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Math: Mathematics and Pupils

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Mathematics is one of the most important parts of a child’s education, since it can impact every aspect of their later lives, including other subjects they may study in the future, such as astronomy or biology. All of us have encountered numbers because of its importance in the real world. Mathematics plays a vital role in the modernization of this civilization. It is everywhere and affects the everyday lives of people. Nature talks to us in the language of mathematics, that is numbers, mathematical rules and equations help us to make sense of the world around us.(The Book of Popular Science, 2002). According to the New Book of Knowledge, 2006, mathematics is the study of numbers, and counting, and measuring, but that is only the beginning. Mathematics involves the study of number patterns and relationship, too.” It is also a way to communicate ideas and perhaps more than anything. It is a way of reasoning that is unique to human beings. Learning mathematics implies living in the world of numbers knowing its concept and strengthening.

Learning the basic concepts of addition and subtraction is the foundation of mastering math. The Four Fundamental Operations are Addition, Multiplication, Subtraction and Division. These four fundamental operations form the basis of the whole study of mathematics and numerical science. These operations form all the other operations that we use in the above specified subjects. So they are called Fundamental Operations because they can’t be derived either in the terms of themselves or any other operator..(Research and Development Institute, Inc. 2006) It is important that students will be equipped with the basic mathematical skills specifically on the four basic operations on whole numbers, fractions and decimals and be aware of its importance to one’s life. In the landmark study showing the impact of basic skills on adult earning, Richard Murname and Frank Levy conclude that the mastery of skills taught in schools at an early grade level is an increasingly important determinant of subsequent wages.

The skills and knowledge students learn in school is correlated with the success later in life.. Basic skills on fundamental operations in fraction, whole numbers and decimals are very necessary to advance in math. Insisting that master computation skills is not to advocate that they should stop at the basics. Basic skills are a floor, not a ceiling. Students must learn the four fundamental operations so that they can move on to more demanding mathematics. An emphasis on the basics should never be used as an excuse to straightjacket students or to slow their progress in the math curriculum. If students have a firm grasp of the fundamentals of math, he will be able to learn more advanced mathematical processes far more easily. Having good math skills will ultimately save time and reduce the need to need remediation. Fundamentals are needed to move on; not having this foundation will result in more time spent on working things that the student should already know. Early success is the beginning of future success.

Since our world is a mathematical world, it logically follows that establishing the simple math skills early on through the heart and desire of the teacher to love and working with it, by doing it one would become an instrument in eradicating number illiteracy in this generation. One of the most common weaknesses of our school children today is ineffective numerical ability. It appears that they are weak not only in fundamental operations such as addition, subtraction, multiplication and division in common and decimal fractions. This inability to solve computational and manipulative problems also contributes to their failure to solve mathematical problems and constitute a strong deterrent to the teaching of problem solving. Inadequate mastery of the four fundamental operations is probably one of the main causes of difficulty encountered by individuals of all ages in dealing with anything of a mathematical in nature.

The source of complaints among teachers in teaching problem solving on four fundamental operations has been the inability to solve mathematical problems due to lack of mastery of the basic fundamental operation on whole numbers. Gabule(2003) emphasized in her study that lack of prior or poor background on the subject leads to student’s poor performance. Hence, since mathematics is sequential, knowledge of its basic skills is necessary. Due to the desire of the researcher to know the mastery level of the four fundamental operations in problem solving among grade five pupils in Lagonglong District, hence this study will be conducted. Conceptual Framework

The Mastery of the four fundamental operations on fractions and decimals is a must for elementary learners. These are tools for them to understand better and love Mathematics as a subject and help children apply in their daily activities. Specifically the need to achieve the mastered skill on four fundamental operations on fractions and decimals is very important prerequisite before one can proceed to solve word problems in Mathematics. For the past twenty years, problem solving has been touted as a primary focus for mathematics instruction at all grade levels (National Council of Supervisors of Mathematics, 1978; National Council of Teachers of Mathematics, 1980, 1989, 2000) A problem-solving model is a systematic approach that reviews student strengths and weaknesses, identifies evidence-based instructional interventions, frequently collects data to monitor student progress, and evaluates the effectiveness of interventions implemented with the student. Problem solving is a model that first solves student difficulties within general education classrooms.

