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1. Chapter 2
REVIEW OF RELATED LITERATURE AND STUDIES
This chapter presents the review of related literature
and studies on National Achievement Test (NAT) performance
of pupils in Mathematics which was gathered and collected
from the different sources to provide guidance and
information pertaining to the study.
The National Achievement Test (NAT)
The National Achievement Test is administered annually
by the Philippine Department of Education (DepEd) and
designed to gauge the academic performance in key subjects
of elementary and secondary students in both public and
private schools. The examination determines the students’
academic strengths and weaknesses in five key-major
subjects: Mathematics, Science, English, Filipino, HeKaSi
(Heograpiya,Kasaysayan at Sibika) in elementary and Araling
Panlipunan in high school. Also the ratings obtained from
NAT for Grade VI and Fourth Year served as a tool so to
measure the school’s competency and effectiveness as well
as the students’ aptitude and mastery towards the basic
learning areas (WebMD, 2010).

2. 20
In addition, the test includes Examinee’s Descriptive
Questionnaire (EDQ) which consists more of a survey of
information about the pupils, like: family background,
school organizations, teacher evaluation, facilities
accessible by the examinee and other related questions.
These types of questions are all in multiple choices and
questions have multiple answers. Moreover, National
Achievement Test is a standardized test used to measure
acquired learning, in a specific subject area such as
reading or arithmetic, in contrast to an intelligence test,
which measures potential ability or learning capacity.
Most pupils view test as a frightful experience. They
experience different levels of nervousness and stress.
Exams are used for assessing the students in a competitive
arena right through this scheme. Pupils either move ahead
to a higher level or repeat their scholastic undertaking
based on achievement test results. However, there is quite
a controversy regarding the importance of these achievement
tests. Criticisms come from educational managers and
policymakers. These exams are deemed to improve the
accountability of students and schools (WebMD, 2010).
Nevertheless, it is not easy to make an accurate
judgment whether it is practical to put an end to this
system or not. These views have elements of impartiality on

3. 21
their varied claims. The contrasting arguments carry must
be taken into consideration. It is mastery of the basic
learning in school that enhances ingenuity and advances
satisfaction in learning, because useful creativity sprouts
from obeying the scholastic rules rather than letting the
mind think without a directing force (WebMD, 2010).
The National Educational Testing and Research Center
(NETRC) is the agency responsible in the implementation
of achievement tests. It is an attached agency of the
Department of Education which leads in research, evaluation
and measurement of the efficiency of education and teaching
which provide information vital of the formulation of
educational policies geared towards the realization of an
empowered and globally competitive Filipino (Department of
Education, 2011).
The key programs of the agency are the National
Achievement Tests which come in two types: (1) the National
Elementary Achievement Test (NEAT), (2) the National
Secondary Achievement Test (NSAT), and (3) the Philippine
Validating Tests (PVT).The National Achievement Tests (NAT)
are aimed in assessing the abilities and skills of
graduating high school students to assess their knowledge
and capabilities in five (5) disciplines such as English,
Filipino, Science, Mathematics and Araling Panlipunan

4. 22
(Social Studies). The Division and Regional Achievement
Tests are derivatives of the NAT.
Mathematics Performance of Pupils
According to the report of Trends in
International Mathematics and Science Study (TIMSS. 2003),
the Philippines showed better improvement in both Math and
Science among 45 countries with 33 and 32 points difference
from 1999 to 2003, respectively. The result of the National
Achievement Test (NAT, 2009) indicates a "steady"
improvement in primary education in the country's public
school system. Among all regions in the country, within
each level, the regions generally ranked the same for both
Math and Science. Grade Six pupils in Calabarzon got the
highest scores in Math and Science, while neighboring
Mimaropa had the lowest in both subjects, in CAR scored the
highest in both subject areas, while Zamboanga Peninsula
was the lowest.
DepEd (2009), reported that they embarked an
intervention programs which aimed at improving key
performance indicators in basic education, teacher
trainings, hiring teachers who have majored in Math,
Science and English, provision of one book each for every
student in core subjects, and food for school.

