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Qualities of effective math teachers have been prioritized in the United States since international tests showed American students’ math and science test scores falling below other students in developed countries.

This research brief examines strategies of effective math teachers and how effectiveness is measured. Current research indicates that building both teacher and student self-efficacy has shown positive outcomes on student achievement and engagement in the classroom. Additionally, current research indicates that when teachers utilize certain strategies they can positively impact student success in mathematics.

This research brief examines strategies of effective math teachers and how effectiveness is measured. Current research indicates that building both teacher and student self-efficacy has shown positive outcomes on student achievement and engagement in the classroom. Additionally, current research indicates that when teachers utilize certain strategies they can positively impact student success in mathematics.

1.
Running head: QUALITIES OF EFFECTIVE MATH TEACHERS 1

Qualities of Effective Math Teachers

Rachel D. Kaboré

University of Nebraska - Omaha

EDL 9550 Symposium on School Leadership

April 17, 2018

Qualities of Effective Math Teachers

Rachel D. Kaboré

University of Nebraska - Omaha

EDL 9550 Symposium on School Leadership

April 17, 2018

2.
QUALITIES OF EFFECTIVE MATH TEACHERS 2

Abstract

Qualities of effective math teachers have been prioritized in the United States since international

tests showed American students’ math and science test scores falling below other students in

developed countries. This research brief examines strategies of effective math teachers and how

effectiveness is measured. Current research indicates that building both teacher and student self-

efficacy has shown positive outcomes on student achievement and engagement in the classroom.

Additionally, current research indicates that when teachers utilize certain strategies they can

positively impact student success in mathematics.

Abstract

Qualities of effective math teachers have been prioritized in the United States since international

tests showed American students’ math and science test scores falling below other students in

developed countries. This research brief examines strategies of effective math teachers and how

effectiveness is measured. Current research indicates that building both teacher and student self-

efficacy has shown positive outcomes on student achievement and engagement in the classroom.

Additionally, current research indicates that when teachers utilize certain strategies they can

positively impact student success in mathematics.

3.
QUALITIES OF EFFECTIVE MATH TEACHERS 3

Title

Qualities of Effective Math Teachers

Research Topic

This research brief explores the factors that distinguish highly effective teachers in the

math classroom. Similarities and differences among elementary, secondary, and collegiate

teachers are considered.

Introduction

Math Achievement Gaps in the United States

Student success in math is essential, as it is the foundation for many science, technology,

and engineering jobs (Martin & Rimm-Kaufman, 2015). Math achievement may be associated

with future economic power and competitiveness of a country thus making it desirable to find

factors associated to positive relationships with mathematics achievement to countries around the

world (Son, 2015). Improving student achievement in mathematics and science has been a

concern in the United States (U.S.) since the early 1980s, when international tests began showing

U.S. students falling behind most developed countries in mathematics and science skills which

painted a less than glamorous picture of the quality of the American math and science teaching

field (Gningue, Peach, & Schroder, 2013; Moyer-Packenham, Bolyard, Kitsantas, & Oh, 2008).

Teacher Effectiveness: Strategies and Measurements

Moyer-Packenham, et al. (2008) identified the most common teacher characteristics

examined include teacher behaviors, practices and beliefs, subject and pedagogical knowledge,

and certification. Surveys, questionnaires, and exams were most commonly used to assess math

teacher quality. This study found while the U.S. has been motivated to hire highly qualified

Title

Qualities of Effective Math Teachers

Research Topic

This research brief explores the factors that distinguish highly effective teachers in the

math classroom. Similarities and differences among elementary, secondary, and collegiate

teachers are considered.

Introduction

Math Achievement Gaps in the United States

Student success in math is essential, as it is the foundation for many science, technology,

and engineering jobs (Martin & Rimm-Kaufman, 2015). Math achievement may be associated

with future economic power and competitiveness of a country thus making it desirable to find

factors associated to positive relationships with mathematics achievement to countries around the

world (Son, 2015). Improving student achievement in mathematics and science has been a

concern in the United States (U.S.) since the early 1980s, when international tests began showing

U.S. students falling behind most developed countries in mathematics and science skills which

painted a less than glamorous picture of the quality of the American math and science teaching

field (Gningue, Peach, & Schroder, 2013; Moyer-Packenham, Bolyard, Kitsantas, & Oh, 2008).

Teacher Effectiveness: Strategies and Measurements

Moyer-Packenham, et al. (2008) identified the most common teacher characteristics

examined include teacher behaviors, practices and beliefs, subject and pedagogical knowledge,

and certification. Surveys, questionnaires, and exams were most commonly used to assess math

teacher quality. This study found while the U.S. has been motivated to hire highly qualified

4.
QUALITIES OF EFFECTIVE MATH TEACHERS 4

teachers since the goal development of No Child Left Behind, there are few instruments

available that effectively measure quality characteristics of mathematics teachers.

While teacher effectiveness is often times measured by student achievement on

standardized assessments, Knight et al. (2015) states that this limits the qualities of effective

teachers to the skills that can be measured by achievement tests. It is suggested that focusing on

teacher inputs and standardized testing effects is a reflection of teacher quality; whereas, a focus

on classroom practice is a reflection of teaching quality. It is therefore encouraged to define

quality in terms of cognitive resources and performance, and to focus on teaching quality

connected to student learning instead of teacher characteristics. Educators are encouraged to

consider teacher affect when defining characteristics of effective teachers. Such teacher affects

may include compassion, fairness and respect, interactions with students both in and out of the

classroom, enthusiasm, motivation, attitudes toward teaching, and reflection.

Teacher effectiveness may also be considered in regards to student expectations in the

classroom. Martin and Rimm-Kaufman (2015) emphasize that ideal math learning is not a

passive process of memorizing and using standard algorithms, instead students engage in

reasoning, problem solving, and discourse with teachers and other students to explore

mathematical problems.

