Contributed by:

The nature of mathematics teachers’ knowledge specific to teaching mathematics is of ongoing concern in mathematics education research (Chapman, 2015). Furthermore, it is well known that teachers have an impact on students' achievement, and for several years mathematics education researchers have been studying teachers’ content knowledge (Levenson, 2013). This naturalistic inquiry revealed teachers’ perceptions about their content knowledge, their own self-efficacy, and their experience impacted student achievement.

Keywords: mathematics education, teacher self-efficacy, content knowledge

Keywords: mathematics education, teacher self-efficacy, content knowledge

1.
Journal of Instructional Pedagogies Volume 21

Mathematics teachers’ efficacy, experience, certification

and their impact on student achievement

Kristina Gonzalez

Texas A&M University-Kingsville

Gerri M. Maxwell

Texas A&M University – Kingsville

The nature of mathematics teachers’ knowledge specific to teaching mathematics is of

ongoing concern in mathematics education research (Chapman, 2015). Furthermore, it is well

known that teachers have an impact on students’ achievement, and for several years mathematics

education researchers have been studying teachers’ content knowledge (Levenson, 2013). This

naturalistic inquiry revealed teachers’ perceptions about their content knowledge, their own self-

efficacy, and their experience impacted student achievement.

Keywords: mathematics education, teacher self-efficacy, content knowledge

Copyright statement: Authors retain the copyright to the manuscripts published in AABRI

journals. Please see the AABRI Copyright Policy at http://www.aabri.com/copyright.html

Mathematics teacher efficacy, Page 1

Mathematics teachers’ efficacy, experience, certification

and their impact on student achievement

Kristina Gonzalez

Texas A&M University-Kingsville

Gerri M. Maxwell

Texas A&M University – Kingsville

The nature of mathematics teachers’ knowledge specific to teaching mathematics is of

ongoing concern in mathematics education research (Chapman, 2015). Furthermore, it is well

known that teachers have an impact on students’ achievement, and for several years mathematics

education researchers have been studying teachers’ content knowledge (Levenson, 2013). This

naturalistic inquiry revealed teachers’ perceptions about their content knowledge, their own self-

efficacy, and their experience impacted student achievement.

Keywords: mathematics education, teacher self-efficacy, content knowledge

Copyright statement: Authors retain the copyright to the manuscripts published in AABRI

journals. Please see the AABRI Copyright Policy at http://www.aabri.com/copyright.html

Mathematics teacher efficacy, Page 1

2.
Journal of Instructional Pedagogies Volume 21

Over the past decade, research has confirmed that teachers have substantial impacts on

their students’ academic and lifelong success (Chetty, Friedman, & Rockoff, 2014). Simply

being knowledgeable in a subject does not necessarily mean one can be effective in teaching it.

Putting knowledge into practice is an endeavor that a teacher must effectively translate to.

(Bartos, S. A., Lederman, N. G., & Lederman, J. S. 2014). Despite concerted efforts to identify

characteristics such as experience, education, and certification that might be correlated with

effectiveness, however, the nature of effective teaching still largely remains a black box (Blazar,

2015). Efforts to uncover this “black box” are evidenced though qualitative research in the form

on naturalistic inquiry.

LITERATURE REVIEW

The nature of mathematics teachers’ knowledge specific to teaching mathematics is of

ongoing concern in mathematics education research (Chapman, 2015). Furthermore, it is well

known that teachers have an impact on students’ achievement, and for several years mathematics

education researchers have been studying teachers’ content knowledge (Levenson, 2013). This

study will explore the following: an elementary teachers’ experience, teacher self-efficacy, and

teaching certification in relation to student achievement. Over time the importance of

mathematics in our society has increasingly been acknowledged which in turn has led to more

intense scrutiny of our mathematics education system (Hourigan & O’Donoghue, 2015). An

elementary teachers’ experience begins with their preservice education. Preservice teachers learn

mathematics in a variety of situations. The most common form of exposing teachers to learn

mathematics is formal in-service courses dealing in a disciplinary-structured way with the

content of mathematics (Julie, 2014). After preservice teachers finish their education, they are

required to become certified. Teachers have the option of which certification test they wish to

pursue. Most elementary teachers receive a generalist certification, which enables them to teach

any subject from early childhood through 6th grade. At times teachers are placed in a position in

which they may not feel comfortable teaching the content, although they are certified to teach the

subject. This is where teachers’ self-efficacy may play a role in student achievement. Once

teachers are in the field of education they are encouraged to continue professional development.

Professional development continues to be the primary vehicle to trigger the increase of

standards-based pedagogies in mathematics classrooms (Polly, Neale, & Pugalee, 2014).

Teachers’ experience and student achievement

Teacher experience and knowledge is essential to engage students in meaningful and

effective mathematical practices in the classroom in order to construct deep understanding of

mathematics (Chapman, 2015). Preservice teacher education and professional development are

factors that may identify a mathematics teachers’ effectiveness in an elementary classroom and

the impact of student achievement in the specific content.

Preservice teachers. A large body of international research suggests that many qualified

and preservice elementary teachers do not possess appropriate mathematics subject matter

Mathematics teacher efficacy, Page 2

Over the past decade, research has confirmed that teachers have substantial impacts on

their students’ academic and lifelong success (Chetty, Friedman, & Rockoff, 2014). Simply

being knowledgeable in a subject does not necessarily mean one can be effective in teaching it.

Putting knowledge into practice is an endeavor that a teacher must effectively translate to.

(Bartos, S. A., Lederman, N. G., & Lederman, J. S. 2014). Despite concerted efforts to identify

characteristics such as experience, education, and certification that might be correlated with

effectiveness, however, the nature of effective teaching still largely remains a black box (Blazar,

2015). Efforts to uncover this “black box” are evidenced though qualitative research in the form

on naturalistic inquiry.

LITERATURE REVIEW

The nature of mathematics teachers’ knowledge specific to teaching mathematics is of

ongoing concern in mathematics education research (Chapman, 2015). Furthermore, it is well

known that teachers have an impact on students’ achievement, and for several years mathematics

education researchers have been studying teachers’ content knowledge (Levenson, 2013). This

study will explore the following: an elementary teachers’ experience, teacher self-efficacy, and

teaching certification in relation to student achievement. Over time the importance of

mathematics in our society has increasingly been acknowledged which in turn has led to more

intense scrutiny of our mathematics education system (Hourigan & O’Donoghue, 2015). An

elementary teachers’ experience begins with their preservice education. Preservice teachers learn

mathematics in a variety of situations. The most common form of exposing teachers to learn

mathematics is formal in-service courses dealing in a disciplinary-structured way with the

content of mathematics (Julie, 2014). After preservice teachers finish their education, they are

required to become certified. Teachers have the option of which certification test they wish to

pursue. Most elementary teachers receive a generalist certification, which enables them to teach

any subject from early childhood through 6th grade. At times teachers are placed in a position in

which they may not feel comfortable teaching the content, although they are certified to teach the

subject. This is where teachers’ self-efficacy may play a role in student achievement. Once

teachers are in the field of education they are encouraged to continue professional development.

