et. al., 2020).
The majority of research on self-regulation among in-service and pre-service teachers focuses on
activities that pertain to their own learning or general teaching practices (Çapa-Aydın et. al., 2009;
Klusmann et al., 2008). Studies examining teachers’ self-regulation in regard to their activities in
the teaching process holistically and within the boundaries of the subject areas are scarce. These
limited number of studies generally focused on teachers’ self-regulation during the planning
process and/or the assessments they made after the instruction (Bozkurt & Yetkin-Özdemir, 2018;
Kurt, 2010; Nathan & Kim, 2009). As a result, little is known about the self-regulation activities of
mathematics teachers during their teaching practices. There are several ways for novice teachers to
get support, particularly when planning lessons (determining goals, making plan etc.), including
speaking with more experienced colleagues and guidance teachers. However, the teacher bears full
responsibility for overseeing the instructional process in the classroom. In order to better
understand this situation, this study aims to describe and investigate the self-regulation processes
connected to the activities (monitoring and control) of novice middle school mathematics teachers.
1.2. The Aim
Previous researchers investigating associations between teaching quality and years of experience
suggested various phases. For instance, while Veenman (1984) defined teachers working in their
second year of the teaching profession as novice teachers, Lavigne (2014) defined teachers who
have five year of teaching experience as new teachers. Another researcher, Turner (1995) stated
that teachers should have at least three to five years of teaching experience so that they are
prepared for any unforeseen events that may arise. Berliner (2001) asserted that the most
reasonable estimate for the development of teaching expertise for the teaching profession is five
years or more. This study focuses on how six middle school mathematics teachers, who are in their
first five years of teaching, regulate their cognitive, motivational, and behavioral processes while
carrying out the tasks associated with teaching mathematics. Because it is crucial to have
information regarding teacher self-regulation, the results of this study will contribute the field by
providing a clearer definition of teacher self-regulation and details on how self-regulated and
strategic teaching can be implemented.
2. Method
2.1. Study Design
A case study is employed as a research design because the content and implementation of teaching
activities cannot be described independently of the setting and conditions under which teachers
work. A case study is a qualitative research design in which researchers examine one or more
bounded systems (cases) using extensive data collection techniques based on a variety of data
sources (observations, interviews, audio-visual materials, documents, reports, etc.) and then report
cases and case-based themes (Creswell, 2007). In this study, in which each teacher was treated as a
separate case, the multiple case study design, one of the case study types, was adopted.
2.2. Participants
Six novice teachers with five or less years of teaching experience (Nihal, Özlem, Ayla, Serkan, Hale
and Ender) took part in the study. Participants were given pseudonyms. Convenience sampling
was used to choose the participants (Yıldırım & Şimşek, 2013). The selection of the participants
was based on their willingness and volunteering to participate in the study. In addition, it was
required that these teachers could share their ideas freely and were not bothered by being
observed in the classroom environment. The teachers who took part in the study were all
undergraduates who had completed a middle school mathematics education program. With five
R. Gürel et al. / Journal of Pedagogical Research, 6(4), 168-189 171
years of teaching experience, Ender and Serkan were the participants with the most experience.
Additionally, these two teachers worked at schools that were situated in a city. Other teachers held
positions at schools in rural areas serving students with poor social and economic circumstances.
Nihal had one year of teaching experience. Two of the teachers, Özlem and Ayla, had two years of
teaching experience. Finally, Hale had four years of teaching experience. While Özlem taught in
the 6th, 7th, and 8th grades during the study, Ayla and Hale taught at all grade levels (5-8 grades).
Other teachers taught at least two different grade levels.
2.3. Data Collection Procedure
Interviews, observations, and document analysis were used to gather the data. Before commencing
the data collection process, an ethical evaluation of the study was confirmed, and the required
ethics certificate was obtained. Additionally, as the study was conducted in public schools, official
approval was obtained from the Ministry of National Education (dated 25.12.2012 and numbered
10230228/44/42696) in addition to an ethics certificate (Hacettepe University Ethical Council’s
permission dated 27.09.2012 and number B.30.2.HAC.0.70.01.00/431-3629). Through the use of
cameras and audio equipment, all observations and interviews were captured. Observations lasted
a total of 61 class hours, and 31 interviews were performed. Table 1 provides information
regarding the observations and interviews.
Pre-interviews and pre-observations with each teacher were performed, as shown in Table 1, in
order to get to know them, learn about the routines they follow in their lessons, and build trust
between the authors and the participants. Their lessons were noted after the preliminary
observations and interviews (nearly 10 class hours). The purpose of the observations was to
identify the control and monitoring behaviors of each teacher during their mathematics
instruction. The author who conducted the observations gathered data from the observations
regarding the behaviors of the teachers during the teaching process and developed self-regulation
interview forms for each instruction. The forms were developed based on the lessons that had been
observed. To improve the validity of data collection, the interview forms were finalized and the
video recording of the lesson observation were shared with another author on the research team.
In the interviews, the teachers were asked to explain the decisions and actions related to the
monitoring and controlling of the instruction. The purpose of the final interview was to enable
teachers to make an overall assessment of their lessons and the semester, and to obtain participant
confirmation of the observation notes. The goal of the document analysis was to obtain data that
would contribute to observation and interview data. To this aim, the textbooks, source books and
class notes prepared by the teachers in the teaching process were examined.
2.4. Data Analysis
The instructional situations that occurred throughout the lesson, as well as the behavior and
decisions of the teacher in relation to these situations, were described in the data analysis process.
To prepare for the interviews regarding the observed lessons, a preliminary analysis of the
observed data was performed. The analysis framework developed during the study study led on
which teacher decisions and behaviors to concentrate on while analyzing the data. The data
analysis was guided by the self-regulation model of Zimmerman (2000) and the self-regulated
teaching model of Yetkin-Özdemir et. al. (2020). The data analysis framework was revised with the
codes identified in the data analysis process which was carried out together with the data
collection process. Table 2 provides the final version of the data analysis framework.
The data obtained for each participant were analyzed using the framework presented in Table
2. The findings are discussed in a comparative manner. Various methods were used to increase the
credibility, transferability and consistency of the findings. In order to increase the transferability of
the findings, the teachers participating in the study and their working environments were defined
in detail. Four methods were used to increase the credibility of the findings. A long-term
Table 1
Information on observations and interviews
Teachers
Observations
Interviews
Nihal
Pre-observation-Measuring length (6-class hours)
Observation I- Polygons and their properties (2-class hours)
Observation II- Perimeter of quadrilaterals (4-class hours)
Observation III- Area measurement (2-class hours)
Observation IV- Area measurement (2-class hours)
Pre-interview (55 min.)
Interview I (47 min.)
Interview II (65 min)
Interview III (61 min.)
Interview IV (48 min.)
Final interview (16 min.)
