Level of Performance of Second Year Students in Complex Numbers

7/25/2019 Level of Performance of Second Year Students in Complex Numbers

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CHAPTER I

INTRODUCTION

Background of the Study

One of the most main goals of education is to prepare the

students to be a globally competitive individual for the

challenges of the future. Wherein, a high level of performance in

Mathematics is required. Since, it is used throughout the world

as an essential partner/tool in many different fields, including

medicine, engineering, natural science, economics and etc. It

also has the largest scope among all the subject areas especially

if the student encountered problem solving activities in the

subjects.

Apparently, most of the students hate Mathematics because it

requires logical reasoning and deductive thinking from the basic

to the complex concepts of Mathematics. They tend to ignore

Mathematics, thus, hinder themselves in many future career

opportunities. Since Mathematics help us to develop skills needed

for the success of our career.

On the other hand, the competence in learning, how to learn

throughout ones life in this changing world entails the

experience and the total training of an individual. It is the


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vehicle for developing students logical thinking and higher-

order cognitive skills. It is our way to our dream since it will

make us smarter and have a great advantaged to those who hate

Math. Students should really continue enhancing their Mathematics

skills.

Learning Mathematics is fun and exciting. Instead of mere

memorization of formulas and procedures and general facts,

different learning activities and exercise should be done to help

students continuous selfimprovement and learning.

The researcher believes that the result of this study would

serve an aid to know the level of performance encountered by the

students in solving complex numbers. Nevertheless, in knowing the

performance level of the students, it is possible to conclude

their difficulties encountered by the students. It also motivates

them that the problem solving involving complex numbers is easy

to understand.


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Statement of the Problem

This study aimed to determine the Level of Performance in

Complex Numbers of the Selected Dormers of MinSCAT Main.

Specifically, this sought to answer the following questions:

1.What is the level of performance in solving complex numbers

of the selected dormers of MinSCAT Main in terms of:

1.1 Addition

1.2 Subtraction

1.3 Multiplication

1.4 Division

2.

Is there a significant difference on the level of

performance in solving complex numbers of the selected

dormers of MinSCAT Main in terms of addition, subtraction,

multiplication and division?


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Statement of Hypothesis

1.

There is no significant difference on the level of

performance of the selected dormers of MinSCAT Main in terms

of addition, subtraction, multiplication and division.

Significance of the Study

The findings of this study bear significance to the

following persons as they would be benefited by the results,

administrators, teachers, students and future researchers.

The results of this study will serve as a guide of the

administrators in upgrading the quality of instruction.

Similarly, this will help teachers to easily determine the

performance of their students in different operations of complex

numbers.

It will also serve for the students as an aid to know their

level of performance in complex numbers. This will serve as their

guide to what extent they will excel to the topic and a basis for

their improvement throughout the learning process.

Lastly, this will serve as the reference of the future

researcher in pursuing the same field of the study and in seeking

for related information/studies needed on their research.


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Scope and Limitation

This study was focused on the level of performance of the in

solving complex numbers in terms of addition, subtraction,

multiplication and division. The respondents of this study are

only second year college dormers of MinSCAT Main, 2015 2016 .

The indicator of the students abilities would be their scores

obtained in the given questionnaires.

Specifically, this study is only limited on answering

specific questions presented in the statement of the problem.

The study was conducted in MinSCAT Main, Alcate, Victoria

last June October, 2015.


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Definition of Terms

The following terms was operationally defined for further

understanding of the study.

Addition is the process of combining two or more

numbers to form one number.

2 Complex Number is the topic used by the researcher. It

refers to the sum of a real number and an imaginary

number.

3 Competency Level it was the researcher wants to

measure. This is ability of the commuters and dormers in

executing different operations in complex numbers.

4 Division the reverse operation of multiplication

5 Imaginary numbers is a multiple of i, where i is the

square root of -1.

6 Mathematics is an exact science that deals which deals

with the study of numbers, figures and other mathematical

concepts.

7 Multiplication is adding the number to itself in

particular number of times

8 Operation was applied in solving a certain problem.

9 Subtraction is an operation that undergoes to the

process of subtracting one number to another number.