Professional development continues to be the primary vehicle to trigger the increase of

standards-based pedagogies in mathematics classrooms (Polly, Neale, & Pugalee, 2014).

Teachers’ experience and student achievement

Teacher experience and knowledge is essential to engage students in meaningful and

effective mathematical practices in the classroom in order to construct deep understanding of

mathematics (Chapman, 2015). Preservice teacher education and professional development are

factors that may identify a mathematics teachers’ effectiveness in an elementary classroom and

the impact of student achievement in the specific content.

Preservice teachers. A large body of international research suggests that many qualified

and preservice elementary teachers do not possess appropriate mathematics subject matter

Mathematics teacher efficacy, Page 2

3.
Journal of Instructional Pedagogies Volume 21

knowledge (MSMK) for teaching (Hourigan & O’Donoghue, 2015). While a majority declare

that elementary mathematics teachers need MSMK, the question remains as to what this means

and how it can best be achieved. In former times, a ‘minimalist’ view was common, where one

was considered to have sufficient knowledge if they could ‘do’ the mathematics covered in the

curriculum (Hourigan & O’Donoghue, 2015). Now this view point has been rejected for the fact

that math content has become more rigorous at the elementary level. If one goal of teacher

education is to ultimately improve teaching, then there needs to be more of a focus on

understanding the knowledge drawn on by teacher educators as they teach content to preservice

teachers (Castro-Superfine, 2014).

Professional development

Professional development in education is of utmost importance in order to keep up with

the demands of more rigorous math standards. In the state of Texas most educators who hold any

teaching certification are required to maintain 150 hours of professional development every five

years. Professional development helps teachers acquire new teaching strategies or ways to

implement content more effectively. Based on the findings from Polly, Neale, and Pugalee

(2014), a professional development program led to statistically significant gains in teachers’

mathematical knowledge for teaching, self-reported enactment of standards-based pedagogies,

and teachers’ beliefs about both mathematics as a content area and the overall teaching and

learning of mathematics.

Teacher efficacy and student achievement

Teacher efficacy is a teachers’ confidence in their ability to promote student learning. It

is, for example, the extent to which teachers believe that they can promote students’ learning,

even if the conditions are difficult (Künsting, Neuber & Lipowsky, 2016). If a teacher has high

confidence in their abilities, student learning and achievement will be greater. Researchers

realize the importance of teacher efficacy construct as a predictor of performance in teaching

mathematics in particular, and in education and research in general (Katz & Stupel, 2016).

Content knowledge and personal teaching efficacy are positively related. No significant

relationship is known for content knowledge and outcome expectancy (Newton, Leonard, Evans

& Eastburn, 2012).

Teachers’ certification and the impact of student achievement

In Texas, the State Board of Education gives prospective educators a certification path in

which an elementary teacher can teach any subject from early childhood through 6th grade.

Educators who choose to receive this certification will be able to teach a subject in which they

can possibly have weak content knowledge. A study indicated that the number of mathematics

teachers’ content courses was a better predictor of student achievement than the number of

mathematics education courses (Telese, 2012). In Texas, with the introduction of the State of

Texas Assessments of Academic Readiness (STAAR), which appears to be a more rigorous state

assessment, and increasing state assessment standards, it is imperative that effective teachers are

in all classrooms (Fox & Peters, 2015). In a state that requires assessments for students to be

promoted, teacher-training programs should also consider adding to their course requirements

Mathematics teacher efficacy, Page 3

knowledge (MSMK) for teaching (Hourigan & O’Donoghue, 2015). While a majority declare

that elementary mathematics teachers need MSMK, the question remains as to what this means

and how it can best be achieved. In former times, a ‘minimalist’ view was common, where one

was considered to have sufficient knowledge if they could ‘do’ the mathematics covered in the

curriculum (Hourigan & O’Donoghue, 2015). Now this view point has been rejected for the fact

that math content has become more rigorous at the elementary level. If one goal of teacher

education is to ultimately improve teaching, then there needs to be more of a focus on

understanding the knowledge drawn on by teacher educators as they teach content to preservice

teachers (Castro-Superfine, 2014).

Professional development

Professional development in education is of utmost importance in order to keep up with

the demands of more rigorous math standards. In the state of Texas most educators who hold any

teaching certification are required to maintain 150 hours of professional development every five

years. Professional development helps teachers acquire new teaching strategies or ways to

implement content more effectively. Based on the findings from Polly, Neale, and Pugalee

(2014), a professional development program led to statistically significant gains in teachers’

mathematical knowledge for teaching, self-reported enactment of standards-based pedagogies,

and teachers’ beliefs about both mathematics as a content area and the overall teaching and

learning of mathematics.

Teacher efficacy and student achievement

Teacher efficacy is a teachers’ confidence in their ability to promote student learning. It

is, for example, the extent to which teachers believe that they can promote students’ learning,

even if the conditions are difficult (Künsting, Neuber & Lipowsky, 2016). If a teacher has high

confidence in their abilities, student learning and achievement will be greater. Researchers

realize the importance of teacher efficacy construct as a predictor of performance in teaching

mathematics in particular, and in education and research in general (Katz & Stupel, 2016).

Content knowledge and personal teaching efficacy are positively related. No significant

relationship is known for content knowledge and outcome expectancy (Newton, Leonard, Evans

& Eastburn, 2012).

Teachers’ certification and the impact of student achievement

In Texas, the State Board of Education gives prospective educators a certification path in

which an elementary teacher can teach any subject from early childhood through 6th grade.

Educators who choose to receive this certification will be able to teach a subject in which they

can possibly have weak content knowledge. A study indicated that the number of mathematics

teachers’ content courses was a better predictor of student achievement than the number of

mathematics education courses (Telese, 2012). In Texas, with the introduction of the State of

Texas Assessments of Academic Readiness (STAAR), which appears to be a more rigorous state

assessment, and increasing state assessment standards, it is imperative that effective teachers are

in all classrooms (Fox & Peters, 2015). In a state that requires assessments for students to be

promoted, teacher-training programs should also consider adding to their course requirements

Mathematics teacher efficacy, Page 3

4.
Journal of Instructional Pedagogies Volume 21

one on preparing teachers for high stakes assessments.