If problem-solving interventions are not successful in general education classrooms, the cycle of selecting intervention strategies and collecting data is repeated with the help of a building-level or grade-level intervention assistance or problem-solving team. Rather than relying primarily on test scores (e.g., from an IQ or math test), the student’s response to general education interventions becomes the primary determinant of his or her need for special education evaluation and services (Marston, 2002; Reschly & Tilly, 1999). Problem Solving is a powerful means to develop the ability to think and indispensable when it comes to achieving a good education. A student, who solves mathematical problems quickly and efficiently, is ready to apply those experiences to solve new problems of everyday life, with the same efficiency and effectiveness.(Cabunoc, 2012)

Figure 1. Schematic Model Showing the Interplay of the Independent and Dependent Variables of the Study

Statement of the Problem
This study aims to find out the problem solving skills of Grade Five Pupils in all schools in the District of Lagonglong, School Year 2012-2013.

Specifically, this study will intend to answer the following questions:
1. What is the mastery level on four fundamental operations in fractions, and decimals of Grade V Pupils in Eleven Schools of Lagonglong, District.
2. What is the level of knowledge among Grade V pupils of Eleven Schools in Lagonglong, District in problem solving along the areas of: 2.1. Adding and Subtracting Similar and Dissimilar Fractions with and without regrouping

2.2 Multiplying fraction
2.3. Adding and Subtracting Decimal Numbers
2.4. Multiplying and Dividing Decimal Numbers
2.5. Finding the percentage, rate, and base
3. Is there a significant relationship between the performance level in problem solving involving fractions, ,decimals and percent on the mastery level on four fundamental operations on fractions and decimals and percent, particularly in mastery level in adding and subtracting similar and dissimilar fractions with and without regrouping, multiplying fraction and mixed numbers, finding the base, percentage and rate.

4. Based on the findings of the study, what learning activity package will be made? Hypothesis

Based on the above stated problem the following null hypotheses will be tested at .05 level of significance. Ho1 :There is no significant relationship between the skills in problem solving using the four fundamental operations on fractions, decimal, percentage and mastery level in adding and subtracting similar and dissimilar fractions with and without regrouping, multiplying fraction and mixed numbers, finding percentage, rate, and base Scope and Limitation of the Study

This study will be limited in finding out the mastery level on fundamental operations in problem solving in Mathematics among Grade Five pupils in Seven Schools of Lagonglong, District, School Year 2012-2013. Problem Solving was limited to the areas in fractions, decimals and percent. The independent variables such as the mastery level on four fundamental operations of fraction, decimals and percent believed to have influence with the problem solving performance. The findings of the research will be limited to the sample grade five pupils. Significance of the Study

The researcher believes that the results of the study will be useful in several ways.
First, the study can be useful to teachers and other people involved in mathematics education because it will provide data as to the performance of the grade five pupils in problem solving. Second, knowing the common weaknesses committed by the children will generate awareness on the part of the administrators and teachers and in turn provide more time in doing activities that will lead to the mastery of basic fundamental operations of fractions, decimals and percent.

Third, for curriculum planners, they can have a clear guide as to the aspects in mathematics which will need enrichment and careful planning to meet the demands of time. Definition of Terms
For better understanding of this research, the following terms which will be used in this study are hereby defined.
Addition of Whole Numbers. This phrase refers to a mathematical operation of getting the sum of two or more addends.
Decimals Numbers. This refers to the phrase taken to mean the grade five lessons involving decimal numbers.
Division of Decimals. This is a mathematical operation of finding the quotient of two decimal numbers.
Fraction. This refers to the expression containing one integer written above another with horizontal line between them. The upper number is called numerator and the lower number is called denominator. The numerator and denominator are called terms of fractions.