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Theoretical Framework

Logic which requires no specific thinking is positive

without any theoretical framework, and research without any

theory is chaotic and incoherent. A theory without facts becomes

fantasy, uncontrolled imagination, a reverie. Based on this

requirement, several theories are presented.

According to Jerome Bruners Constructivist Theory, as cited

by Hurst, the purpose of education is not to impart knowledge,

but instead to facilitate a childs thinking and problem solving

skills which can then be transferred to a range of situations.

Specifically, education should also develop symbolic thinking in

children. Also, curriculum should foster the development of

problem solving skills through the processes of inquiry and

discovery. It should be designed so that the mastery of skills

leads to the mastery of still more powerful ones.

On the other hand, Bandura noted on his theory the social

influences on learning and distinguished between learning and

performance, distinction behaviorists would not make. Learning is

the acquisition of some symbolic representation that serves to

guide future behavior. The future behavior may or may not

actually occur. Bandura believes that in naturalistic settings we

learn new behaviors through observation of models and the results

of their own actions. Cognitive processes also play an important


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role in our learning, a specially our sense of self efficacy.

According to Bandura, our self-efficacy, our beliefs about our

ability to perform a specific task, play a major role both in the

effort that we put forward and resulting learning. (Hannum, 2008)

Likewise, cognitive and associative learning play an

important role in the performance of the students in the problem

solving because these processes involve continuous learning

process which is necessary to determine the level of skills and

ability in some areas may greatly affect ones performance for

the learning cannot be connected from one idea to another.

Moreover, Bruner believed that the subject matter should be

represented in terms of the childs way of viewing the world and

advocated teaching by organizing concepts and learning by

discovery. He also asserted culture should shape notions through

which people organize their views of themselves and others and

the world in which they live. Also, that intuitive and analytical

thinking should both be encouraged and rewarded.

Also, Lewins Theory of Learning, as cited by Ceraspe,

believed that an individual lives in space which is usually his

environment. He suggested that the development of an individual

was the product of the interaction between inborn predispositions

(nature) and life experiences (nurture). The behavior of an

individual is always geared toward some goal or objective and it


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is precisely this intention that matters most in the performance

of behavior. These intentions supposedly follow field principles

and are influenced by psychological forces such as how the

individual perceives a situation.

Vygotsky thought that the social world played a primary role

in cognitive development. He saw language as a major tool not

only for communications but also for shaping individual thought.

He started cognition within a historical and cultural framework

because he believes that was the only way that cognition could be

understood. Vygotsky placed an emphasis on social and cultural

aspects of learning. Certain aspects of Vygotskys work have

influenced education, especially his concept of the zone of

proximal development. (Hannum, 2005).

Calderon (2004) cites that trial and error theory involves

that trying a series of solution using all available information

and techniques known until the correct solution to a problem is

found. Insight, understanding and systematic procedure are used

in trying to solve a problem especially in Mathematics.

Furthermore, the Theory of Cognitive Development proposed by

Jean Piaget focused on how learners interact with their

environment to develop complex reasoning and knowledge. Students

in a constructivist classroom learn concepts while exploring

their application. During this application process, students


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explore various solutions and learn through discovery. Throughout

the learning experience, meaning is constructed and reconstructed

based on the previous experiences of the learner.

As teachers, there are specific things that they can do to

help pupils remember what they learn. One of these is to make

sure that the pupils see the relationship between the information

they learned and reduce memorization to a minimum.


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Conceptual Model

On the basis of the forgoing theoretical framework, the

Conceptual Framework is shown in Figure 1.

Figure 1. Hypothesized difference among the variables of the

study.

Figure 1 shows the hypothesized difference on the level of

performance in complex numbers of the selected dormers of MinSCAT

Main.

Specifically, as shown above, the major variable of the

study is the level of performance of the selected dormers in

complex numbers. These are measured in terms of addition,

subtraction, multiplication and division of the complex numbers.

This study tried to determine the significant difference in

solving complex numbers as performed by the respondents. This was

indicated by the double-headed arrow.