Özlem
Pre-observation- Circle and segment - Basic elements of prisms (5-class hours)
Observation I- Surface area of prisms (2-class hours)
Observation II- Surface area of cone and pyramid (2-class hours)
Observation III- Volume of prisms (4-class hours)
Observation IV- Pie chart (2- class hours)
Pre-interview (29 min.)
Interview I (24 min.)
Interview II (31 min.)
Interview III (45 min.)
Interview IV (31 min.)
Final interview (12 min.)
Ayla
Pre-observation- Measuring liquids -Measuring area- Area and volume of prisms (6-class
hours)
Observation I- Circles (2-class hours)
Observation II- Basic elements of prisms (4-class hours)
Observation III- Angles in circles (2-class hours)
Observation IV- Surface area of cones (2- class hours)
Pre-interview (45 min.)
Interview I (42 min.)
Interview II (53 min.)
Interview III (61 min.)
Interview IV (43 min.)
Final interview (13 min.)
Serkan
Pre Observation - Probability- Addition and subtraction of fractions (6-class hours)
Observation I- Probability (4-class hours)
Observation II- Multiplication and division of fractions (3-class hours)
Observation III- Decimals (2- class hours)
Pre interview (55 min.)
Interview I (49 min.)
Interview II (53 min.)
Final interview (12 min.)
Ender
Pre observation- First order equations with one unknown - Frequency table Bar graph (5-
class hours)
Observation I- Coordinate system and linear relations (3-class hours)
Observation II- Basic geometric concepts (5-class hours)
Observation III- Direct and inverse proportion (4-class hours)
Pre interview (51min.)
Interview I (56 min.)
Interview II (72 min.)
Interview III (50 minutes)
Final interview (28 minutes)
Hale
Pre-Observation- Operations with natural numbers-Angles- Addition and subtraction of
fractions (5-class hours)
Observation I- Multiplication and division of fractions (4-class hours)
Observation II- Basic geometric concepts (6-class hours)
Pre-interview (38 minutes)
Interview I (73 minutes)
Interview II (84 minutes)
Final interview (10 minutes)
R. Gürel et al. / Journal of Pedagogical Research, 6(4), 168-189 172
R. Gürel et al. / Journal of Pedagogical Research, 6(4), 168-189 173
Table 2
Data analysis framework
Categories
Themes
Explanation
Monitoring
Student-oriented
Cognitive: It includes cognitive monitoring of students. It is the process of
observing the solutions offered by the students, their answers to the
questions and explanations.
Behavioral: It includes behavioral monitoring of students. It is the process
of observing the psychomotor skills of the students, such as working in
groups, participating in the lesson, and expressing their ideas.
Affective: It includes the monitoring of the students from a motivational
point of view. It includes monitoring student interest in the subject and
their self-confidence, etc.
Teaching- oriented
It includes the monitoring of the decisions and actions of the teachers
regarding the teaching activities. It involves observing the
appropriateness/correctness of the explanations, directions, etc. made to
the students. It also includes the observations about the course content, the
variety of problems. It covers the monitoring of the positive/negative
effects of teaching practices on student performance.
Control behavior
In regard to the course
content
It includes the decisions taken and practices to follow, limit or expand the
content planned within the scope of the stated objectives specified for the
relevant grade level in the mathematics education program.
In regard to the
lectures
It includes the decisions related to the instructional materials, the way
they are presented and / or the order in which they will be discussed and
taught in the lesson and the decisions taken regarding the teaching
methods and techniques.
association with the participants which lasted approximately three months was achieved through
the interviews and observations. Diverse techniques were used for gathering the data. During the
data collection and analysis processes, all researchers collaborated and shared information.
Additionally, member checking was applied during the final interview as well as the interim
interviews regarding the lectures. The techniques for data collecting and analysis were thoroughly
outlined in order to improve consistency. Furthermore, the findings obtained from the
observations, interviews and document analysis were examined comparatively, and the
consistency of the findings was tested. During the coding process, the researchers collaborated and
discussed through any coding issues.
3. Findings
The regulation activities of the teachers regarding their teaching activities were examined in terms
of two basic processes, namely, monitoring and control. First of all, the findings on student-
oriented and teaching-oriented monitoring behaviors were presented. The findings are then
discussed in relation to the teachers’ controlling behaviors of the course content, mathematical
tasks, and teaching methods and techniques.
3.1. Monitoring Behavior
3.1.1. Student-oriented Monitoring
The findings regarding the student-oriented monitoring behaviors of each teacher are presented in
Table 3.
R. Gürel et al. / Journal of Pedagogical Research, 6(4), 168-189 174
Table 3
Student-oriented monitoring behaviors
Nihal
Ayla
Özlem
Hale
Serkan
Ender
Cognitive factors
Conceptual understanding
Procedural skills
Basic skills (connections, communication, etc.)
Behavioral factors (e.g., psychomotor skills)
Affective factors (e.g., interest)
Table 3 shows that the participants frequently monitored the cognitive status and activities of
the students. Concerning the cognitive monitoring, they focused on students’ procedural skills.
Throughout the lesson, teachers observed their students to see if they correctly applied the rules or
relations (formulas for surface area or volume of geometric objects, etc.), followed the algorithms
(multiplication / division algorithms in fractions, etc.), and used the symbols (line, line segment,
ray symbols, etc.) in an appropriate manner. In line with their goals, they concentrated on how
well their students performed, paying particular attention to their procedural knowledge and
abilities. As they stated in their goals, they focused on the performance of their students, especially
in relation to their procedural knowledge and skills, and checked the students’ notebooks to
monitor whether they made any operational mistakes. For instance, Hale claimed that during these
observations, she concentrated on the students' achievements on the topics she gave priority to in
the class and on the points she projected they could find challenging.
Hale: I pay close attention to some aspects and I monitor them such as finding the common
denominators in fractions, inverting [referring to invert-and-multiply algorithm] in division, using
symbols, or using brackets correctly when using symbols. (Multiplication and division by fractions)
Asking students if there is anything they do not understand and monitoring their reactions is
another action teacher do to monitor their students’ cognitive performance. This behavior was
found to be frequently exhibited by Özlem, Hale and Ender. Özlem claimed that when she asks
her students if they understand, she often observes their responses and analyzes them. Making
inferences about the class as a whole by focusing on the behaviors or reactions of particular
students is another reported monitoring behavior of teachers. Ayla's report demonstrates this
tendency. In relation to this strategy which makes the monitoring process easier, she stated, "There
are some students that provide me feedback. Using their feedback, I deliver the lesson”. In a
similar vein, Ayla claimed that she payed attention to her students' verbal cues and that when she
received brief responses to her inquiries, she assumed that the content was not grasped.
The majority of the students' performance was monitored based on their procedural knowledge
or problem-solving skills. This is consistent with teachers’ goal orientations related to standard
testing and their low expectations from the students (Yetkin-Özdemir, 2015; Yıldız et. al., 2021).
Only Nihal, Ayla, and Serkan, albeit rarely, focused on their students’ conceptual understanding.