5. 23
According to the study of Makilan as cited by Salaver
(2007) and Urquiza (2014), the level of academic
performance of Grade 6 pupils in Mathematics was average
with 70.79 mean percentile. Again in the study of Urquiza
(2014), she found out that the level of Division Unified
test performance of third year high school students in
Mathematics in the Division of La Carlota City mean
percentile was average and it belongs to average mastery
level.
Gender and Pupils’ Performance in Mathematics
There were studies showing the relationship between
gender and pupil’s performance in Mathematics. For
instance Flores (2009) as cited by Urquiza (2014) revealed
that Filipino women are better in Math than their male
counterparts.
In the study of Hyde (2009), she emphasized that
researchers have all but debunked the idea that girls are
innately worse at Math than boys. But psychologists have
identified other factors that might set girls back. Most
experts agree that if gender differences do exist, they are
small and likely to affect specific areas of math skill at
the highest end of the spectrum and there’s no indication
that women cannot succeed in mathematically demanding

6. 24
fields. Still, women continue to be underrepresented in
Math, Science and engineering-related careers, and there’s
evidence that girls can lose ground in Math under certain
circumstances. One factor inhibiting girls is self-
confidence, even when girls are getting better grades, boys
are more confident in math. It’s important to understand
what might be sapping girls’ confidence.
Ceci and Williams (2003) concluded that lack of self-
assurance likely stems from culture. After reviewing
decades of research on gender differences, culture plays a
bigger role in men and boys’ higher interest and
achievement in Mathematics. In 1983, the study showed that
out of 10,000 pupils, 13 boys in every 1 girl scoring top
in Mathematics. Since then, until 2007, that gap has shrunk
to somewhere between 2.8 and four boys for every girl. So
if the difference was just in the genome, there would not
be that improvement. Rather, shifts like that are due in
large part to increase in the number of girls who take
higher level math courses in high school, where girls
traditionally began falling behind boys. They appear to be
taking more math courses because changing cultural norms
make it more acceptable.
Hyde and her colleagues (2009) found out that the more
gender equity contribute in the increase of school

7. 25
enrollment, for women share research jobs and the more
women’s parliamentary representation the smaller its Math
gender gap.
As Carr (2003) stated that girls are less confident
than boys in their Math abilities, and found out that girls
use different strategies and have different motivations to
do Math. Boys tend to use memory to retrieve sums and are
motivated by a sense of competition to get the answer fast,
even if they sacrifice accuracy. Girls care less about
speed than accuracy and more often rely on “manipulatives”
— counting on their fingers or a counting board. Girls
used manipulatives even when they might be able to
retrieve. They need an added push that boys don’t need to
start using cognitive strategies.
The study of Beilock (2010) showed that girls’
confidence and their interest in becoming “fluent” are
influenced by Math anxiety among their predominantly female
elementary school. It started with these facts that more
than 90 percent of elementary school teachers are women,
and studies show that elementary education majors have
higher levels of math anxiety than any other major. The
researchers then assessed Math anxiety in 17 female first
and second-grade teachers, as well as Math achievement and
gender stereotypes among 52 boys and 65 girls from their

8. 26
classes. At the start of the school year, the researchers
found no link between teacher anxiety and student Math
achievement. But by school year’s end, the more anxious
teachers were about Math, the more likely girls, but not
boys, agreed with the statement, “Boys are good in Math and
girls are good in reading.” In addition, girls who accepted
this stereotype performed significantly worse on math
achievement measures than girls who did not and boys
overall. Interestingly, on average, girls and boys
performed the same. Only the girls who endorsed the
stereotype showed a drop in math performance. Others have
done on “stereotype threat,” which shows that people
perform poorly when a negative stereotype is in play. It’s
also not surprising that girls picked up on their teachers’
anxiety and not boys because research shows that young
children are more likely to emulate adults of the same
gender.
Economic Status and Pupils’ Performance in Mathematics
In the study of Jordan, et al. (2007) pupils who come
from low economic status backgrounds enter school far
behind their peers who come from higher economic status
backgrounds and understand less mathematical topics
including but not limited to counting, and number

9. 27
relations. Although there has been much research about
parental involvement on students’ Mathematics achievement,
little attention has been placed on the reasons for the
Mathematics achievement gap between low-and middle-income
students.
Cross et al. (2009) added that there was a huge
Mathematics achievement gap between low-and middle-
economic status students even before they enrolled in
elementary school, suggesting that low-economic status
parents can support their children’s informal mathematical
knowledge and skills by enhancing their readiness before
they start school; thus reducing the gap between low-
economic status students and high-economic status. However,
this support may be improved by providing information about
early and later mathematical development, and its
connection to parental support. Once parents believe their
support is of importance to their children’ s mathematical
development, they will try to provide as many opportunities
as they can, and students who have had opportunities at
home to learn mathematics demonstrated more mathematical
achievement than their peers who lacked such opportunities.
In addition, Zadeh, Farnia and Ungerleider (2010)
showed that providing an enriched home environment was
essential for the reading and Mathematics achievement of

10. 28
both boys and girls, and they indicated that providing an
enriched home environment was one of the options available
to influence children’s Mathematics achievement,
particularly that of children of less well-educated
mothers.
Crosnoe and Cooper (2010) noted that the achievement
gap due to the students’ economic background was larger for
reading but more related to family socialization factors in
Mathematics.
Guo and Harris (2000) found out that the economic
status of parents has had significant effects on
Mathematics achievement during early childhood, but its
effects have not been shown to be as noteworthy as during
later childhood. It is because there is a vital period in a
child’s life when development of cognitive skills is
greatest and when involvement by parents is generally the
highest. In other words, the worst effects of poverty on
children can be explained by a lack of early cognitive
development within the home.
Unfortunately, according to Blevins-Knabe & Musun-
Miller (1999) emphasized that low- economic status pupils
receive less support in their home environment to develop
their Mathematical skills than their middle and high-peers.