Level of Performance in Complex Numbers

of the selected dormers of MinSCAT Main in terms of:

Addition,

Subtraction,

Multiplication, and

Division


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CHAPTER II

REVIEW OF RELATED LITERATURE

In this portion of the study, literature and studies found

in books, articles and magazines and even in the internet about

the students level of performance are presented and reviewed.

The purpose is to show that the content and subject matter in

this study are supported by the authorities.

Related Literature

Dicdican (2007) stressed that pupils performance lies on

the expertise of the teacher, his effectiveness to attain the

objectives of the lesson, willingness to provide varied learning

activities for interactive or cooperative learning and initiative

to ask questions that develop critical thinking skills.

While, according to Zanzali (2006), the levels of content

mastery and the skills necessary to carry out certain standard

algorithms are satisfactory. The mastery of problem solving

skills, however, among the students is still at low. Efforts to

upgrade and thus help students to mastery the problem solving

skills should be planned and implemented. It is hoped that the


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data generated by this research can contribute towards the

upgrading of teaching and learning mathematics in Malaysia.

Also, according to him, there is a general agreement among

mathematics educators that students need to acquire problem

solving skill, learn to communicate using mathematical knowledge

and skills, and develop mathematical thinking and reasoning, to

see the interconnectedness between mathematics and other

disciplines. Based on this perspective, this research looked into

the levels of problem solving ability amongst selected Malaysian

secondary school students. Research findings also showed that

students have fairly good command of basic knowledge and skills,

but did not show the use of problem solving strategies as

expected. Generally, these students have a low command on problem

solving skills. Most of the students were unable to use correct

and suitable mathematical symbols and vocabulary in providing

reasons and explanations for certain problem-solving procedures.

It is hope that these findings will serve as a reference for

educators in improving the learning and teaching of mathematics

in general and problem solving instruction in particular.

Likewise, Jakimovik in 2010, problem-solving competencies of

the majority of students are of very low levels. Each year more

than half of students didnt even attempt to solve the problems,

and only a small percent of those who tried did it correctly. the


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diagnostic testing on these two context problems show serious

lack of understanding of these types of problems and very low

levels of strategic competence of the majority of the first year

students, prospective elementary school teachers. Approximately

93 %, 91 %, 94 % and 98 %, each year respectively, earned 0

points on the first problem, and 88 %, 89 %, 94% and 91%, each

year respectively, earned 0 points on the second problem. The

reasons behind the high percent of students who earned 0 points

on each problem are indeed complex and require a substantial in

depth investigation. A list of some of the possible related

factors, a set of goals of mathematics education for elementary

school teachers and the necessary changes in planning and

practicing mathematics instruction at teacher training

departments.

On the other hand, Fisico (2005) suggested that pupils

should be given more opportunities to expose and engage

extensively in mathematical and logical problem solving

situations. Schools may indulge in mathematics competitions. Such

competitions help students make sound and logical conclusions

promote discipline as students to solve as many problems as

possible in the process. Today, mathematics competitions are

being held and intensified in the elementary, secondary and


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tertiary levels to motivate and arouse students interest,

prestige and achievement in mathematics.

Furthermore, Knuth et. al. (2005) stated that a multiple

values response to the literal symbol interpretation task was

associated with success which is larger task that a relational

view of the equal sign was associated with success on the

equivalent equations talk. Additionally, the likelihood that the

student would use the recognize equivalence strategy in eight

grade was greater than the acquired relational understanding of

the equal sign in the sixth and seventh grade, suggesting it

matters when students acquire a relational understanding of the

equal sign. That teachers failed to see these connections is not

necessarily surprising, given these tasks are not ones typically

posed to students.

Related Studies

Berguera (2009) in her study entitled Level of Performance

in Solving number and Word Problems in Algebra of Second Year

Students in Selected National High Schools in Naujan South and

East District found out that student respondents from Naujan

South have better performance than student respondents from

Naujan East in solving number problems while they have shown the


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same level of performance in word problems. She recommended that

students should be given more exercises in solving both number

and word problems to enhance their abilities and master some

techniques in interpreting mathematical problems to further

improve students problem solving ability.