Fundamental Operations. These are addition, subtraction, multiplication, division
Multiplication of Fractions. This is a mathematical operation of finding the products of two of two fractions.
Mathematics. This is a science that deals with the systematic treatment of magnitude, relationship between figures and forms, and relation between figures and forms, and relation between quantities expressed symbolically and supported by facts and principles.

Problem Solving. This refers to involves more than merely finding solutions or the verbal problems presented in the textbooks (Spencer as cited by Lagrimas, 1990:352). In this study it is taken to mean mathematical problems for grade five pupils.

Pupils. This refers to the grade five children enrolled seven schools comprising central and non- central schools in District of Lagonglong, Lagonglong, Misamis Oriental.
Whole Numbers. These are sets of counting numbers that start from one and go on in their natural order. This number does not contain a fraction and a decimal.

Chapter 2
This chapter presents a review of relevant information from books, periodicals and unpublished studies that have effects on Mathematics
education and are related to the present investigation. This literature will deal about the mastery level on four fundamental operations in problem solving. Related Literature and Studies in Foreign Setting

The mastery of four fundamental operations is a must for an elementary learners. These are tools for them to better understand and appreciate Mathematics as a subjects and help them in their day to day activities. A learner needs to sharpen his computation skills on basic operations through varied exercises and drills. Fractions, decimals and percent are some areas in problem solving which are observed to be less mastered by the elementary learners. Low mastery level in performing fundamental operations contributed to the low performance of pupils working on problem solving .Curriculum must prepare children to become effective problem solvers (Burns, 2000). Problem solving requires mastery on four fundamental operations on the part of the students in order to give solution and arrive at correct answer. Parents and teachers have direct influence to the students.

There is a need for them to work hand in hand in developing the problem solving skills necessary for his future survival. Suydam (2001) stated that problem solving is the foundation of all mathematical activity. In order to function in our complex and challenging society, people need to be able to solve a wide variety of problems. The elementary Mathematics curriculum must prepare children to become effective problem solvers( Burns, 2000) Although problem solving is an integral part of all Mathematics, many students struggle with solving problems. In fact student’s ability to solve word problems falls below their ability to compute.(Burns, 2000). Research shows that this discrepancy is not because children have poor computation or reading skills but because children do not know how to choose the correct operation to apply to the problem.

Varied studies conducted by the Mathematics Education Research (MER) as well as Aron(2004), Schoeberger and Liming (2001) cited some causes of student’s inabilities to effectively solve multi-step problems involving mathematical vocabulary and higher- order cited numerical operations as well as factors that contribute to student’s weakness in thinking skills. A very good point cited by Jones and Morgan (2007) is that developing thinking enables learners to gain a deeper understanding of topics, to be more critical about evidence. To think flexibility and to make reasoned judgements and decisions rather than jumping to conclusions. These qualities in thinking are needed both in school and in the wider world. Learners need to develop a repertoire of thinking strategies to be drawn on when encounter new situations. Swets(2003) stressed that the formation of mathematical concepts in the minds of learners can take place at these several events of cognitive involvement. These levels differ in their intellectual demands and lend themselves as a basis for establishment of specific objectives or goals for individual classroom lessons.

Writing and problem not only deepen students understanding, they also help students apply and relate the Mathematics they learned in the classroom to the real world(Aber;2000 Albert& Antos, 2000).

Problem solving is present in several aspects of mathematical activities, from games to real life problems. Leitze and Melser (2005) said that if students were able to connect what they have learned inside the class with the events outside, they were able to maintain and appreciate information better.

