11
PERFORMANCE AND DIFFICULTIES ENCOUNTERED IN
BASIC MATHEMATICAL
OPERATIONS__________________________________________
A Thesis Presented to the
Faculty of the Graduate School
University of Cebu
Cebu City
__________________________________________
In Partial Fulfillment
Of the Requirements for the Degree
Master in Science Teaching, major in Mathematics
__________________________________________
By Eunice L. Manugas
February 2011
APPROVAL SHEET
This thesis entitled, PERFORMANCE AND DIFFICULTIES ENCOUNTERED
IN BASIC MATHEMATICAL OPERATIONS, prepared and submitted by MISS
EUNICE L. MANUGAS, in partial fulfillment of the requirements for
the degree of MASTER IN SCIENCE TEACHING (MST) MAJOR IN MATHEMATICS
has been examined and is recommended for acceptance and approval
for Oral Examination.
THESIS COMMITTEEAGAPITO P. PINO, JR., DM AdviserRENATO C.
SAGAYNO, MST Math
MA. NILA R. SABAL, MST MathMember
MemberYOLANDA C. SAYSON, Ed. DChairmanPANEL OF EXAMINERS
Approved by the Committee on Oral Examination with a grade of
Passed.
AGAPITO P. PINO, JR., DM AdviserRENATO C. SAGAYNO, MST Math
MA. NILA R. SABAL, MST MathMember
MemberYOLANDA C. SAYSON, Ed. DChairman
Accepted and approved in partial fulfillment of the requirements
for the degree Master in science Teaching (MST), major in
Mathematics.
Comprehensive Examination: Passed
February 17, 2011
DR. YOLANDA SAYSONDate of Oral Examination
Dean, Graduate School
ACKNOWLEDGEMENT
The researcher would like to recognize and acknowledge these
people who, directly or indirectly, contributed to the preparation
of this intellectual work in terms of motivation, encouragement,
support and assistance. Atty. Augusto W. Go, for the financially
aid and other privileges he has extended to this researcher;Dr.
Agapito P. Pino, Jr., the well-educated adviser, who devoted ample
time to correct her works thus leading to an improved completion of
her research;The members of the panel, Prof. Renato Sagayno and
Prof. Ma Nila Sabal for their invaluable comments and suggestions
for the improvement of this work;Dr. Yolanda Sayson, the Graduate
School Dean and the Chair of the Thesis Committee, for her
suggestions for the improvement of this study; Prof. Marcial Chiu,
the researchers censor, for his patience in correcting the grammar
and spelling to make the material more comprehensive. The Grad
School staff and working scholars headed by Maam Ann who rendered
excellent service by answering all the researchers queries,
accommodating her requests and assisted her from the start;Mr.
Precellano Comon, the School Head of San Fernando National High
School, who willingly welcomed the researcher and approved the
four-hour request to administer the four sets of test
questionnaires to the high school freshmen within a week;The San
Fernando NHS Faculty and Staff, for their understanding and help in
the adjustment of their daily schedule so as to give the researcher
an hour a day;Special citation is given to Mr. and Mrs. Diogenes
and Estrella Manugas, for the dearly treatment and for being the
researchers main support system;Gesture of gratitude is given to
Ms. Janice Maraviles, the researchers bestfriend, for all the
motivation.Above all, the researcher is grateful to the Lord
Almighty who is her strength booster, provider and protector.
Dedication
This piece of work is heartily dedicated to
my loving parents, Pa Deo and Ma Estring,my only brother
Eugene,
my adorable niece, Divine Hannahmy second family Aunty Fe, Uncle
Dodong,
and to my cousins, Jessa, Kim and Lowe.TABLE OF CONTENTS1CHAPTER
1
1THE PROBLEM AND ITS SCOPE
1INTRODUCTION
2Theoretical Background
8THE PROBLEM
8Statement of the Problem
9Statement of Null Hypothesis
9Significance of the Study
11RESEARCH METHODOLOGY
12Research Environment
14Research Respondents
14Research Instruments
15Research Procedures
17DEFINITION OF TERMS
19CHAPTER 2
19PRESENTATION, ANALYSIS AND INTERPRETATION OF DATA
19PROFILE OF HIGH SCHOOL FRESHMEN
23PERFORMANCE ON BASIC MATHEMATICAL OPERATIONS
28DIFFICULTIES ENCOUNTERED IN BASIC MATHEMATICAL OPERATIONS
37CHAPTER 3
37SUMMARY, FINDINGS, CONCLUSIONS AND RECOMMENDATIONS
37SUMMARY
39FINDINGS
43CONCLUSIONS
43RECOMMENDATIONS
45REFERENCES
APPENDICES47Appendix A-1 Transmittal Letter
48Appendix A-2 Transmittal Letter
49Appendix B The Research Instrument
58Appendix C Results on Difficulties Encountered
62Appendix D Relationship between Performance and Difficulties
Encountered
63Appendix E Proposed Remedial Class
65CURRICULUM VITAE
LIST OF TABLES AND FIGURESTable
Page
1Distribution of Respondents According to Gender19
2Distribution of Respondents According to Age19
3First Grading Period grades of the Respondents20
4Second Grading Period grades of the Respondents21
5Distribution of the Respondents According to their Performance
in Addition23
6Distribution of the Respondents According to their Performance
in Subtraction24
7Distribution of the Respondents According to their Performance
in Multiplication25
8Distribution of the Respondents According to their Performance
in Division26
9Difficulties encountered by the respondents on Addition27
10Difficulties encountered by the respondents on
Subtraction29
11Difficulties encountered by the respondents on
Multiplication31
12Difficulties encountered by the respondents on Division33
13Chi-square Test on Relationship34
FigurePage
1The Research Flow11
2Location Map12
University of Cebu
Cebu City
GRADUATE SCHOOL
Thesis Abstract
Title:PERFORMANCE AND DIFFICULTIES ENCOUNTERED IN BASIC
MATHEMATICAL OPERATIONSAuthor:Eunice L. ManugasDegree:Master in
Science Teaching major in MathematicsSchool:University of
CebuAdviser:Dr. Agapito P. Pino, Jr., D.M.Place of
Publication:University of CebuDate:March 2011Pages:65ABSTRACT
The ability to perform the basic mathematical operations
(addition, subtraction, multiplication and division) is a
pre-requisite for all high school freshmen to understand high
school mathematics. All freshmen are expected to add, subtract,
multiply and divide whole numbers, fractions and decimals. This
means that one cannot fully grasp new learning without
understanding the previous one which calls the attention of
teachers to practice the law of readiness in learning.
To comprehend the concepts of basic mathematical operations is a
significant tool to students performance because it is an
indicatory factor of how far they understood the mathematical
operations. How the students categorize an item according to the
level of difficulty also tells the teacher what topic needs to be
retaught or reinforced. The findings point out that the freshmen
had a difficulty in the operations involving fractions and decimal
numbers. This suggests that they are not yet ready to learn
Mathematics for high school.
Considering the findings of this study, it revealed that the
respondents perform satisfactorily in addition and subtraction but
their performance is less satisfactory in the operations of
multiplication and division. Basing from the aggregate mean, they
have a less satisfactory performance in the basic mathematical
operations. They also found the basic mathematical operations to be
difficult. CHAPTER 1
THE PROBLEM AND ITS SCOPEINTRODUCTIONRationale
In the current education system of the Philippines, Arithmetic
is generally taught by Elementary teachers both in the public and
private schools. The 6-year stage of learning process evolves on
real numbers and complex numbers under the four basic mathematical
operations: addition, subtraction, multiplication and division.
Napoleon Abasolo, the School Principal of Tubod National High
School who is also teaching Math, during the 2009 Math Contest
said: It is alarming that some; if not most of the high school
freshmen in the public schools have difficulty with the basic
operations. On a timed set of examination, they have trouble with
long addition and when challenged with multiplication they result
to using addition instead. A domino effect is observed when one is
unable to master multiplication; he cannot be performing well in
division. This has been the major problem of the high school math
teacher because to reteach Arithmetic will definitely consume time
and effort. Inability of the students to fully grasp the concept of
the four basic mathematical operations implies that they are not
ready to learn higher math.
The NCBTS 2009 Report on the San Fernando academic performance
revealed that high school students in general had a high Mean
Percentage Score in English and Filipino but low in Math.