For instance, Nihal challenged fifth-grade students to determine the side length of the square
whose area is given as a perfect square integer while teaching the topic of the area of the square.
She stated that she wondered how the students would respond when she posed this issue, which
calls for a high level of thinking for a student in the fifth grade. Serkan, on the other hand,
emphasized the invert-and-multiply algorithm in the division of fractions and did not include any
activity to make sense of the operation. However, later in the lesson while tackling the problem of
, he surprised that the students used the algorithm. He expressed his surprise as follows:
“How many
are there in
? There is one. I looked for anyone who would give this answer, but no
one gave this answer.” As can be seen from this example, Serkan questioned his students to
monitor their understanding of the procedure. However, because there had never been any
activity to explain this procedure, he was forced to draw a poor conclusion about his students'
mathematical reasoning as a result of this monitoring activity.
R. Gürel et al. / Journal of Pedagogical Research, 6(4), 168-189 175
Another important finding regarding the student-oriented monitoring behaviors is that the
teachers did not monitor the development of the skills related to mathematical connections (i.e.,
making connections with other disciplines and daily life) among the students. The fact that Nihal
and Ender did not follow up on this skill during the lesson, although it was included in their goal
statements, may be related to the fact that they cared less about this goal than other goals.
It is revealed that Nihal and Ayla did, albeit minimally, monitor their students' behavior. These
teachers particularly monitored the students' note-taking habits and their their ability to use
tools (protractor, compass, ruler, etc.). It can be seen in the following excerpt from Nihal's reports:
Nihal: Because there is very little space left before the zero with the ruler, students can take that into
account. Alternately, they can start from 1. I observed it to watch out for it... Because I know their
mistakes. (Measuring area in polygons)
The teachers also monitored the motivational status of their students throught the lesson. Only
Nihal was not found to make any monitoring behavior in this regard. The teachers exhibited
various behaviors in order to maintain the lesson by supporting the motivation of the students. For
example, Hale tried to track both the overall motivation of the class and the motivations of
individual students during the lesson. Especially when she used a novel instructional material
(such as using a rope in teaching basic geometric concepts), she monitored the participation and
interest of the students. In this process, she focused on the quantity of participation (the fact that
most students were attracted to the lesson) rather than the quality of participation (does the
concrete material help students understand the concept/ how?).
Hale: In mathematics, it's difficult to visualize much. This course is abstract. The students didn't lose
interest in listening to the lesson at least while they were learning something. They made an effort to
participate in the class, as I could see. That's why I believe it helps. (Basic geometric concepts)
3.1.2. Teaching-oriented Monitoring
The monitoring behaviors of the participants that are focused on teaching are shown in Table 4.
Table 4
Teaching-oriented monitoring behaviors
Nihal
Ayla
Özlem
Hale
Serkan
Ender
Monitoring of the content
Monitoring the variety of the problems
Monitoring the adequacy of
explanations/descriptions
Monitoring instructional behaviors (response time,
intervention, time management)
Experimenting with different teaching practices and
monitoring their results
The majority of the teachers' monitoring of their own teaching performance consisted of
adhering to the content-related curriculum. It has been observed that all of the teachers constantly
monitor their own progress in covering the content of the lesson. It is also found that they employ
textbooks as a tool to achieve this goal. For instance, Hale's monitoring behavior throughout the
lecture was to adhere to the textbook in order to avoid skipping over any of the lesson content.
Researcher: Throughout the class, I have noticed that you occasionally glanced at the book. What are
you looking at in the book?
Hale: I checked to see if there was anything I had neglected. Or, if the book provided a different
example. I do not want to miss the information provided in the book we are writing. I then looked at
the book. (Basic geometric concepts)
R. Gürel et al. / Journal of Pedagogical Research, 6(4), 168-189 176
Ender, on the other hand, mostly followed the source book to check the lesson content. It was
also observed that Ender used the notes he had prepared before the class. He reported this as
follows:
Ender: I wonder if there is a point I skipped. We solve examples pertaining to each topic after the
topic has been taught. I checked it because I was unsure whether there was anything I missed or did
not do according to the plan. I took a look at it to see if there was a more intriguing question that I
had prepared. (Linear and inverse proportion)
Because they did not systematically monitor their own teaching practices, the teachers were
unable to implement some of the activities they had intended. Instead of adding the entire portions
of two integer fractions and then continuing the procedure, the students in Hale's class turned both
fractions into composite fractions when faced with a question that required an operation with
brackets. Hale mentioned in this question that she wanted the students to continue the process by
understanding this relationship, but she made no comments in this regard. It was noted that she
was unable to follow up in a systematic manner; hence this learning opportunity was missed. She
provided the following reports:
Researcher: In this question, adding the integer parts makes 6. Did you specifically choose this
question?
Hale: Yes, but students could not solve it. Instead, they converted it into a compound fraction. But
my purpose in giving this question was different. I do not remember if I said it in class but I took it
to highlight it.
Researcher: I guess you did not say it.
Hale: I honestly do not remember if I said it or not, but I chose it with that in mind. 4 whole and 1
whole are 5 whole. Actually, I would, but it may have been overlooked. (Multiplication and division
by fractions)
Another important finding is that teachers monitored the diversity of the problems they use in
their lessons. They used the textbooks and workbooks for this purpose. For example, Ender
checked the question styles in the book. Similarly, Nihal’s statements “I looked to see if there were
any other question styles in the book. ... I wanted to see if I missed any question style. That's why I
looked at the book.” also indicate that she employed the textbooks to offer various examples of
questions to their students.
The teachers stated that they also monitored the accuracy of the definitions they used and the
adequacy of their explanations during the lesson. It has been noted that they occasionally
consulted the textbooks, workbooks, and notes for this reason. Serkan, for instance, claimed that he
utilized the book to confirm the veracity of the definitions he provided in the class. Nihal's
decision to alter the way the lesson was taught was influenced by her observations of her own
teaching behaviors. For example, she gave a more detailed explanation when she recognized that
her explanation was insufficient in regard to the calculating the area of compound figures and to
direct her students to calculate the area by converting the shape into a rectangle. Here, Nihal’s
decision and practice can be seen as a result of her monitoring, focusing on both student
performance and her own teaching behavior. She stated that, “I suddenly thought about it.
Because I realized that my previous explanation was insufficient. That’s why I felt the need to
make such a statement (Measuring area in polygons).”
The teachers’ monitoring of their own teaching behaviors or habits is found to be quite limited.
Among the teachers, Ayla was the most frequent and regular self-observer in this regard. For
example, Ayla, whose most obvious teaching goal was to give her students more voice and not be
intrusive, stated that she often watches herself in these aspects during the lesson. Nihal, on the
other hand, stated that she paid attention to whether she allowed her students enough waiting
time for an answer. In her statement below, Nihal expresses her views about the monitoring and
evaluating her own performance in terms of giving her students a voice.