STATEMENT OF THE PROBLEM

There is a problem in South Texas elementary math classrooms. Despite the fact that

teachers should be competent and effective in their subject matter, many still lack the knowledge

needed to perform at a level essential for students’ long term success. Studies conducted

throughout America show that teachers lack essential knowledge for teaching mathematics

(Tchoshanov, 2011). This problem negatively impacts student achievement because, the lack of

teacher effectiveness in the content in which they teach inhibits student learning. A possible

cause of this problem is a teachers’ lack of experience, their self-efficacy and the teaching

certification they hold. Elementary teachers across Texas who hold a generalist certification may

teach any subject kindergarten through sixth grade. However, teachers are sometimes placed in a

core subject area, such as math, in which they lack the content knowledge needed to perform at a

required professional level. Perhaps a study which investigates mathematics teachers’ view on

teaching mathematics, their efficacy, and thoughts on teacher certification, by a qualitative

naturalistic inquiry, could be a step closer to remedy the situation.

PURPOSE OF THE STUDY

The purpose of this study is to describe how teachers in three rural South Texas

elementary schools view teaching mathematics and their perception of content knowledge

certification impacting student achievement.

CONTRIBUTION OF THE STUDY

This study will contribute the knowledge of the field of mathematics in the area of

teacher content knowledge and their effectiveness in the classroom. Furthermore, this study will

determine if teacher self-efficacy and a teachers’ certification impacts student achievement in

mathematics. Individuals and societies that can use mathematics effectively in this period of

rapid changes will have a voice on increasing the opportunities and potentials which can shape

their future (NCTM, p.40).

The research methodology utilized for the project was qualitative in nature, specifically,

naturalistic inquiry. A naturalistic study is usually never fully established before the study

begins, but rather it emerges as data are collected, preliminary analysis is conducted, and the

context becomes more fully described (Erlandson, Harris, Skipper, & Allen, 1993). Furthermore,

naturalistic studies are impossible to design in any absolute way before the study is actually

undertaken (Lincoln & Guba, 1985).

Mathematics teacher efficacy, Page 4

one on preparing teachers for high stakes assessments.

STATEMENT OF THE PROBLEM

There is a problem in South Texas elementary math classrooms. Despite the fact that

teachers should be competent and effective in their subject matter, many still lack the knowledge

needed to perform at a level essential for students’ long term success. Studies conducted

throughout America show that teachers lack essential knowledge for teaching mathematics

(Tchoshanov, 2011). This problem negatively impacts student achievement because, the lack of

teacher effectiveness in the content in which they teach inhibits student learning. A possible

cause of this problem is a teachers’ lack of experience, their self-efficacy and the teaching

certification they hold. Elementary teachers across Texas who hold a generalist certification may

teach any subject kindergarten through sixth grade. However, teachers are sometimes placed in a

core subject area, such as math, in which they lack the content knowledge needed to perform at a

required professional level. Perhaps a study which investigates mathematics teachers’ view on

teaching mathematics, their efficacy, and thoughts on teacher certification, by a qualitative

naturalistic inquiry, could be a step closer to remedy the situation.

PURPOSE OF THE STUDY

The purpose of this study is to describe how teachers in three rural South Texas

elementary schools view teaching mathematics and their perception of content knowledge

certification impacting student achievement.

CONTRIBUTION OF THE STUDY

This study will contribute the knowledge of the field of mathematics in the area of

teacher content knowledge and their effectiveness in the classroom. Furthermore, this study will

determine if teacher self-efficacy and a teachers’ certification impacts student achievement in

mathematics. Individuals and societies that can use mathematics effectively in this period of

rapid changes will have a voice on increasing the opportunities and potentials which can shape

their future (NCTM, p.40).

The research methodology utilized for the project was qualitative in nature, specifically,

naturalistic inquiry. A naturalistic study is usually never fully established before the study

begins, but rather it emerges as data are collected, preliminary analysis is conducted, and the

context becomes more fully described (Erlandson, Harris, Skipper, & Allen, 1993). Furthermore,

naturalistic studies are impossible to design in any absolute way before the study is actually

undertaken (Lincoln & Guba, 1985).

Mathematics teacher efficacy, Page 4

5.
Journal of Instructional Pedagogies Volume 21

Research Design

There has been a void in the literature of teachers’ describing their efficacy, experiences,

and perceptions of teaching mathematics in regards to their teaching certification. This void also

fails to examine the impact of student achievement in respect to the aforementioned description

of teachers. The most suitable research design for this naturalistic small scale study was a case

study design. This case study examined teachers’ perceptions of teaching mathematics, focusing

on teacher efficacy, experience, and certification and the impact of student achievement. Data

from interviews was coded and analyzed for themes.

Naturalistic inquiry demands a human instrument (Lincoln & Guba, 1985; Patton, 2002)

as the primary source of data gathering. The researcher, in this study, conducted semi structured

interviews which were recorded, transcribed, and examined for themes. Semi-structured

interviews are open-ended, but generally follow a script and covers a list of topics (Bernard,

2002). In this study, the interview followed a scripted list of interview questions and stayed

within the general scheme of questions throughout each interview.

All sampling is conducted with some purpose in mind (Lincoln & Guba, 1985). The

respondents chosen were 3 teachers who have taught K-3 math and an administrator who serves

as a math facilitator at an elementary campus, each are key figures in the interviews that were

conducted (Erlandson, et al. 1993). All respondents were from south Texas elementary schools,

two of whom the researcher works with. A fifth participant, who was a 4th grade math teacher,

was unable to participate in a scheduled interview due to personal reasons. Rescheduling became

an issue and therefore was not able to participate in the research. Participants were interviewed

on their perceptions of teaching elementary mathematics. The participants were contacted in

person or by phone to explain the purpose of the research and to set up interviews. Once

agreement was made for an interview, the researcher proceeded to meet face to face with the

participants at individually scheduled times. Before the interview began, the researcher provided

an informed consent document in which the participant agreed and signed.

Site Selection

“The researcher should seek to find the best site possible within the boundaries of his or

her resources, and the primary guides for the site selection are the specific research topic

problem and questions” (Erlandson, et al., 1993, p. 54). This small-scale study focused on south

Texas elementary schools, therefore any south Texas elementary school would suffice for this

particular study. The site selection chosen was based on accessibility to the researcher. The four

participants work at schools within a thirty-mile radius of one another.