11. 29
Demir, Kilic, and Unal (2010) found that parents’
educational background was also an important indicator for
pupils’ Mathematics achievement, and noted that if parents
had higher educational background, this could increase
their children’s later Mathematics success.
Starkey and Klein (2000) noted the gap between
students’ Mathematics achievement associated with their SES
background was not only explained by parents’ financial
resources, but it was mostly based on parents’ educational
background and exposure to Mathematics. For example,
although providing board game materials was cheap, and
could be easily made at home, most Head Start children were
not provided these activity games at home. While 80% of
middle-income children reported that they played one or
more board games activities at home, only 47% of Head Start
children reported that they did. This demonstrates one of
the reasons for the gap associated with SES background and
why it is more likely due to parents’ educational
background rather than their financial resources.
Demir, Kilic, and Unal (2010) reported that students
whose parents were highly educated and exposed to
Mathematics before in their lives tended to show more
success in Mathematics than their peers whose parents were
less educated and not being exposed to Mathematics.

12. 30
Furthermore, Alomar (2006) stated that highly educated
parents knew the learning requirements and had the
opportunity to provide the best educational environment for
their children.
Study Habits and Pupils’ Performance in Mathematics
The studies conducted by Patel (1997) and
Panchalingappa (1995) indicated that Habit is defined as a
conformed way of doing things. Study habits are a well
planned and way of studying and preparing lessons to
achieve and to attained a form of consistency in the
academic improvements and passing. Among the learner
factors that are important for high achievement, study
habit is one. Study habit and academic achievement are
directly related. Beside, Patel (1997) compared pupils who
differ on different problems they have covering areas like
health, monetary, personal, social, religious cum sex, and
educational
Generally, Yoloye (1999) stressed out that successful
achievement in any form of activity is based upon study,
interpretation and application; and that study should have
a purpose. It therefore depends on individual to decide
why he or she wants to study either to gain new ideas or to
find out relationship between two different things. What

13. 31
one learns as a result of study depends on the degree at
which one succeeds in achieving that aim or purpose.
Isangedighi (1997) relates the strong correlation
between study habits and academic achievement of elementary
pupils. The researcher concluded that “a reduction in
test-anxiety is no guarantee of subsequent improvement in
academic performance when the level of study habit
competence is ignored. Some researchers have found that
note taking activity as study habit variable is beneficial
to students.
On the otherhand Fagbemi, (2001) stated that the
degree of learning depends on the amount of time the child
is actively engaged in learning. The time spent on
studying helps to retain the materials learnt, which will
eventually boost the pupil performance outcome during tests
or examinations.
Khan (2011) reported regarding students who failed to
engage in the coursework and spent little or no time
studying. Students were disengaged from their learning
responsibilities and the derailing of their studying began
as early as elementary school. Early on, students
struggled and faced constant frustration on a series of
topics: long division, fractions, negative numbers, and
word problems. These discouraged students and led to a

14. 32
decreased interest in engaging in the classroom or
completing homework. The competency was low yet students
still continued on to the next grade despite their lack of
knowledge and understanding around basic algebraic
concepts. He concluded that the real problem was making
those poor habits an excuse for the wrong initiatives.
Attitude of Pupils and their Performance
in Mathematics
According to Allport (2001), an attitude is a mental
and neutral state of readiness organized through
experience, exerting a directive or dynamic influence upon
the individual response to all subjects and situation with
which it is related. Attitude underlies many of the
significant dramatic instances of man’s behavior.
Evans (2002) relates that in elementary stage the base
on Mathematics should be imposed to develop mental
observation and creativity or innovativeness. Due to the
lack of proper knowledge on Mathematics the student suffer
in all spheres of life. There is a general consensus among
educators that Mathematics is an important and useful
subject for development in every country. It is the key to
technology. Despite its importance and influence, it is a
subject most feared by students of the primary school.
Today in the modern world there are more applications of