Nihal: While teaching the subjects, I try to involve the students in the process. As far as I can tell, I
undoubtedly have some weaknesses. I think I should wait a little while giving a word to the
R. Gürel et al. / Journal of Pedagogical Research, 6(4), 168-189 177
students. But I guess I answer the questions myself, thinking that they cannot answer them. I noticed
it. (Calculating perimeter in polygons)
It has been observed that the teachers only monitored the effects of teaching process when they
used a material or model that they had not used before in their lessons. In particular, Ender stated
that he observed the results when he tried different teaching practices. For example, he stated that
students made measurements on length and land measurements in the school garden, had poster
work on geometric shapes and that he observed that this activity was effective for student learning
and motivation. Nihal also stated that she observed that drawing the unit squares while teaching
area measurement increased the motivation of the students. In a similar vein, Hale claimed that the
students' interest in the lesson was boosted by the use of models like rope and pencil in the lesson
in which she taught geometric concepts such as line, line segment, and parallelism. The cognitive
impacts of these activities on students' learning, however, were not thoroughly and in-depth
monitored by the teachers. It is observed that none of the teachers had the habit of systematic
monitoring and record keeping of students’ performance or their own teaching performance. In
this process, only Ayla stated that she recorded the information she obtained as a result of her
teaching-oriented follow-ups, on a notebook or a book, although not regularly.
Ayla: Yes, I take notes on my difficulty during the lessons, the difficulty of the students and on what
I should do to avoid such problems. But, I do not take such notes regularly… When I regard
something very important I take notes about it, since later I may forget about it. It would have been
much better if I had noted down what I did last year and where the students were having trouble.
As I look at these notes, I probably understand what I taught so that it does not need to be repeated.
(Angles in the circle)
3.2. Control Behavior
3.2.1. Controlling the course content
Table 5 presents teacher behavior about the controlling the content in a comparative manner.
Table 5
Control behavior concerning the course content
Nihal
Ayla
Özlem
Hale
Serkan
Ender
Following what was planned
Expanding the content
Narrowing or limiting the content
Table 5 shows that the teachers generally followed the content they had planned by engaging in
a few rourtine control behaviors. The follow-up of the textbook is identified as a routine that they
frequently refer to. For example, Ayla stated that she tried to follow the book, especially checking
whether the process in the book and the process in her mind matched. She also stated that she
used the textbook specifically to ensure that the definitions were error-free. Nihal, on the other
hand, usually observed the textbook, but did not follow the book exactly. However, she adhered to
the textbook on the subjects that she did not think she had sufficient knowledge and experience or
on the subjects that she did not have the necessary confidence in terms of field knowledge (such as
measurement estimation). Below are her opinions in this regard:
Nihal: I did not have any formal training on the methods of estimation. So, I do not have necessary
knowledge about it. I should follow the textbook concerning this topic. That’s why I used the
textbook in relation to estimation. (Measurement estimation)
Another routine control behavior that the teachers performed in order to maintain the content
they planned is to start each lesson by making a short explanation about the content of the lesson
and reminding the students of the subject they covered in the previous lessons. For instance,
Hale’s views are as follows:
Hale: Sometimes students forget what they have been taught. For example, students forget to invert
and multiply in the division. I am going this way so that the children will not be disappointed and
R. Gürel et al. / Journal of Pedagogical Research, 6(4), 168-189 178
that they do not feel sorry for not being able to do it, and to remind them from the beginning. I
remind them to take precautions. I remind the basics before starting the lesson. (Multiplication and
division by fractions)
The teachers introduced a problem, example or explanation in the introduction to a new topic
and then asked students to solve similar examples, this may be seen as another control behavior of
teachers to follow the lesson plan. In addition, they explained the solutions to questions. The
teachers did not give their students many opportunities to do the problem solving and explain the
solutions. Serkan’s statements in this regard are presented below as follows:
Serkan: When students solve the problems themselves, they cannot understand the process.
Moreover, there is time constraints which do not allow me to make each student solve the problems.
I therefore prefer solving the problems and explaining how to do so to the students. (Probability)
In general, the teachers did not go beyond the course content they planned and made limited
extensions to the content in line with the interests and needs of the students. However Nihal, Hale
and Serkan occasionally did. For example, although it was not included in the curriculum, Nihal
asked her students to find the side lengths of a square whose area is given (in the form of a perfect
square like 16, 64). Nihal stated that this control behavior aimed at expanding the content and also,
at increasing the cognitive complexity in order to test the performances of the students. Similarly,
Hale included the concept of right angle, which is not included in the educational program, as a
result of a student’s question about angles. Serkan’s decisions to expand/enrich the content are
mostly aimed at supporting students’ procedural skills or eliminating deficiencies in their prior
knowledge. For instance, he focused on a strategy to develop mental processing skills of the
students which is not directly related to the learning outcome. He showed his students how to use
"computing by dividing numbers", one of the mental calculation strategies, in solving a problem
that requires multiplication in probability calculations. In the interviews held after the lessons, the
teachers stated that these additions they made to the content of the lesson were based on the
decisions they made during the lesson without making any plans. Extensions other than these
examples are additions made as a reminder to the relevant preliminary topics, which are mostly
included in the lesson plan. For example, Ender briefly mentioned the concept of ratio before the
subject of proportion, and Nihal emphasized the concept of polygons in the introduction to the
subject of quadrilaterals. Likewise, Özlem made reminders about the area formulas of the
polygons that make up the surfaces, about the surface areas of the prisms.
The teachers did not decide to restrict the content they planned during the classes, nor did they
include the topics they believed their students would struggle to understand or that they would
find challenging to teach. The fact that Hale did not include the use of models in the division of
fractions is one example. Similarly, Nihal adhered to the content she planned during the lesson but
made some limitations by not going deep into the issues that she thought were not important or
that students might have difficulty with. For example, in problems related to calculating the areas
of compound shapes, she focused on the method of dividing the shape into squares or rectangles
but did not include the method of converting the shape into a square or rectangle, although it was
included in the textbook. She stated that she understood the fragmentation method better and that
her students would not understand the converting method as the reasons for this decision.
When students experienced difficulty throughout the lesson, the teachers did not cut back on
the information they had intended. However, they either took on the duty of finishing the
assignment themselves or provided basic and straightforward examples to teach the subject. The
only instance we observed where a decision was made to restrict (narrow) the subject while
teaching was in Serkan's class. Serkan's exam-oriented objectives were effective in supporting him
narrow the content, particularly during preparation and class activities. For instance, despite the
fact that it was in the curriculum, he decided not to utilize a model for the division of fractions
since he had problems multiplication of fractions. Likewise, for dividing fractions, identifying
common denominators then dividing the numerators and denominators separately were not
included in the lesson. The invert-and-multiply algorithm was the sole algorithm presented in the
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course. He preferred to incorporate algorithms that would drive students to the outcome fast, as
can be seen from his comments below, and he limited the content in this way.