Data Collection Process

Lincoln and Guba note that sometimes the only data collection instrument utilized in a

naturalistic inquiry is the inquirer, the sources that instrument utilizes may be both human and

Mathematics teacher efficacy, Page 5

Research Design

There has been a void in the literature of teachers’ describing their efficacy, experiences,

and perceptions of teaching mathematics in regards to their teaching certification. This void also

fails to examine the impact of student achievement in respect to the aforementioned description

of teachers. The most suitable research design for this naturalistic small scale study was a case

study design. This case study examined teachers’ perceptions of teaching mathematics, focusing

on teacher efficacy, experience, and certification and the impact of student achievement. Data

from interviews was coded and analyzed for themes.

Naturalistic inquiry demands a human instrument (Lincoln & Guba, 1985; Patton, 2002)

as the primary source of data gathering. The researcher, in this study, conducted semi structured

interviews which were recorded, transcribed, and examined for themes. Semi-structured

interviews are open-ended, but generally follow a script and covers a list of topics (Bernard,

2002). In this study, the interview followed a scripted list of interview questions and stayed

within the general scheme of questions throughout each interview.

All sampling is conducted with some purpose in mind (Lincoln & Guba, 1985). The

respondents chosen were 3 teachers who have taught K-3 math and an administrator who serves

as a math facilitator at an elementary campus, each are key figures in the interviews that were

conducted (Erlandson, et al. 1993). All respondents were from south Texas elementary schools,

two of whom the researcher works with. A fifth participant, who was a 4th grade math teacher,

was unable to participate in a scheduled interview due to personal reasons. Rescheduling became

an issue and therefore was not able to participate in the research. Participants were interviewed

on their perceptions of teaching elementary mathematics. The participants were contacted in

person or by phone to explain the purpose of the research and to set up interviews. Once

agreement was made for an interview, the researcher proceeded to meet face to face with the

participants at individually scheduled times. Before the interview began, the researcher provided

an informed consent document in which the participant agreed and signed.

Site Selection

“The researcher should seek to find the best site possible within the boundaries of his or

her resources, and the primary guides for the site selection are the specific research topic

problem and questions” (Erlandson, et al., 1993, p. 54). This small-scale study focused on south

Texas elementary schools, therefore any south Texas elementary school would suffice for this

particular study. The site selection chosen was based on accessibility to the researcher. The four

participants work at schools within a thirty-mile radius of one another.

Data Collection Process

Lincoln and Guba note that sometimes the only data collection instrument utilized in a

naturalistic inquiry is the inquirer, the sources that instrument utilizes may be both human and

Mathematics teacher efficacy, Page 5

6.
Journal of Instructional Pedagogies Volume 21

non-human (1985). Human sources include taped interviews, (Lincoln & Guba, 1985) which is

the type of data collection that was utilized in this study. There are different types of interviews.

According to Bernard, the concept of interviewing covers a wide array, from unstructured

interactions, through semi-structured interviews, and to highly formal interactions (2002). For

this study, data was collected through a series of four semi-structured interviews.

Data Analysis

“Qualitative inquiry demands meticulous attention to language and deep reflection on the

emergent patterns and meanings of human experience,” (Saldana, 2013, p. 10). Data analysis for

this study was done by manually coding transcriptions of the participant’s interviews. Saldana

mentions that coding requires that one wear a researcher’s analytic lens (2013). Upon the first

interview, data was being analyzed. Themes did emerge, however they were not fully evident as

more research and interviews needed to be conducted. Transcriptions were typed in a Word

document. Coding was input in a color-coded table, also in a Word document.

Trustworthiness and Credibility

“Trustworthiness is established in a naturalistic inquiry by the use of techniques that

provide truth value through credibility, applicability through transferability, consistency through

dependability, and neutrality through confirmability” (Erlandson et al., 1993, p. 132).

Techniques that the researched used to establish trustworthiness and credibility included:

member checking and purposive sampling. Member checking was conducted by emailing

interview transcriptions to participants for a review. Participants were also able to add additional

comments if they felt the need; however, all participants said the transcriptions were accurate

and did not wish to add any additional comments. Purposive sampling is used to maximize

information, rather than to facilitate generalization (Erlandson et. al., 1993). Participants were

purposefully selected as to gain credible information on the study being conducted. The

participants ranged from kindergarten through third grade and a math facilitator from an

elementary campus was also selected with a purpose in mind.

Significance and Summary

Through qualitative naturalistic inquiry the researcher was able to interview mathematics

teachers in order to gain insight into their perceptions of teaching mathematics. Their voice has

made a contribution to the literature in respect to the impact they have on student achievement

based on their efficacy, experience, and certification.

After thorough analysis of data collected, it is evident that the teachers interviewed feel

much the same when it comes to teaching elementary mathematics, they feel somewhat guarded

since it is elementary math, yet find it challenging as rigor increases. Melanie, who was a

previous high school math teacher, now an elementary math facilitator had a different

Mathematics teacher efficacy, Page 6

non-human (1985). Human sources include taped interviews, (Lincoln & Guba, 1985) which is

the type of data collection that was utilized in this study. There are different types of interviews.

According to Bernard, the concept of interviewing covers a wide array, from unstructured

interactions, through semi-structured interviews, and to highly formal interactions (2002). For

this study, data was collected through a series of four semi-structured interviews.

Data Analysis

“Qualitative inquiry demands meticulous attention to language and deep reflection on the

emergent patterns and meanings of human experience,” (Saldana, 2013, p. 10). Data analysis for

this study was done by manually coding transcriptions of the participant’s interviews. Saldana

mentions that coding requires that one wear a researcher’s analytic lens (2013). Upon the first

interview, data was being analyzed. Themes did emerge, however they were not fully evident as

more research and interviews needed to be conducted. Transcriptions were typed in a Word

document. Coding was input in a color-coded table, also in a Word document.

Trustworthiness and Credibility

“Trustworthiness is established in a naturalistic inquiry by the use of techniques that

provide truth value through credibility, applicability through transferability, consistency through

dependability, and neutrality through confirmability” (Erlandson et al., 1993, p. 132).

Techniques that the researched used to establish trustworthiness and credibility included:

member checking and purposive sampling. Member checking was conducted by emailing

interview transcriptions to participants for a review. Participants were also able to add additional

comments if they felt the need; however, all participants said the transcriptions were accurate

and did not wish to add any additional comments. Purposive sampling is used to maximize

information, rather than to facilitate generalization (Erlandson et. al., 1993). Participants were

purposefully selected as to gain credible information on the study being conducted. The

participants ranged from kindergarten through third grade and a math facilitator from an

elementary campus was also selected with a purpose in mind.

Significance and Summary

Through qualitative naturalistic inquiry the researcher was able to interview mathematics

teachers in order to gain insight into their perceptions of teaching mathematics. Their voice has

made a contribution to the literature in respect to the impact they have on student achievement

based on their efficacy, experience, and certification.