Moreover, after the three years at San Fernando NHS, this
researcher noticed that the teachers usually commented that most of
the students have difficulty in the four basic mathematical
operations. They can add, subtract, multiply and divide two-digit
numbers; however, when they are presented with longer ones, they
generally ignore them.Determining the level of performance and the
difficulties encountered in the basic mathematics operations as
well as determining if there is a significant relationship between
the two has geared the researcher to conduct her studies at the
said school.Theoretical BackgroundThis study is anchored on Blooms
Theory (1976) which stated that when the students do not know the
basic skills, then it follows that they are not ready to receive
the next step of learning. Learners who mastered the first course
in a subject to a high level have the tendency to learn the
succeeding courses in the same subject to a high level in less time
and with less help from the teacher.
This theory is supported by Bruner (2000) who also stated that
when students fail to master a certain skill, instruction for
another skill is postponed until they are more ready. Math is like
a pyramid. Every new skill requires an understanding of
prerequisites to do well. He added, by the same token, before
learning pre-algebra, a good understanding of basic mathematics is
important. And before learning algebra, a solid understanding of
pre-algebra is a must.That is why high school Math teachers,
especially those who are handling Elementary Algebra expect the
freshmen to be skillful in addition, subtraction, multiplication
and division. Although granted that a three-month review on
Arithmetic is administered, teachers still presume their students
to have functional learning on their previous math lessons
specifically the basic mathematical operations. According to Sidhu,
(2005), Arithmetic was developed out of a need for a system of
counting. It has been considered to be essential for efficient and
successful living. The need of a good command of arithmetic by a
house-wife, by a modern farmer, by a successful merchant, by a
skilled worker, and by a progressive professional man; is too
obvious to need any discussion. Also its utilitarian, cultural and
disciplinary values are too obvious to need any argument at this
stage. The teaching of arithmetic has to fulfill two major
responsibilities: (1) the inculcation of an appreciative
fundamental processes; (2) the socialization of number
experiences.
He also stated that for some years every young learner is
concerned mainly with the so-called four simple rules. Proficiency
in these processes is very important. The student has to depend on
these at all the states of learning mathematics. These are
foundation. It is customary and natural to enable the child to
acquire speed and accuracy in these in the very beginning.
Furthermore, he cited that the most important thing in teaching
these rules is that the preliminary experiences should be given in
an inter-connected form with the help of concrete material.
Ultimately, for the purpose of practice, their teaching will take
abstract form. Their operations have to be taught side by side as
far as possible. The teacher must impress upon the students the
educational values and necessity of the avoidance of errors in
these operations and of their careful execution. He must not allow
any such errors to persist, otherwise the learners later
performance are bound to be defective. The DepEds Basic Education
Curriculum for SY 2010-2011 on Mathematics, mandated that
Mathematics in Grades 1 and 2 should include the study of whole
numbers, addition and subtraction, basic facts of multiplication
and division, basics of geometry, fractions and metric and local
measurements, the use of money and their application to practical
problems on real life activities. Grades 3 and 4 deals with the
study of whole numbers, the four fundamental operations, fractions
and decimals including money, angles, plane figures, measurements
and graphs. In Grades 5 and 6 the child is expected to have
mastered the four fundamental operations of whole numbers, performs
skills in decimals and fractions, conceptualize the meaning of
ration and proportion, percent, integers, simple probability,
polygon, spatial figures, measurement and graphs. However, Brown
(2004) said in his studies that in the typical elementary
classroom, students are expected to learn and master their addition
facts through countless practice problems and rote memorization.
Yet for many teachers, the biggest mathematical frustration is
students not knowing their basic facts. For students, this creates
a problem as the mathematical concepts build on each other and
become more difficult. Students work with applications of new
ideas, yet without a firm grasp of basic mathematics they become
bogged down in the simple computations. The longer students go
without knowing their facts, the longer they struggle through the
related mathematical topics.
Brown (2004) also added that the students who successfully
master their basic mathematics facts quickly are able to create
mental schemes each time they encounter a fact. Although students
as well as adults may not consciously think of it, when we see a
problem like 8 + 5 = 13 we think of some strategy (for example, we
might add 2 to 8to obtain 10, and then add 3 to 10 to get the final
result). As adults, we have mastered these strategies to a point
that we know the solution to a problem instantly because the
strategies are automatic for us.
Escalera (1987) in his study revealed that an error in
computation is one of the major difficulties in the work with
fractions. This could be traced to inadequacy in the basic
combination on the four fundamental processes of Mathematics. He
added that the major difficulties that ran true in all processes
were lack of comprehension of process involved. This was the result
when pre-requisite skills were not drilled to the point of mastery.
This has been supported by Tesorio (1998) in his studies who
affirmed that in Mathematics, if mastery of the basic skills would
not be achieved then one would be confronted with a difficulty in
coping with the higher skills. In like manner, Butler (1965) stated
that students tend to remain interested in those things which they
can do most successfully and which they understand most completely.
Therefore, understanding the concepts of the basic mathematical
operation is important in learning Mathematics because it
determines the interest level of the learners.Eslabon (2003)
recommended that teachers should be encouraged to attend in-service
training activities or seminars and conferences to update their
teaching strategies and they should scholarly assist students in
their activities to help build good foundations and concepts in
Mathematics.
Boaler (2002) further stated that learning happens through
participation in social practices. By including all students in
meaningful interaction within the Mathematics classroom, the
diversity of perspectives and problem solving approaches that
ensues is critical for the intellectual healthy both the classroom
and the disciplines of study as a whole. Teenagers, of course
represent an age group that has challenged adults since the
beginning of time, and that many teachers are finding it more
difficult to reach them. (Kranendonk, 2010)Teachers must also be
able to deliver the subject matter efficiently and effectively. The
truism that one cannot teach a subject effectively unless his
knowledge and understanding go well beyond the scope of that which
he is expected to teach. (Schaaf, 1967)Furthermore, many
researchers have found out that students who feel they have
supportive, caring teachers are more strongly motivated to engage
in academic work than students who do not have. Teachers must
address the attitude of many high school students. In many
Mathematical classrooms, students (especially teenagers) evince
boredom, restlessness and a general inability to pay attention to
details of a teachers lecture. Teachers need to incorporate a more
extensive range of instructional strategies that will provide
opportunities to expand students thinking. (Mayer, 2006)From these
theories, this study intends to assess the level of performance and
the difficulties encountered by the high school freshmen in basic
mathematical operation. THE PROBLEMStatement of the ProblemThe main
purpose of this study is to determine the level of performance in
the basic mathematical operation and the difficulties encountered
by the high school freshmen of San Fernando National High School
for the School Year 2010-2011. Based on the findings, remedial
measures were proposed.
Specifically, it seeks to answer the following questions:
1. What is the profile of the high school freshman as
regards
1.1 gender,
1.2 age,
1.3 grades in Math, and 1.4 school of origin?2. What is the
performance of the high school freshmen under study in the basic
mathematical operations concerning whole numbers, fractions and
decimal numbers in terms of:
2.1 addition,
2.2 subtraction,
2.3 multiplication, and
2.4 division?
3. What are the difficulties encountered by the high school
freshmen in the basic mathematical operation?
4. Is there a significant relationship between the performance
of basic mathematical operation and their difficulties encountered
by the high school freshmen in the basic mathematical
operations?
5. What remedial measures may be proposed to make the high
school freshmen become ready for the Elementary Algebra on the
findings of the research?
Statement of Null Hypothesis
The following null hypothesis was tested in this study:
H0: There is no significant relationship between the high school
freshmens performance and difficulties encountered in the basic
mathematical operations.Significance of the Study
This study would be beneficial to the following:
DepEd. The findings of the study would aid DepEd in improving
the Budgeted Lessons which is the teaching guide of the public
school teachers. San Fernando National High School. The findings of
the research would be influential in achieving an increase in the
Mean Percentage Score (MPS) in Periodical and achievement test from
forty-five percent (45%) to at least seventy-five percent
(75%).
Principals of San Fernando District. In-service trainings topics
are decided by principals and school heads, this study will guide
the principals on which Math lessons are to be included during the
training.
Mathematics Coordinator. This would become a reference for the
Public School Math Coordinators which will guide them to study
methods, strategies and techniques that are likely acceptable to
students. Knowing their performance level and determining the
difficulties would help the coordinators map out the necessary
steps to improve students performance in the basic mathematical
operations. Mathematics Teachers. This would be a helpful tool to
teachers in dealing with students having difficulty in the basic
mathematical operation skills. They will be able to decide which
teaching technique to use as discussed by the Math
Coordinators.
Freshman Students. Knowing the causes of students difficulty in
learning the four basic mathematical operations will be remedied
through a proposed remedial measure. This will then lead to
respondents responsive and participative attitude in Mathematics 1
(Elementary Algebra).
The Researcher. The study would make the researcher
knowledgeable on the causes of students inability to master the
basic mathematical operation skills that will lead her to propose a
remedial measure.