Serkan: As confusion could arise, when division [referring to invert-and-multiply algorithm] was
completely understood by students, I did not make the process much more complex by including
finding the common denominators and dividing the numerators and denominators separately.
Students rarely encounter this topic. So in our test sources, they do not come across such topics
elsewhere. Therefore, I did not focus on it very much. (Multiplication and division in fractions)
3.2.2. Controlling the mathematical tasks
Table 6 compares the control behavior of the teachers in relation to the mathematical tasks.
Table 6
Control behavior concerning the mathematical tasks
Nihal
Ayla
Özlem
Hale
Serkan
Ender
Classifying the similar tasks to make the content
more varied
Breaking down and simplifying the task
Complicating the task
Variation in representation of the tasks (materials,
models/shapes, verbal problems, etc.)
Table 6 shows that the teachers' control behaviors toward the mathematical tasks mostly
involve an effort to carry out their planned lesson or routines. To do this, they divided the
mathematical activities into groups and tried to include a range of examples in the lesson. These
groupings were often ranked by teachers from simple to complex. The teachers in whom this
behavior is most obviously manifested are Nihal, Ayla, Serkan, and Ender. Serkan divided the
fraction division problems into three categories: division of a natural number by a fraction,
division of a fraction by a fraction, and division of two integer fractions by each other. He covered
the problems that could be an example for each group. Ender stated that he chose examples from
the types of questions that students might encounter (problems such as distance-time, number of
worker-time, etc.) in the subjects of direct and inverse proportion and included them in the lesson.
Similarly, Ayla first included activities to find the surface area of the unfolded cone, and then she
moved on to activities involving finding the surface area of the cones, which were given folded.
Likewise, Nihal first focused on the problems involving calculating the perimeter of a square of
which side length is given. Then, she focused on situations involving finding the side length of the
square of which perimeter is given. Teachers stated that students should work on different types of
examples and problems in order to learn mathematics. For this reason, they made an effort to
increase diversity by constantly monitoring the examples and problems they presented to their
students in their lessons.
Teachers' student-oriented monitoring has been effective in their instructional decisions. Some
of these decisions were in the form of complicating the content or breaking down or simplifying
the task. They supported students to focus on the main concepts by using simple numerical values
so that students could focus on important mathematical ideas by reducing the cognitive load in the
transition to a new topic, albeit at a limited level. For example, Özlem stated that she aimed to
make students easily establish the relationship between the angle of the circle slice and the data set
by choosing the data set from numerical values that can be easily processed on the subject of pie
graph. Similarly, Ayla included examples containing reference values such as 45, 90 and 180 angle
degrees so that students could see the relationship between the inscribed angle and the central
angle subtending the same arc of the circle. However not all of the teachers used examples that
might be easily connected to what students already know. For instance, while Serkan and Hale
could use simple numerical values (such as
or
) to make sense of multiplication
R. Gürel et al. / Journal of Pedagogical Research, 6(4), 168-189 180
and division operations with fractions, they focused on the application of the algorithm and did
not include such examples that could support conceptual understanding of the students.
Another way to simplify the task is to break it down into sub-tasks, making it a step-by-step
process. For example, Özlem first drew the closed shape for each geometric object in the lessons
where she taught the surface area, and then went on to solve sample problems after unfolding the
shape and developed the formula for surface area. In this way, breaking up the teaching task is a
control behavior that facilitates the operation. Nihal's most obvious control behavior for the lesson
was the breaking down the task to reduce cognitive complexity. For example, while teaching the
subject of calculating the area of compound shapes, she reminded her students that they should
find the side lengths that were not given first to calculate the area.
Nihal: We can proceed in steps. The aim is to make students achieve it themselves. ... Or they follow
me after each step. At the end the students can solve the problems fast. When we proceed step-by-
step they can do it. It's considerably better, in my opinion. (Measurement of area)
Decisions and practices aimed at complicating the task are often arrangements that can support
the development of computing skills, requiring the use of fractions, decimals, or square roots when
performing operations, or converting the different units of measurement. It is observed that Nihal,
Ayla, Serkan and Ender included challenging problems that require high-level skills that enable
students to think more deeply about concepts. However, they took an active role in solving these
problems. Nihal, as a result of her observations on student performance, decided to use different
units in the values she gave for the edge lengths in the problem of finding perimeters. She stated
that she took a decision in this direction in order to remind the students of prior subjects and make
the question more difficult.
The teachers rarely included different forms of representation (material, model/shape, verbal
problem, etc.) in their lessons depending on the nature of the subject they were teaching. Nihal,
Ayla, Özlem, Hale and Ender, whose lessons we observed including geometry subjects, benefited
from geometric object models, drawings and materials such as rope. However, no variation was
observed in terms of teaching method or technique in the use of materials and models. The model
use occurred generally in the form of teaching the subject through teacher-oriented question-
answers. In the lessons, prototype examples were rarely exceeded, and the drawings and models
mostly reflected typical examples. In addition, the teachers did not deal with different
representations of the same concept together and did not make associations between different
representations. For example, Serkan, who dealt with the multiplication of fractions through area
model, did not include the relationship between the solutions through this model and the
solutions using symbols in his lesson.
3.2.3. Controlling teaching methods and techniques
Table 7 presents the participants’ control behavior in relation to teaching methods and techniques
in a comparative manner. It has been observed that the teachers lacked flexibility when it came to
modifying the lesson. Additionally, they did not moderate the lesson based on the students'
existing or emerging knowledge and abilities. This tendency was very clear in the introduction
sections of the lesson. The teachers usually started their lessons by reminding the students of
related past topics. In this process, they were more active than the students themselves, and they
presented the preliminary information that the students had difficulty in remembering in the form
of explanations. They did not use these introductory activities for monitoring and organizing the
lesson. For example, Ender routinely reminded students of the preliminary information about the
subject, but he did not change the sequence of the lesson according to this introductory activity.
This also applies to other activities. Similarly, the concluding activities of the lesson were not
modified according to the situations that emerged in the teaching and learning activities, and the
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Table 7
Control behavior concerning teaching methods and techniques
Nihal
Ayla
Özlem
Hale
Serkan
Ender
Organizing the sequence of the lesson according to the
events in the lesson, flexibility
Using different/various methods in different
situations (question-answer, explanation,
demonstration, discussion, group work, etc.)
Highlighting rules, algorithms, and potential errors
Taking responsibility for completing the task in
challenging situations
Using explanation, repetition and demonstration as
plan B
Skimming/ superficial explanations
Limiting/ignoring the right to speak
lessons were carried out as planned. It was observed that Özlem did not go beyond the practices
she planned in her lessons, and she mostly used the same type of teaching methods and techniques
in her lessons. Therefore, Özlem's monitoring and control behaviors are mostly limited and aimed
at maintaining the lesson plan. In all of Özlem’s observed lessons, the students’ prior knowledge
was checked by questions at the beginning of the lesson, and the teacher herself explained the
missing subjects. In addition, the teacher presented the definitions and drawings related to the
subject on the board and solved the first example herself. Then she asked the students to solve
similar examples. Özlem continued to use these methods and techniques even when she faced
with an unexpected situation. Only Ayla stated that she often revised the sequence of the lesson
according to the reactions of her students. However, she stated that for this reason she could not
teach her lessons as she planned. Her views are given as follows:
Researcher: You said that the lesson went completely different from what you had in your mind.
