Math Teachers: What Influences Their Teaching Methods?

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There’s not one type of pedagogical technique that produces an engaging teacher. Teachers are shaped by various experiences, training, and personality. There are also factors like the qualifications of being a math major and personal motivations are not as important in influencing teachers’ teaching styles and their level of engagement. The most important aspect is that teachers need to initially have a strong background in teaching, where there needs to be quality and quantity amount of teaching experience, in order for these teacher qualities to be influential.
1. Trinity College
Trinity College Digital Repository
Senior Theses and Projects Student Scholarship
Spring 2010
Math Teachers: What Influences Their Teaching Methods?
LiJin Yan
Trinity College
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Part of the Education Commons
Recommended Citation
Yan, LiJin, "Math Teachers: What Influences Their Teaching Methods?". Senior Theses, Trinity College,
Hartford, CT 2010.
Trinity College Digital Repository,
2. Math Teachers:
What Influences Their Teaching Methods?
LiJin Yan
Educational Studies Program
Senior Research Project
Trinity College
Hartford, CT
Professor Sandler
December 2009
Many students have different opinions about the subject of mathematics. During my time
in public schools, I have met some American students who are enthusiastic about learning math
and plan to pursue a career that involve the use of math. But there are also many students who
despise math and struggle hard to grasp the basic concepts of math in high school. The U.S is
known for low achievement rates in mathematics but there are obviously some students in our
schools that enjoy and excel in math. Students need to be engaged in the lesson through
discussion, group work and less chalk and talk from the teacher. All teachers have different
teaching styles and approaches to making sure their students are participating and learning the
subject. But what influences math teachers to teach differently? The teacher’s education
background, personality, social background, experiences in the field, or mastery of the skill may
affect his or her teaching methods in the math classroom.
When students are learning math, the teacher’s teaching method is a crucial factor to how
much the student would understand and retain the material. Teachers appear to lecture and use
teacher directed instruction more frequently than using student centered methods to instruct math.
(McKinney et al., 2009). They also found that many teachers spend more time on teaching basic
computational skills rather than engaging the students in mathematically rich problem-solving
experiences. Furthermore, in high poverty schools, teachers implement the “pedagogy of poverty”
when they teach their students. The “pedagogy of poverty” is a curriculum that follows a fixed
sequence, concentrates on just teaching the students basic skills without enough emphasis on
problem solving and reasoning. (McKinney et al., 2009). This article is relevant to what I want to
research because it demonstrates that teachers in high poverty schools have the tendency to use
4. traditional teaching methods, which limit the students’ ability to fully understand. They teach
less challenging math curriculums rather than implementing methods that are more student and
inquiry centered, and offer more challenging math curriculum.
The impact of teaching methods on students’ understanding of math can also be seen in
Bayazit and Gray’s study. Bayazit and Gray (2004) found that teaching practices that differ in a
qualitative way will produce qualitatively different learning outcomes. They concluded that
using real life situations to convey inverse functions might help students develop conceptual
understanding of the topic. A better way to ensure that students are constructing meaningful
understanding of inverse functions is to use a variety of appropriate representational systems,
examining the concept through conceptually focused and cognitively challenging tasks, and
ensuring active involvement of the students in the classroom. This study emphasizes the need for
teachers to use visual aids like Venn diagrams and graphs to help students develop a rich
understanding in the math concepts that are introduced in the classroom. This finding is
important to educational research because teachers and administrators need to know that using
qualitative methods would help increase students’ engagement in classrooms.
So far, I have talked about how traditional methods of teacher centered lessons are
dominant in math classrooms, even though it has been demonstrated by studies that when math
lessons are more student centered, the students actually develop a better understanding of the
math concepts. Wilson and Gwendolyn (2000) conducted a study where they implemented the
Core-Plus Mathematics Project, which is based on the belief that all students can make sense of
mathematics. This project encourages the teachers to organize students into groups and class
discussions, where they can work together to explore mathematical problems and ideas. The
three teachers in the study have taught math for 10 years and have struggled with sharing math
5. authoritative power with the students. They have problems with sharing math authoritative
power with the students because the attention in the classroom is no longer on them, but on the
students instead. (Wilson and Gwendolyn, 2000). Teachers also struggle to realize that students
can make important connections through group work, even without direct teacher explanation.
