Qualities of Effective Math Teachers

Contributed by:
Jonathan James
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.
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 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.
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.
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
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
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
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,
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
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
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
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;
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.
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
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
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.
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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.