Summary of Findings

Characteristics of Teacher Quality in the Math Classroom

Through a review of literature on mathematics and science teacher quality, Bolyard and

Moyer-Packenham (2008) identified six primary characteristics as indicators of teacher quality:

general ability; experience; pedagogical knowledge; subject knowledge; certification status; and

teacher behaviors, practices, and beliefs with a focus on student achievement as the dependent

teachers since the goal development of No Child Left Behind, there are few instruments

available that effectively measure quality characteristics of mathematics teachers.

While teacher effectiveness is often times measured by student achievement on

standardized assessments, Knight et al. (2015) states that this limits the qualities of effective

teachers to the skills that can be measured by achievement tests. It is suggested that focusing on

teacher inputs and standardized testing effects is a reflection of teacher quality; whereas, a focus

on classroom practice is a reflection of teaching quality. It is therefore encouraged to define

quality in terms of cognitive resources and performance, and to focus on teaching quality

connected to student learning instead of teacher characteristics. Educators are encouraged to

consider teacher affect when defining characteristics of effective teachers. Such teacher affects

may include compassion, fairness and respect, interactions with students both in and out of the

classroom, enthusiasm, motivation, attitudes toward teaching, and reflection.

Teacher effectiveness may also be considered in regards to student expectations in the

classroom. Martin and Rimm-Kaufman (2015) emphasize that ideal math learning is not a

passive process of memorizing and using standard algorithms, instead students engage in

reasoning, problem solving, and discourse with teachers and other students to explore

mathematical problems.

Summary of Findings

Characteristics of Teacher Quality in the Math Classroom

Through a review of literature on mathematics and science teacher quality, Bolyard and

Moyer-Packenham (2008) identified six primary characteristics as indicators of teacher quality:

general ability; experience; pedagogical knowledge; subject knowledge; certification status; and

teacher behaviors, practices, and beliefs with a focus on student achievement as the dependent

5.
QUALITIES OF EFFECTIVE MATH TEACHERS 5

variable. They found studies generally point to a positive relationship between teachers’ general

and verbal ability and student achievement in mathematics. The relationship between teaching

experience and mathematics achievement provided mixed results; however, more studies found a

positive relationship, especially at the secondary level (Moyer-Packenham et al., 2008).

When measuring qualities of effective math teachers by student engagement, it is helpful

to understand what student engagement entails. For the purpose of their study, Martin and

Rimm-Kaufman (2015) recognized emotional and social engagement. They describe emotional

engagement as a student’s enjoyment and interest in math, which they considered critically

important to motivation and success. Social engagement includes positive exchanges between

peers that connect to the instruction with an understanding that when students feel effective in

math, they are more comfortable working with a group and helping others. Student engagement

stems from internal processes and external supports including classroom experiences, and a

student’s sense of self-efficacy in math and supportive teacher-student interactions. Some of the

ways teachers provide support include being caring and aware of student interests and needs,

having clear expectations, providing explicit feedback, and creating opportunities for conceptual

thinking (Martin & Rimm-Kaufman, 2015).

Qualities of Effective Teachers in Elementary Math

Elementary education majors have the highest levels of math anxiety of any college

major (Hembree, 1990), and children are more likely to emulate the behavior and attitudes of

same gender adults (Bussey & Bandura, 1984); therefore, when female elementary teachers are

anxious about math, there are negative consequences for their female students. In their research

on first and second grade teachers and students, Beilock, Gunderson, Ramirez, and Levine

(2010) found that girls’ math achievement is related to traditional gender ability beliefs; girls

variable. They found studies generally point to a positive relationship between teachers’ general

and verbal ability and student achievement in mathematics. The relationship between teaching

experience and mathematics achievement provided mixed results; however, more studies found a

positive relationship, especially at the secondary level (Moyer-Packenham et al., 2008).

When measuring qualities of effective math teachers by student engagement, it is helpful

to understand what student engagement entails. For the purpose of their study, Martin and

Rimm-Kaufman (2015) recognized emotional and social engagement. They describe emotional

engagement as a student’s enjoyment and interest in math, which they considered critically

important to motivation and success. Social engagement includes positive exchanges between

peers that connect to the instruction with an understanding that when students feel effective in

math, they are more comfortable working with a group and helping others. Student engagement

stems from internal processes and external supports including classroom experiences, and a

student’s sense of self-efficacy in math and supportive teacher-student interactions. Some of the

ways teachers provide support include being caring and aware of student interests and needs,

having clear expectations, providing explicit feedback, and creating opportunities for conceptual

thinking (Martin & Rimm-Kaufman, 2015).

Qualities of Effective Teachers in Elementary Math

Elementary education majors have the highest levels of math anxiety of any college

major (Hembree, 1990), and children are more likely to emulate the behavior and attitudes of

same gender adults (Bussey & Bandura, 1984); therefore, when female elementary teachers are

anxious about math, there are negative consequences for their female students. In their research

on first and second grade teachers and students, Beilock, Gunderson, Ramirez, and Levine

(2010) found that girls’ math achievement is related to traditional gender ability beliefs; girls

6.
QUALITIES OF EFFECTIVE MATH TEACHERS 6

who believed boys were better than girls at math were outperformed by girls who did not hold

this viewpoint, and female teacher anxiety affects these beliefs. In these classrooms, the

academic achievement of boys were not affected by the anxiety of their female teachers. While

elementary math majors have high levels of math anxiety, Bolyard and Moyer (2008) found that

at the elementary level, it is more beneficial for teachers to have degrees in education than

mathematics; however, the study noted that it is rare to find elementary teachers with degrees in

mathematics which may influence the data. It was also suggested that requiring teachers to study

more math is only helpful if teachers are learning the math in ways that will help them better

instruct their students in the area of mathematics.

In their study of fifth grade students, Martin and Rimm-Kaufman (2015) found students

with higher levels of self-efficacy reported greater levels of engagement in math class, and

students who were in classrooms with high levels of emotional support also reported similar

levels of engagement, regardless of initial self-efficacy. Moreover, students at risk for problems

in school due to low self-efficacy appeared to benefit more from high quality emotional support

than those students without risk. Students high in self-efficacy are engaged regardless of teacher

support; however, the engagement of students low in self-efficacy fluctuate based on teacher

support (Martin & Rimm-Kaufman, 2015).