While the teachers used the Core-Plus Curriculum, they implemented it along with their own
teaching styles and preferences. This finding helped me realize that when I am observing the
math classrooms in an urban middle school, I might actually see alterations of student centered
lessons. This shows that teacher’s input and teaching styles have an influence on the curriculum,
even if they are all instructed to teach in one specific way. If administrators can find out what
exactly influences the teachers’ way of teaching in the classrooms, then it can help them recruit
teachers who can implement successful engaging strategies that are similar to the Core-Plus
The teacher is a crucial tool when we want to ensure that students are developing a
concrete understanding of all the math concepts. Therefore we need to also focus on what kind
of teachers are instructing math in the public schools. One of the factors that might influence the
way the teacher instructs is his or her cultural and social class background. Cahnmann and
Remillard (2002) analyzed the challenges that Arieto, a bilingual Puerto Rican teacher, and
Kitcher, a white teacher who mainly teaches minorities, face as they try implementing
mathematics reform in a high poverty school. Cahnmann and Remillard (2002) discovered that
these two teachers need to teach from perspectives that are unfamiliar to them. Kitcher needs to
know how to relate to the students by examining her own cultural assumptions, and realize her
expectations of her students. On the other hand, Arieto needs more experience with exploring
math ideas more deeply, and use instructive practices that actually engage the students in rich
6. mathematical thinking. This study showed me that in order to achieve better participation in the
math classrooms; teachers need to continuously apply mathematical representations and
language from a mathematical and cultural perspective. Administrators need to keep this finding
in mind in order to find the best teachers that can relate to the students and teach them
Another factor that may affect the teachers’ teaching methods is the training that the
teachers received, education background, and experience in math instruction. There are three
professional development interventions that demonstrated a shift in the prospective teachers’
beliefs about reform-oriented mathematics learning and teaching practices, which are problem
solving journals, structured interviews, and peer teaching (Timmerman, 2004). Teachers who
were exposed to these interventions were able to easily instruct math in their classroom using
innovative and engaging ways. During my interviews, I would be paying close attention to
whether or not these teachers received these types of training.
Teachers’ own motivation can also affect the way they plan their math lessons and
instruct in the classroom. Mok (2002) found that teachers’ development is due to self-as-agent,
meaning their own personal values and fulfillment of the self’s personality motivates them to
continue teaching and improving in their areas. The teachers’ self-confidence in their capabilities
and own personal values can shape their attitudes towards teaching students. It’s an important
point because teachers, who don’t have a goal and high confidence level, would more likely not
care about the students’ performance.
Along with personal goals and values, educational background can also be another factor
that determines how teachers instruct. Teachers who have midrange years of teaching experience,
7. supervised more than five field experience students, work closely with an university supervisor,
and have graduate-level preparation in supervision tend to be more effective teachers (Killian &
Wilkins, 2009). Teachers who have a combination of these different qualities usually are able to
create and have various types of learning methods to engage the students in math. In addition,
many of the effective teachers also have master’s degrees in teacher leadership. Teachers who
have degrees in teacher leadership are more successful in flawlessly instructing the class without
having trouble with classroom management. Also, teachers who had been exposed to a field of
studies that show the usefulness for student achievement, testing and grading techniques were
more likely to incorporate these foundations in their teaching methods as well (Gentile, 2003). If
teachers are able to personally experience and be involved in various assessment tools, then they
would have knowledge on the best way to use these tools in their classrooms. These additional
educational backgrounds result in better teaching styles that produce more engagement within
the classroom.
Along with educational background, the teachers’ college major may not play an
important role in the quality of the teachers’ teaching methods. According to Cavanagh (2009),
qualified teachers do not necessary need to have a math major in order to improve student
learning in elementary and middle school. “Just superimposing a math major isn’t going to
guarantee anything. Teachers need to know their stuff, and they need to know how to apply it”
(Cavanagh, 2009). He is arguing that it is not always about the teachers’ knowledge of math
content, but it is also crucial that the teacher knows how to convey these concepts to the students
in the best possible way. Teachers who possess the “mathematical knowledge for teaching” are
more likely to be able to explain the meaning of math problems to students in several ways,
know how to use math language in class and keep track of where students get confused on the
8. problems, while at the same time teachers need to be adept in covering all of the important math
concept (Cavanagh, 2009). This shows that the requirement of teachers having to be math majors
in college does not necessary mean that they will be the most effective math teachers. Instead,
administrators and researchers should pay more attention on how well the teachers know their
math materials and if they are capable of conveying this math information in the most concise
and understanding format. I will keep this in mind as I am doing my research on the factors that
influence effective engaging teachers’ teaching methods.