Similarly, Castillo (2009) revealed in her study, Level of

Performance in Problem Solving in Mathematics of Grade Six Pupils

in Selected Public Intermediate Schools in Bongabong South

District, S.Y. 2008-2009, that majority of the pupil respondents

have a good performance in problem solving achievement, however

there is still a need among the pupils to improve and increase

mean performance in mathematics. She recommended that the teacher

should exert more effort in improving the level of performance in

problem solving of pupils. They should assist pupils in problem

solving difficulties by introducing varied activities and

involving them to unusual degree of realism. Teachers should also

make problem solving interesting, allow pupils to experience

success and introduce varied problem solving activities. Teachers

should emphasize reading carefully and analytically in order to

understand the meanings of the word problems.

Perez (2010) in her study, Problem Solving Performance in

Algebra of Second Year Students in Three Selected National High

School in Naujan found out that the respondents from three


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schools have varying levels of performance in solving word

problems such as age problem, work problem, mixture problem,

investment problem, and uniform motion problem since they have

different kinds of learning system.

Likewise, based on the finding on the study Level of

Performance in Solving Word Problems involving two and three

dimensions among third year students in Two National High Schools

of Naujan West Ditrict conducted by Fababaer (2010), revealed

that student respondents in School A generally have demonstrated

a very high performance in area of rectangle, high in area of

square, low in triangle and very low in trapezoid. But they were

able to identify the given and formula to be used. While on

School B shown a very high performance in area of rectangle,

averge in square and very low in triangle and trapezoid.

Also, it was concluded that in terms of volume of

rectangular prism and volume of triangular prism, pyramid,

cylinder and sphere, the both School A and B got a low and very

low performance respectively.

Furthermore, in the study conducted by Montana (2011), the

Level of Performance in Signed Numbers, gender, dialect, family

income and organizational involvement do not affect the mastery

and competency level of the students. Also the educational

materials have no significant relationship with the students


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performance level. Though, if these materials were used properly,

these would be a great help with their studies. The study

revealed that the performance of students in solving problems

involving signed numbers is differing to each other.

Silmilarly, in the study, Gender Disparity in Mathematics

Performance of Selected Students at Mindoro State College of

Agriculture and Technology, Arenillo (2008) found out that the

male and female students have demonstrated varying levels of

performance in Mathematics across four year levels. Second year

students have shown invariably good performance. Generally, both

gender groups performed very satisfactorily in their mathematics

courses. Results further indicate that mathematics performance of

the students is not influenced by the gender except in the third

year level where males have outperformed the females. She

recommended that the Mindoro State College of Agriculture and

Technology faculty in Mathematics should engage their students in

more problem solving tasks to come up with empirical evidences of

the conceptual and procedural knowledge level of their students.

Results, in turn may give better dimensions of gender difference.


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CHAPTER III

RESEARCH METHODOLOGY

This chapter presents the methodology research design,

research locale, respondents of the study, sampling technique,

research instrument, scoring and quantification, data gathering

procedure, data processing method and statistical treatment of

data employed in analyzing and interpreting data pertaining to

the variables of the study. This chapter presents the

Research Design

The descriptivecomparative method of research was employed

in this study to describe and compare the level of performance of

the students in solving complex numbers.

This research design describes systematically, factually,

accurately and objectively a phenomenon. Zulueta (2003) defined

this design as a method which considers two entities without

manipulating their values but rather establishing a formal

procedure for obtaining criterion data on the basis of which one

can compare and conclude which of the two variables is better.


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Research Locale

This study was conducted in Mindoro State College of

Agriculture and Technology located at Alcate, Victoria, Oriental

Mindoro. It was 15 km away from the town proper of Victoria.

Specifically, this school satisfied the criterion in the

selection of the research locale.

Respondents of the Study

The respondents of the study were composed of 15 Second Year

College dormers of the given locale. The distribution of these

respondents was shown in Table I.

Table I. Distribution of the Respondents

Respondents Population Sample

Dormers 680 15

Sampling Technique

A systematic random sampling technique was used to determine

the number of the respondents of the study.


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Research Instrument

The major instrument of the study used is a set of forty

(40) item test. This set of test was selfstructured and other

was generated from the lessons in complex numbers. This is

composed of four parts.