15. 33
Mathematics and new field of research has been developed
that a pupil can generate their knowledge. For this
attitude towards Mathematics, the general tendency of an
individual and to act in a certain way under certain
condition and to determine whether the student likes
Mathematics.
Al ken (1976) noted that there is relationship between
attitude towards Mathematics and achievement in Mathematics
is positive at elementary level and secondary school level
but may not always reach statistically significant.
The National Council of Supervisors of Mathematics
(1977) asserted that learning to solve problems is the
principal reason for studying Mathematics.
As Eshun (2002) defines an attitude towards
Mathematics as “a disposition towards an aspect of
Mathematics that has been acquired by an individual through
his or her beliefs and experiences but which could be
changed.” When emphasizing the importance of individual
experiences, the contexts where students interact with
others and with Mathematics become important focal points.
From the study of Fraser and Kahle (2001), they have
highlighted this aspect in research which shows that
learning environments at home, at school, and within the
peer group accounted for a significant amount of variance

16. 34
in student attitudes and, furthermore, that class ethos had
a significant impact on the scores achieved by students for
these attitudes. Attitudes can be seen as more or less
positive. A positive attitude towards Mathematics reflects
a positive emotional disposition in relation to the subject
and, in a similar way, a negative attitude towards
Mathematics relates to a negative emotional disposition.
These emotional dispositions have an impact on an
individual’s behavior, as one is likely to achieve better
in a subject that one enjoys, has confidence in or finds
useful. For this reason positive attitudes towards
Mathematics are desirable since they may influence one’s
willingness to learn and also the benefits one can derive
from Mathematics instructions.
Nicolaidou and Philippou (2003) showed that negative
attitudes are the result of frequent and repeated failures
or problems when dealing with mathematical tasks and these
negative attitudes may become relatively permanent.
According to these authors when children first go to school
they usually have positive attitudes towards Mathematics.
However, as they progress their attitudes become less
positive and frequently become negative at high school.
Kogce, et al. (2001) found significant differences
between younger and older students’ attitudes towards

17. 35
Mathematics with 8th graders having lower attitudes than
6th graders. There are a number of factors which can
explain why attitudes towards Mathematics become more
negative with the school grade, such as the pressure to
perform well, over demanding tasks, uninteresting lessons
and less than positive attitudes on the part of teachers.
Technological Gadgets and Pupils’
Performance in Mathematics
Norman (1993) stated that technology has a pivotal
role in students’ research. Among the technological
gadgets, the use of cell phones and internet is common to
students. Thus most of the students are not involved in
extracurricular activities. Likewise, there is a massive
consumption of TV among student compared to radio and
newspapers as media of information. The media provides
minimal help in their studies. Technology, media, and
study habits are said to have a direct causal relationship
to the performance of the students in the National
Achievement Test.
Moreover, Norman (1993) stressed that since computers
entered the schools, and it seems reasonable to foresee
that "new technologies" will be quickly and definitely
included in school practice. Thus, it becomes more and more

18. 36
urgent to identify the crucial points around which organize
the discussion on the use of computers and all the new
technologies related to them: how and why new technologies
influence, and are going to influence in the future,
education and in particular Mathematics education.
Likewise, Sfard and Leron (1996) discussed on the
impact of computer programming on learning Mathematics. The
authors described as how the presence of the computer might
change the standard way of conceiving the difficulty of a
problem; and in so doing the computer shows its
potentialities in upsetting and transforming the norms of
school practice.
Lo, Ji, Syu, You, and Chen (2008) stated that as a
medium for learning, digital games provide promising
possibilities to motivate and engage students in subject
learning. Recently, game-based learning is regarded as a
promising vehicle for facilitating students’ active
participation and engaged learning.
On one hand, Prensky (2008) believed that since
digital games own a number of characteristics to engage
students, such as imaginary, challenges, competition,
fantasy, curiosity, uncertainty, goal, decision,
discussion, and emotional connection, a well-incorporation

19. 37
of some of these characteristics might make a boring
learning be interesting and joyful.
Teachers’ Gender and Pupils’
Performance in Mathematics
Steele (2003) stated that the more anxious female
teachers are in Math classes and the more likely female
students are to endorse the stereotype “boys are good at
Math, and girls are good at reading,” the lower the Math
achievement of female students relative to male students or
female students without such a belief. In particular, the
gender differences in children’s self perceptions about
ability and their awareness of commonly held beliefs about
gender stereotypes start emerging between the ages of 7 and
12.
Furthermore, he mentioned that over the years,
educational researchers have investigated many factors
considered to affect student learning. At the heart of this
line of inquiry is the core belief that teachers make a
difference. The difference that has quality results, the
process to achieve this requires great effort and sacrifice
that contribute to the success of the institution. Indeed,
teacher plays an important role in the intellectual