These relevant research articles provided me with background knowledge on which type
of methods would yield higher students’ engagement and participation. I have basic knowledge
now that factors like mastery learning knowledge, work experience with a supervisor, teachers’
personal drive, strong teacher-student relationships and the quality of the teachers’ knowledge on
math can affect how engaging teachers are in instructing and leading students. With this
information, I want to further to examine what kind of teaching methods are currently being
implemented in an urban middle school to engage students in math. I also want to observe if
there are other factors that can influence teachers’ math teaching styles that may or may not
result in engaging students.
Research Question
What types of teaching methods do teachers use to engage students in Math departments
in an urban middle school?    What are the influential factors that play a role in the methods that
Math teachers use inside the classroom?    
9. I decided that I want to use qualitative research methods of interviews to conduct my
study because I wanted to personally experience the different math teaching styles that are used
inside an urban classroom. Also, I wanted to interview the teachers myself so I can have a better
understanding of who they individual are and how their characteristics relate to the way they
teach inside the classroom. After deciding this, I gained permission to an urban middle school,
and this urban middle school will be known as the H school in my paper. I was only able to
interview and observe four math teachers at the H school. Each interview was about forty
minutes long, and all the interview questions were open-ended questions. I initially constructed a
structure set of questions for all of the four teachers but then I altered the questions depending on
each teacher’s responses during the interview (see attached appendix for the list of interview
questions). The teachers’ were randomly selected at the school.
During my time at the urban middle school, I defined and determined what it means to be
an “engaging teacher”. I also investigated the types of teachers that are in the math classrooms
and if their methods are engaging to their students. All of the teachers had to sign a consent form
before I started the interview and classroom observations. Throughout this whole paper, I have
given the school and the teachers a pseudonym in order to ensure confidentiality and protect the
privacy of the teachers.
Data & Analysis
In the H school, there are several different and interesting teaching methods that teachers
use inside the urban middle school classrooms, which involve a combination of direct instruction,
verbal interactions and hands on activities. The individual teacher’s teaching methods can be
10. influence by various types of experience, training, and personality, which are crucial for
becoming an engaging teacher. Furthermore, teachers do not necessary need to be math majors in
order to be qualify to teach engagingly in the classroom. Most important of all, teachers need to
have a strong foundation in teaching from the very beginning in order to be an engaging teacher.
It’s the quality and quantity of the teacher’s teaching experience that would affect how engaging
the teacher can be in a math classroom.
Engaging Teachers
For my project, I determined engaging teachers as teachers who frequently use verbal
instruction in the lessons. There also needs to be a high rate of student participation in the math
classroom. The teachers also need to be able to implement innovative methods and develop a
strong and trusting relationship with the students.
Ms. Bush
Many of these students in his class are alert and attentive. When the students in his class
become rowdy and start talking, he either just needs to put his arms up to quiet them down or
give them a stern look. The students automatically focus on their work. Based on my
observations in the H school, Ms. Bush is one of the most engaging math teachers out of the four
I interviewed because instead of just direct instruction, she is constantly involved in verbal
instruction with the students. In the beginning of the class, she would have music playing in the
background for four minutes, so the students would settle in and be ready to do the “Do Now”.
The “do now” are a set of questions that the teacher assigns to the students in the beginning of
the class that will cover materials from the previous lessons and homework problems. She
believes that you need to “try as much as you can to make the math problems real to the kids’ life
11. in some way. If your teaching fractions, you know cut up a pizza, don’t just cut up a rectangle on
the board” (Ms. Bush). Furthermore, she permits the students to have an open discussion with
him when they do not agree on a solution to a problem. This grants the students the opportunity
to explore and develop a better understanding of the math concepts on their own. One day during
his 8th grade geometry class, she drew a rectangle with two congruent angles and asked the class,
“If these two sides do not exist, will you still have two parallel lines?” Everyone agrees but then
a student asked “what if you erase the other sides of the diagram, would the angles still be
congruent?” The teacher does not immediately correct the student, instead she draws out the
scenario that the student is posing and she guides the student with questions. This discussion
continues for at least fifteen more minutes, with several students participating and going up to
the board to demonstrate what they think the answer is.