Part I deals with adding complex numbers with 10 items

scored as 10 points.

Part II contracts with subtracting complex numbers with 10

items scored as 10 points.

Part III deals with multiplying complex numbers with 10


Part IV contracts with dividing complex numbers with 10



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Scoring and Quantification

The result of test obtained by the student respondents will

be described using the following:

Score Description

910 Very High

78 High

56 Average

34 Low

1-2 Very Low

Data Gathering Procedure

The researcher distributed personally the set of

questionnaires to the respondents. Direction for answering the

test was explicitly stated to guide the students in answering the

test. It was also read and explained for the respondents to

answer properly. The researcher retrieved the materials and made

sure they were returned completely.


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Data Processing Method

After the retrieval of the questionnaire, the researcher

tabulated and processed the data manually through the use of the

description in the scoring and quantification presented above.

Quantitative data were analyzed and the results were interpreted.

Data table was made to organize, summarize and analyze the data

on how variables differ with each other.

Statistical Treatment of Data

After tabulating the data gathered from the questionnaire,

they were analyzed and interpreted using Frequency and Percentage

Distribution, Mean and OneWay Analysis Of Variance.

The following statistical formulas were used in the study.

1.

Frequency and Percentage Distribution

Formula:

where:

percentage

frequency

total number of respondents


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2.

Mean

Formula:

where:

= mean

= symbol for summation

X = nthindividual observation

n = total number of observation

3.

One Way Analysis of Variance (ANOVA)

Table:

Source of

Variation

Degree of

Freedom

Sum of

Squares

Mean of

SquaresF-ratio

Critical

ValueResults

Between

Groups

Within

Groups

Total

Formula:

mean square between

mean square within


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sum of square between

sum of square within

degrees of freedom between

degrees of freedom within


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CHAPTER IV

RESULTS AND DISCUSSION

This chapter presents the results and discussions of data

generated based on the problems of the study.

1. Level of performance in complex numbers of the dormers

1.1 Addition of Complex Numbers

Table 1.1 shows the frequency and percentage distribution of

the level of performance in adding complex numbers of the

dormers.

It can be noted that 10 or 66.67% of the respondents got

scores between 9 to 10. Three or 20% obtained scores between 78.

Only 2 (or 13.33%) scored between 56.

Based on the foregoing results, it implies that the

respondents have a high level of performance in adding complex

numbers as shown by the computed mean of 8.57.

This can be denoted that the most of the respondents are

familiar with the rules of adding complex numbers in order to

arrive with the correct answers.


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Table 1.1 Frequency and Percentage distribution of the

respondents level of performance in complex numbers in terms of

addition.

Level of

PerformanceFrequency Percentage Description

910 10 66.67 Very High

78 3 20 High

56 2 13.33 Average

34 0 0 Low

12 0 0 Very Low

Total 15 100

Mean: 8.57 Description: High

1.2 Subtraction of Complex Numbers

Table 1.2 presents the frequency and percentage distribution

of the level of performance in subtracting complex numbers of the

dormers.

Most of the respondents (66.67% or 10 out of 15)fell within

910 brackets. There are three (or 20%) who got scores between 5

to 6. While, two (or 13.33 %) were scored between 78.


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The computed mean of 8.43 denotes that the respondents have

a high level of performance in subtracting complex numbers.

Specifically, it can be inferred that majority of the

respondents got the correct answer since they know the rules

involved in subtracting complex numbers.



subtraction.

Level of


910 10 66.67 Very High

78 2 13.33 High

56 3 20 Average

34 0 0 Low

12 0 0 Very Low

Total 15 100



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1.3 Multiplication of Complex Numbers

Frequency and percentage distribution of the level of

performance in multiplying complex numbers of the dormers is

shown in Table 1.3.

Ten (10) or 66.67% of the respondents scored between 9 to

10. Twenty percent or three (3) of the respondents got scores

between 12. Two (or 33.33%) who got scores between 56.

The findings showed as indicated by the computed mean of

7.63 that the level of performance of the dormers in multiplying

complex number is high.

This suggests that the respondents have enough knowledge on

the rules concerning multiplication of complex numbers in order

to arrive with the correct answer.