After thorough analysis of data collected, it is evident that the teachers interviewed feel

much the same when it comes to teaching elementary mathematics, they feel somewhat guarded

since it is elementary math, yet find it challenging as rigor increases. Melanie, who was a

previous high school math teacher, now an elementary math facilitator had a different

Mathematics teacher efficacy, Page 6

7.
Journal of Instructional Pedagogies Volume 21

perspective. She said: “Even though it seems easy, we can say, “oh it’s the easiest thing to do,

anybody can teach math at the elementary level,” not everybody can teach math.” For this very

reason, this study was conducted. Often administrators, even teacher preparation programs feel a

generalist certification will suffice at the elementary level. However, student achievement may

be negatively impacted as a result. The following section will describe the participants of the

study. Participants were given pseudonyms as to keep their Reponses confidential. Further, the

findings will be outlined based on the themes that emerged from the data collected.

DESCRIPTION OF PARTICIPANTS

Cassidy was the first participant interviewed. She had previously taught seven years of

high school English and is currently in her third year of teaching first grade. Cassidy is certified

to teach English Language Arts 8-12, Speech 8-12, and EC-6th Generalist. Cassidy had this to

say about teaching mathematics to elementary students: “I have seen it’s changed from when, of

course, I was younger. The way they learn the math is different, it is more difficult to me, in my

The second interviewee was Melanie, who is not an elementary mathematics teacher, but

rather an administrator serving as a math instructional facilitator at the elementary level. Melanie

was a high school mathematics teacher for 17 years, a high school counselor for 3 years, and is

currently an instructional facilitator at an elementary campus. Melanie is certified in secondary

mathematics 6-12 and EC-12 School Counselor. Although Melanie is not actively teaching

elementary mathematics, she is able to observe other teachers teaching math.

I don’t have teaching experience at the elementary level, but I’ve observed elementary

math classrooms. I can coach teachers and tell them what they could be doing differently

and making sure they’re using the correct math terminology.

Alaina, an EC-4 certified teacher, was the third participant interviewed for the study. Of

the participants interviewed, Alaina has the most experience teaching elementary math. She has

taught 2nd and 3rd grade math for a combined total of nine years. She had this to say about

teaching math: “Teaching elementary mathematics has been kind of a rollercoaster ride. I’ve

seen everything from the simplest curriculum to the most difficult, which is where we are now.”

Jasmine, who is a first-year teacher, was the last participant interviewed for the study.

She has been around the education field for six years serving as a substitute teacher. Her

certification is EC-6 Generalist. She is currently teaching kindergarten, but has had experience

substitute teaching all grades of elementary math. When asked about her experience teaching

Mathematics teacher efficacy, Page 7

perspective. She said: “Even though it seems easy, we can say, “oh it’s the easiest thing to do,

anybody can teach math at the elementary level,” not everybody can teach math.” For this very

reason, this study was conducted. Often administrators, even teacher preparation programs feel a

generalist certification will suffice at the elementary level. However, student achievement may

be negatively impacted as a result. The following section will describe the participants of the

study. Participants were given pseudonyms as to keep their Reponses confidential. Further, the

findings will be outlined based on the themes that emerged from the data collected.

DESCRIPTION OF PARTICIPANTS

Cassidy was the first participant interviewed. She had previously taught seven years of

high school English and is currently in her third year of teaching first grade. Cassidy is certified

to teach English Language Arts 8-12, Speech 8-12, and EC-6th Generalist. Cassidy had this to

say about teaching mathematics to elementary students: “I have seen it’s changed from when, of

course, I was younger. The way they learn the math is different, it is more difficult to me, in my

The second interviewee was Melanie, who is not an elementary mathematics teacher, but

rather an administrator serving as a math instructional facilitator at the elementary level. Melanie

was a high school mathematics teacher for 17 years, a high school counselor for 3 years, and is

currently an instructional facilitator at an elementary campus. Melanie is certified in secondary

mathematics 6-12 and EC-12 School Counselor. Although Melanie is not actively teaching

elementary mathematics, she is able to observe other teachers teaching math.

I don’t have teaching experience at the elementary level, but I’ve observed elementary

math classrooms. I can coach teachers and tell them what they could be doing differently

and making sure they’re using the correct math terminology.

Alaina, an EC-4 certified teacher, was the third participant interviewed for the study. Of

the participants interviewed, Alaina has the most experience teaching elementary math. She has

taught 2nd and 3rd grade math for a combined total of nine years. She had this to say about

teaching math: “Teaching elementary mathematics has been kind of a rollercoaster ride. I’ve

seen everything from the simplest curriculum to the most difficult, which is where we are now.”

Jasmine, who is a first-year teacher, was the last participant interviewed for the study.

She has been around the education field for six years serving as a substitute teacher. Her

certification is EC-6 Generalist. She is currently teaching kindergarten, but has had experience

substitute teaching all grades of elementary math. When asked about her experience teaching

Mathematics teacher efficacy, Page 7

8.
Journal of Instructional Pedagogies Volume 21

math, this is what she had to say: “Teaching elementary mathematics has been rather interesting;

teaching in the kindergarten level has also been fun.”

After analyzing data from interviewing the respondents the study revealed several

themes. The themes that emerged included: being knowledgeable in content aids in student

achievement, having a passion and motivation or a positive self-efficacy for a particular subject

supports knowledge of that subject and the experience one has can be a determining factor in

success or lack of success in a subject that is being taught.

Knowledgeable in math content

One theme revealed that being knowledgeable in content aids in student achievement. For

instance, Cassidy stated the following:

I also feel the knowledge the teacher has with the math, and especially the mistakes,

common mistakes that students make. Right away, we can pick up on it, and they can fix it. That

comes from knowledge of math, like, ‘Oh, I have a student that,’ or ‘They're making this mistake

because,’ and then they can fix it.

Likewise, Melanie said:

Students that are already weak in math tend to be at a disadvantage when the teacher does

not know exactly what she's supposed to be teaching conceptually. So, they do the best

they can, but is it the best for the students?

Melanie stated it best with her last statement: “So they do the best they can, but is it the best for

the students?” Often teachers do the best they can with the math knowledge they have. At times

though, that knowledge may be limited to what the student needs. Hence, is it best for the

students? Furthermore, Alaina stated the following: “Math knowledge in relation to student

achievement, I think, is pretty important only because if you don’t know what you’re teaching,

then they’re not going to know what to learn.” Jasmine continued with the same premise on her

thoughts of how important it is for teachers to be knowledgeable in math content in order to have

successful students. She believes:

A teacher should be very knowledgeable in math . . . teaching elementary mathematics

sets the foundation for the students as they get older. If they have a very poor

mathematics foundation, they will only struggle as they get into junior high and high

school.