20. 38
development and other aspect of the learners, using various
assessments. Ultimately, teaching is about engaging and
guiding students to learning. The nature of the students in
a classroom is, hence, a major preoccupation on the part of
the teacher. Seen another way, the nature of student
population is a major mediating variable in any connections
between policy and teaching.
According to Biddle (2001), the general aim of
education is to provide opportunity for the fullest
development of the students' thoughts, feelings, and
conduct, so that they will realize their potentialities for
the good of themselves and society. Important in the
realization of such aim is the teacher, who plays many
roles: that of mentor, parent, morale builder, motivator,
stimulator and so on. In performing varied roles, the
teacher, decidedly, affects the total development of the
student. To be effective in teaching, a teacher should have
a broad background of rich experiences, and professional
competencies integrated with cultural heritage.
In addition he added that the teachers, for instance,
should look into the multi-faceted relationship of pupils
with them as teachers, and with their parents and peers,
because this relationship influences their learning, daily
styles life, and even their self perception. The students’

21. 39
problems affect not only their daily interactions, but also
their goals in life. The teachers have a vast and broad
opportunity for inspiring the youth to learn and to grow,
and be worthy members of society. They can use personal
approaches that create a conducive-environment for
learning. They can make the students' life miserable or
joyous, can torture or inspire, humiliate or induce humor,
hurt or heal. It is imperative, then, to love the teaching
profession which may not be financially rewarding, but the
dedication in molding the youth and services the nation, is
invaluable. The teacher should be concerned with other
things, other than the preoccupation with pupils’ classroom
experiences, teaching methods, and enrichment of subject-
matter content. This is so because teaching is a
personalized matter. No factor is so vital to the students’
welfare as the impact of the teachers upon the total
development of the students. Since teaching is a multi-tech
job, the teachers need help in the task of making students
become responsive, well-adjusted individuals. One such help
concerns looking into students' problems, for this is an
avenue by which the teacher can understand the students
better. Obviously, such an understanding will facilitate
the teaching learning process. As human beings with unique
wants, desires, hopes, fears, and aspirations, the students

22. 40
should be understood. The teachers are in the best position
to manifest their understanding of the students. Once the
teachers understand the students' behavior, they can
readily spot the root causes of their students' undesirable
behavior.
In addition Bursal and Pagnozas (2006) and Gresham
(2007), stated that while Math anxiety among elementary
school teachers is found to be a commonplace phenomenon.
This observation is also true to teachers at higher levels
of education, particularly highly selective post-secondary
institutions, when given the same level of their academic
training in Math.
Finally, Beilock (2010) examined the relative
effectiveness of male and female teachers on the
achievement outcomes (Math and Reading) of male and female
students. These affect the quality of teaching in
Mathematics and as well on the part of the learners. If
the Math anxiety hypothesis is the main factor behind the
negative effect of female teachers on female student Math
achievement as these authors claim, then we there is no
impact of having a female teacher (relative to having a
male teacher) on reading for female students or test scores
(reading or Math) for male students. Moreover, there is a
negative effect to either disappear or in fact become

23. 41
positive, as in the economics literature, for female
students taught by teachers who have a strong Math
background and are therefore less likely to suffer from
Math anxiety. Using a unique data set where students are
assigned to classrooms randomly at the beginning of the
academic year, they found that female students who were
assigned to a female teacher, as opposed to a male teacher,
suffered from lower Math test scores at the end of the
academic year. Furthermore, using an indirect test of the
Math anxiety hypothesis, they found the this negative
effect in Math not only seems to disappear but becomes
(marginally) positive in the classrooms where the female
teacher had a Math or a Math-related major in college/post-
college yet persisted in classrooms where the female
teacher did not have a strong background in Math. Also,
they have not found any effect of having a female teacher
on male students’ test scores (Math or Reading) or female
students’ reading test scores.
Sparks (2010) cited on her study that Female
elementary school teachers' comfort with Mathematics has an
outsize effect on the girls they teach, according to new
research. Girls taught by a female teacher got a learning
boost if that teacher had a strong Math background, but had
consistently lower Math performance by the end of the

24. 42
school year if she didn't, according to a study presented
at the American Economic Association's annual conference.
By contrast, boys' Math scores were not affected by having
a female Math teacher, regardless of the teacher's
background in that subject, and there were no differences
in Math performance among male and female students of male
teachers of different math backgrounds. The study adds to
growing evidence that children's gender biases can
significantly affect their own ability.
Other authors were University graduate students
Elizabeth Gunderson and Gerardo Ramirez as well as Susan
Levine, the Stella M. Rowley Professor of Psychology at the
University of Chicago (2000) stated that more than 90
percent of elementary school teachers in the country are
women, and often they get their teaching certificates with
little Mathematics preparation. Other research shows that
elementary education majors have the highest rate of
Mathematics anxiety of any college major. The potential of
these teachers to impact girls' performance has important
consequences. Teachers' anxiety might undermine female
students' confidence in learning Mathematics and also may
decrease their performance in math-dependent subjects such
as science and engineering.