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multiplication.

Level of


910 10 66.67 Very High

78 2 13.33 High

56 0 0 Average

34 0 0 Low

12 3 20 Very Low

Total 15 100


1.4 Division of Complex Numbers

Table 1.4 illustrates the frequency and percentage

distribution of the level of performance in dividing complex

numbers of the dormers.

Specifically, it can be seen that 10 (or 66.67%) out of the

15 respondents obtained scores between 7-8. Two (or 13.33%) who


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got scores between 9-10 and also, between 56. Only 1 (or 6.67%)

was scored between 34.

Based on the findings, it entails that the respondents have

a high level of performance in dividing complex numbers as shown

by the computed mean of 7.23.

This can be meant that the most of the respondents managed

to get the correct answers because they were acquainted with the

rules in division of complex numbers.



division.

Level of


910 2 13.33 Very High

78 10 66.67 High

56 2 13.33 Average

34 1 6.67 Low

12 0 0 Very Low

Total 15 100



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2. Differences in the level of performance in complex numbers of

dormers

Table 2.1 Summary Table of Oneway ANOVA of the respondents

level of performance in complex numbers

Source of

Variation

Degree of

Freedom

Sum of

Squares

Mean of

Squares

F-ratio

F

Critical

Value

Results

Between

Groups3 28.87 9.62

2.26 2.77Not

SignificantWithin

Groups56 238.7 4.26

Total 59 267.57

Table 2.1 shows the difference in the level of performance

of dormers in addition, subtraction, multiplication and division

of complex numbers.

As indicated, since the computed Fratio of 2.26 is less

than the tabular value of 2.77 at 0.05 level of significance

using the degrees of freedom (3,56), thus, the null hypothesis

was accepted. It means that there is no significant difference in

the level of performance in complex numbers of dormers.


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It can be suggested that the level of performance of dormers

in terms of adding, subtracting, multiplying and dividing complex

numbers were almost the same and do not differ with each other.

This may be due to the familiarity of the respondents on the

rules involved in the four fundamental operations used in complex

numbers. It is also possible that the students mastered the

complex numbers because it was taught to them by their teacher

effectively.

The findings affirm the study conducted by Dicdican (2007),

which found out that pupils performance lies on the expertise of

the teacher and his effectiveness to attain the objectives of the

lesson.

Likewise, it was upheld by Arenillo (2008) which revealed

that students have shown good performance in Mathematics.

Lastly, the result of the study denotes that dormers have a

high level of performance in complex numbers and they do not

differ significantly.


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CHAPTER V

SUMMARY, CONCLUSIONS AND RECOMMENDATIONS

This chapter presents the summary, conclusions and

recommendations made by the researcher.

Summary

1. Level of performance in complex numbers of the dormers

1.1 Addition of Complex Numbers

Results showed that 10 or 66.67% of the respondents got

scores between 9 to 10. Three or 20% obtained scores between 78.

Only 2 (or 13.33%) scored between 56. The mean score was 8.57.

1.2 Subtraction of Complex Numbers

Most of the respondents which is 66.67% (or 10 out of 15)

fell within 910 brackets. There are three (or 20%) who got

scores between 5 to 6. While, two (or 13.33 %) were scored

between 78. The mean score was 8.43.


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1.3 Multiplication of Complex Numbers

Of 15 respondents, ten (10) or 66.67% scored between 9 to

10. Twenty percent or three (3) of the respondents got scores

between 12. Two (or 33.33%) who got scores between 56. The

computed mean score was 7.63.

1.4 Division of Complex Numbers

As shown in the results, 10 (or 66.67%) out of the 15

respondents obtained scores between 7-8. Two (or 13.33%) who got

scores between 9-10 and also, between 56. Only 1 (or 6.67%) was

scored between 34. 7.23was the computed mean score.

2. Differences in the level of performance in complex numbers of

dormers

There is no significant difference in the level of

performance in complex numbers of dormers since the computed

Fratio of 2.26 is less than the tabular value of 2.77 at 0.05

level of significance using the degrees of freedom (3,56).


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Conclusion

The researcher has come up with the following conclusions

based on the findings of the study.