In a study regarding teachers’ ability and help attributions in relation to children’s math

performance and task persistence amongst third graders in Estonia, Tõeväli and Kikas (2016)

found that the more teachers attributed children’s math success to teacher help or math failure to

lack of ability, the poorer the children’s math performance was. The task persistence of the

students also had a positive effect on their math performance; the more persistence students

demonstrated in second grade, the better their math performance was in third grade. In addition,

who believed boys were better than girls at math were outperformed by girls who did not hold

this viewpoint, and female teacher anxiety affects these beliefs. In these classrooms, the

academic achievement of boys were not affected by the anxiety of their female teachers. While

elementary math majors have high levels of math anxiety, Bolyard and Moyer (2008) found that

at the elementary level, it is more beneficial for teachers to have degrees in education than

mathematics; however, the study noted that it is rare to find elementary teachers with degrees in

mathematics which may influence the data. It was also suggested that requiring teachers to study

more math is only helpful if teachers are learning the math in ways that will help them better

instruct their students in the area of mathematics.

In their study of fifth grade students, Martin and Rimm-Kaufman (2015) found students

with higher levels of self-efficacy reported greater levels of engagement in math class, and

students who were in classrooms with high levels of emotional support also reported similar

levels of engagement, regardless of initial self-efficacy. Moreover, students at risk for problems

in school due to low self-efficacy appeared to benefit more from high quality emotional support

than those students without risk. Students high in self-efficacy are engaged regardless of teacher

support; however, the engagement of students low in self-efficacy fluctuate based on teacher

support (Martin & Rimm-Kaufman, 2015).

In a study regarding teachers’ ability and help attributions in relation to children’s math

performance and task persistence amongst third graders in Estonia, Tõeväli and Kikas (2016)

found that the more teachers attributed children’s math success to teacher help or math failure to

lack of ability, the poorer the children’s math performance was. The task persistence of the

students also had a positive effect on their math performance; the more persistence students

demonstrated in second grade, the better their math performance was in third grade. In addition,

7.
QUALITIES OF EFFECTIVE MATH TEACHERS 7

the stronger a student’s math performance was in second grade, the more persistence showed

later. The authors noted that boys showed lower levels of persistence than girls did in this study.

O’Donnell (2009) studied the work of elementary teachers who created and maintained

instructional environments that promoted mathematical learning through problem solving.

Through these studies, she found Carol. Carol’s strategies include holding high expectations by

not setting limits on what students were capable of learning; allowing students time to think

through processes such as think-pair-share so they had both individual and group problem

solving; giving students responsibility to discuss problems, pose possible strategies to solve

problems, make connections between mathematical concepts, and present answers; and accepting

the idea that some students will not get the answer because their reasoning is flawed. O’Donnell

also met Brenda and Laurel who had similar strategies that include anticipating students’ tension

as anxiety leads students to focus on memorization and causes them to lose self-esteem which

inhibits their abilities to learn the big ideas and concepts; and fostering quality interactions by

using effective questioning techniques and making conscientious decisions about when and how

to provide information.

Qualities of Effective Teachers in Secondary Math

Bolyard and Moyer (2008) found that at the secondary level, teachers who hold a degree

in mathematics appears to have positive impacts on student achievement while there is little or

even negative impact on student achievement for teachers to have education degrees without a

mathematics degree. However, teacher coursework taken specifically in the area of mathematics

has a positive relationship on student achievement; yet, this seems to be limited, as one study

found the impact diminishes after a certain number of courses and is influenced by the level of

course. Overall, teachers who have degrees in mathematics have positive impacts on student

the stronger a student’s math performance was in second grade, the more persistence showed

later. The authors noted that boys showed lower levels of persistence than girls did in this study.

O’Donnell (2009) studied the work of elementary teachers who created and maintained

instructional environments that promoted mathematical learning through problem solving.

Through these studies, she found Carol. Carol’s strategies include holding high expectations by

not setting limits on what students were capable of learning; allowing students time to think

through processes such as think-pair-share so they had both individual and group problem

solving; giving students responsibility to discuss problems, pose possible strategies to solve

problems, make connections between mathematical concepts, and present answers; and accepting

the idea that some students will not get the answer because their reasoning is flawed. O’Donnell

also met Brenda and Laurel who had similar strategies that include anticipating students’ tension

as anxiety leads students to focus on memorization and causes them to lose self-esteem which

inhibits their abilities to learn the big ideas and concepts; and fostering quality interactions by

using effective questioning techniques and making conscientious decisions about when and how

to provide information.

Qualities of Effective Teachers in Secondary Math

Bolyard and Moyer (2008) found that at the secondary level, teachers who hold a degree

in mathematics appears to have positive impacts on student achievement while there is little or

even negative impact on student achievement for teachers to have education degrees without a

mathematics degree. However, teacher coursework taken specifically in the area of mathematics

has a positive relationship on student achievement; yet, this seems to be limited, as one study

found the impact diminishes after a certain number of courses and is influenced by the level of

course. Overall, teachers who have degrees in mathematics have positive impacts on student

8.
QUALITIES OF EFFECTIVE MATH TEACHERS 8

achievement, and there is a positive relationship between subject-specific certifications and

student achievement. While there is a positive relationship between mathematics courses and

student achievement, Bolyard and Moyer, 2008, indicate that preparation in pedagogy is also

important. Programs that compromise on subject matter training with teachers having a limited

mathematical understanding of the content has detrimental effects on pedagogical content

knowledge and negative effects on instructional quality and student progress which persist across

their entire teaching careers (Baumert et. al, 2010).