25. 43
To determine the impact of teachers' mathematics
anxiety on students, the team assessed teachers' anxiety
about math. Then, at both the beginning and end of the
school year, the research team tested the students' level
of mathematics achievement and their gender stereotypes.
To assess stereotypes, the students were told gender-
neutral stories about students who were good at mathematics
and reading, and then were asked to draw each type of
student. Researchers were interested in examining the
genders of the drawings that children produced for each
story. At the beginning of the school year, student math
achievement was unrelated to teacher math anxiety in both
boys and girls. By the end of the school year, however, the
more anxious teachers were about math, the more likely
girls, but not boys, were to endorse the view that "boys
are good at math and girls are good at reading." Girls who
accepted this stereotype did significantly worse on math
achievement measures at the end of the school year than
girls who did not accept the stereotype, and than boys
overall. Girls who confirmed a belief that boys are better
in math scored six points lower in math achievement than
did boys or girls who had not developed a stereotype (102
for the girls who accepted the stereotype, versus 108 for
other students). Other research has shown that adults'

26. 44
attitudes strongly influence elementary school children,
and that this relationship is strongest for students and
adults of the same gender. "Thus it may be that first- and
second-grade girls are more likely to be influenced by
their teachers' anxieties than their male classmates,
because most early-elementary school teachers are female,
and the high levels of math anxiety in this teacher
population confirm a societal stereotype about girls' math
ability.
The authors suggest that elementary teacher
preparation programs could be strengthened by requiring
more mathematics preparation for teachers and by addressing
their issues of math attitudes and anxiety.
Teacher’s Educational Qualifications
and Pupils’ Performance
In the study of Braun, (2005); McCaffrey, Lockwood,
Koretz, Louis, & Hamilton, (2004), Sanders, (2000) and
Sanders and Rivers (1996) proved that with the increased
demands for accountability in line with performance
standards and with the growing demand for evidence-based
policymaking, student achievement is considered an accurate
measure of teacher effectiveness and has become a basis for
value-added teacher assessment systems.

27. 45
Cochran-Smith (2001) stated that the notions have also
found favor in regard to the effectiveness of teacher
education systems. After tracing the development and reform
of teacher education in terms of the major questions
shaping this field of education, she argues that “the
outcome” question is what currently motivates teacher
education research and policymaking. She set down three
ways in which the outcomes of teacher education are
constructed. One of them, long-term impact outcomes, refers
to the relationships between teacher qualifications and
student learning. Teachers’ qualifications encompass
teachers’ scores on tests and examinations, their years of
experience, the extent of their preparation in subject
matter and in pedagogy, what qualifications they hold in
their area of expertise, and their ongoing professional
development. Student learning is taken simply as the gain
scores students attain on achievement tests.
In addition, Cochran-Smith (2001) went on to posit the
relationship between teacher qualification and student
learning as the percentage of variance in student scores
accounted for by teacher qualifications when other
variables are held constant or adjusted.
Betts, Zau and Rice (2003), Ferguson & Ladd, (1996),
Goldhaber & Brewer, (1997, 2000), Rowan, Chiang, and Miller

28. 46
(1997), found that teachers’ academic degrees (Bachelor’s,
Master’s, doctorate, and other) are inconclusive. Some
studies show positive effects of advanced degrees; others
show negative effects. According to Murnane (1996), he
stated that some researchers maintain that the requirement
for teachers to have a second degree raises the cost,
financially as well as in time, of teacher education, which
may prevent quality candidates from choosing this
profession.
Furthermore, Darling-Hammond (1999), Goldhaber &
Brewer (2000), Guyton & Farokhi (1987) stated that this
characteristic is related to the subject-matter knowledge
teachers acquire during their formal studies and pre-
service teacher education courses. The evidence from
different studies is contradictory. Several studies show a
positive relationship between teachers’ preparation in the
subject matter they later teach and student achievement,
while others have less unequivocal results.
Monk and King (1994) found both positive and negative
effects of teachers’ in-field preparation on student
achievement.
Goldhaber and Brewer (2000) found a positive
relationship for students’ Mathematics achievement but no
such relationship for science. Rowan, et al. (1997)

29. 47
reported a positive relationship between student
achievement and teachers with a major in Mathematics. Monk
(1994) however, found that while having a major in
Mathematics had no effect on student achievement in
mathematics, having a substantial amount of under- or post-
graduate coursework had a significant positive effect on
students in physics but not in life sciences.
Teachers’ Length of Service
and Pupils’ Performance
According to the studies of Klitgaard and Hall (1974),
& Murnane and Phillips (1981) about the effect of teacher’s
experience on student learning showed that there is a
positive relationship between teachers’ effectiveness and
their years of experience, but the relationship observed is
not always a significant or an entirely linear one. The
evidence currently available suggests that while
inexperienced teachers are less effective than more senior
teachers, the benefits of experience level off after a few
years.
Based on the findings of Harris and Sass (2007), the
relationship between teacher experience and student
achievement is difficult to interpret because this variable
is highly affected by market conditions and/or motivation
of women teachers to work during the child-rearing period.