If students are able to see Mathematics as interesting and exciting, it is important that they see the relevance between Mathematics and their everyday life (Albert & Antos, 2000). Teachers can nurture intellectual excitement by connecting reading, writing to real life experiences through tasks and activities that have a problem solving- solving focus. Adams (2003) followed that” doing Mathematics is reading Mathematics.” Because it is the word symbols and numerals that give Mathematics its substance and framework, these same words, symbols and numerals must be used to communicate the problem solution to students so that students can use them to perform procedures, solve problems and explain processes. Sometimes , students are quick to only look at the numbers and then put operation symbols between them in one- step problem. These students are rushing into finding a calculation ( Lee, 2007).

Lee(2007) wrote articles explaining their findings of how mathematical technology affects students being able to translate word problems into algebraic terms using numbers and symbols. She reflected on the problem solving process and instrumental strategies that may improve student success in the Math classroom such as modeling and reflection. Thomson and Shackow (2005) highlighted that the National Council of Teachers of Mathematics (NTCM) stressed the importance of confidence, interest, perseverance, and curiosity in learning Mathematics. The recommendations encourage teachers to replace emphasizing low- level computation with active classrooms focusing on higher- level thinking. Several researchers have found that positive attitudes can increase the tendency of individuals to select Mathematics courses and consider careers in Mathematics related fields. Page (2003) stated that number of students of all ages fail to demonstrate proficiency in problem solving and do not have the skills necessary to solve mathematical- related problems in their everyday lives or in their future work situations. Related Literature and Studies in Local Setting

In the classroom setting, students are faced with more challenges as they accomplish academic tasks requiring the comprehension of reading materials written or in case of Philippines, in the third language(Manaay, 2007) Bigornia (2000), in her study, claimed that pupils’ background and communication skills were found to have highly significant relationship with pupil’s mathematical achievement and educational attainment of parents, and reading comprehension skills of the pupils had affected Mathematics achievement. However, there was no significant evidence seen to show significant relationship between pupil’s skills in Mathematics and the pupil factors such as mother’s educational attainment and family annual income. As pointed by Bigonia (2000), teacher competence was found to have highly significant relationship with student’s Mathematics achievement.

Dicdican (2007) pointed out that pupil’s performance lies on the expertise of a teacher. Applied to classroom setting, expertise connotes the effectiveness of the teacher to attain the objectives of the lesson, the willingness of the teacher to provide varied learning activities to the pupils for interactive/ cooperative learning, and the initiative of the teacher to ask questions that develop critical thinking skills. Solano- Flores (2003) stressed that Mathematics learning must be accursed. Students must know first how to add and subtract before they can learn how to multiply and divide, and must learn multiplication and division before learning ratio. In addition, as students’ progress in Mathematics, content and textbooks become more difficult. They added that Math vocabulary not commonly used in daily settings is technical in nature, and is narrowly defused. Language is also as essential part of Mathematics construct because language is an indispensable tool in Mathematics. In the study of Olavides (2000), the finding revealed that manipulative approach made the children positive attitude and resulted in high achievement in Mathematics.

On the other hand, Costa (2001) said that intelligent human beings learn from experience. When confronted with a new and perplexing problem, they will draw forth experiences from their past. They call upon their store of knowledge and experiences as sources of data to support theories to explain or processes to solve each new challenge. Several researcher conducted studies in order to cause of the pupil’s inability to solve problems. Some studies included here were conducted and it was conducted and it was found out that the difficulties on problem solving correlated the skills that begin from the elementary grade and its relationship with reading achievement. The difficulties felt by the high school students reflect what they had been taught in the elementary grades. Capili (1999) cited in her research that difficulty in problem solving is caused by the inability of the pupil to understand situation, their failure to determine the process and the lack of masters of the basic facts in solving the fundamental operations.