Future Researchers. The study would help future researchers on
the implications and reasons of students inability to master the
basic mathematical operation skills. The researcher suggests that
they look deeper on the reasons why these difficulties occur.
RESEARCH METHODOLOGY
This study made use of the Descriptive Survey Method. Figure 1
shows the research process.
Figure 1. The Research Flow
Research Environment
Figure 2. Location Map of San Fernando National High School
The study was conducted at San Fernando National High School
located in South Poblacion, San Fernando, Cebu. It is alongside the
road going to Tapon, South Poblacion and is at the back of Nexus
Subdivision. Students nearby can walk to school. The common means
for transportation is the famous choppy, a remodeled tricycle.
The 5,000 square meter lot was donated by the Benedictos to
DepEd last 2008. It was August 2009 when the first two classrooms
were constructed. The following year, 4th of January2010, the
studentry and the faculty and staff moved in. The school is under
the 1st Congressional District of Cebu Province along with Sibonga,
Carcar, Naga, Minglanilla and Talisay. Moreover, it is supervised
by Mrs. Laurencia Suening, District supervisor and managed by the
Area Consultant who hails from Barili.
As documented, San Fernando National High School first operated
last 2007 with 150 high school freshmen, because the school
location was yet to be decided, temporarily, the students were
housed at the South Poblacion Barangay Hall. On the following year,
the increase of the students population cited a major problem. The
teachers opted to use the San Fernando Sports Complex just to
accommodate the sophomores. In August 2009, the construction of the
two-room building commenced and on January 4, 2010, San Fernando
NHS moved to its school building.
Most of the students were from South Poblacion proper and the
nearby barangays. It offers First to Third year secondary education
for the time being. Fourth year secondary education will be offered
the next school year. The school is headed by Mr. Precellano Comon,
Head Teacher III. It has three (3) regular/permanent teachers who
are nationally funded and two (2) locally funded teachers whose
compensations are taken from the Government Special Education
Fund.
Research Respondents
The research respondents were the 112 high school freshmen of
San Fernando National High School enrolled this school year
2010-2011 who were taking up Elementary Algebra. Research
Instruments
The tools used in this research were as follows: Teacher-made
Test in Arithmetic, Researcher-made Likert Scale Test and a form
necessary for respondents profile.An hour of Teacher-made
Arithmetic Test on basic mathematical skills was administered in
four days which covered the four basic mathematical operations. The
students were required to write their age and gender as these were
beneficial for the profiling. Each operation had 15-items
subdivided into three test types of 5-items each: Test I - Whole
Numbers, Test II - Fractions and Test III - Decimal Numbers.
The Researcher-made Likert Scale Test was designed to gather
information required for the study to determine the difficulties
encountered in the basic mathematical operations. It is
administered shortly after the high school freshmen had answered
the Teacher-Made Arithmetic Test.
It consisted of 20-items. The respondents were given the
opportunity to identify whether the item is very difficult (4),
difficult (3), easy (2) or very easy (1).The following ranges were
given as the descriptive interpretation of the weighted mean
scores.
Ranges
Interpretation
3.25 4.00
Very Difficult
2.50 3.24
Difficult
1.75 2.49
Easy
1.00 1.74
Very Easy
Research ProceduresGathering of Data. The researcher submitted a
transmittal letter to the School Head of San Fernando National High
School for approval on Nov 17, 2010. The researcher commenced the
research and administered the test on Dec 13, 2010 which culminated
on the 17th.The Arithmetic test was given to students followed by
the Lickert-Scale made test. Treatment of Data. Data collected and
gathered were analyzed using appropriate statistical tool. All
information was tabulated, quantified and appropriate rank-order
scales were given, and then it was analyzed and interpreted
correspondingly using frequency distributions, weighted means,
simple percentages, standard deviation and Chi Square test.
DEFINITION OF TERMSThe following words are defined by the
researcher to provide clarity and substance to the research:
Addition
In this research, addition refers to the process of finding the
total of two or more numbers in whole numbers, fractions and
decimals only.
Basic Mathematical Operations
This covers the four fundamental operations of Math: the
addition, subtraction, multiplication and division.
Difficulties Encountered
These are the levels of difficulties encountered by the freshmen
in the basic mathematical operations. Division
In this research, this refers to the operation of determining
the number of times one quantity is contained in another among
whole numbers, fractions and decimals only.
High School Freshmen
This refers to the respondents.Multiplication
In this research, an arithmetical operation, defined initially
in terms of repeated addition in whole numbers, fractions and
decimals only.
Performance
Performance means the students ability to apply their knowledge
and understanding on the basic mathematical operations.Profile
Refers to the gender, age, grades in Mathematics and school of
originProposed Remedial Measures
This refers to a proposal to remedy the inability of freshman
students to master the basic mathematical operations.
Subtraction
In this research, an arithmetic operation in which the
difference between two numbers is calculated in whole numbers,
fractions and decimals only.CHAPTER 2
PRESENTATION, ANALYSIS AND INTERPRETATION OF DATA
This chapter presents, analyzes and interprets the data on the
profile of the respondents, their performance and the difficulties
encountered in the basic mathematical operations concerning whole
numbers, fractions and decimals, and the significant relationship
between their performance and the difficulties encountered in the
basic mathematical operations. To facilitate presentation and
clarify purposes, the data are presented in tabular form followed
by brief discussions.
PROFILE OF HIGH SCHOOL FRESHMENThe first four tables reveal the
profile of the one hundred and twelve (112) high school freshmen of
San Fernando National High School for the school year 2010-2011.
Table 1 shows the gender of the respondents. Table 2 shows the age
in years. The third and the fourth tables are the grades in Math
for the First and Second grading. A short description on the high
school freshmens school of origin was also provided. Frequencies
are shown with their corresponding proportions in percentages.
These are between or among the identified categories.Gender
Table 1
Distribution of Respondents According to Gender
GenderFrequencyPercentage (%)
Male 6255
Female5045
Total112100
Table 1 shows that of the hundred and twelve (112) respondents,
sixty-two (62) or fifty-five percent (55%) were males and fifty
(50) or forty-five percent (45%) were females. It depicts that
respondents were dominated by males.Age
Normal age for the high school freshmen is at 11 13 years old.
Table 2 shows the distribution of students ages.
Table 2
Distribution of Respondents According to Age
Ages in yearsFrequencyPercentage (%)
17+109
14-163733
11-136558
Total112100
Ten (10) among the high school freshmen aged 17 years and above,
thirty-seven (37) were at the bracket of 13-16 years and sixty-five
(65) were aged 11-13 years. These are equivalent to nine percent
(9%), thirty-three percent (33%) and fifty-eight percent (58%)
respectively. It implies that normal age for high school freshmen
which should be at 11-13 dominates.
Grades in Math
To determine the respondents learning capabilities, the
researcher had requested the school registrar as approved by the
school principal to furnish a copy of the first and second grading
grades of the high school freshmen. These are depicted in Table 3
and Table 4. It is important to consider that the passing grade is
75 and up whereas 70 to 74 is a failing mark.
Table 3
First Grading grades of the Respondents
Mark for the
1st GradingFrequencyPercentage (%)
90-9444
85-8954
80-8487
75-794641
70-744944
Total112100
Table 3 shows the frequencies of the respondents grades during
the First Grading in Math. Four (4) respondents or four percent
(4%) received the mark 90-94. Five (5) respondents or four percent
(4%) were marked 85-89. Eight (8) among them or seven percent (7%)
had a grade of 80-84. Forty-six (46) or forty-one percent (41%)
were marked 75-79. This means that fifty-six percent (56%) passed
during the first grading which leaves to forty-nine students (49)
or forty-four percent (44%) who received a failing mark of
70-74.
Table 4
Second Grading grades of the Respondents
Mark for the
2nd GradingFrequencyPercentage (%)
90-9433
85-8998
80-843632
75-794944
70-741513
Total112100
As presented in table 4, three or three percent (3%) among the
respondents were graded 90-94. Nine respondents or eight percent
(8%) received the mark 85-89, thirty-six or thirty-two percent
(32%) were marked 80-84 and forty-nine (49) respondents or
forty-four percent (44%) had 75-79. Fifteen (15) high school
freshmen or thirteen percent (13%) has a failing mark. This implies
that eighty-seven percent (87%) passed the second grading period, a
positive inclination of thirty-one percent (31%) as compared to
their first grading.
