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

54

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

55

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.