Some failures are brought about by pupil’s carelessness in computations. She also concluded that mastery of the subject matter prescribed for each grade was far from being satisfactory. It has been observed that grade six pupils were weak in operations involving integer, fractions and decimals. They lack complete mastery of the basic facts in addition, subtraction multiplication and division. Several studies attempted to evaluate the mathematical difficulties of high school students in problem solving and analysis. And it was found out that the most common weakness of high school students then was ineffective numerical ability. Students were weak not only in the fundamental operations such as addition, subtraction, multiplication and division but also in decimal fraction. According to Bautista (1977), pupils relatively underachievers in problem solving due to their limited due to their limited exposure to word problems in mathematics and their ability to comprehend the problems in mathematics. When given the problems to solve, pupils in intermediate grades cannot decide whether they are going to add, subtract, multiply or divide. The aforementioned related literature and studies of the other researchers have provided further significant insights and important information in this study.

This chapter will deal with the methods used in the study. It includes the following sections: the instruments, data collection and statistical treatment of the data. Research Design

This study will include descriptive evaluative method of research. The descriptive method emphasizes the present condition of the phenomena under study, describes the current situation determining the nature of the prevailing practices This design provides descriptive information of the demographic nature of the population/ respondents considered in this study. This study includes a detailed description, recording, analysis and interpretation of the data gathered. Research Profile

This study will be conducted all schools of Lagonglong District, Lagonglong, Misamis Oriental for school year 2001-2012. Seven schools are directly headed by head teachers and four schools are headed by principals and district supervisor. Respondents of the Study

The population of this study will be the Grade V pupils of the eleven (11) schools of Lagonglong District. The schools are Lagonglong Central School, Dampil Elementary School, Kabulawan Elementary School, Tabok Elementary School, Kauswagan Elementary School, Umagos Elementary School, Lumbo Elementary School, Gasto Elementary, C. Gadrinab Elementary, Manaol Elementary, Kamansi Elementary. These eleven schools consist of 466 grade 5 pupils. With that population, a total of 215 will be selected as respondents of the study. The number of respondents per School is shown in Table 1 below.

The Sampling Procedure
The population of this study will be the grade five pupils of the eleven schools of District of Lagonglong, Lagonglong, Misamis Oriental. The distribution of the population is shown in Table 1 above.

As shown in Table 1, there are 466 grade five pupils from eleven schools and to have an idea on the sample size, the Slovin Formula (1960) below is to be used. n = ______N__________
1 + N(e) 2
Where: n= sample size N= population size e= desired margin of error pegged at 0.05 level
For this formula, out of 466 population, there 215 grade five pupils served as the minimum number of respondents.
To determine the sample schools the simple random sampling procedure will be adopted and the respondents of this study will be determined through sampling proportionate to size population per school. Table 1 shows the computation of the number of respondents per school. Research Instruments

To gather the necessary data, a researcher will formulate a Mathematics problem solving test to get the mastery level of pupils on four fundamental operations on fractions, decimals and percent to determine the skills of the grade five pupils in eleven schools. The questionnaires are so designed to generate information which has relevance to the present study.

The problem solving test will ask questions that calls for problem solving analysis as what are given, what is asked, what operation will be used, what is the number equation and the solution. The topics to cover will be fractions, decimals, and percent. This test will consist of 10 items and is distributed as follows 4 items for fraction and 4 items for decimal and 2 items for percent.

Validity and Reliability Research Instrument
The construction of the problem solving test for grade five will be based on the Basic Education Curriculum ( Philippine Elementary Learning Competencies). This test will use questions which are easy to understand by the pupils.

The researcher will prepare the Table of Specification to guide the researcher in the distribution of items in each content area.
The test on determining the mastery level on fundamental operation on fractions, decimals and percent will be designed base on PELC for grade five. Data Gathering Procedure

Before administering the research instruments, the researcher will secure a written permit from the Schools Division Superintendent of Misamis Oriental to allow him to float her questionnaire and to gather pertinent data. After being granted with permit, the researcher will personally administer the questionnaires. The researcher will see to it that prior instructions are understood by the Mathematics teacher and the pupils. Immediately after the questionnaires are answered they will be retrieved, checked, tabulated and analyzed by the researcher himself. Categorization of Variables

The problem solving test will be scored by giving one point for every correct answer.
The variables used in this study will be treated in the following manner: A. Independent variables