School of origin
All one hundred and twelve (112) high school freshmen or
one-hundred percent (100%) graduated from public schools and none
from private schools.PERFORMANCE ON BASIC MATHEMATICAL
OPERATIONSThe tables 5 to 8 reveal the high school freshmens
academic performance in Mathematics in the basic mathematical
operations concerning whole numbers, fractions and decimals. Four
sets of Teacher-made Test in Arithmetic were administered in four
days. Each questionnaire had two parts. Part 1 determines the
performance of the respondents in the basic mathematical operations
and part 2 identifies the difficulties encountered. This section
will focus Part 1.
Part 1 has a total of 15 items equally divided into three test
types: Whole numbers, Fractions and Decimals. To identify the
categories where the respondents belong, the researcher took the
mean and the standard deviation. There are four categories namely:
Very Satisfactory (VS), Satisfactory (S), Less Satisfactory (LS)
and Poor (P).Addition
Table 5Distribution of the Respondents
According to their Performance in Addition
CategoryFrequencyPercentage (%)
Very Satisfactory (13 15)33
Satisfactory (10 12)8878
Less Satisfactory (7 9)1917
Poor (4 6)22
Total112100
Mean= 9.545SD
= 1.792
Table 5 reveals the distribution of the respondents in terms of
their performance in addition. The categories used were Very
Satisfactory (score ranges from 13-15), Satisfactory (score ranges
from 10-12), Less Satisfactory (score ranges from 7-9) and Poor
(score ranges from 4-6).
The table shows that of the one hundred and twelve (112)
respondents, the majoritys performance in addition was satisfactory
at seventy-eight percent (78%) or eighty-eight respondents.
Nineteen (19) or seventeen percent (17%) belonged to the category
of less satisfactory. There were three respondents or three percent
(3) who performed very satisfactorily and only two respondents or
two percent (2%) had a poor performance.SubtractionTable
6Distribution of the Respondents
According to their Performance in
SubtractionCategoryFrequencyPercentage (%)
Very Satisfactory (12 15)00
Satisfactory (8 11)5549
Less Satisfactory (4 7)4439
Poor (0 3)1312
Total112100
Mean= 8.027SD
= 2.586Table 6 reveals the distribution of the respondents in
terms of their performance in addition. The categories used were
Very Satisfactory (score ranges from 12-15), Satisfactory (score
ranges from 8-11), Not Satisfactory (score ranges from 4-7) and
Poor (score ranges from 0-3).
Table 6 shows that nobody can be categorized as very
satisfactory; fifty-five (55) or forty-nine percent (49%) were
within the satisfactory category; forty-four (44) or thirty-nine
percent (39%) were within the less satisfactory category; and,
thirteen (13) or twelve percent (12%) performed poorly. This show
that majority of the respondents performed satisfactorily in the
mathematical operation of subtraction.MultiplicationTable
7Distribution of the Respondents
According to their Performance in
MultiplicationCategoryFrequencyPercentage (%)
Very Satisfactory (10 12)11
Satisfactory (7 9)109
Less Satisfactory (3 6)6760
Poor (0 2)3430
Total112100
Mean= 5.777SD
= 2.207Table 7 reveals the distribution of the respondents in
terms of their performance in addition. The categories used were
Very Satisfactory (score ranges from 10-12), Satisfactory (score
ranges from 7-9), Not Satisfactory (score ranges from 3-6) and Poor
(score ranges from (0-2).
Table 7 shows that only one or one percent (1%) was categorized
as very satisfactory; ten (10) or nine percent (9%) were
categorized as satisfactory; sixty-seven (67%) or sixty percent
(60%) were categorized as Less satisfactory; and, thirty-four (34)
or thirty percent (30%) were categorized as poor. It means then
that majority of the students did not perform well in
multiplication hence they were categorized as less satisfactory.
DivisionTable 8Distribution of the Respondents
According to their Performance in
DivisionCategoryFrequencyPercentage (%)
Very Satisfactory (9 11)00
Satisfactory (6 8)54
Less Satisfactory (3 5)6457
Poor (0 2)4339
Total112100
Mean= 4.875SD
= 2.027Table 8 reveals the distribution of the respondents in
terms of their performance in addition. The categories used were
Very Satisfactory (score ranges from 9-11), Satisfactory (score
ranges from 6-8), Less Satisfactory (score ranges from 3-5) and
Poor (score ranges from (-1)-2).
As presented in table 8, nobody belonged to very satisfactory
category; five (5) or four percent (4%) belong to satisfactory
category; sixty-four (64) or fifty-seven percent (57%) belong to
Less satisfactory category; and, forty-three (43) or thirty-nine
percent (39%) belonged to poor category. This implied that majority
did not perform well in division.DIFFICULTIES ENCOUNTERED IN BASIC
MATHEMATICAL OPERATIONS
Tables 9 to 12 present the result on the difficulties
encountered by the respondents on the basic mathematical
operations. To determine the difficulties encountered by the
respondents, the researcher made a 20-item Lickert-Scale. Table
9Difficulties encountered by the respondents on Addition
IndicatorsWeighted MeanInterpretation
1. adding one digit number 2.29Easy
2. adding two-digits 2.06Easy
3. adding three-digits2.39Easy
4. adding whole numbers2.52Difficult
5. adding similar fractions2.42Easy
6. adding dissimilar fractions 2.46Easy
7. adding mixed fractions 2.58Difficult
8. adding proper fraction and proper fraction2.68Difficult
9. adding proper fraction and improper
fractions2.71Difficult
10. adding improper fraction and improper
fraction2.69Difficult
11. adding mixed fraction and mixed fraction2.63Difficult
12. addition rules of adding similar fractions2.60Difficult
13. addition rules of adding dissimilar
fractions2.51Difficult
14. adding fractions2.71Difficult
15. adding numbers with one decimal places 2.45Easy
16. adding two decimal places2.53Difficult
17. adding three decimal places2.47Easy
18. adding decimals2.54Difficult
19. addition as a process2.57Difficult
20. general approach to addition.2.64Difficult
Aggregate Mean2.52Difficult
Table 9 clearly shows that the high school freshmen find adding
two-digit number, one-digit number, three digit-numbers, similar
fractions, dissimilar fractions and three decimal places easy. The
ratings were 2.06, 2.29, 2.39, 2.42, 2.45 and 2.47, respectively.
The highest rating of 2.71 was tied between adding fractions and
specifically adding proper fractions with an improper fraction. The
respondents also find the following to be difficult: adding
improper fraction with another improper fraction, adding proper
fraction with another proper fraction, general approach to
addition, adding mixed fraction with another mixed fraction,
addition rules of adding similar fractions, adding mixed fractions,
addition as a process, adding decimals, adding two decimal places,
adding whole numbers and addition rules of adding dissimilar
fractions. It shows that high school freshmen were able to add
whole numbers and that their difficulty were more on fractions and
decimals. Based on the researchers calculated aggregate mean of
2.52, it shows that the majority of the respondents find the
mathematical operation involving addition difficult.
This implies that the Math teacher handling the high school
freshmen must allocate time to reteach the basic rules of adding
fractions and decimal numbers. Hence basic rules involving addition
of fractions and decimal numbers apply in higher math. If students
do not fully understand or grasp the addition concept of fractions
then they could not understand the basics of Elementary Algebra.
The teacher must also reinforce addition of whole numbers.
Table 10Difficulties encountered by the respondents on
Subtraction
IndicatorsWeighted MeanInterpretation
1. subtracting one digit number from one digit
number2.14Easy
2. subtracting two-digit number from two digit
number2.46Easy
3. subtracting two-digit number from three digit
number2.42Easy
4. subtracting three-digit number from three digit
number2.38Easy
5. subtracting whole numbers2.54Difficult
6. subtracting similar fractions2.62Difficult
7. subtracting dissimilar fractions 2.70Difficult
8. subtracting mixed fractions 2.58Difficult
9. subtracting proper fraction from proper
fraction2.80Difficult
10. subtracting proper fraction from improper
fractions2.76Difficult
11. subtracting improper fraction from improper
fraction2.73Difficult
12. subtracting mixed fraction from mixed
fraction2.71Difficult
13. rules of subtracting similar fractions2.85Difficult
14. rules of subtracting dissimilar fractions2.92Difficult
15. subtracting one decimal place number from one decimal place
number2.77Difficult
16. subtracting two decimal places number from two decimal
places number2.71Difficult
17. subtracting two decimal places number from three decimal
places number2.74Difficult
18. subtracting decimals2.61Difficult
19. subtraction as a process2.83Difficult
20. general approach to subtraction.2.87Difficult
Aggregate Mean2.66Difficult
Table 10 shows that of the 20 indicators only 4 of them were
easy according to the high school freshmen. Subtracting one-digit
number from one-digit number got the lowest rating of 2.14.
