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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
items scored as 10 points.
Part IV contracts with dividing complex numbers with 10
items scored as 10 points.
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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.
Table 1.2 Frequency and Percentage distribution of the
respondents level of performance in complex numbers in terms of
subtraction.
Level of
PerformanceFrequency Percentage Description
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
Mean: 8.43 Description: High
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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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Table 1.3 Frequency and Percentage distribution of the
respondents level of performance in complex numbers in terms of
multiplication.
Level of
PerformanceFrequency Percentage Description
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
Mean: 7.63 Description: High
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.
Table 1.4 Frequency and Percentage distribution of the
respondents level of performance in complex numbers in terms of
division.
Level of
PerformanceFrequency Percentage Description
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
Mean: 7.23 Description: High
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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