Mastery Level
86%-96%Closely Approximating Mastery(CAM)
66%-85%Moving Towards Mastery(MTM)
35%-65%Average Mastery(AM)
15%-34%Low Mastery(LM)
5%-14%Very Low Mastery
0%-4%Absolutely No Mastery(ANM)
B. Dependent variables
Analysis of the Problem
Fraction and Decimal
The number of correct answers will be analyzed using the measure which will be categorized in the following manner: 1. Fraction and Decimals
19 -Very Good
17-18 -Good
15 –16 – Passing
14 and below- Needs Improvement

2. Percent
9.31 – 10.00- Excellent
8.71 – 9.30- Very Good
8.01 – 8.70- Good
7.50 – 8.00- Passing
7.49 and below- Needs Improvement

Statistical Treatment
The study will employ the following statistical treatment data: The level of knowledge in problem solving involving fractions, decimals will be interpreted and analyzed through the use of mean and standard deviation. The Pearson Product Moment Correlation ( r) with the formula below will be adopted to determine the Significance in pupil’s skills in problem solving and the their mastery level on four fundamental operations in fraction, decimals and percent. r=NΣX – ΣXΣY[NΣX2 -(ΣN)2 ][NΣX2 -ΣY2 ]

Where: r – correlation
X -mean
Y – variable
N – number of cases
Σ -summation


A. Books
The New Book of Knowledge , 2006
Research and Development Institute, Inc., 2006
Keenedy, Leonard. Guiding Children’s Learning of Mathematics. California, Wadsworth Book, 1984 Charles, R.I. and Mason, R.P.Problem Solving Experiences in Mathematics. Addison Wesley Publishing Company, 1985. The Book of Popular Science. 2002

Dolan, D.T. and Williamson, J. Teaching Problem Solving Strategies, Addison Wesley Company, 1983 The Grolier Encyclopedia. Vol.1. Connecticut: Houghton Miffin Co., 1980 Van Cleaves, Janice. Mathematics for Every Kids. New York: Jon Wiley and Sons, 1991 B. Unpublished Studies

Alingig, Emmanuel B..” Computational Skills in Decimals of Grade V Pupils in City Central School, Cagayan de Oro City S.Y. 2001-2001. Unpublished Thesis, Xavier University, 2007 Ballenas, Gilbert J. “ Computational Skills in Fractions and decimals of Grade V Pupils, Xavier University, SY 2009-2010.Unpublished Master’s Thesis Xavier University, 2010 Taucan, L.H. (2007). “ Teacher’s Competence and Student’s Performance in Elementary Mathematicsin the Catholic Schools of Iligan City” Thesis. St. Michael’s College, Iligan City. Capili, Lina N.(1999). Problem Solving Skills in Mathematics among the Grade V Pupils of El Salvador District, Misamis Oriental, SY 1998-1999. Cabunoc, Emere S. (2012). Reading Comprehension and Common Errors in Mathematical problem Solving Committed by the Grade Four Pupils in Central Schools in the Eastern Part of the Division of Misamis Oriental C. Journals/ Periodicals and Magazines

Swetz, Frank J. (2003). Teaching Mathematics to Children. Quezon City:
Office of Research and Publications, Ateneo de Manila University Lee, Q.N. (2006). “Math Anxiety”. The Philippine Journal of Education, Vol. 85, No. 4
p. 155. Dicdican, R.C. (2007) “The Role of Classroom Teacher in developing Critical Creative Thinking in Mathematics among School children.” The Modern Teacher, Vol. LVI No. 4 p. 135 Arellano, Renato . Teach Mathematics the Meaningful Way.The Filipino Teacher, September., 1983 D. Internet Sources

Lending Club. The Importance of Basic Math Skills 2008
Kilpatrick, Kelly. Become A Teacher in Florida
http://wik.ed.uiuc.edu/index.php/Problem_solving-Elementary_level http://www.poweroften.ca/

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