By the end of the 15 minutes, the students concluded that “they can prove the top and
bottom angles are congruent but the z on the other side might or might not be congruent because
we don’t know any more information about the other two sides.” Ms. Bush then gets up from her
seat and confirms this finding by telling them “you need more information to prove if the lines
are parallel” (Ms. Bush). All the students continue to ask questions and every single student in
this class was actively participating. When some students are not participating, Ms. Bush would
call on them to answer her question, in order to pull them into the lesson. Ms. Bush can obtain
and retain the students’ attention throughout the 80 minutes of class and she does this with her
ability to discipline her students in a structured classroom setting.
12. Ms. Top
Ms. Top can also be considered one of the most efficient teachers in math engagement at
H school. In her class, students are attentively taking notes and raising their hands to answer her
questions. She uses the smart board to demonstrate diagrams and word problems, but at the same
time she asks questions that require several students to answer as she explains the problems.
Many students would raise their hands and patiently wait to be called on and she would also call
on unexpected students to answer as well. She is constantly monitoring the room to assist any
students who may need her help. When she notices a student is looking into space and talking to
other people, she would walk to him and kneel down to help him refocus on the problem. Her
tone is soft but serious at the same time. She would raise her voice if she needs to calm the class
down. She tends to give a lot of quizzes and vocabulary sheets to the class because she believes
that it will help track their progress and allow the student to figure out where he or she still needs
to work on.
Ms. Smiley
Ms. Smiley is the third most engaging math teacher at H school. Within her classroom,
she tries hard to engage her students with limited direct instruction with combination of verbal
discussion between the teacher and the kids, and the regular use of games. She teaches two
regular math classes and one special education math class. In her special education classes, most
of the kids are interactive with her, while she teaches. The students are constantly raising their
hands and asking questions about things that they need clarification on. Half of the class would
be involved in her verbal discussions. She also engages the students to a certain extent by
implementing games that enable the students to experience probability with their own eyes and
13. hands. Some of the students would get restless as class progress and start to have their own
conversations. She tries to quiet her student down and make them re-focus when they get rowdy
but she is not as successful as Ms. Bush or Ms. Top in achieving a focus classroom. Most of the
time, 4 or 5 students would be roaming around the classroom, while she is involved in a class
discussion with the class.
Ms. Reese
Ms. Reese is the fourth engaging teacher because she often lectures in front of the
classroom, while the students listen and take notes. She tries to have a verbal interaction during
this direct instruction but many students tend to not participate. There are a lot of worksheets and
homework problems that they work on during class. The pace of the class is pretty slow because
she frequently has to stop to take care of students’ misbehavior. In her math classes, she
struggles just as much as Ms. Top in class management. One day two students were arguing in a
corner about which sneakers are better and four students eventually became involved in the
conversation as well when they were supposed to be working on their worksheets. Teacher 4 was
helping a student on the other side of the room and she doesn’t address this until four minutes,
while the noise level from that group were pretty loud. When she approaches them, she tells
them to focus on their work but this was not effective at all. The students after a second started
talking to other people again. These side conversations and student outbursts constantly happen
in her 80 minute lesson plan, which interferes with her goal of trying to engage these students.
Only 3 students were regularly participating when she is instructing to the class and the rest were
either staring into space or walking around and talking to their neighbors.
14. Influential Factors
After interviewing the teachers, I found that the most influential factors that influence
teachers’ teaching method are the quality and quantity of the teaching experience, quality of the
teaching training, and the personality of each individual. In addition, I found that personal
motivations and qualities of being a college math major have no influence on teachers’ teaching
Ms. Bush
Teacher 3 describes himself as “a big old guy with a deep booming voice, 6’2, weighing
240 pounds” (Ms. Bush). She never had a problem with public speaking and she is very
confident in speech. She is not shy and not afraid to tell students what they need to do in her
classroom. She definitely does not have any problems with class management because as she
says, “I am absolutely intimidating and it can be useful if I need to quiet them down” (Ms. Bush).
But because of her intimidating nature, she has to rein that in a bit because she had experienced
kids who are afraid to ask her questions. But she learned to balance it by kneeling next to the
kids and being a jokester with silly ties and jokes. This allows the students to respect Ms. Bush
but at the same time they seem to feel comfortable to approach her for help.
