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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).
In addition, the test includes Examinee’s Descriptive
Questionnaire (EDQ) which consists more of a survey of
20
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
their varied claims. The contrasting arguments carry must be
21
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
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
23
and English, provision of one book each for every student in
core subjects, and food for school.
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
24
the highest end of the spectrum and there’s no indication
that women cannot succeed in mathematically demanding
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
25
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
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
26
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 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
27
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 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
28
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
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.
29
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.
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.
30
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.
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
31
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 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.
32
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 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.
33
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
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.
34
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 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
35
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
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
36
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 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
37
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 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
38
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
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
39
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’
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
40
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 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.
41
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 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
42
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 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
43
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.
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
44
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' 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
45
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.
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
46
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
(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,
47
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) 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
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significant positive effect on students in physics but not
in life sciences.
Teachers’ Length of Serviceand 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. 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
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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 Trainingsand 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 student outcomes are mixed. Some studies on
in-service professional development have found no
relationship to student achievement.
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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.
Teachers’ Styles and Strategies in Teaching Mathematics and Pupils’ Performance
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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 programs, children can
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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
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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
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shown to 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
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curriculum standards have been condensed from an original
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
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imagination free rein! (National Council of Teachers of
Mathematics, 2000).
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
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questions related to multiplying or subtracting the number
of characters or incidents. This content area should be
taught with manipulative resources. 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.