You said that neither where nor how did it go, it never went the way you planned, remember that??
Ayla: The questions they ask are sometimes those that I can answer very briefly and I may continue
to teach the topics. But sometimes they confuse the topics. I cannot continue with the topics without
eliminating this confusion. Therefore, the reactions from the students guide me about how I will
teach the lesson. (Basic elements of prisms)
The teachers preferred different teaching methods in different parts of the lesson in order to
continue their lesson as they planned. These behaviors come to the fore especially in the
introduction phase of the lessons. For example, Hale, Serkan and Ender generally started their
lessons with a short explanation (writing the title, or talking about the importance of the topic)
about the content of the lesson. After the introduction, the teachers made the transition to the new
topic by presenting a definition and explanation or using the question-answer method. For
example, at the beginning of the subject of quadrilaterals, Nihal asked her students to show
examples of the quadrilaterals they saw around them. She then asked her students about the
properties of each quadrilateral such as sides and corners. Similarly, Serkan studied experimental,
subjective and theoretical probabilities by asking questions related to weather forecasting. The
question-answer activity mostly took place between the teacher and a student and then ended with
the teachers’ evaluation (true-false). No observation was made in which students can discuss the
topics with each other, allowing them to explore concepts and rules and to ask questions and
explain them. A definition, a rule or generalization was mostly presented by the teacher. Then
sample problem solutions were made in which the teacher was more active. The students took a
more active role in individual problem solving processes, which mostly took place at the end of the
lesson.
Situations supporting student explanations and/or solutions were not observed. Even if the
student solution was correct, the teachers often took on the task of explaining the solution method.
R. Gürel et al. / Journal of Pedagogical Research, 6(4), 168-189 182
Serkan himself explained the problem solutions in his classes. He stated that a student who could
not explain the solution well could cause confusion among the others. At the beginning of Ender’s
routine behaviors, his students listened to him while he was explaining the subject and took notes
later. He made frequent statements in this direction during the lesson and reminded the students
of this expectation. Only Ayla encouraged her students to develop their own ideas and find their
own solutions, and tried to create opportunities to develop through these ideas. She expressed her
views as, “A student is solving a problem. I know that there is another solution. I want them to
find it, these solutions should not be the same as I provided.” One of the practices that support this
view is asking her students to draw different chords of a circle in their notebooks.
The most typical practice to maintain the sequence of the lesson plan was to highlight the
definitions, rules, or algorithms associated with the topic covered in the lesson. All of the teachers
emphasized the points they deem important about the subject by writing or repeating. However,
these practices differed slightly among the participants. For example, Nihal stated that she
consciously expressed the definition in the book with her own words and Hale stated that she
included especially important points and possible mistakes and emphasized these statements in
the definitions. Ender, on the other hand, stated that he used bullets to highlight the key points in
definitions because he thought they were more memorable. Serkan and Hale, who are more senior
teachers, frequently emphasized typical student mistakes. Serkan emphasized important points
and possible student mistakes about dependent and independent events in probability. For
example, he stated “It [referring to the probability of compound events] is multiplied in both the
dependent and the independent [events]. There is no such thing as adding [the probability]” and
“If the numerator and denominator do not decrease, they are independent [events], if they do, they
are dependent [events].” Hale and Serkan emphasized that denominators do not have to be equal
in multiplication and division algorithms for fractions. Such practices were especially observed as
a defining feature of Hale’s lectures. Hale, frequently emphasizes about possible mistakes and
error-free solutions without allowing students to make mistakes.
Teachers’ monitoring and evaluation of student performance affected their decisions about the
ways of teaching. The typical control behavior observed among all teachers is that they are active
in a new or different situation or in solving a problem. They took the responsibility of completing
the task when they thought that their students might have difficulties, and they retreated in
subsequent similar situations and gave the students the opportunity to deal with it on their own.
For example, Serkan presented a probability problem that he had not solved before and stated that
he wanted his students to follow him while he was solving it. Similarly, Özlem carried out the
tasks of understanding the problem situation on the surface areas of geometric objects and forming
the relation herself, and the students were left only to write the numerical values in the relation
and to perform operations. Özlem, who stated that she had low expectations from her students,
took the responsibility of completing the mathematical tasks in almost all stages of her lessons.
Nihal herself took an active role in most of her lessons, especially when she thought that her
students might have difficulties, and gave her students the right to speak in second or later similar
examples. Even when she gave her students autonomy, she took an active role in reaching a
solution with her guidance and hints. In order to prevent her students from finding incorrect
solutions, she started to manage the process herself when she saw that they had difficulties.
Teachers frequently referred to pertinent previous courses or reiterated what they believed
were key themes when they noticed that the students were having difficulty in understanding the
topic. For example, Nihal’s explanation to her students, who confused the rules for area and
perimeter of the square, was to repeat these two rules. Only once did she use a verbal daily life
situation (the perimeter and area of Uncle Ahmet's garden) to show the difference between the
concepts of perimeter and area. She did not use other different methods (showing the area and the
perimeter with different colored pencils, establishing a relationship between the drawing and the
rules, etc.) to make students understand the difference between these concepts. On the other hand,
it is observed that Serkan and Ender became a model for their students by giving clues, thinking
R. Gürel et al. / Journal of Pedagogical Research, 6(4), 168-189 183
aloud, using simplification or a different teaching method (visualization, explanation, etc.) in
problem solving when they felt that the students did not understand the subject.
The teachers glossed over or gave superficial explanations when answering the students’
questions that they thought might negatively affect the direction of the lesson or they would have
difficulty explaining. For example, Serkan and Hale glossed over the questions of the students who
asked why the invert-and-multiply algorithm worked on division by fractions. Likewise, Özlem
did not explain the relationship between the volumes of the right cylinder and the right cone of the
same height. Nihal, too, could not provide an adequate explanation to her student who asked why
they were making calculations about estimation.
Another control behavior, which is used with the aim of maintaining the sequence of the lesson
plan, is to ask for explanations from students who can explain their ideas well, to give the students
the right to speak only on simple and basic issues, to ignore the suggestions of the students or to
postpone the discussion of ideas in cases where they think that the subject may be disintegrated.