Her major was history and economics. She did not intend to become a math teacher, in
fact she was horrible at math as a student. The reason she chose to teach math was because of
economic issues. “I pursued teaching math because I need a job” (Ms. Bush). It is quite
interesting that her personal motivation was not his passion for math, instead it was the desire for
a job but she is still successful in student engagement in his classroom. Furthermore, her major
was not math; therefore personal motivations and majoring in math may not be the most
15. important factor in deciding if a teacher is effective in math student engagement. It may vary
from teacher to teacher.
Furthermore, teaching experience plays a key role in Ms. Bush teaching methods. H
school is her third school and this is her twenty-six years of teaching, with eight years at H
school. As mentioned before she didn’t plan to become a teacher, therefore she did not enroll in
any education courses in college. Instead after a couple years in construction work, she decided
it’s was too hard. She ended up getting her master and student teaching at a university. She
actually did not get many teaching experiences before she taught at her first school but she was
excited to just started teaching in front of the kids during her master program. “By the end of the
first week, I just started teaching” (Ms. Bush). It wasn’t a challenge for her to just dive into
teaching and she liked it a lot. Experience definitely helped her develop strategies that worked in
student engagement but it seems that she was just a natural to begin with. But experience can
really make a difference for teachers who already have a strong foundation in instructing from
the beginning.
Ms. Top
Ms. Top has been teaching for 30 years. She definitely has a lot of teaching experience,
just like Ms. Bush, and this seems to work in her favor. She taught at high schools for 23 years
and now she has been teaching at H school for 7 years. She had formal training at a university
right after college.
One of the most significant differences between Teacher 1 and Teacher 3 is Teacher 1’s
personal motivation. She chooses to teach math, not because she wanted a job, but because
“math is so important. It comes up everywhere in their life later on and I found it easier to
16. convince students how important the subject I was teaching in” (Ms. Top). She made a decision
to teach math because she wants to help and prepare students for whatever comes next and it was
so clear to her that they need math in order to move on in life. This motivated her to continuously
altering her lesson plans every year until she is satisfied with it. Her passion for math and her
two majors allowed her to build a strong foundation for teaching, along with the help of
experience over the 30 years. Her major actually helped her realize that she wanted to teach math
more than history, whereas majors had no relevance to Ms. Bush’s teaching methods.
Ms. Top is not as outspoken and as strict as Ms. Bush. She is a perfect example of how
teachers do not all have to be necessary strict but need to know how to balance out between
being too soft and too strict. “I think I am strict although I also think I am not as strict as some
people I know. I am I am too soft” (Ms. Top). Although she has a problem with disciplining her
kids, she found a solution which is to keep them busy and engage. “But with do now’s, I see a
change in the class, it sets the tone of the class for the next 80 minutes, so I think that has always
been my answer to what I can do to make them engaged” (Ms. Top). She has a different
personality than Ms. Bush but she still is able to engage the students with her type of personality.
Her methods are different from Ms. Bush who believes in a combination of direct
instruction, problems that involve real life situations and verbal instruction. “I think I am also
more sensitive to where I think the CMT did a disservice, where everything was hands on, but
not everything will be hands on in reality” (Ms. Top). Due to this belief, she insists on building
in tests and quizzes in her classroom to prepare the kids for reality. “I am a big believer in lots of
quizzes along the way. The fact that my quizzes are always small points, most of the kids are
going to say it’s a fair system and they will respond well to it” (Teacher 1). Her quizzes are
17. supposed to let them know they are in the learning stage and allow them to assess how well they
are doing.
Ms. Smiley
Ms. Smiley is one of those teachers that people would label as a teacher with potential.
She just started her first year of teaching at H school. She is from a family of educators. Her
education and job experience, personality and personal motivation impacted her teaching styles
tremendously. For several years, she was a engineer. She then worked for an educational
consultant and designed teacher booklets for No Child Left Behind and title 1 schools. She did
not start teaching the traditional way; instead she worked in private tutoring in math and reading
in her kids’ schools whenever she was available. “I knew I wanted to be an engineer. I eventually
wanted to go into teaching because my own math experiences were horrible until I got to college”
(Ms. Smiley). The switch from mechanical engineer was not a sudden career move. She first
wanted the practical experience of applying math on a daily basis before becoming a teacher. Her
personal experience with math and science was horrible but if it wasn’t for her family’s
encouragement, she would have turned away from these two fields. “I am a not a traditional
teacher. I don’t believe that is the best way to learn math and I knew I wanted to do it differently
when I have the chance” (Ms. Smiley). Therefore, her education experience influenced her
teaching methods because she refuses to teach traditionally in terms of basing her lessons on the
textbooks and constantly using worksheets.