All four participants felt strongly that if students are to be successful in math, the teacher

teaching must know the content, no matter how simple it may seem. Teachers need to be able to

understand the how and why students are making the mistakes they make. Common

misconceptions of math content also should be acknowledged.

Teacher Self-Efficacy

A second theme showed that being motivating, confident and passionate about math

supports teacher knowledge and student achievement. Teacher self-efficacy is a term used to

Mathematics teacher efficacy, Page 8

math, this is what she had to say: “Teaching elementary mathematics has been rather interesting;

teaching in the kindergarten level has also been fun.”

After analyzing data from interviewing the respondents the study revealed several

themes. The themes that emerged included: being knowledgeable in content aids in student

achievement, having a passion and motivation or a positive self-efficacy for a particular subject

supports knowledge of that subject and the experience one has can be a determining factor in

success or lack of success in a subject that is being taught.

Knowledgeable in math content

One theme revealed that being knowledgeable in content aids in student achievement. For

instance, Cassidy stated the following:

I also feel the knowledge the teacher has with the math, and especially the mistakes,

common mistakes that students make. Right away, we can pick up on it, and they can fix it. That

comes from knowledge of math, like, ‘Oh, I have a student that,’ or ‘They're making this mistake

because,’ and then they can fix it.

Likewise, Melanie said:

Students that are already weak in math tend to be at a disadvantage when the teacher does

not know exactly what she's supposed to be teaching conceptually. So, they do the best

they can, but is it the best for the students?

Melanie stated it best with her last statement: “So they do the best they can, but is it the best for

the students?” Often teachers do the best they can with the math knowledge they have. At times

though, that knowledge may be limited to what the student needs. Hence, is it best for the

students? Furthermore, Alaina stated the following: “Math knowledge in relation to student

achievement, I think, is pretty important only because if you don’t know what you’re teaching,

then they’re not going to know what to learn.” Jasmine continued with the same premise on her

thoughts of how important it is for teachers to be knowledgeable in math content in order to have

successful students. She believes:

A teacher should be very knowledgeable in math . . . teaching elementary mathematics

sets the foundation for the students as they get older. If they have a very poor

mathematics foundation, they will only struggle as they get into junior high and high

school.

All four participants felt strongly that if students are to be successful in math, the teacher

teaching must know the content, no matter how simple it may seem. Teachers need to be able to

understand the how and why students are making the mistakes they make. Common

misconceptions of math content also should be acknowledged.

Teacher Self-Efficacy

A second theme showed that being motivating, confident and passionate about math

supports teacher knowledge and student achievement. Teacher self-efficacy is a term used to

Mathematics teacher efficacy, Page 8

9.
Journal of Instructional Pedagogies Volume 21

describe such passion, confidence, and motivation. For instance, Melanie was passionate about

teaching math and made the following statement:

Then, looking at the teachers that are passionate about math because they like it, they do

so much better with it versus those that just go through the motions because they put

them to teach something that they don't really want to be doing.

Hand in hand with passion, is motivation. Furthermore, Cassidy had this to say:

“In terms of teaching math? Okay, I teach 1st grade presently. I feel that right now, I could be

motivating and I’m pretty competent.” If a teacher is motivating and passionate about the subject

they teach, it supports the knowledge and competence that they possess in order to teach the

subject that is being presented. Student achievement, thus results in positive outcomes. Jasmine

had the following to say about her efficacy in terms of teaching mathematics:

I feel rather confident and I know if I do encounter some problem or question, I can go to

somebody higher and find a solution to what I might not have the answer to or not

understand complexly. I can just go ask somebody . . . an upper grade teacher.

Keep in mind, Jasmine teaches kindergarten and knows that there is a possibility that she might

not know it all. Alaina, who is our veteran elementary math teacher describes her efficacy as

In the beginning, I felt pretty confident when I first started teaching because, like I said, it

was so simple, and within the past three years when the state changed, it got a little

complex not only for the students, but more for me because it was a whole new . . . It felt

like a whole new subject. It felt like I wasn't teaching second grade anymore. It felt like I

was teaching more fourth grade, more fifth grade.

Being confident, motivating, and passionate about teaching math will impact student

achievement in a positive way since, as evidenced by the participants, stems from math

A third theme indicated that the experience one has can be a determining factor in

success or lack of success in a subject that is being taught. Two of the participants were previous

high school teachers. Cassidy taught English at the high school level, now currently teachers 1st

I am not a math major, or an education major, so I went and got my certification through

an alternative certification. I didn't have to take any kind of math class. I did have to pass

the test, however, it was elementary math. It wasn't very difficult.

Cassidy, as previously mentioned teaches 1st grade and mentioned that she is “pretty competent”

when it comes to teaching math. She also stated the following: “However, like I said, maybe 4th,

5th, and 6th grade math, I would have to really do research before I taught. Really learn it first.”

Melanie, who previously taught high school math, now an elementary math facilitator makes note

of the following:

I’ve been a mathematics teacher for 17 years at the secondary level. As far as content, I

know content. I can tell you what needs to be taught, how it should be taught as far as math

vocabulary, looking at different data, what the students are weak in, where we need to go

with it.

Of the two participants who taught at the high school level, Melanie seems to have more experience

with math. Although, she does not directly teach math to elementary students, her knowledge in

Mathematics teacher efficacy, Page 9

describe such passion, confidence, and motivation. For instance, Melanie was passionate about

teaching math and made the following statement:

Then, looking at the teachers that are passionate about math because they like it, they do

so much better with it versus those that just go through the motions because they put

them to teach something that they don't really want to be doing.

Hand in hand with passion, is motivation. Furthermore, Cassidy had this to say:

“In terms of teaching math? Okay, I teach 1st grade presently. I feel that right now, I could be

motivating and I’m pretty competent.” If a teacher is motivating and passionate about the subject

they teach, it supports the knowledge and competence that they possess in order to teach the

subject that is being presented. Student achievement, thus results in positive outcomes. Jasmine

had the following to say about her efficacy in terms of teaching mathematics:

I feel rather confident and I know if I do encounter some problem or question, I can go to

somebody higher and find a solution to what I might not have the answer to or not

understand complexly. I can just go ask somebody . . . an upper grade teacher.

Keep in mind, Jasmine teaches kindergarten and knows that there is a possibility that she might

not know it all. Alaina, who is our veteran elementary math teacher describes her efficacy as

In the beginning, I felt pretty confident when I first started teaching because, like I said, it

was so simple, and within the past three years when the state changed, it got a little

complex not only for the students, but more for me because it was a whole new . . . It felt

like a whole new subject. It felt like I wasn't teaching second grade anymore. It felt like I

was teaching more fourth grade, more fifth grade.