30. 48
They point to a selection bias that can affect the validity
of conclusions concerning the effect of teachers’ years of
experience: if less effective teachers are more likely to
leave the profession, this may give the mistaken appearance
that experience raises teacher effectiveness. Selection
bias could, however, work in the opposite direction if the
more able teachers with better opportunities to earn are
those teachers most likely to leave the profession.
Teachers’ Seminars and Trainings
and Pupils’ Performance
Jacob and Lefgren (2004) stated that professional
development activities can be conducted by many different
organizations, in school and out of school, on the job or
during sabbatical leave. On these occasions, practicing
teachers update their content knowledge and teaching skills
so they can meet the requirements of new curricula,
consider new research findings on teaching and learning,
and adapt to changes in the needs of the student
population, and so on. Criticism has been leveled against
the episodic nature of these activities and concern
expressed that very little is known about what these
activities really comprise and involve. Conclusions in the
literature on the relationship between teachers’
participation in professional development activities and

31. 49
student outcomes are mixed. Some studies on in-service
professional development have found no relationship to
student achievement.
Likewise Brown, Smith, and Stein (1995) and Cohen and
Hill (1977), Wiley and Yoon (1995) added that other studies
have found higher levels of student achievement linked to
teachers’ participation in professional development
activities directly related to the area in which they are
teaching.
Wenglinsky (2000) found a positive correlation between
professional development activities aimed at the needs of
special education students, and students’ higher-order
skills and laboratory skills in science. More recently,
Harris and Sass (2007) identified what they call the
“lagged effect of professional development,” that is, the
larger effect of teachers’ professional development on
student outcomes not becoming apparent until three years
after the teachers had completed their courses. The
interpretation of the positive effect of participation in
teacher professional development activities is not clear
cut, as this variable is confounded with other teacher
attributes, that is, teachers who participate in these
activities are also likely to be more motivated and,
usually, more specialized in the subjects they teach.

32. 50
Teachers’ Styles and Strategies in Teaching
Mathematics and Pupils’ Performance
According to Best Evidence Encyclopedia (2009),
Elementary Math is a subject which many students struggle
to grasp. The material often requires extra attention and
differs with each student. It has found out that there is a
large achievement gap between black, Hispanic and white
elementary students. Thus the book suggests that are some
of the best and most effective methods of teaching math
which may work to close the learning gap and help those who
often experience learning hurdles in the classroom are: the
use of textbooks visuals and graphics for students to learn
from. These are crucial elements to accompany text and help
get the concepts across to students. However, according to
the National Council of Teachers of Mathematics, the use of
graphics appeared to be much more effective when paired
with specific practice or guidance. This guidance could be
coming from the teacher or from another classroom tool.
According to Burke (2000), teachers are starting to
implement computerized learning into the classroom for a
more personalized learning approach. In fact, more
than four in 10 teachers report the use of e-readers and
tablet computers in their classrooms to complete
assignments and assist in learning. With virtual math

33. 51
programs, children can not only see these graphics, but
they can revisit concepts that were especially difficult.
They are able to learn at their own pace and won't feel
rushed to move onto a concept they are not yet ready to
tackle.
Furthermore, Burke (2000) stated that the process of
having students verbalize step-by-step how they got to the
answer they did may help other students to learn basic
procedures. Since, many students are hesitant to raise
their hands in class to ask questions for fear of sounding
unintelligent. If those in the class are required to
explain how they got to that answer, they may be helping
their classmates in the process. The act of students
explaining their process may also help them to learn how to
do a certain problem. This helps them to recognize the
strategies they're using and potentially apply them to
other areas of learning.
According to the Institute of Education Sciences
(2010), many students benefit from specific teacher
feedback about what they did correctly and where and how
they can improve next time. Teachers should also present
their students with opportunities to correct their answers
and see what errors they made. Instead of simply giving the
correct answer and telling them where they went wrong, it