The Mathematics Teacher Transformation Institute measured effectiveness of teaching by

measuring student engagement in math; Gningue et al. (2013) found that teachers who employed

a high level of student-centered, inquiry-based pedagogy were more effective algebra and

geometry teachers than those who did not. However, they also found there was no relationship

between the increase in content knowledge and a teacher’s use of student-centered teaching. Son

(2015) found in a study of eighth grade students in the United States and Korea that while

teachers’ educational backgrounds are not associated with high-quality mathematics instruction

in Korea, the opposite is true in the United States where teachers who majored in both education

and mathematics are 2.4 times more likely to be classified into the high quality group than

teachers who did not major in education or mathematics and used an alternative path to the

teaching profession. Professional development opportunities were a distinguishing factor for

teachers who had high-quality instruction but low self-efficacy and for teachers who had low-

quality instruction but high self-efficacy from those that were low in both quality instruction and

self-efficacy. In the United States, there is a positive relationship between mathematical

instruction, teacher self-efficacy, and student achievement in mathematics; however, in Korea,

there is no significant relationship amongst the three. The discrepancy regarding the

achievement, and there is a positive relationship between subject-specific certifications and

student achievement. While there is a positive relationship between mathematics courses and

student achievement, Bolyard and Moyer, 2008, indicate that preparation in pedagogy is also

important. Programs that compromise on subject matter training with teachers having a limited

mathematical understanding of the content has detrimental effects on pedagogical content

knowledge and negative effects on instructional quality and student progress which persist across

their entire teaching careers (Baumert et. al, 2010).

The Mathematics Teacher Transformation Institute measured effectiveness of teaching by

measuring student engagement in math; Gningue et al. (2013) found that teachers who employed

a high level of student-centered, inquiry-based pedagogy were more effective algebra and

geometry teachers than those who did not. However, they also found there was no relationship

between the increase in content knowledge and a teacher’s use of student-centered teaching. Son

(2015) found in a study of eighth grade students in the United States and Korea that while

teachers’ educational backgrounds are not associated with high-quality mathematics instruction

in Korea, the opposite is true in the United States where teachers who majored in both education

and mathematics are 2.4 times more likely to be classified into the high quality group than

teachers who did not major in education or mathematics and used an alternative path to the

teaching profession. Professional development opportunities were a distinguishing factor for

teachers who had high-quality instruction but low self-efficacy and for teachers who had low-

quality instruction but high self-efficacy from those that were low in both quality instruction and

self-efficacy. In the United States, there is a positive relationship between mathematical

instruction, teacher self-efficacy, and student achievement in mathematics; however, in Korea,

there is no significant relationship amongst the three. The discrepancy regarding the

9.
QUALITIES OF EFFECTIVE MATH TEACHERS 9

effectiveness of teacher coursework or content knowledge can be explained by the process of

measuring effectiveness; when evaluating student achievement there is a positive correlation;

whereas, when evaluating student engagement there was no relationship.

While Bolyard and Moyer’s (2008) research focused on teacher coursework, Judson

(2017) focused on practices of math teachers in different courses including advanced placement

(AP), honors, and regular classes. While he did not evaluate the effectiveness of teacher

strategies on student outcomes, Judson (2017) did find significant differences in expectations.

Math teachers who taught a combination of AP, honors and regular math classes indicated they

believe students in AP classes should be assigned homework on a more regular basis and the

lessons should have more explicit structure than in regular math courses. In their honors math

courses, teachers felt it was better to go into more depth on fewer topics; whereas, in the AP

courses, teachers did not hold this view and may have felt they were not allowed to omit any

topics. In their AP classes, teachers indicated placing significantly greater emphasis on

understanding mathematical ideas, emphasizing mathematical practices, understanding real-life

application, increasing interest in math and preparing for further study in mathematics than in

their regular math courses.

Compared to their honors classes, teachers indicated placing significantly greater

emphasis on developing computation speed, understanding mathematical ideas, developing

mathematical practices, and integrating real-life applications in their AP courses. While writing

reflections was not reported as common in math courses, teachers did report that it occurred

significantly more often in AP courses than regular courses. In general, AP courses were

reported as being more student-centered and engaging than regular math courses where students

effectiveness of teacher coursework or content knowledge can be explained by the process of

measuring effectiveness; when evaluating student achievement there is a positive correlation;

whereas, when evaluating student engagement there was no relationship.

While Bolyard and Moyer’s (2008) research focused on teacher coursework, Judson

(2017) focused on practices of math teachers in different courses including advanced placement

(AP), honors, and regular classes. While he did not evaluate the effectiveness of teacher

strategies on student outcomes, Judson (2017) did find significant differences in expectations.

Math teachers who taught a combination of AP, honors and regular math classes indicated they

believe students in AP classes should be assigned homework on a more regular basis and the

lessons should have more explicit structure than in regular math courses. In their honors math

courses, teachers felt it was better to go into more depth on fewer topics; whereas, in the AP

courses, teachers did not hold this view and may have felt they were not allowed to omit any

topics. In their AP classes, teachers indicated placing significantly greater emphasis on

understanding mathematical ideas, emphasizing mathematical practices, understanding real-life

application, increasing interest in math and preparing for further study in mathematics than in

their regular math courses.

Compared to their honors classes, teachers indicated placing significantly greater

emphasis on developing computation speed, understanding mathematical ideas, developing

mathematical practices, and integrating real-life applications in their AP courses. While writing

reflections was not reported as common in math courses, teachers did report that it occurred

significantly more often in AP courses than regular courses. In general, AP courses were

reported as being more student-centered and engaging than regular math courses where students

10.
QUALITIES OF EFFECTIVE MATH TEACHERS 10

are less engaged with practices which promote critical thinking and reflection which Judson

(2017) identifies as valuable practices that should occur in all levels of math.

In a study focused on secondary math teachers from Teach For America (TFA), an

alternative route to teacher certification, Chiang, Clark and McConnell (2017) found that TFA

teachers outperformed comparison teachers on both the Praxis II Mathematics Content

Knowledge Test and the Praxis II Middle School Mathematics Test. The two-year study

compared TFA teachers and teachers from other certification routes teaching the same math

course, typically at the same class period. Fewer TFA teachers had majored in mathematics or

secondary math education, but more TFA teachers had majored in other math-related subjects

than the comparison teachers; 59% of the comparison teachers were from traditional education

programs and 41% were from alternative certification programs other than TFA. Based on

student scores on end-of-year math assessments, the researchers found TFA teachers to be more

effective than comparison teachers teaching the same math courses in the same schools.