Subtracting three-digit number from three-digit number had a rating
of 2.39. Subtracting two-digit number from three-digit number and
subtracting two-digit number from two-digit number had a close
interval at 2.42 and 2.46. The 16 indicators were interpreted as
difficult. The indicator that had the highest rating was rules of
subtracting dissimilar fractions at 2.92. This implies that the
freshmen can subtract whole numbers however they have difficulty
with fractions and decimals. The teacher must reteach the basic
concepts on how to subtract fractions starting from similar ones.
The teacher must reinforce the learning through activities and
assignments. If students are doing well in subtracting similar
fractions, then it is ample time to introduce the rules of
subtracting dissimilar fractions hence this is deemed hardest
according to the result. If the high school freshmen have fully
understood the concept of subtracting fractions already, then they
are expected to perform well on subtracting decimals.
The aggregate weighted mean of 2.66 means that the students find
the mathematical operation involving subtraction as difficult.
Table 11Difficulties encountered by the respondents on
Multiplication
IndicatorsWeighted MeanInterpretation
1. multiplying one digit number with another one digit
number2.39Easy
2. multiplying two-digit number with one digit
number2.41Easy
3. multiplying two-digit number with another two-digit
number2.67Difficult
4. multiplying three-digit number with one digit
number2.54Difficult
5. multiplying three-digit number with two digit
number2.51Difficult
6. multiplying whole numbers 2.64Difficult
7. multiplying similar fractions 2.56Difficult
8. multiplying dissimilar fractions2.73Difficult
9. multiplying mixed fraction with mixed
fraction2.76Difficult
10. multiplying proper fraction with a proper
fractions2.71Difficult
11. multiplying proper fraction with and improper
fraction2.61Difficult
12. multiplying improper fraction with another improper
fraction2.65Difficult
13. multiplying fractions2.54Difficult
14. multiplying one decimal place with another one decimal place
2.48Easy
15. multiplying two decimal place with one decimal
place2.64Difficult
16. multiplying two decimal place with two decimal
place2.60Difficult
17. multiplying three decimal place with two decimal
place2.54Difficult
18. multiplying decimals2.54Difficult
19. multiplication as a process2.72Difficult
20. general approach to multiplication.2.78Difficult
Aggregate Mean2.60Difficult
As presented in table 11, only 3 indicators out from 20 were
easy according to the respondents. The least rating of 2.39 was for
the indicator multiplying one-digit number with another one-digit
number. Multiplying two-digit number with one-digit number had a
rating of 2.41 and multiplying one-decimal place with another
one-decimal place had a rating of 2.48. The 17 indicators were
branded as difficult with a highest rating of 2.78 for the
indicator general approach to multiplication.
This table clearly shows that the high school freshmen have the
ability to multiply whole numbers and small value places decimal
numbers however they have difficulty understanding the rules of
multiplying fractions. With a rating of 2.76, multiplying mixed
fraction with another mixed fraction proved to be difficult to
them. This can be eased if the freshmen knew how to change mixed
fractions to improper fractions before they can proceed to
multiplication.
If the freshmen have a sound learning in addition, then it would
have been easier for them to master or at least comprehend the
concept of multiplication. Hence multiplication is just a
duplication or replication of addition.
The aggregate weighted mean of 2.60 meant that the respondents
find the mathematical operation involving multiplication to be
difficult.
Table 12Difficulties encountered by the respondents on
Division
IndicatorsWeighted MeanInterpretation
1. dividing one digit number with another one digit
number2.52Difficult
2. dividing two-digit number with one digit
number2.58Difficult
3. dividing two-digit number with another two-digit
number2.63Difficult
4. dividing three-digit number with one digit
number2.66Difficult
5. dividing three-digit number with two digit
number2.73Difficult
6. dividing whole numbers 2.72Difficult
7. dividing similar fractions 2.80Difficult
8. dividing dissimilar fractions2.84Difficult
9. dividing mixed fraction with mixed fraction2.90Difficult
10. dividing proper fraction with a proper
fractions2.80Difficult
11. dividing proper fraction with and improper
fraction2.79Difficult
12. dividing improper fraction with another improper
fraction2.96Difficult
13. dividing fractions2.77Difficult
14. dividing one decimal place with another one decimal place
2.85Difficult
15. dividing two decimal place with one decimal
place2.79Difficult
16. dividing two decimal place with two decimal
place2.82Difficult
17. dividing three decimal place with two decimal
place2.96Difficult
18. dividing decimals2.83Difficult
19. division as a process2.79Difficult
20. general approach to division.2.81Difficult
Aggregate Mean2.78Difficult
Table 12 clearly shows that of the 20 indicators of the
difficulties encountered by the respondents in the basic
mathematical operations on division, they find all of them as
difficult. The indicators dividing improper fraction with another
improper fraction and dividing three-decimal places with
two-decimal places tied at a rating of 2.96. The table presents
that the freshmen do not understand the concept and the basics of
dividing whole numbers, fractions and decimals. This can be traced
from their less performance in the operations of addition,
subtraction and multiplication. Table 13Chi-square Test on
RelationshipPaired VariableComputed
X2dfc.v at 0.05Significance
Performance and difficulties
encountered77.554916.92Significant
Table 13 presents the results of the test on the significant
relationship between the performance and the difficulties
encountered in the basic mathematical operations. The table shows
that the obtained value of X2 which is 77.554 is greater than the
critical value of 16.92 at 9dfat 0.05 level of significance. It is
clear that there is a significant relationship between the
freshmens performance and the difficulties encountered in the basic
mathematical operations. It also implies that the lesser is the
respondents performance on the mathematical operations, the greater
is the difficulty they have encountered. Thus, the null hypothesis
which states that there is no significant relationship between the
high school freshmens performance and difficulties encountered in
the basic mathematical operations is rejected.
Furthermore, the result supported Blooms Theory which stated
that when the students do not know the basic skills, then it
follows that they are not ready to receive the next step of
learning. Learners who mastered the first course in a subject to a
high level have the tendency to learn the succeeding courses in the
same subject to a high level in less time and with less help from
the teacher.CHAPTER 3SUMMARY, FINDINGS, CONCLUSIONS AND
RECOMMENDATIONS
This chapter provides the summary and findings of the study, and
based upon these findings, a conclusion is drawn.
SUMMARYThe main purpose of this study is to determine the level
of performance in the basic mathematical operation and the
difficulties encountered by the high school freshmen of San
Fernando National High School for the School Year 2010-2011. Based
on the findings, remedial measures will be proposed.
Specifically, it seeks to answer the following questions:1. What
is the profile of the freshman students as regards
1.1 gender,
1.2 age,
1.3 grades in Math, and
1.4 school of origin?
2. What is the performance of the high school freshmen under
study in the basic mathematical operations concerning whole
numbers, fractions and decimal numbers in terms of:
2.1 addition,
2.2 subtraction,
2.3 multiplication, and
2.4 division?
3. What are the difficulties encountered by the high school
freshmen in the basic mathematical operation?
4. Is there a significant relationship between the performance
of basic mathematical operation and their difficulties encountered
by the high school freshmen in the basic mathematical
operations?
5. What remedial measures may be proposed to make the highs
school freshmen become ready for the Elementary Algebra on the
findings of the research?
The research methodology used was the Descriptive Survey Method.
It was conducted in San Fernando National High School, San
Fernando, Cebu. The 112 freshmen were the respondents. The tools
used in this research were as follows: Teacher-made Test in
Arithmetic, Researcher-made Likert Scale Test and a form necessary
for respondents profile.
FINDINGS
After the data were gathered, tabulated, analyzed and
interpreted, the following are the findings of the study:1. The
profile of the respondents as revealed in Tables 1 to 5 are as
follows: 1.1 A majority of the respondents were males.1.2
Two-thirds of the students age was the normal age for first year
high school student which is 12 - 13.1.3 First grading marks of the
students increased on the second grading. 1.4 All of the freshmen
were from public elementary schools 2. Performance of freshmen in
the basic mathematical operation.2.1 Majority of the students have
a satisfactory performance in the basic mathematical operation
involving addition.2.2 Almost half of the number of the respondents
has a satisfactory performance in the basic mathematical operation
involving subtraction.
2.3 Three-fifths of the freshmen have a not satisfactory
performance in the basic mathematical operation involving
multiplication.
2.4 More than half of the freshmen have a not satisfactory
performance in the basic mathematical operation involving
division.
3. Difficulties encountered by the freshmen in the basic
mathematical operations
3.1 On Addition
The freshmen have difficulties in: adding whole numbers, adding
mixed fractions, adding proper fraction and proper fraction, adding
proper fraction and improper fractions, adding improper fraction
and improper fraction, adding mixed fraction and mixed fraction,
addition rules of adding similar fractions, addition rules of
adding dissimilar fractions, adding fractions, adding two decimal
places, adding decimals, addition as a process, general approach to
addition.