1. Most of the respondents have a high level of performance in

adding complex numbers because of their familiarity with the

rules in addition of complex numbers to arrive with the correct

answers.

2. Majority of the respondents have a high level of performance

in subtracting complex numbers because they were aware in the

rules employed in subtracting complex numbers.

3. The level of performance in complex numbers of the majority of

the respondents is high because they have enough knowledge on the

rules concerning multiplication of complex numbers.

4. Most of the respondents have a high level of performance in

dividing complex numbers because they were acquainted with the

rules involved in dividing of complex numbers.

5. The study revealed a no significant difference on the level of

performance in complex number operations of the dormers.


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Recommendations

Based on the findings and conclusions of the study, the

following are recommended:

1. The students are encouraged to familiarize themselves with the

rules in adding, subtracting, multiplying and dividing complex

numbers.

2. Teachers should give focus on making their students acquainted

on the rules employed in the four fundamental operations of

complex numbers.

3. Students should also be exposed to different operations and

must be equipped with the skills because four operations will

always be applied in everyday life.

4. Similar studies should be conducted about complex numbers to

verify the results of the study.


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BIBLIOGRAPHY


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Perez, C. O. (2010) Problem Solving Performance in Algebra of

Second Year Students in Three Selected National High School

in Naujan

Fababaer, L. M. (2010) Level of Performance in Solving Word

Problems involving two and three dimensions among third year

students in Two National High Schools of Naujan West Ditrict


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APPENDICES


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APPENDIX ARESEARCH INSTRUMENT


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Name: Date:

Course and Year:

Dorm Number:

Direction: Perform the indicated operations and reduce to the

form a + bi.

I. Addition

1. (5+11i) + (7+4i) =

2. 15 + (-2+3i) =

3. (2+5i) + (6+7i) =

4. (3+2i)+(45i)+(5+8i) =

5. (1511i)+(45i)+2i =

6. i + 7i + (4) =

7. 25 + 4i=

8. (2+3i) + (16)+7 =

9. 3 + (72i) =

10. (6+2i) + (46i) =

II. Subtraction

1. (1+6i) (8+2i) =

2. (52i)(35i) =

3. (27i)(313i) =

4. 4 (i+7) =

5. 25i=

6. 4+7) (2+3i)=

7. 15 (3i21) =

8. 3 74)=

9. 25 6i (2i) =

10. (14+5i) (6+i) =


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III. Multiplication

1. (7+2i)(2+7i) =

2. 2i(5+6i) =

3. (73i)(4+25) =

4. 100(38i) =

5. 6(5+i) =

6. (4+7)(3i) =

7. (i+7i)(4) =

8. 3(7+4) =

9. (256i)(4+2i) =

10. (14+5i)(6+i) =

IV. Division

1.(-4+2i)

-2=

2.25

()=

3.24i

3i=

4.i2+2i+1

i+1=

5.i

3i=

6.(-36)

2i=

7.()

5=

8.24i

3=

9.i+3i+1

i+1=

10.66i

11=


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APPENDIX BCURRICULUM VITAE


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CURRICULUM VITAE

Personal Data

Name:Desiree B. Evangelista

Address:Poblacion III, Victoria, Oriental Mindoro

Birthdate:December 21, 1996

Age:18

Civil Status:Single

Religion:Roman Catholic

Email Address:[email protected]

Educational Attainment

Undergraduate Course

Bachelor of Secondary Education Major in Mathematics

Mindoro State College of Agriculture and Technology

Main Campus

Alcate, Victoria, Oriental Mindoro


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Secondary

Aurelio Arago Memorial National High School

Main Campus

Leido, Victoria, Oriental Mindoro

S.Y. 2012 2013

Salutatorian

Academic Excellence in Mathematics Awardee

Most Outstanding Researcher Awardee

Active Girl Scouts of the Philippines Awardee

Elementary

Simon Gayutin Memorial Elementary School

Malayas, Poblacion III, Victoria, Oriental Mindoro

Salutatorian

Level of Performance of Second Year Students in Complex Numbers

Documents

Transcript of Level of Performance of Second Year Students in Complex Numbers