Our study provides experimental evidence from multiple school districts that TFA’s

distinctive model of recruiting, selecting, training, and supporting its teachers is capable

of raising both the quantity and quality of teachers in a hard-to-staff subject area within

high-poverty schools. (Chiang et al., 2017, p. 35)

While students were not brought up to the mean of the general population on their end-of-year

math assessments, the gap was narrowed.

While O’Donnell (2009) primarily studied elementary teachers with effective math

strategies, she did gain some insight from Belinda, a middle grades teacher. Belinda’s lesson

strategies include researching each problem by dissecting the mathematical concept, determining

potential strategies students may use, and preparing connections to other mathematical concepts;

are less engaged with practices which promote critical thinking and reflection which Judson

(2017) identifies as valuable practices that should occur in all levels of math.

In a study focused on secondary math teachers from Teach For America (TFA), an

alternative route to teacher certification, Chiang, Clark and McConnell (2017) found that TFA

teachers outperformed comparison teachers on both the Praxis II Mathematics Content

Knowledge Test and the Praxis II Middle School Mathematics Test. The two-year study

compared TFA teachers and teachers from other certification routes teaching the same math

course, typically at the same class period. Fewer TFA teachers had majored in mathematics or

secondary math education, but more TFA teachers had majored in other math-related subjects

than the comparison teachers; 59% of the comparison teachers were from traditional education

programs and 41% were from alternative certification programs other than TFA. Based on

student scores on end-of-year math assessments, the researchers found TFA teachers to be more

effective than comparison teachers teaching the same math courses in the same schools.

Our study provides experimental evidence from multiple school districts that TFA’s

distinctive model of recruiting, selecting, training, and supporting its teachers is capable

of raising both the quantity and quality of teachers in a hard-to-staff subject area within

high-poverty schools. (Chiang et al., 2017, p. 35)

While students were not brought up to the mean of the general population on their end-of-year

math assessments, the gap was narrowed.

While O’Donnell (2009) primarily studied elementary teachers with effective math

strategies, she did gain some insight from Belinda, a middle grades teacher. Belinda’s lesson

strategies include researching each problem by dissecting the mathematical concept, determining

potential strategies students may use, and preparing connections to other mathematical concepts;

11.
QUALITIES OF EFFECTIVE MATH TEACHERS 11

using challenging problems to extend student reasoning and build mathematical understanding;

and not giving up on students or on self by recognizing students learn from their mistakes and

she can learn from her shortcomings.

Urdan and Schoenfelder (2006) identified teaching strategies that lead to academic

success in the classroom such as emphasizing students’ efforts in learning, helping students make

connections between tasks, modeling strategies, and scaffolding that allows students to take

Qualities of Ineffective Teachers in College Courses

A study was conducted to gain knowledge on not-so-good instructors at the collegiate

level. The researchers found that poor teaching is not necessarily the inverse of good teaching

but is based on key reciprocals including being disrespectful, offering unrepresentative and

unfair student learning assessments, having unrealistic expectations for student learning, and

being less than knowledgeable on course content. They recommended that all teachers, not just

college and university teachers, should avoid these qualities (Busler, Kirk, Keeley, & Buskist,

Summary of the Characteristics of Effective Teachers and Student Self-Efficacy

Student success in the area of mathematics is influenced by both the teacher and the

student. Qualities of effective math teachers that build student self-efficacy and encourage

success in the math classroom in the U.S. include providing emotional support, believing

students can be successful in math regardless of gender, attributing student success to the

student, maintaining high expectations in a student-centered, inquiry-based classroom, and

having solid content knowledge.

using challenging problems to extend student reasoning and build mathematical understanding;

and not giving up on students or on self by recognizing students learn from their mistakes and

she can learn from her shortcomings.

Urdan and Schoenfelder (2006) identified teaching strategies that lead to academic

success in the classroom such as emphasizing students’ efforts in learning, helping students make

connections between tasks, modeling strategies, and scaffolding that allows students to take

Qualities of Ineffective Teachers in College Courses

A study was conducted to gain knowledge on not-so-good instructors at the collegiate

level. The researchers found that poor teaching is not necessarily the inverse of good teaching

but is based on key reciprocals including being disrespectful, offering unrepresentative and

unfair student learning assessments, having unrealistic expectations for student learning, and

being less than knowledgeable on course content. They recommended that all teachers, not just

college and university teachers, should avoid these qualities (Busler, Kirk, Keeley, & Buskist,

Summary of the Characteristics of Effective Teachers and Student Self-Efficacy

Student success in the area of mathematics is influenced by both the teacher and the

student. Qualities of effective math teachers that build student self-efficacy and encourage

success in the math classroom in the U.S. include providing emotional support, believing

students can be successful in math regardless of gender, attributing student success to the

student, maintaining high expectations in a student-centered, inquiry-based classroom, and

having solid content knowledge.

12.
QUALITIES OF EFFECTIVE MATH TEACHERS 12

Implication of the Findings and Application to MOEC

Implication of the Findings

In their study of Slovene eighth grade students, Puklek Levpušček and Zupančič (2009)

found parental academic pressure appeared to be the strongest predictor of mastery goal

orientation, academic self-efficacy, and achievement in math; the counterproductive effect of

student-rated parental academic pressure was demonstrated through the negative effect on

students’ self-efficacy in math and that parental academic pressure and support were negatively

related to students’ math grades. On the other hand, there was a positive relationship between

math teaching and student self-efficacy, mastery goal orientation, and achievement in the math

domain. Their study also revealed that students’ self-efficacy in math significantly contributes to

their final math grade. Puklek Levpušček and Zupančič (2009) realize a combined effect of both

student-rated family and classroom context on eighth grade math performance is stronger than

the effect of either one alone. They also found teachers’ classroom behaviors predominantly

contributed to students’ grades by building students’ self-efficacy in math; therefore, focusing

professional development on instructional practices and communication skills that build self-

efficacy should be considered when striving to improve student achievement in the area of

Both preservice and inservice professional development seems to be a powerful tool in

improving the quality of teaching and raising student achievement. Math anxiety of elementary

teachers can be reduced through math training and education (Gresham, 2007). In the United