3.2 On Subtraction
The freshmen have difficulties in: subtracting whole numbers
subtracting similar fractions, subtracting dissimilar fractions,
subtracting mixed fractions, subtracting proper fraction from
proper fraction, subtracting proper fraction from improper
fractions, subtracting improper fraction from improper fraction,
subtracting mixed fraction from mixed fraction, rules of
subtracting similar fractions, rules of subtracting dissimilar
fractions, subtracting one decimal place number from one decimal
place number, subtracting two decimal places number from two
decimal places number, subtracting two decimal places number from
three decimal places number, subtracting decimals, subtraction as a
process, general approach to subtraction.
3.3 On Multiplication
The freshmen have difficulties in: multiplying two-digit number
with another two-digit number, multiplying three-digit number with
one digit number, multiplying three-digit number with two digit
number, multiplying whole numbers, multiplying similar fractions,
multiplying dissimilar fractions, multiplying mixed fraction with
mixed fraction, multiplying proper fraction with a proper
fractions, multiplying proper fraction with and improper fraction,
multiplying improper fraction with another improper fraction,
multiplying fractions, multiplying two decimal place with one
decimal place, multiplying two decimal place with two decimal
place, multiplying three decimal place with two decimal place,
multiplying decimals, multiplication as a process, general approach
to multiplication3.4 On Division
The freshmen have difficulties in: dividing one digit number
with another one digit number, dividing two-digit number with one
digit number, dividing two-digit number with another two-digit
number, dividing three-digit number with one digit number, dividing
three-digit number with two digit number, dividing whole numbers,
dividing similar fractions
dividing dissimilar fractions, dividing mixed fraction with
mixed fraction, dividing proper fraction with a proper fractions,
dividing proper fraction with an improper fraction, dividing
improper fraction with another improper fraction, dividing
fractions, dividing one decimal place with another one decimal
place, dividing two decimal place with one decimal place, dividing
two decimal place with two decimal place, dividing three decimal
place with two decimal place
dividing decimals, division as a process, general approach to
division.
4. There was a significant relationship between the freshmens
performance in the basic mathematical operations and the
difficulties encountered.CONCLUSIONS
The high school freshmen had a satisfactory performance in
Addition and Subtraction and a less satisfactory performance in
Multiplication and Division and their difficulties encountered were
mostly on the operations involving fractions and decimals.
RECOMMENDATIONS
Based on the findings of the study, the researcher recommends
the following:
1. The high school freshmen can add, subtract, multiply and
divide whole numbers. However, there is a need to reinforce
operations on fractions and decimals. 2. The high school freshmen
need to be taught again by Math 1 teacher the concept of the four
basic mathematical operations stressing the need of the students in
understanding the operations on fractions and decimals. New methods
and strategies should be introduced by the teacher. 3. To adopt the
proposed remedial measures:
a. Teaching seminars and trainings. The researcher finds it
significant for the Math teacher to undergo seminars and trainings
about new methods, strategies and approaches they will use to
reteach the operations on fractions and decimals. b. 2-Hour
Remedial Classes in Basic Mathematics. This will be done during
Saturdays. It will be participated by the high school freshmen. A
topic will be discussed per session and reinforcement will be
given. (See Appendix E) c. Peer-teaching. High school freshmen who
have a satisfactory performance in the basic mathematical
operations are encouraged to teach their
classmates.REFERENCESBooks
Bloom, B. (1976). Human characteristics and school learning.New
York: Wiley McGraw Hill Book Company.
Butler, C. (1965). The teaching of secondary mathematics. New
York: Wiley McGraw Hill Book Company.
Mayer, R. (2006). Learning and instruction. New Jersey: Prentice
Hall.
Schaaf, W. (1967). Basic concept of elementary mathematics.New
York: Wiley.
Sidhu, Kaulbir Singh. (2005). The teaching of mathematics. New
Delhi: Sterling Publishers.
Internet Sources
Bruner, Jerome. (2000). Philosophical insights from Jerome
Bruner. Retrieved October 2010 from
http://www.uk.edu/~eushe2/quotations/bruner.html.
Brown, T. (2004). Helping third grade students with addition
facts. Retrieved October 2010 from
http://www.bsu.edu/web/math/exchange/02-02/brown.pdf.
Boaler, Jo (2002). Experiencing school mathematics traditional
and reform approaches to teaching and their impact on student
learning. Retrieved November 2010 from
http://www.questiaschool.com/read/110691058.
DepEd Elementary (2010). Curriculum in mathematics. Retrieved
November 2010 from
http://www.deped.gov.ph/cpanel/uploads/issuancelmg/Math-Elementary.pdf.
Periodical
Kranendonk, H. (2010, February). Can we make high school more
relevant? Mathematics teachers.pp. 392-393.
Unpublished Materials
Dayonot, J. J. (2001). The intra-extra psychological
difficulties of freshman college in St. Catherine's College: A
difficulty-based skills reinforcement material. Unpublished
master's thesis, Cebu Normal University, Cebu City.
Escalera, A. (1987). Learning difficulties in fractions, grades
V and VI, schools district of Canduay, Division of Bohol,
1986-1987: A proposed remedial teaching program of fractions for
the intermediate grades. Unpublished master's thesis, Cebu Normal
University, Cebu City.
Eslabon, R. (2003). The level of performance in algebra of
freshman education students of West Negros College, school year
2002-2003: Proposed Remedial Measures. Unpublished master's thesis,
University of Cebu, Cebu City.
Tesorio, G. (1998). Learning difficulties in the operations of
basic and algebraic fractions of the freshman computer science
students at the University of Cebu, Cebu City, school year
1997-1998: Implications to curriculum revision, enrichment and
teacher preparation. Unpublished master's thesis, University of
Cebu, Cebu City.
Appendix A-1TRANSMITTAL LETTER November 17, 2010MR. PRECELLANO
C. COMON, M.A., Ed. School Head Teacher San Fernando National High
SchoolSan Fernando, CebuDear Sir:
The undersigned is now writing her thesis entitled PERFORMANCE
AND DIFFICULTIES ENCOUNTERED IN BASIC MATHEMATICAL OPERATION
SKILLS, as required for the degree of Master of Science Teaching
major in Mathematics.
With this view, she would like to request your permission to
allow him to conduct the afore-mentioned study in San Fernando
National High School especially to the freshmen.
Your approval of this request is a step toward the success of
this endeavor and will be beneficial to the academic progress of
your school.
Thank you and God bless!
Very truly yours,
EUNICE L. MANUGAS
MasterandDR. AGAPITO P. PINO JR.AdviserAppendix A-2TRANSMITTAL
LETTER November 17, 2010MRS. CRESCEL SORIANOSchool Registrar San
Fernando National High SchoolSan Fernando, CebuDear Madam:
The undersigned is a masterand of UC Graduate School and who is
now writing her thesis entitled PERFORMANCE AND DIFFICULTIES
ENCOUNTERED IN BASIC MATHEMATICAL OPERATION SKILLS, as required for
the degree of Master of Science Teaching major in Mathematics.
Moreover, the researcher will conduct her study in the San Fernando
National High School especially to the freshmen as approved by the
proposal hearing last November 8, 2010.
It is in this light that she would like to request your good
office an authenticated copy of the first two grading period marks
only in Mathematics I as the basis for evaluating their academic
performance in Mathematics.
Rest assured that the data provided will be handled with
confidentiality and will be used only for this research and will
hold the researcher liable ones it is violated.
Thank you and God bless!