Being confident, motivating, and passionate about teaching math will impact student

achievement in a positive way since, as evidenced by the participants, stems from math

A third theme indicated that the experience one has can be a determining factor in

success or lack of success in a subject that is being taught. Two of the participants were previous

high school teachers. Cassidy taught English at the high school level, now currently teachers 1st

I am not a math major, or an education major, so I went and got my certification through

an alternative certification. I didn't have to take any kind of math class. I did have to pass

the test, however, it was elementary math. It wasn't very difficult.

Cassidy, as previously mentioned teaches 1st grade and mentioned that she is “pretty competent”

when it comes to teaching math. She also stated the following: “However, like I said, maybe 4th,

5th, and 6th grade math, I would have to really do research before I taught. Really learn it first.”

Melanie, who previously taught high school math, now an elementary math facilitator makes note

of the following:

I’ve been a mathematics teacher for 17 years at the secondary level. As far as content, I

know content. I can tell you what needs to be taught, how it should be taught as far as math

vocabulary, looking at different data, what the students are weak in, where we need to go

with it.

Of the two participants who taught at the high school level, Melanie seems to have more experience

with math. Although, she does not directly teach math to elementary students, her knowledge in

Mathematics teacher efficacy, Page 9

10.
Journal of Instructional Pedagogies Volume 21

the subject matter will be beneficial to elementary math teachers whom she coaches. Cassidy’s

experience has been very minimal at the elementary level, however still feels “pretty confident” in

teaching her first graders. Jasmine, although has yet to teach a full year, has had experience being

a substitute, teaching elementary grades up to 6th grade. Through her experience, she feels: “At all

grade levels you must have a lot of hands on, because often times many of the students do not

grasp the information just by working out a problem, they want to see concrete examples.” Her

response is indicative of a typical elementary teacher. In most elementary classroom students are

learning through hands on experiences. Alaina, who has only taught elementary math to second

and third graders had the following to say about her experience:

Teaching elementary mathematics has been kind of a rollercoaster ride. I've been teaching

for nine years and I've seen everything from the simplest curriculum to the most difficult,

which is where we're at now. I believe when I started, the math was very general. It didn't

seem so . . . rigorous.

Based on the participant data, all participants agreed that strong math content is

significant to student achievement and that minimal content knowledge is insufficient.

Participants also concurred that their own efficacy to be successful was important to student

achievement. Finally, actual classroom experience with students at varied grade levels was also

shared by participants as significant to positive student achievement in mathematics.

Bernard, H.R. (2002). Interviewing: Unstructured and semi-structured (pp 203-239). In H.R.

Bernard, Research methods of anthropology. Walnut Creek, CA; Alta Mira Press. (ROC).

Blazar, D. (2015). Effective teaching in elementary mathematics: Identifying classroom practices

that support student achievement. Economics of Education Review, 4816-29.

doi:10.1016/j.econedurev.2015.05.005

Castro-Superfine, A., & Li, W. (2014). Exploring the Mathematical Knowledge Needed for

Teaching Teachers. Journal of Teacher Education, 65(4), 303-314.

doi:10.1177/0022487114534265

Chapman, O. (2015). Reflective Awareness in Mathematics Teachers’ Learning and Teaching

Eurasia Journal of Mathematics, Science & Technology Education, 2015, 11(2), 313-324

Chetty, Raj, John N. Friedman and Jonah E. Rockoff. 2014. "Measuring the Impacts of Teachers

II: Teacher Value-Added and Student Outcomes in Adulthood." American Economic

Review, 104(9): 2633-79. doi:10.1257/aer.104.9.2633

Erlandson, D., Harris, E, Skipper, B., Allen, S. (1993) Doing Naturalistic Inquiry. Newberry

Park, CA: Sage.

Fox, A. and Peters, M. (2013). First year teachers: certification program and assigned subject on

their self-efficacy. Current Issues in Education,16(1).

Hourigan, M., & O’Donoghue, J. (2015). Addressing prospective elementary teachers’

mathematics subject matter knowledge through action research. International Journal Of

Mathematical Education In Science & Technology, 46(1), 56-75.

doi:10.1080/0020739X.2014.936977

Mathematics teacher efficacy, Page 10

the subject matter will be beneficial to elementary math teachers whom she coaches. Cassidy’s

experience has been very minimal at the elementary level, however still feels “pretty confident” in

teaching her first graders. Jasmine, although has yet to teach a full year, has had experience being

a substitute, teaching elementary grades up to 6th grade. Through her experience, she feels: “At all

grade levels you must have a lot of hands on, because often times many of the students do not

grasp the information just by working out a problem, they want to see concrete examples.” Her

response is indicative of a typical elementary teacher. In most elementary classroom students are

learning through hands on experiences. Alaina, who has only taught elementary math to second

and third graders had the following to say about her experience:

Teaching elementary mathematics has been kind of a rollercoaster ride. I've been teaching

for nine years and I've seen everything from the simplest curriculum to the most difficult,

which is where we're at now. I believe when I started, the math was very general. It didn't

seem so . . . rigorous.

Based on the participant data, all participants agreed that strong math content is

significant to student achievement and that minimal content knowledge is insufficient.

Participants also concurred that their own efficacy to be successful was important to student

achievement. Finally, actual classroom experience with students at varied grade levels was also

shared by participants as significant to positive student achievement in mathematics.

Bernard, H.R. (2002). Interviewing: Unstructured and semi-structured (pp 203-239). In H.R.

Bernard, Research methods of anthropology. Walnut Creek, CA; Alta Mira Press. (ROC).

Blazar, D. (2015). Effective teaching in elementary mathematics: Identifying classroom practices

that support student achievement. Economics of Education Review, 4816-29.

doi:10.1016/j.econedurev.2015.05.005

Castro-Superfine, A., & Li, W. (2014). Exploring the Mathematical Knowledge Needed for

Teaching Teachers. Journal of Teacher Education, 65(4), 303-314.

doi:10.1177/0022487114534265

Chapman, O. (2015). Reflective Awareness in Mathematics Teachers’ Learning and Teaching

Eurasia Journal of Mathematics, Science & Technology Education, 2015, 11(2), 313-324

Chetty, Raj, John N. Friedman and Jonah E. Rockoff. 2014. "Measuring the Impacts of Teachers

II: Teacher Value-Added and Student Outcomes in Adulthood." American Economic

Review, 104(9): 2633-79. doi:10.1257/aer.104.9.2633

Erlandson, D., Harris, E, Skipper, B., Allen, S. (1993) Doing Naturalistic Inquiry. Newberry

Park, CA: Sage.