States, to improve student achievement in mathematics, there must be a focus on cognitively

demanding instruction and teacher self-efficacy (Son, 2015). With a focus on tying classroom

Implication of the Findings and Application to MOEC

Implication of the Findings

In their study of Slovene eighth grade students, Puklek Levpušček and Zupančič (2009)

found parental academic pressure appeared to be the strongest predictor of mastery goal

orientation, academic self-efficacy, and achievement in math; the counterproductive effect of

student-rated parental academic pressure was demonstrated through the negative effect on

students’ self-efficacy in math and that parental academic pressure and support were negatively

related to students’ math grades. On the other hand, there was a positive relationship between

math teaching and student self-efficacy, mastery goal orientation, and achievement in the math

domain. Their study also revealed that students’ self-efficacy in math significantly contributes to

their final math grade. Puklek Levpušček and Zupančič (2009) realize a combined effect of both

student-rated family and classroom context on eighth grade math performance is stronger than

the effect of either one alone. They also found teachers’ classroom behaviors predominantly

contributed to students’ grades by building students’ self-efficacy in math; therefore, focusing

professional development on instructional practices and communication skills that build self-

efficacy should be considered when striving to improve student achievement in the area of

Both preservice and inservice professional development seems to be a powerful tool in

improving the quality of teaching and raising student achievement. Math anxiety of elementary

teachers can be reduced through math training and education (Gresham, 2007). In the United

States, to improve student achievement in mathematics, there must be a focus on cognitively

demanding instruction and teacher self-efficacy (Son, 2015). With a focus on tying classroom

13.
QUALITIES OF EFFECTIVE MATH TEACHERS 13

practice to student learning, preservice and inservice professional development aligned to

increasing quality of teaching and learning is imperative (Knight et al., 2015). Knight et al.

(2015) further explains that quality teaching will depend on teachers who enter the profession

with a solid foundation and build on that foundation throughout their careers which includes the

ability to assess student knowledge and content needs and effectively respond to those needs, a

commitment to lifelong learning through professional development. These teachers must also

value the individual and sociocultural knowledge of diverse learners and know how to connect

and built on that knowledge.

When students feel challenged in math, effective teachers help students understand that

although the work seems hard, they are capable of meeting the high expectations. Student self-

efficacy in math can be enhanced by promoting a growth mindset rather than a fixed mindset

sending the message that with effort, ability can be developed. Building teacher-student

relationships is one way to improve emotional and social engagement (Martin & Rimm-

Kaufman, 2015).

If the mathematical success of children is attributed to help from teachers, children may

feel they have little control over their performance; therefore lowering overall performance. The

reactions of teachers and their casual attributions may affect children’s learning and motivation;

therefore teachers should be aware of the message they are sending students through comments,

feedback, praise, etcetera (Tõeväli & Kikas, 2016).

Application to Metropolitan Omaha Educational Consortium (MOEC)

The MOEC Achievement Plan Strategic Framework indicates a strategic priority to focus

on increasing the number of highly qualified educational professionals with a focus on high need

areas. MOEC’s shared metrics include students meeting academic proficiency in reading and

practice to student learning, preservice and inservice professional development aligned to

increasing quality of teaching and learning is imperative (Knight et al., 2015). Knight et al.

(2015) further explains that quality teaching will depend on teachers who enter the profession

with a solid foundation and build on that foundation throughout their careers which includes the

ability to assess student knowledge and content needs and effectively respond to those needs, a

commitment to lifelong learning through professional development. These teachers must also

value the individual and sociocultural knowledge of diverse learners and know how to connect

and built on that knowledge.

When students feel challenged in math, effective teachers help students understand that

although the work seems hard, they are capable of meeting the high expectations. Student self-

efficacy in math can be enhanced by promoting a growth mindset rather than a fixed mindset

sending the message that with effort, ability can be developed. Building teacher-student

relationships is one way to improve emotional and social engagement (Martin & Rimm-

Kaufman, 2015).

If the mathematical success of children is attributed to help from teachers, children may

feel they have little control over their performance; therefore lowering overall performance. The

reactions of teachers and their casual attributions may affect children’s learning and motivation;

therefore teachers should be aware of the message they are sending students through comments,

feedback, praise, etcetera (Tõeväli & Kikas, 2016).

Application to Metropolitan Omaha Educational Consortium (MOEC)

The MOEC Achievement Plan Strategic Framework indicates a strategic priority to focus

on increasing the number of highly qualified educational professionals with a focus on high need

areas. MOEC’s shared metrics include students meeting academic proficiency in reading and

14.
QUALITIES OF EFFECTIVE MATH TEACHERS 14

mathematics, hiring highly qualified professionals having certification and degrees in high need

areas, and graduating students from high school who are prepared for postsecondary and career

success (MOEC, 2018). MOEC is comprised of twelve public school districts, two educational

service units, a metropolitan university, and two community colleges; because MOEC serves a

large portion of educators in the metropolitan area, it would be beneficial for this consortium to

plan both preservice and inservice professional development opportunities to build self-efficacy

of elementary math teachers and to guide instructional practices to enhance student self-efficacy.

It would also be worthwhile to have discussions amongst the school districts to evaluate

expectations in all math classes and how they relate to students’ academic outcomes.

Professional development in the area of student-centered inquiry-based classrooms would also be

beneficial, as studies have found positive correlations to student achievement and engagement.

mathematics, hiring highly qualified professionals having certification and degrees in high need

areas, and graduating students from high school who are prepared for postsecondary and career

success (MOEC, 2018). MOEC is comprised of twelve public school districts, two educational

service units, a metropolitan university, and two community colleges; because MOEC serves a

large portion of educators in the metropolitan area, it would be beneficial for this consortium to

plan both preservice and inservice professional development opportunities to build self-efficacy

of elementary math teachers and to guide instructional practices to enhance student self-efficacy.

It would also be worthwhile to have discussions amongst the school districts to evaluate

expectations in all math classes and how they relate to students’ academic outcomes.

Professional development in the area of student-centered inquiry-based classrooms would also be

beneficial, as studies have found positive correlations to student achievement and engagement.