Very truly yours,
EUNICE L. MANUGAS
MasterandDR. AGAPITO P. PINO JR.AdviserAppendix BTHE RESEARCH
INSTRUMENTAdditionWhole numbers, Decimals and FractionsName:
________________________Yr. & Sec.: ___________________Gender:
_______________________Age: ________________________Instruction:
Solve the following basic mathematical operations on whole numbers,
fractions and decimals. Use the back page of the questionnaire for
your solutions.Test I. Addition A. Whole Numbers 1. 4 + 9 =2. 37 +
46 =3. 29 + 22 =4. 972 + 491 =5. 694 + 512 = B. Fraction
1. 2. 3. 4. 5. C. Decimals
1. 49. 5 + 29.6 =
2. 94.68 + 33.79 =
3. 64.09 + 65.68 =
4. 67.618 + 44.408 =
5. 34.133 + 33.846 =
Name: ________________________________________________Note: This
questionnaire is designed to determine the difficulties encountered
by the high school freshmen in the basic mathematical operation
skills. Honesty is requested to obtain accurate answers. This will
not affect grades of the respondents Researcher-made Likert scale
testBelow is a list of attitudes toward the basic mathematical
operation skills. Please encircle the number which corresponds to
the level of difficulty in each of the category. 4 VERY DIFFICULT3
DIFFICULT 2 EASY 1 VERY EASYADDITION - I find 4321
1. adding one digit number 4321
2. adding two-digits 4321
3. adding three-digits4321
4. adding whole numbers4321
5. adding similar fractions4321
6. adding dissimilar fractions 4321
7. adding mixed fractions 4321
8. adding proper fraction and proper fraction4321
9. adding proper fraction and improper fractions4321
10. adding improper fraction and improper fraction4321
11. adding mixed fraction and mixed fraction4321
12. addition rules of adding similar fractions4321
13. addition rules of adding dissimilar fractions4321
14. adding fractions4321
15. adding numbers with one decimal places 4321
16. adding two decimal places4321
17. adding three decimal places4321
18. adding decimals4321
19. addition as a process4321
20. general approach to addition.4321
SubtractionWhole numbers, Decimals and FractionsName:
________________________Yr. & Sec.: ___________________Gender:
_______________________Age: ________________________Instruction:
Solve the following basic mathematical operations on whole numbers,
fractions and decimals. Use the back page of the questionnaire for
your solutions.Test II. SubtractionA. Whole Numbers
1. 9 4= 2. 42 34 =3. 81 12 =4. 783 87=5. 968 439=B.
Fractions
1. 2. 3. 4. 5. C. Decimal Numbers 1. 95.4 82.7 = 2. 94.81 83.17
= 3. 55.14 41.04 = 4. 93.147 92.71 = 5. 93.476 51.873 = Name:
________________________________________________Note: This
questionnaire is designed to determine the difficulties encountered
by the high school freshmen in the basic mathematical operation
skills. Honesty is requested to obtain accurate answers. This will
not affect grades of the respondents Researcher-made Likert scale
testBelow is a list of attitudes toward the basic mathematical
operation skills. Please encircle the number which corresponds to
the level of difficulty in each of the category. 4 VERY DIFFICULT3
DIFFICULT 2 EASY 1 VERY EASYI find 4321
1. subtracting one digit number from one digit number4321
2. subtracting two-digit number from two digit number4321
3. subtracting two-digit number from three digit number4321
4. subtracting three-digit number from three digit number
5. subtracting whole numbers4321
6. subtracting similar fractions4321
7. subtracting dissimilar fractions 4321
8. subtracting mixed fractions 4321
9. subtracting proper fraction from proper fraction4321
10. subtracting proper fraction from improper fractions4321
11. subtracting improper fraction from improper fraction4321
12. subtracting mixed fraction from mixed fraction4321
13. rules of subtracting similar fractions4321
14. rules of subtracting dissimilar fractions4321
15. subtracting one decimal place number from one decimal place
number4321
16. subtracting two decimal places number from two decimal
places number4321
17. subtracting two decimal places number from three decimal
places number4321
18. subtracting decimals4321
19. subtraction as a process4321
20. general approach to subtraction.4321
MultiplicationWhole numbers, Decimals and FractionsName:
________________________Yr. & Sec.: ___________________Gender:
_______________________Age: ________________________Instruction:
Solve the following basic mathematical operations on whole numbers,
fractions and decimals. Use the back page of the questionnaire for
your solutions.Test III. MultiplicationA. Whole Numbers
1. 7 8 =2. 42 9 =3. 49 17 =4. 638 8 = 5. 695 43 =B.
Fractions
1. 2. 3. 4. 5. C. Decimal Numbers1. 70.9 60.3=
2. 95.85 73.4 =
3. 80.65 57.78 =
4. 72.383 67.5 =
5. 93.488 6.71 =
Name: ________________________________________________Note: This
questionnaire is designed to determine the difficulties encountered
by the high school freshmen in the basic mathematical operation
skills. Honesty is requested to obtain accurate answers. This will
not affect grades of the respondents Researcher-made Likert scale
testBelow is a list of attitudes toward the basic mathematical
operation skills. Please encircle the number which corresponds to
the level of difficulty in each of the category. 4 VERY DIFFICULT3
DIFFICULT 2 EASY 1 VERY EASYI find 4321
1. multiplying one digit number with another one digit
number4321
2. multiplying two-digit number with one digit number4321
3. multiplying two-digit number with another two-digit
number4321
4. multiplying three-digit number with one digit number4321
5. multiplying three-digit number with two digit number4321
6. multiplying whole numbers 4321
7. multiplying similar fractions 4321
8. multiplying dissimilar fractions4321
9. multiplying mixed fraction with mixed fraction4321
10. multiplying proper fraction with a proper fractions4321
11. multiplying proper fraction with and improper
fraction4321
12. multiplying improper fraction with another improper
fraction4321
13. multiplying fractions4321
14. multiplying one decimal place with another one decimal place
4321
15. multiplying two decimal place with one decimal place4321
16. multiplying two decimal place with two decimal place4321
17. multiplying three decimal place with two decimal
place4321
18. multiplying decimals4321
19. multiplication as a process4321
20. general approach to multiplication.4321
DivisionWhole numbers, Decimals and FractionsName:
________________________Yr. & Sec.: ___________________Gender:
_______________________Age: ________________________Instruction:
Solve the following basic mathematical operations on whole numbers,
fractions and decimals. Use the back page of the questionnaire for
your solutions.Test IV. C. DivisionA. Whole Numbers
1. 9 0 =
2. 81 3 =
3. 64 16 =
4. 763 6 =
5. 288 36 =
Name: ________________________________________________Note: This
questionnaire is designed to determine the difficulties encountered
by the high school freshmen in the basic mathematical operation
skills. Honesty is requested to obtain accurate answers. This will
not affect grades of the respondents Researcher-made Likert scale
testBelow is a list of attitudes toward the basic mathematical
operation skills. Please encircle the number which corresponds to
the level of difficulty in each of the category. 4 VERY DIFFICULT3
DIFFICULT 2 EASY 1 VERY EASYI find 4321
1. dividing one digit number with another one digit
number4321
2. dividing two-digit number with one digit number4321
3. dividing two-digit number with another two-digit
number4321
4. dividing three-digit number with one digit number4321
5. dividing three-digit number with two digit number4321
6. dividing whole numbers 4321
7. dividing similar fractions 4321
8. dividing dissimilar fractions4321
9. dividing mixed fraction with mixed fraction4321
10. dividing proper fraction with a proper fractions4321
11. dividing proper fraction with and improper fraction4321
12. dividing improper fraction with another improper
fraction4321
13. dividing fractions4321
14. dividing one decimal place with another one decimal place
4321
15. dividing two decimal place with one decimal place4321
16. dividing two decimal place with two decimal place4321
17. dividing three decimal place with two decimal place4321
18. dividing decimals4321
19. division as a process4321
20. general approach to division.4321
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _ _ _ _This section is to be filled in by the school
registrar.1. Did the student graduate from a Public or Private
School? (tick the box of the appropriate answer)
Public
Private
Name of School:
____________________________________________________
2. Academic Performance in Mathematics I
First Grading Period
: _____________________
Second Grading Period: _____________________
_______________________School Registrar Appendix CResults on
Difficulties Encountered for Addition
ADDITION - I find VD4D3E2VE1TotalWM
1. adding one digit number 83648201122.29
2. adding two-digits 102343361122.06
3. adding three-digits203232281122.39
4. adding whole numbers243038201122.52
5. adding similar fractions173244191122.42
6. adding dissimilar fractions 134241161122.46
7. adding mixed fractions 233342141122.58
8. adding proper fraction and proper fraction23364761122.68
9. adding proper fraction and improper
fractions25384181122.71
10. adding improper fraction and improper
fraction23404091122.69
11. adding mixed fraction and mixed fraction213843101122.63
12. addition rules of adding similar
fractions214232171122.60