While this behavior may have been necessary to preserve the integrity of the lesson, it precluded
the opportunity for students to discuss their developing ideas. For example, Ender ignored the
student questions about whether parallel lines could be in different directions (except for vertical
and horizontal directions) on basic geometric concepts because this question did not fit the
sequence of the lesson plan. In a later part of the lesson, he explained the student’s question about
the parallel lines himself. However, the question of the student could have been directed to other
students and they could be asked to reason about the answer to think about the concept of
parallelism and the students could be made to think about the concept more actively.
4. Discussion and Conclusion
It is evident from the results of the study that the teachers monitored and controlled the lessons in
accordance with their preparation goals. Because they generally set goals for the correct use of
rules and algorithms, they regularly followed up on the accuracy of the student answers, whether
algorithms, rules and symbols were used appropriately during the lesson. They rarely observed
the development of students’ conceptual understanding. These results suggest that novice teachers
tend to focus on procedural knowledge, which supports the results of Arani (2017). Arani (2017)
reported that the experienced teachers focus on conceptual understanding while novice teachers
focus on procedural knowledge. Another remarkable result of the study is that the teachers did not
monitor the development of the skills related to the mathematical connections that they stated in
their objective statements. These results suggest that some goals were not given importance as
much as that to others. Therefore, it can be argued that there is no regular and systematic
monitoring of whether these goals are achieved or not.
Compared to student-oriented monitoring, teaching-oriented monitoring was quite limited.
Following a course book or notes was the most frequently observed monitoring behavior for
teaching performance. Although at a more limited level, the teachers attempted to diversify the
problems included in the lesson and to ensure the accuracy of the explanations/definitions
presented. However, it is observed that there are mathematically incorrect or incomplete
definitions that were modified to make them easier to understand. It is also observed that these
incorrect statements were not noticed and corrected because there was no careful and systematic
monitoring. Another remarkable finding is that only the two least experienced teachers (Nihal and
Ayla) are found to monitor their own teaching behaviors (e.g., response time, intervention).
Almost all of the teachers participated in the study monitored the effectiveness of the new or
different instructional practices (the use of novel materials, models, etc.). However, this monitoring
mostly focused on changes in the student interest and participation. There was no in-depth
monitoring of how these practices affected students’ understanding of concepts (e.g., How did the
material make the concept easier or difficult to understand for the students?). This may be due to
the teachers’ limited knowledge about the effects of material use on learning or their inability to
use this knowledge effectively for monitoring purposes. The studies suggest that teachers’ purpose
R. Gürel et al. / Journal of Pedagogical Research, 6(4), 168-189 184
of using concrete materials is generally to increase student interest and participation in the lesson
(Grant & Peterson, 1996; Moyer, 2001). These findings provide explanatory information about the
tendency of the teachers participated in the study to focus on the motivational dimension during
material use.
Grossman et al. (2009) suggested that teacher training programs should be organized around
specific practices (learning practices) that guide teaching, rather than around what teachers should
know. However, it is emphasized that teacher trainers should address not only the practical aspect
(how to do it?), but also the conceptual aspect (why should we do it?) of these practices. The
findings of this study show that one of the learning practices that teachers need to gain experience
should be towards student understanding and their ability to monitor their own teaching
behaviors during the lesson. In the teacher training some approaches such as the Cognitively
Guided Instruction (Fennema et. al., 1996; Franke et al., 2001; Franke & Kazemi, 2001) and the
Hypothetical Learning Trajectories (Simon, 1995) might provide the pre- and in-service teachers
opportunities to focus student thinking. In order to acquire this habit of keeping regular and
systematic records on students' learning processes, teachers, especially those in the first years of
the teaching profession, need to engage in practices (workshops, seminars, group activities, and
cooperative professional development programs) based on the above-mentioned approaches.
It appears that teachers mostly adhered to the content and process of the lesson they planned.
Content was rarely expanded or narrowed based on the development of the lesson, and the outline
of the lesson was rarely changed. In the studies comparing the behavior of novice and experienced
teachers’ teaching performances, it is reported that novice teachers are overly dependent on lesson
plans in the teaching process (Borko & Livingston, 1989; Westerman, 1991). It is also reported that
the priorities of novice teachers in the teaching process are to attract student attention to teaching
tasks and to complete the lesson as planned (Chubbuck et al., 2001; Housner & Griffey, 1985).
Zimmerman (2015) argues that novice teachers have four different types of practical intentions in
the teaching process: keeping the lesson momentum; covering the content; supporting the student
needs and encouraging the independent student thinking. The findings obtained in this study
show that the teachers exhibited monitoring and control behaviors in order to cover the content
they planned, to maintain the momentum of the lesson (maintaining the order in the lesson plan)
and to support student needs (academic-procedural and emotional). However, very limited
behavior was observed in only one teacher regarding the intention to encourage independent
student thinking.
According to Dreher and Kuntze (2015), representations are an important aspect of mathematics
teaching and learning. Furthermore, the related studies show that it is impossible to teach a
mathematical object or idea coherently when using only one representation, and that the
meaningful use of multiple representations in the process of establishing relationships and
teaching is beneficial for students to obtain a coherent understanding of mathematics (e.g. Cengiz
et. al., 2011; Duval, 2006). It was observed that the teachers used different materials and models
during the lessons. However, they did not use different forms of representation in completing a
particular mathematical task. Therefore, it was not observed that different forms of representation
of a concept are employed together and the relations are established between these
representations. The inability to make adequate regulations during the lesson in terms of using
multiple representations may be due to the teachers’ lack of knowledge about the structure and
properties of teaching materials and their effects on student learning, or their ineffective use.
The most obvious control behaviors of the teachers were emphasizing rules, algorithms and
possible errors, and taking responsibility for completing the task in challenging situations.
However, such activities did not go beyond showing the correct solution by informing the
students about possible mistakes that could be made. Therefore, such behaviors prevented
students developing mathematical understandings through discussing incorrect or incomplete
ideas. Another control behavior that is carried out in order to maintain the planned sequence of the
lesson is to give a voice only to students who can express their opinions well. This practice also
R. Gürel et al. / Journal of Pedagogical Research, 6(4), 168-189 185
prevented students from learning from mistakes. Similarly, the teachers’ taking the responsibility
of completing the task in challenging situations caused the students not to have opportunities to
develop their mathematical thinking. Such practices may be related to teachers’ low expectations
for their students, their knowledge of how to learn mathematics, their beliefs and approaches. This
finding shows that there is a need for practices (such as workshops, seminars, group activities,
cooperative professional development programs) that will question the current approaches of
novice teachers to teach mathematics.
Teachers mostly used explanation, repetition, or demonstration as their plan B when their
students encountered problems or made mistakes. These results indicate that the teachers are
incapable of pedagogical content knowledge for a problematic situation during their instruction.
The fact that they avoided unexpected student questions about the ways of the rules or algorithms
work, or give superficial answers to them, also supports this interpretation. Related studies also
report that novice teachers have difficulty in producing appropriate answers or explanations for
students’ questions and comments for which they are not prepared, and that they do not change
their lesson plans in line with student needs (Borko & Livingston, 1989; Livingston & Borko, 1989;
Westerman, 1991).