15.
QUALITIES OF EFFECTIVE MATH TEACHERS 15

References

Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., . . .Tsai, Y-M. (2010).

Teachers' mathematical knowledge, cognitive activation in the classroom, and student

progress. American Educational Research Journal, 47(1), 133-180.

doi:10.3102/0002831209345157

Beilock, S. L., Gunderson, E. A., Ramirez, G., & Levine, S. C. (2010). Female teachers' math

anxiety affects girls' math achievement. Proceedings of the National Academy of Sciences of

the United States of America, 107(5), 1860-1863. doi:10.1073/pnas.0910967107

Bolyard, J. J., & Moyer-Packenham, P. S. (2008). A review of the literature on mathematics and

science teacher quality. Peabody Journal of Education, 83(4), 509-535.

doi:10.1080/01619560802414890

Busler, J., Kirk, C., Keeley, J., & Buskist, W. (2017). What constitutes poor teaching? A

preliminary inquiry into the misbehaviors of not-so-good instructors. Teaching of

Psychology, 44(4), 330-334. doi:10.1177/0098628317727907

Bussey, K., & Bandura, A. (1984). Influence of gender constancy and social power on sex-linked

modeling. Journal of Personality and Social Psychology, 47(6), 1292-1302. 10.1037/0022-

3514.47.6.1292 Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/6527216

Chiang, H. S., Clark, M. A., & McConnell, S. (2017). Supplying disadvantaged schools with

effective teachers: Experimental evidence on secondary math teachers from teach for

America. Journal of Policy Analysis and Management, 36(1), 97-125.

doi:10.1002/pam.21958

Gningue, S. M., Peach, R., & Schroder, B. (2013). Developing effective mathematics teaching:

Assessing content and pedagogical knowledge, student-centered teaching, and student

References

Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., . . .Tsai, Y-M. (2010).

Teachers' mathematical knowledge, cognitive activation in the classroom, and student

progress. American Educational Research Journal, 47(1), 133-180.

doi:10.3102/0002831209345157

Beilock, S. L., Gunderson, E. A., Ramirez, G., & Levine, S. C. (2010). Female teachers' math

anxiety affects girls' math achievement. Proceedings of the National Academy of Sciences of

the United States of America, 107(5), 1860-1863. doi:10.1073/pnas.0910967107

Bolyard, J. J., & Moyer-Packenham, P. S. (2008). A review of the literature on mathematics and

science teacher quality. Peabody Journal of Education, 83(4), 509-535.

doi:10.1080/01619560802414890

Busler, J., Kirk, C., Keeley, J., & Buskist, W. (2017). What constitutes poor teaching? A

preliminary inquiry into the misbehaviors of not-so-good instructors. Teaching of

Psychology, 44(4), 330-334. doi:10.1177/0098628317727907

Bussey, K., & Bandura, A. (1984). Influence of gender constancy and social power on sex-linked

modeling. Journal of Personality and Social Psychology, 47(6), 1292-1302. 10.1037/0022-

3514.47.6.1292 Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/6527216

Chiang, H. S., Clark, M. A., & McConnell, S. (2017). Supplying disadvantaged schools with

effective teachers: Experimental evidence on secondary math teachers from teach for

America. Journal of Policy Analysis and Management, 36(1), 97-125.

doi:10.1002/pam.21958

Gningue, S. M., Peach, R., & Schroder, B. (2013). Developing effective mathematics teaching:

Assessing content and pedagogical knowledge, student-centered teaching, and student

16.
QUALITIES OF EFFECTIVE MATH TEACHERS 16

engagement. The Mathematics Enthusiast, 10(3), 621-646. Retrieved

from http://search.ebscohost.com.leo.lib.unomaha.edu/login.aspx?direct=true&db=psyh&A

N=2014-21464-004&login.asp&site=ehost-live&scope=site

Gresham, G. (2007). A study of mathematics anxiety in pre-service teachers. Early Childhood

Education Journal, 35(2), 181-188. 10.1007/s10643-007-0174-7 Retrieved

from http://search.ebscohost.com.leo.lib.unomaha.edu/login.aspx?direct=true&db=eue&AN

=508004775&site=ehost-live&scope=site

Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. Journal for Research

in Mathematics Education, 21(1), 33-46. Retrieved from http://www.jstor.org/stable/749455

Judson, E. (2017). How science and math teachers address different course levels: Advanced

placement (AP), honors, and regular. The High School Journal, 100(4), 226-249.

doi:10.1353/hsj.2017.0010

Knight, S. L., Lloyd, G. M., Arbaugh, F., Gamson, D., McDonald, S. P., Nolan, J., & Whitney,

A. E. (2015). Reconceptualizing teacher quality to inform preservice and inservice

professional development. Journal of Teacher Education, 66(2), 105-108.

doi:10.1177/0022487115570564

Martin, D. P., & Rimm-Kaufman, S. E. (2015). Do student self-efficacy and teacher-student

interaction quality contribute to emotional and social engagement in fifth grade

math? Journal of School Psychology, 53(5), 359-373. doi:10.1016/j.jsp.2015.07.001

Metropolitan Omaha Educational Consortium. (2018, March). MOEC achievement plan:

Strategic framework. Retrieved from https://www.unomaha.edu/college-

ofeducation/moec/index.php

engagement. The Mathematics Enthusiast, 10(3), 621-646. Retrieved

from http://search.ebscohost.com.leo.lib.unomaha.edu/login.aspx?direct=true&db=psyh&A

N=2014-21464-004&login.asp&site=ehost-live&scope=site

Gresham, G. (2007). A study of mathematics anxiety in pre-service teachers. Early Childhood

Education Journal, 35(2), 181-188. 10.1007/s10643-007-0174-7 Retrieved

from http://search.ebscohost.com.leo.lib.unomaha.edu/login.aspx?direct=true&db=eue&AN

=508004775&site=ehost-live&scope=site

Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. Journal for Research

in Mathematics Education, 21(1), 33-46. Retrieved from http://www.jstor.org/stable/749455

Judson, E. (2017). How science and math teachers address different course levels: Advanced

placement (AP), honors, and regular. The High School Journal, 100(4), 226-249.