13. addition rules of adding dissimilar
fractions183839171122.51
14. adding fractions27334481122.71
15. adding numbers with one decimal places 153449141122.45
16. adding two decimal places203345141122.53
17. adding three decimal places173446151122.47
18. adding decimals193644131122.54
19. addition as a process184140131122.57
20. general approach to addition.292939151122.64
Aggregate Mean2.52
Results on Difficulties Encountered for Subtraction
I find VD4D
3E
2VE
1TotalWM
1. subtracting one digit number from one digit
number192031421122.14
2. subtracting two-digit number from two digit
number203338211122.46
3. subtracting two-digit number from three digit
number212840231122.42
4. subtracting three-digit number from three digit
number192842231122.38
5. subtracting whole numbers243139181122.54
6. subtracting similar fractions262749101122.62
7. subtracting dissimilar fractions 24384281122.70
8. subtracting mixed fractions 183945101122.58
9. subtracting proper fraction from proper
fraction29383961122.80
10. subtracting proper fraction from improper
fractions21493661122.76
11. subtracting improper fraction from improper
fraction25403981122.73
12. subtracting mixed fraction from mixed
fraction25393991122.71
13. rules of subtracting similar fractions30393941122.85
14. rules of subtracting dissimilar fractions29473421122.92
15. subtracting one decimal place number from one decimal place
number26413871122.77
16. subtracting two decimal places number from two decimal
places number25364561122.71
17. subtracting two decimal places number from three decimal
places number28354181122.74
18. subtracting decimals213841121122.61
19. subtraction as a process353334101122.83
20. general approach to subtraction.295022111122.87
Aggregate Mean2.66
Results on Difficulties Encountered for Multiplication
I find VD4D3E2VE1TotalWM
1. multiplying one digit number with another one digit
number202742231122.39
2. multiplying two-digit number with one digit
number163736231122.41
3. multiplying two-digit number with another two-digit
number273732161122.67
4. multiplying three-digit number with one digit
number164338151122.54
5. multiplying three-digit number with two digit
number174038171122.51
6. multiplying whole numbers 283432181122.64
7. multiplying similar fractions 213738161122.56
8. multiplying dissimilar fractions27373991122.73
9. multiplying mixed fraction with mixed
fraction18553361122.76
10. multiplying proper fraction with a proper
fractions23414081122.71
11. multiplying proper fraction with and improper
fraction174637121122.61
12. multiplying improper fraction with another improper
fraction25314881122.65
13. multiplying fractions184039151122.54
14. multiplying one decimal place with another one decimal place
144534191122.48
15. multiplying two decimal place with one decimal
place254029181122.64
16. multiplying two decimal place with two decimal
place233540141122.60
17. multiplying three decimal place with two decimal
place194134181122.54
18. multiplying decimals193840151122.54
19. multiplication as a process283637111122.72
20. general approach to multiplication.28364351122.78
Aggregate Mean2.60
Results on Difficulties Encountered for Division
I find VD4D3E2VE1TotalWM
1. dividing one digit number with another one digit
number253427261122.52
2. dividing two-digit number with one digit
number283033211122.58
3. dividing two-digit number with another two-digit
number253439141122.63
4. dividing three-digit number with one digit
number283434161122.66
5. dividing three-digit number with two digit
number333721211122.73
6. dividing whole numbers 293732141122.72
7. dividing similar fractions 27443381122.80
8. dividing dissimilar fractions32393291122.84
9. dividing mixed fraction with mixed fraction33423071122.90
10. dividing proper fraction with a proper
fractions343628141122.80
11. dividing proper fraction with and improper
fraction323829131122.79
12. dividing improper fraction with another improper
fraction413722121122.96
13. dividing fractions313633121122.77
14. dividing one decimal place with another one decimal place
35333681122.85
15. dividing two decimal place with one decimal
place284625131122.79
16. dividing two decimal place with two decimal
place29393951122.82
17. dividing three decimal place with two decimal
place36393341122.96
18. dividing decimals393536121122.83
19. division as a process363033131122.79
20. general approach to division.373228151122.81
Aggregate Mean2.78
Appendix DRelationship between Performance and Difficulties
EncounteredPerformance
CategoryFrequencyPercentage (%)
Very Satisfactory (41 53)65
Satisfactory (29 40)5045
Not Satisfactory (17 28)4641
Poor (4 16)109
Total112100
Difficulties Encountered
CategoryFrequencyPercentage (%)
Very Difficult(229 247)87
Difficult (211 228)4641
Easy (193 210)5247
Very Easy (175 192)65
Total112100
Relationship
PerformanceDifficulties EncounteredTotal
Very DifficultDifficultEasyVery Easy
Very Satisfactory (41 53)00426
Satisfactory (29 40)01334350
Not Satisfactory (17 28)23013146
Poor (4 16)631010
Total846526112
Appendix E
San Fernando National High School
San Fernando, Cebu
Proposed Remedial Classes for the Freshmen Students
of San Fernando National High School
in Basic Mathematical Operations
Title:
This proposed remedial class for the high school freshmen of San
Fernando National High School is entitled, DEVELOPING STUDENTS
MASTERY ON THE FOUR FUNDAMENTAL OPERATIONS OF MATH.
Description:
DEVELOPING STUDENTS MASTERY ON THE FOUR FUNDAMENTAL OPERATIONS
OF MATH is a 2-hour weekend remedial class for 6 sessions and
participated by all high school freshmen and conducted by Math
teachers. A topic will be discussed every session and reinforcement
will be given.Objectives
This proposal aims to enhance the high school freshmens
performance on the basic mathematical operations. More
specifically, after the remedial classes, the high school freshmen
are expected to:
1. Acquire a thorough knowledge on the basic mathematical
operations
2. Comprehend the concept of the basic mathematical
operation
3. Perform satisfactorily in the operations involving fractions
and divisions
4. Become ready for high school mathematics
Scheme of Implementation
In the process of working for the implementation of the proposed
remedial class, the researcher will ascertain that the various
phases of the program will be taken cared of:
Planning. The researcher shall present the result of this study
to the principal of San Fernando National High School and request
that a meeting with the faculty be held in order to discuss the
findings of the research and the implementation of the remedial
class. The meeting should cover the planning of the remedial
measure.
Organizing. The students will be grouped according to section.
Each Math teachers are to follow the program given to them to
administer learning in an hour and an hour of series of activities
and reinforcement.
Supervision. The teachers are to determine their students
performance before they are going to proceed to another topic. They
should see to it that the students have mastered the topic
discussed during the session.
Evaluation. The principal will evaluate the performance of the
high school freshmen on the basic mathematical operations.
ContentSessionTopics
1Rules of Adding and Subtracting Fractions
2Rules of Multiplying and Dividing Fractions
3Long quiz on operations involving Fractions
4Addition and Subtraction of Decimals
5Multiplication and Division of Decimals
6Long quiz on operations involving Decimals
CURRICULUM VITAE
PERSONAL DATA
Name :Eunice Lawas Manugas
Age :26
Date of Birth :Jan 11, 1985
Gender :Female
Civil Status :Single
Nationality :Filipino
Religion:Christian
Permanent Address:291 South Poblacion, San Fernando, Cebu,
Philippines
EDUCATION
LEVELSchool / University Date of Completion
Post Graduate:MST Math
University of Cebu Grad School
Sanciangko St., Cebu City
March 2011
Tertiary:BSED Math
University of Cebu
Sanciangko St., Cebu City
October 2006
Secondary:Notre Dame Academy
South Poblacion, San Fdo., Cebu
March 2002
Elementary:North Central Elementary School
North Poblacion, San Fdo., CebuMarch 1998
SCHOLARSHIP ENJOYED
College :JAASH
CIVIL SERVICE ELIGIBILITIES
LicenseLicense No. Date
1.LET Examination for Teachers0975xxxAug 15, 2007
WORK EXPERIENCE
1.Position:Administrative Assistant
Duration:Aug 2010 present
e-School:Fortress Learning
Location:Brisbane, Australia
2.Position:Faculty Member, Class Adviser, Math Teacher
Duration:Jun 15, 2009 July 1, 2010
School:San Fernando National High School
Location:San Fernando
3.Position:Sales Representative
Duration:Jun 15, 2008 - Jun 1, 2009 (1 yr.)
Organization:iCOMM Phil. Inc.
Location:Lahug, Cebu, Phil.
4.Position:Faculty Vice-president, teacher
Duration:Jun 1, 2007 - Mar 31, 2008 (1 School Year)
School:Notre Dame Academy
Location:San Fernando
5.Position:Technical Service Representative
Duration:Nov. 2006May 2007
Organization:Qualfon Phil. Inc.
Location:Lahug, Cebu, Phil.
SKILLS
1.Hosting
2.Computer/Internet Savvy
3.Sketching
4.Debating
5.Indoor games player
6.Facilitating/organizing events
Profile of the high school freshmen
Performance in basic mathematical operation
Difficulties encountered by the high school freshmen in basic
mathematical operation
Significant relationship between the performance and
difficulties encountered
INPUT
Descriptive Survey Method using Teacher-made Test in Arithmetic,
Researcher-made Likert scale test Gathering of Data
Data processing, analysis and interpretation
PROCESS
Proposed Remedial Measures
OUPUT