34. 52
helps for students to be guided in that direction so they
can figure it out for themselves. Also, educators are
aware that not all students learn in the same manner.
However, it is difficult to reach all learners all of the
time. Often it is the students who understand and
participate in the lesson that drive the instruction,
leaving the student who “hides in the back” completely
lost. The teaching strategies provided in this collection
are intended to help teachers differentiate their lessons
to reach those students who are struggling with
mathematics. These resources are comprised of webpages,
articles, and research reports showcasing teaching
strategies to reach these struggling learners, whether they
are struggling due to a learning disability or they just
have difficulty with Math. These resources provide
techniques teachers can use to assess and intervene when
students are struggling in mathematics. There are tips on
how to engage struggling learners, strategies for improving
problem solving, and suggestions for intervention models.
Several resources suggest interventions that address
students’ needs in reading while learning math, as well as
for English language learners. Three of the resources
discuss the specifics of choosing and integrating
technology into instruction, which has been shown to

35. 53
benefit all learners. There are also some longer items
that include research studies on effective teaching
strategies and response to intervention. Differentiation
is often associated with reaching students who need more
assistance, re-teaching, or intervention. However,
differentiation should be used with all levels of learners.
Since we know that students have a preferred learning
style, it makes sense to provide tasks that
reflect students' abilities and preferences, and that
challenge them at the appropriate level.
Burke (2000), added that elementary school teaching
practices constantly are being re-evaluated and revised.
Many movements, such as the: experimental curricular
projects of the 1950s and 1960s; back-to-basics movement
that has been regenerated every other decade or two; “new”
math, integrated curricula, Cooperative Learning, and
“thinking skills”, have each attempted to change basic math
programs by inserting innovative aspects. Now the
new National Council of Teachers of Mathematics, 2000:
Principles and Standards for School Mathematics (NCTM,
2000) is the most recent call for improved math strategies.
Since major emphasis has been on increased student
engagement and the use of improved math strategies, various
curriculum standards have been condensed from an original

36. 54
list of 13 to10 of which 5 describe the math content that
students should learn. These include: numbers and
operations; patterns, functions, and algebra; geometry and
spatial sense; measurements; and data analysis, statistics,
and probability (National Council of Teachers of
Mathematics, 2000).
Hands-on styles and strategies that make sense to
global, tactual, and kinesthetic learners are: Numbers and
operations. It is important that students understand number
concepts and how these relate to their everyday
experiences-- not merely recite them by rote. Using hands-
on models like counters, Cuisenaire rods, multi-base
blocks, chips, abaci, wooden cubes, and counting sticks
would be perfect for students like Raphael—the boy who
vibrated with continuous energy. After Raphael masters
computation concretely, he then can use semi-concrete and
abstract resources with number lines, charts, computers,
calculators, and other activities such as card and board
games that you, he, and other similar students can create.
Tactual students often design better and more intricate
tactual instructional resources that we teachers! Give them
a concrete model and easy-to-follow, illustrated directions
and give their imagination free rein! (National Council of
Teachers of Mathematics, 2000).

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Patterns, functions, and algebra. When math teachers
bring abstract symbols and generalizations to elementary-
school pupils, they need to explain the concept
through real life situations. Elementary pupils need
problem solving in the context of their own personal
situations. They need to generate tables and graphs and
name variables for a purpose. For example, they can create
bar graphs to determine the number of pupilsd who prefer
various flavors of ice cream in preparation for a class
party (National Council of Teachers of Mathematics, 2000).
Measurement. Most measurements require tools and the
materials for teaching them include the standard measuring
instruments. Have children use rulers, meter sticks, tape
measures, trundle wheels, graduated beakers, measuring cups
and spoons, bathroom scales, thermometers, timers, and
protractors. Place assignments on the board, allow them to
work either alone or in a pair to complete the tasks, and
walk among them to assist. Use children’s storybooks to
teach global students math concepts such as time, money,
measurement, and problem-solving techniques. Make math
games and quizzes as an outcome of story lines or
happenings. Pose questions related to multiplying or
subtracting the number of characters or incidents. This
content area should be taught with manipulative resources.

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Some of these materials include dice, coins, cards, colored
cubes, chips, spinners, graph paper, squares, and objects
for making concrete graphs and, of course, calculators and
computers (National Council of Teachers of Mathematics,
2000).
Moreover, Saritas (2004) stated that it is important
for educators to adopt instructional design techniques to
attain higher achievement rates in Mathematics. Considering
students’ needs and comprehension of higher-order
mathematical knowledge, instructional design provides a
systematic process and a framework for analytically
planning, developing, and adapting Mathematics instruction.
Instructional design is an effective way to alleviate many
pressing problems in education. Instructional design is a
linking science a body of knowledge that prescribes
instructional actions to optimize desired instructional
outcomes, such as achievement and effect.