Her training and teaching experience are the reasons why she is struggling with
classroom management. Her methods are successful in achieving student math engagement most
of the time but her lack of behavior management interferes with that engagement. “The only
18. special education class I took at a college, which did not prepare me for the level of needs that
these children need in my special education classes. I am modifying more work for that class
with my gut feel” (Ms. Smiley). She even admits that she does not have adequate amount of
special education training that allows her to really teach and manage these kids. She is planning
on going back to school to get more training in this area. She also lacks the experience to know
how to deal with classroom management. “It’s a difficult thing, as a new teacher, classroom
management probably is one of my biggest challenges. I haven’t found anything that really
works. The level of chitchat during class, I don’t know how to deal with it yet” (Ms. Smiley).
But although she is at a disadvantage, she is willing to change her ways by over planning every
day because “if you have to kept them busy, because if you don’t, they will keep you busy” (Ms.
Smiley). This is her personality, which is willing to work hard because her passion is to teach
these kids in the best possible way. Unlike Ms. Bush and Ms. Top, she doesn’t have the 30 or 26
years of knowledge of how to deal with talking and behavior issues. Teachers that have an
adequate amount of training in various education areas and a huge amount of experience would
definitely be more effective in classroom management that would not interfere with the student
math engagement.
Ms. Reese
She was a math major in college and decided to teach because she always had a passion
for math. “Well, I thought I was good at explaining math but I don’t know anymore. I always
had a gift in communicating mathematics to my peers, so I thought I was going to be good in the
classrooms” (Ms. Reese). Her personal motivation to teach was that she was passionate about
math but she now seems to have doubt about how well she actually can teach. “I think one of the
reasons why I am having a hard time because I think I am not challenging them enough. I need to
19. work on challenging them more” (Ms. Reese). It’s interesting that she acknowledges that her
teaching methods are not stimulating enough for these students, which fails to draw their
attention and interest in math. According to Ms. Reese, these students at H school are smarter
and at a higher level of learning than at the other schools she taught at. Furthermore, this
demonstrates that Ms. Reese lacks a strong foundation in engaging students from the beginning.
Ms. Reese is actually an interesting case because she has 19 years of teaching experience
in public schools but she is still struggling with class management and student engagement in her
math classrooms. She has more experience than Ms. Smiley but Ms. Smiley, who just started
teaching this year, is actually more successful in student math engagement than Teacher 4. Ms.
Reese has taught at high schools for 17 years and this is her 2nd year at H school. Her total 19
years of teaching did not aid her at all in keeping her students under control and fail to engage
students at the same time. Teaching experience was an essential factor in the other three teachers
but this indicates that only having teaching experience is just not enough.
She is also very soft spoken and not very strict, just like Ms. Top but she doesn’t have
any strategies to help her be firm on the students. The students tend to take advantage on her
being too nice, although she does try to send misbehaved students to the principal, but it doesn’t
seem to scare any of the students at all. Ms. Reese’s personality didn’t help her at all in engaging
her students as much as Ms. Bush, Ms. Top, and Ms. Smiley’s personality did.
Limitations and Challenges
One major limitation to this study is the amount of teachers I was able to interview and
observe. Initially, I wanted to study high school math classrooms and teachers because they
might have more freedom with playing around with the math curriculum. After many attempts to
20. gain access into the high schools, I was not successful but instead I was able to gain permission
from the Principal at the H middle school. Due to the fact that it took me a whole month to gain
access to a school, the math director at the H school was only able to give me four math teachers
to work with. Therefore, my sample size is small and I know if I have a bigger sample size, I
might have been able to find more differences between the teachers. I also wanted to compare
the math teachers in different schools but due to access issues and time constraints, I was not
able to implement this in my study. It would be interesting to see if the teacher qualities and
teaching methods in one school are the same or different in other schools.