Fox, A. and Peters, M. (2013). First year teachers: certification program and assigned subject on

their self-efficacy. Current Issues in Education,16(1).

Hourigan, M., & O’Donoghue, J. (2015). Addressing prospective elementary teachers’

mathematics subject matter knowledge through action research. International Journal Of

Mathematical Education In Science & Technology, 46(1), 56-75.

doi:10.1080/0020739X.2014.936977

Mathematics teacher efficacy, Page 10

11.
Journal of Instructional Pedagogies Volume 21

Julie, C. (2014). Emergences and affordances as opportunities to develop teachers’ mathematical

content knowledge. International Journal of Mathematical Education In Science &

Technology, 45(3), 428-437. doi:10.1080/0020739X.2013.851809

Katz, S., & Stupel, M. (2016). Enhancing elementary-school mathematics teachers' efficacy

beliefs: a qualitative action research. International Journal of Mathematical Education In

Science & Technology, 47(3), 421-439. doi:10.1080/0020739X.2015.1080314

Künsting, J., Neuber, V., & Lipowsky, F. (2016). Teacher self-efficacy as a long-term predictor

of instructional quality in the classroom. European Journal of Psychology Of Education -

EJPE (Springer Science & Business Media B.V.), 31(3), 299-322. doi:10.1007/s10212-

015-0272-7

Lincoln, Y. & Guba, E. (1985) Naturalistic Inquiry. Newberry Park, CA: Sage.

Levenson, E. (2013). Policy, Practice, and Readiness to Teach Primary and Secondary

Mathematics in 17 Countries: Findings from the IEA Teacher Education and

Development Study in Mathematics. Comparative Education Review, 57(4), 740-742.

NCTM. Principles and standards for school mathematics. Reston (VA): NCTM; 2000; p. 40.

Newton, K. J., Leonard, J., Evans, B. R., & Eastburn, J. A. (2012). Preservice Elementary

Teachers' Mathematics Content Knowledge and Teacher Efficacy. School Science &

Mathematics, 112(5), 289-299. doi:10.1111/j.1949-8594.2012.00145.x

Patton, M.Q. (2002) Fieldwork strategies and observation methods. In, Qualitative evaluation

and research methods. 3rd edition. Thousand Oaks, CA: Sage.

Polly, D., McGee, J., Wang, C., Martin, C., Lambert, R., & Pugalee, D. K. (2015). Linking

professional development, teacher outcomes, and student achievement: The case of a

learner-centered mathematics program for elementary school teachers. International

Journal of Educational Research, 7226-37. doi:10.1016/j.ijer.2015.04.002

Polly, D., Neale, H., & Pugalee, D. (2014). How Does Ongoing Task-Focused Mathematics

Professional Development Influence Elementary School Teachers' Knowledge, Beliefs

and Enacted Pedagogies?. Early Childhood Education Journal, 42(1), 1-10.

doi:10.1007/s10643-013-0585-6Saldana, J. (2013) The Coding Manual for Qualitative

Researchers. Sage.

Tchoshanov, M. A. (2011). Relationship between teacher knowledge of concepts and

connections, teaching practice, and student achievement in middle grades mathematics.

Educational Studies In Mathematics, 76(2), 141-164. doi:10.1007/s10649-010-9269-y

Telese, James A. Journal of Educational Research. 2012, Vol. 105 Issue 2, p102-111. 10p. 1

Diagram, 3 Charts. DOI: 10.1080/00220671.2010.521209. Database: Academic Search

Complete

Mathematics teacher efficacy, Page 11

Julie, C. (2014). Emergences and affordances as opportunities to develop teachers’ mathematical

content knowledge. International Journal of Mathematical Education In Science &

Technology, 45(3), 428-437. doi:10.1080/0020739X.2013.851809

Katz, S., & Stupel, M. (2016). Enhancing elementary-school mathematics teachers' efficacy

beliefs: a qualitative action research. International Journal of Mathematical Education In

Science & Technology, 47(3), 421-439. doi:10.1080/0020739X.2015.1080314

Künsting, J., Neuber, V., & Lipowsky, F. (2016). Teacher self-efficacy as a long-term predictor

of instructional quality in the classroom. European Journal of Psychology Of Education -

EJPE (Springer Science & Business Media B.V.), 31(3), 299-322. doi:10.1007/s10212-

015-0272-7

Lincoln, Y. & Guba, E. (1985) Naturalistic Inquiry. Newberry Park, CA: Sage.

Levenson, E. (2013). Policy, Practice, and Readiness to Teach Primary and Secondary

Mathematics in 17 Countries: Findings from the IEA Teacher Education and

Development Study in Mathematics. Comparative Education Review, 57(4), 740-742.

NCTM. Principles and standards for school mathematics. Reston (VA): NCTM; 2000; p. 40.

Newton, K. J., Leonard, J., Evans, B. R., & Eastburn, J. A. (2012). Preservice Elementary

Teachers' Mathematics Content Knowledge and Teacher Efficacy. School Science &

Mathematics, 112(5), 289-299. doi:10.1111/j.1949-8594.2012.00145.x

Patton, M.Q. (2002) Fieldwork strategies and observation methods. In, Qualitative evaluation

and research methods. 3rd edition. Thousand Oaks, CA: Sage.

Polly, D., McGee, J., Wang, C., Martin, C., Lambert, R., & Pugalee, D. K. (2015). Linking

professional development, teacher outcomes, and student achievement: The case of a

learner-centered mathematics program for elementary school teachers. International

Journal of Educational Research, 7226-37. doi:10.1016/j.ijer.2015.04.002

Polly, D., Neale, H., & Pugalee, D. (2014). How Does Ongoing Task-Focused Mathematics

Professional Development Influence Elementary School Teachers' Knowledge, Beliefs

and Enacted Pedagogies?. Early Childhood Education Journal, 42(1), 1-10.

doi:10.1007/s10643-013-0585-6Saldana, J. (2013) The Coding Manual for Qualitative

Researchers. Sage.

Tchoshanov, M. A. (2011). Relationship between teacher knowledge of concepts and

connections, teaching practice, and student achievement in middle grades mathematics.

Educational Studies In Mathematics, 76(2), 141-164. doi:10.1007/s10649-010-9269-y

Telese, James A. Journal of Educational Research. 2012, Vol. 105 Issue 2, p102-111. 10p. 1

Diagram, 3 Charts. DOI: 10.1080/00220671.2010.521209. Database: Academic Search

Complete

Mathematics teacher efficacy, Page 11