Experiencing unexpected situations may assist teachers' professional development and allow
them to develop better plans for their next teaching cycle of similar concepts (Smith et. al., 2008).
Stockero and Van Zoest (2013) defined the pivotal teaching moment (PTM) as moments when
teachers notice such situations and take action and change the sequence of instruction based on the
students’ views, unexpected comments and questions based on misconceptions or confusion.
During the unexpected situations in the classroom environment, teachers may choose to ignore
PTMs or build their lessons on these moments to extend the lesson they had previously planned
(Stockero & Van Zoest, 2013). The results obtained in this study show that the teachers generally
ignore these moments and do not prefer to make a change in the lesson based on their students’
thinking. One reason for this situation may be that teachers’ contingency, defined as necessary
teacher knowledge that helps them to face unexpected moments when they have to deviate from
their plans, is not sufficiently developed (Rowland et al., 2015).
According to the teachers who participated in the study, they were able to follow the lesson
plan they developed. Only Ayla stated that she often could not implement the decisions she made
before the lesson to increase the participation of her student. In other studies, it has been reported
that novice teachers can get away from their goals during the lesson compared to senior teachers
(Borko & Livingston, 1989; Livingston & Borko, 1989; Westerman, 1991).
The teachers generally went through previous material associated with the present subject at
the beginning of their lessons. However, they often took an active role rather than giving students
opportunity to think about their prior learning. In addition, they did not change their lesson
according to this introduction process and continued the lesson as they planned by making
explanations about the deficiencies in the students’ prior knowledge. The following behaviors
observed in senior teachers were not observed among the participants: associating with prior
learning (Griffey & Housner, 1991), encouraging students to participate in classroom discussion
(Arani, 2017), and allowing students to ask questions and make comments (Borko & Livingston,
1989; Livingston & Borko, 1989; Westerman, 1991). Reform studies in mathematics education call
for teachers to shape the teaching process depending on the developments in the lesson, especially
the students’ thoughts, for effective mathematics teaching (Anthony et al., 2015; National Council
of Teachers of Mathematics [NCTM], 2014). It is also stated that recognizing students’
mathematical thinking is of critical importance for high-quality mathematics teaching (Jacobs et al.,
2010; Walkoe et al., 2020). However, the findings of this study indicate that the teachers did not
shape the teaching process based on the situations that developed in the lesson. This finding is
consistent with the finding of Arani (2017) that novice teachers do not very often modify the lesson
based on the students’ thoughts. Complex teaching tasks such as supporting the student
(simplifying the task, offering clues, etc.), managing effective classroom discussion, and
R. Gürel et al. / Journal of Pedagogical Research, 6(4), 168-189 186
responding appropriately to a student question require skills that teachers can acquire over the
years. In order for novice teachers to develop such complex skills, it can be ensured that they focus
on sub-skills that include these complex skills, so that they experience and become competent in
one sub-skill at a time (Grossman et. al., 2009; Kazemi et al., 2009). For instance, in order to gain an
ability to conduct effective classroom discussions, the related sub-skills (identifying a debatable
problem situation, creating productive questions, vocalizing student answers, etc.) can be focused
on individually and practiced one at a time. Novice teachers need to be supported by experts
(experienced teachers, academics, etc.) with these skills in order to gain such experiences.
5. Suggestions for Further Studies
In this study, teachers’ self-regulation behaviors in teaching mathematics were examined based on
Zimmerman's (2000, 2002) self-regulation model. It is found that the forethought and self-reflection
processes in this model are successful in explaining the preparation for teaching and self-
regulation after teaching (Bozkurt & Yetkin-Özdemir, 2018; Bozkurt et. al. 2022; Yetkin-Özdemir,
2015; Yıldız et. al., 2021). In other words, the processes such as goal setting, planning, evaluation,
and self-reflection accounted for the regulating teaching as well as regulating learning. However, it
is observed that it is insufficient to explain the regulation regarding the control and monitoring
processes during the actual teaching. For this reason, the monitoring process in this study is
defined as 1) student-oriented monitoring and 2) teaching-oriented monitoring. Similarly, the
control behaviors are defined as the regulation of content and processes during the lesson.
However, since the aim of the control behaviors of the novice teachers is mostly to continue the
lesson as planned, the situations of making changes/regulations during the lesson were observed
at a very limited level. For this reason, it is suggested to examine the monitoring and control
behaviors of middle school mathematics teachers, who are especially qualified as senior.
Comparative studies with novice and senior teachers are also necessary in order to be able to
define teaching self-regulation activities in more detail and to see about which regulation activities
novice teachers need support.
In this study, teachers’ monitoring behaviors in the lessons were examined through interviews
made after the lesson. The use of other methods (i.e., eye tracking) that will help determine the
situations that teachers focus and follow during the lessons can support a better understanding of
this process (Sherin et al., 2011). It is suggested to use such methods in future studies.
In this study, teachers who have not completed their first five years in the teaching profession
were defined as novice teachers. However, the findings suggest that there were differences in
terms of self-regulation even within this group. For example, it is observed that the goals of the
teachers who did not complete their first two years in teaching are more compatible with the
curriculum, and that they formed more specific criteria in terms of evaluating their teaching
performance. It is also observed that the conditions at the schools where the teachers work also
play an active role in self-regulation. However, the findings of this case study, which was
conducted with a small number of participants, do not make it possible to produce generalizable
conclusions regarding the effects of seniority and environmental factors on self-regulation. For this
reason, there is a need for research with more participants to examine how self-regulation
activities for teaching differ in terms of variables such as seniority, school environment, and
teacher beliefs.
The concept of professional vision is defined on the basis of two processes: noticing and
reasoning based on knowledge (Seidel & Stürmer 2014; van Es & Sherin, 2008). Noticing is the
ability of teachers to direct their attention to related classroom situations (van Es & Sherin, 2008),
and knowledge-based reasoning refers to the teachers’ cognitive processing of perceived
instructional events based on their knowledge of teaching and learning (Borko, 2004; Sherin, 2017;
van Es & Sherin, 2008). While noticing can be associated with the monitoring behaviors which are
described in this study, knowledge-based reasoning is related to the teachers’ control behaviors
depending on the monitoring process. In this context, examining the regulation skills of teachers
R. Gürel et al. / Journal of Pedagogical Research, 6(4), 168-189 187
for the teaching process in their professional vision and teaching awareness studies may offer
different perspectives in terms of understanding these concepts.
Author contributions: All authors have sufficiently contributed to the study, and agreed with the
results and conclusions.
Funding: This study is derived from the project study numbered 113K316 carried out within the
scope of the 1001 program of The Scientific and Technological Research Council of Turkey
(TÜBİTAK). The project study was supported by TUBITAK, Social and Humanities Research
Support Group (SOBAG).
Declaration of interest: No conflict of interest is declared by authors.
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