doi:10.1353/hsj.2017.0010

Knight, S. L., Lloyd, G. M., Arbaugh, F., Gamson, D., McDonald, S. P., Nolan, J., & Whitney,

A. E. (2015). Reconceptualizing teacher quality to inform preservice and inservice

professional development. Journal of Teacher Education, 66(2), 105-108.

doi:10.1177/0022487115570564

Martin, D. P., & Rimm-Kaufman, S. E. (2015). Do student self-efficacy and teacher-student

interaction quality contribute to emotional and social engagement in fifth grade

math? Journal of School Psychology, 53(5), 359-373. doi:10.1016/j.jsp.2015.07.001

Metropolitan Omaha Educational Consortium. (2018, March). MOEC achievement plan:

Strategic framework. Retrieved from https://www.unomaha.edu/college-

ofeducation/moec/index.php

17.
QUALITIES OF EFFECTIVE MATH TEACHERS 17

Moyer-Packenham, P. S., Bolyard, J. J., Kitsantas, A., & Oh, H. (2008). The assessment of

mathematics and science teacher quality. Peabody Journal of Education, 83(4), 562-591.

doi:10.1080/01619560802414940

O'Donnell, B. (2009). What effective math teachers have in common. Teaching Children

Mathematics, 16(2), 118-125. Retrieved from http://www.jstor.org/stable/41199387

Puklek Levpušček, M., & Zupančič, M. (2009). Math achievement in early adolescence: The role

of parental involvement, teachers’ behavior, and students’ motivational beliefs about

math. The Journal of Early Adolescence, 29(4), 541-570. doi:10.1177/0272431608324189

Son, J-W. (2015). Quality instruction, teachers' self-efficay, and student math achievement in

Korea and the United States. Conference Papers -- Psychology of Mathematics & Education

of North America, 1142-1145. Retrieved

from http://search.ebscohost.com.leo.lib.unomaha.edu/login.aspx?direct=true&db=eue&AN

=118477085&site=ehost-live&scope=site

Tõeväli, P-K., & Kikas, E. (2016). Teachers' ability and help attributions and children's math

performance and task persistence. Early Child Development and Care, 186(8), 1259-1270.

doi:10.1080/03004430.2015.1089434

Urdan, T., & Schoenfelder, E. (2006). Classroom effects on student motivation: Goal structures,

social relationships, and competence beliefs. Journal of School Psychology, 44(5), 331-349.

10.1016/j.jsp.2006.04.003 Retrieved

from https://www.sciencedirect.com/science/article/pii/S0022440506000380

Watson, S., Miller, T., Davis, L., & Carter, P. (2010). Teachers' perceptions of the effective

teacher. Research in the Schools, 17(2), 11-22. Retrieved

from https://search.proquest.com/docview/906329046

Moyer-Packenham, P. S., Bolyard, J. J., Kitsantas, A., & Oh, H. (2008). The assessment of

mathematics and science teacher quality. Peabody Journal of Education, 83(4), 562-591.

doi:10.1080/01619560802414940

O'Donnell, B. (2009). What effective math teachers have in common. Teaching Children

Mathematics, 16(2), 118-125. Retrieved from http://www.jstor.org/stable/41199387

Puklek Levpušček, M., & Zupančič, M. (2009). Math achievement in early adolescence: The role

of parental involvement, teachers’ behavior, and students’ motivational beliefs about

math. The Journal of Early Adolescence, 29(4), 541-570. doi:10.1177/0272431608324189

Son, J-W. (2015). Quality instruction, teachers' self-efficay, and student math achievement in

Korea and the United States. Conference Papers -- Psychology of Mathematics & Education

of North America, 1142-1145. Retrieved

from http://search.ebscohost.com.leo.lib.unomaha.edu/login.aspx?direct=true&db=eue&AN

=118477085&site=ehost-live&scope=site

Tõeväli, P-K., & Kikas, E. (2016). Teachers' ability and help attributions and children's math

performance and task persistence. Early Child Development and Care, 186(8), 1259-1270.

doi:10.1080/03004430.2015.1089434

Urdan, T., & Schoenfelder, E. (2006). Classroom effects on student motivation: Goal structures,

social relationships, and competence beliefs. Journal of School Psychology, 44(5), 331-349.

10.1016/j.jsp.2006.04.003 Retrieved

from https://www.sciencedirect.com/science/article/pii/S0022440506000380

Watson, S., Miller, T., Davis, L., & Carter, P. (2010). Teachers' perceptions of the effective

teacher. Research in the Schools, 17(2), 11-22. Retrieved

from https://search.proquest.com/docview/906329046

18.
QUALITIES OF EFFECTIVE MATH TEACHERS 18

Author’s Information

Rachel Kaboré is a doctoral student at the University of Nebraska at Omaha. Prior to her

doctoral work, Rachel earned her master’s degree in Educational Leadership from Doane

College and her bachelor’s degree in Education from the University of Nebraska at Lincoln.

Rachel is currently a curriculum coordinator for the Elkhorn Public Schools. In her role as

curriculum coordinator, Rachel works with teachers on district common assessments, manages

online textbooks, and provides professional development. Prior to her work as a curriculum

coordinator, Rachel taught middle school reading, language arts, and math for the Elkhorn Public

Schools and was a member of the school improvement team and the student assistance team

leader. Rachel values providing opportunities for students that open doors to their futures.

Author’s Information

Rachel Kaboré is a doctoral student at the University of Nebraska at Omaha. Prior to her

doctoral work, Rachel earned her master’s degree in Educational Leadership from Doane

College and her bachelor’s degree in Education from the University of Nebraska at Lincoln.

Rachel is currently a curriculum coordinator for the Elkhorn Public Schools. In her role as

curriculum coordinator, Rachel works with teachers on district common assessments, manages

online textbooks, and provides professional development. Prior to her work as a curriculum

coordinator, Rachel taught middle school reading, language arts, and math for the Elkhorn Public

Schools and was a member of the school improvement team and the student assistance team

leader. Rachel values providing opportunities for students that open doors to their futures.