MST_MATH_Thesis - Performance and Difficulties Encountered in Basic Mathematical Operations

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 (%)




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 (%)




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 (%)




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


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


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


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


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


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


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




Not Satisfactory (17 28)4641

Poor (4 16)109

Total112100

Difficulties Encountered


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



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

Documents

MST_MATH_Thesis - Performance and Difficulties Encountered in Basic Mathematical Operations