This study is significant because Math is an important subject that all students would
need in their future endeavors. Math is such a fundamental tool that everyone needs in their daily
life. Therefore, we need to ensure that we have adequate teachers that can engage our students to
learn the math concepts they need to know. Furthermore, this study can play an important role in
the math teacher hiring process. Administrators can use the findings from this study as a guide to
help them figure out what type of teacher qualities they should pay attention to in order to ensure
that they hire teachers that are capable of engaging the students in math.
Ms. Bush and Ms. Top both are very qualified in their teaching experience, training,
education background, personal motivation, and personality. Although they differ in many
aspects of these factors, these factors primarily shape how they engage their students. This
allows them to use combinations of worksheets, games and verbal discussion styles with the
students. Ms. Smiley is third in line to be considered in effectively engaging her students because
21. she has a lot of personality, personal motivation, and unique education background. But she still
lacks in areas such as teaching experience and extensive training. As for Ms. Reese, she has a lot
of teaching experience but the quality of her teaching experience is lacking. She is still learning
to manage her class in terms of behavior and engaging them in the lesson. She isn’t as qualified
in the different influential factors like Ms. Bush, Ms. Top, and Ms. Smiley are.
There’s not one type of pedagogical technique that produces an engaging teacher. Teachers
are shaped by various experiences, training, and personality. There are also factors like the
qualifications of being a math major and personal motivations are not as important in influencing
teachers’ teaching styles and their level of engagement. The most important aspect is that
teachers need to initially have a strong background in teaching, where there needs to be quality
and quantity amount of teaching experience, in order for these teacher qualities to be influential.
22.   Bibliography
Bayazit, Ibrahim & Gray, Eddie. “Understanding Inverse Functions: The relationship between
Teaching Practices and Student Learning.” International Group for the Psychology of
Mathematics Education 28 (2004): 1-8. Web. 5 Oct. 2009.
Cahnmann, Melisa S. & Remillard, Janine T. “What counts and how: mathematics teaching in
culturally, linguistically, and socioeconomically diverse urban settings.” The Urban
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24. Appendix A
Teacher Interview Questions
Personal Information
1. What is your name?
2. What are the math levels and grades that you currently teach?
3. How long have you been teaching at Hartford Magnet Middle School?
4. Can you tell me about where you are from originally? How would you compare it to Hartford?
Would you describe it as really different or similar to Hartford? Are you living in Hartford
currently or still living in your hometown?
5. What was your first reaction when you first started working at the H School? Can you please
describe your transition period? Did it take you a long time to adapt to the new environment or
you felt right at home with all the students and teachers?
Teaching Styles
6. Can you please elaborate for me regarding your education background, starting from
elementary school? Like, what type of school was it? (private or public, school size, racial
7. I would like to know more about your educational background. Can you talk more in detail
about where you went to undergraduate school and the road you took to get here today? What
major? How did you get involved in this major? (Where did you attend undergraduate school?
Where did you attend graduate school? Did you work closely with any of the professors there?)
8. Why did you pursue teaching math? Are you going to keep pursuing this career or is this just
for now?
25. 9. What motivates you to do this?
10. Can you talk more about what jobs you work at before you took this teaching job here?
(What kind of experience did you have before teaching here? What kind of training for
education were you involved in?)
11. Describe the students’ interest in math at H school for me please. Do you think these students
would consider math as one of their favorite academic subjects? Is it a struggle for them?
12. Please talk about the types of expectations you have for your students in your math
classroom. How would you describe their math performance? Do you have different expectations
for different math levels and does that affect your teaching style?
13. Can you please talk about how you begin your math lessons? What type of method do you
prefer using? I notice there are smart boards, whiteboards, and a lot of worksheets given out. Is
that helpful in students’ engagement in the lesson? Which one do you use the most? (Do you
prefer having students involve in group work and discussion style or do you like to just lecture
and have the students answer one by one?) (Do you like to implement innovative methods in
your classroom or do you like to follow by the books?)
14. Do you think your students are comfortable approaching you at anytime for help? How do
you offer your help? (like do you have hours after school for extra help, do you make yourself
15. I would like to know more about you as a person. Can you describe yourself to me? (like
would you describe yourself as outgoing, shy, funny, strict and so on?) Are you comfortable
26. with public speaking? (presenting in front of students – is that easy for you or you have to prep
yourself every day?) Did this take years to perfect?
16. Also, I have seen that some of your classes have behavior problems, like tend to act out, and
walk around. How would you deal with that on a regular day? Can you explain in detail? (do you
stop the whole class to quiet him or her down or do you keep going hoping that they would get
the idea?)
27.                                    Appendix  B  
Table 1
Engaging Teachers
Rank  of  Engaging          
Teachers   Teaching  Methods   Reasons  Why  Teachers  Are  Engaging  
"try  as  much  as  you  can  to  make   1.  Students  respect  Mr.  Bush.                                                                            
the  math  problems  real  to  the   2.  A  lot  of  student  participation.                                                                        
 Mr.  Bush  is  the  most       kids'  life  in  some  way.  If  you're   3.  Students  are  actively  asking  
engaging  teacher   teaching  fractions,  you  know  cut   questions.                                                                                                      
up  a  pizza,  don’t  just  cut  up  a   4.  Fast  pace  lesson  and  lot  of  good  
rectangle  on  the  board."       content.  
"I  am  a  big  believer  in  lots  of   1.  Students  are  constantly  asking  
quizzes,  they  are  always  small   questions  and  actively  listening.                                                  
   Ms.  Top  is  the  second  
points,  most  of  the  kids  are  going   2.  Uses  a  lot  of  worksheets  as  she  
most  engaging  teacher.  
to  say  it's  a  fair  system  and  they   lectures.                                                                                                              
will  respond  well  to  it."   3.    Lots  of  diagrams.  
1.  Students  somewhat  participate.                                                    
Engage  her  students  with  limited   2.  Struggle  with  classroom  
 Ms.  Smiley  is  the  third  
direct  instruction  with   management.                                                                                                
engaging  teacher.  
combination  of  verbal  discussion   3.  Uses  mints  as  incentives.                                                                        
between  the  teacher  and  the   4.  A  lot  of  games.  
students.  Constant  use  of  games.  
1.  Only  3-­‐4  students  are  listening  and  
Ms.  Reese  is  the  fourth   participating.                                                                                                          
engaging  teacher   Direct  instruction  with  verbal   2.  Students  are  constantly  walking  
interaction  but  at  a  very  slow   around  having  conversations.                                                                              
pace,  due  to  poor  class   3.  Worksheets  are  usually  
management  skills.   incomplete.  
28. Appendix C
Table 2: Influential Factors
Teachers    Training   Personality    Majors   Personal  Motivation  
Master  program  
at  University  of  
"I  am  absolutely  
Arlington  after  
intimidating  and  it  can  
   Mr.   26  years  at  3   college.  "By  the   Economic  
be  useful  if  I  need  to  
Bush   schools   end  of  the  first   and  History  
quiet  them  down.  I  am  
week,  I  just  
also  a  jokester."  
started   "I   pursued   teaching   math  
teaching."   because  I  needed  a  job."  
Formal  education   "I  think  I  am  strict,   "Math  is  so  important.  It  
training  right   although  I  also  think  I   History   comes  up  everywhere  in  
30  years  at  4  
   Ms.  Top     after  college  at   am  not  as  strict  as   Major  and   their  life  later  on  and  I  
University  of   some  people  I  know.  I   Math  minor   found  it  easier  to  convince  
Hartford.   am  too  soft."   students  how  important  
the  subject  I  was  teaching  
Worked  as  a  
mechanical   "I  like  to  over  plan  
engineer  for   every  day  because   "I  am  not  a  traditional  
Ms.   many  years.   "you  have  to  keep   Mechanical   teacher.  I  don't  believe  
         1st  year  
Smiley   Went  back  to   them  busy,  because  if   Engineer     that  it  is  the  best  way  to  
school  last  year   you  don’t,  they  will   learn  math  and  I  knew  I  
to  get  teaching   keep  you  busy."   wanted  to  do  it  differently  
certificate.     when  I  have  the  chance."  
Formal  education  
19  years  at  2   training  after  
Ms.   schools,   college  but   "I  think  I  am  too  soft   "I  like  Math  since  I  was  
Math  Major   young  and  thought  I  was  
Reese   tutoring   started  working   and  nice."  
programs   in  tutoring   good  at  explaining  it  to  
centers  first.   people,  so  I  pursued