Difficulties In Solving Mathematical Word Problem.docx

CHAPTER I THE PROBLEM AND ITS BACKGROUND Introduction “Mathematical problems are really difficult to be solved”. Students do not know how to do it. That is why they do not like the subject especially problem solving as a skill, the more that students hate mathematics when they are given a test in problem solving. However, they cannot avoid this challenge being an important skill to be acquired. In fact, problems are spices in life. So, it is a “must” for us to solve problems to make on life meaningful and fruitful. Problem solving in mathematics is not a topic but a process underlie the whole mathematics programmes which contextually helped concepts and skills to be learned (Ibrahim 1997). It is true that problem solving in mathematics is not a topic but a process on how to solve or deal with mathematical problems. This mathematical problems serves as a guide on how to apply its process in solving our daily life problems. Many mathematical skills are involved in problem solving. Mathematical difficulties are frequently characterized by cognitive deficits such as ineffective problem solving strategies, lack of comprehension and computational fluency. Leongson (2003) reveals that Pilipino students excel in knowledge acquisition but fare considerably low in lessons requiring higher order thinking skills. This disappointing condition is evident in the performance of students in national and international surveys on mathematics and science competencies. The Third International Mathematical Science Study (TIMMS,2000) examined patterns of student’s achievement in mathematics and found out that the school effectiveness 1

and teachers competency impact learning and promote higher level of achievements. In addition, the quality of instruction and effective instructional design are necessary to alleviate problems related to teaching and learning mathematics (Dursun & Dede,2004). In the 21st century, one shifting paradigm in education is about teacher’s role and competencies. Competent mathematics teachers provide a roadmap to guide students to an organized understanding of mathematical concepts, to reflective learning, to critical thinking, and ultimately to mathematical achievement. Problem solving is the real test in mathematical abilities. It concerns understanding of the problem which practically demands reading comprehension. It also requires the appropriate formula that is needed to get what is required. It also requires the proper operation of the numbers/ expressions involved. These are some of the common steps in solving problem. It must be noted that in every problem there is a solution. It is then a challenge for every problem solver to find some ways and measures to find the solution of the problem. Any student who lacks knowledge and skills in solving problem in mathematics in general (Algebra, Arithmetic, Geometry, etc.) will find difficulties in order to arrive the correct solution, thus, this study.

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Statement of the Problem The purpose of this study is to identify students’ difficulties in solving mathematical word problems through a self-made test whose validity and reliability are determined. This study also investigates what teaching strategies are used to foster success tostudents difficulties in solving mathematical word problem. Specifically this study intends to answer the following questions: 1. What is the demographic profile of the student as described in: 1.1 age; 1.2 gender; and 1.3 grade 2. What is the demographic profile of the teachers as described in: 2.1 age; 2.2 gender; 2.3 civil status; 2.4 highest educational attainment; and 2.5 teaching position 3. What are the difficulties of the studentsin solving mathematical word problems? 4.What are the factors that affect students’ difficulty in solving mathematical word problem? 5. What teaching practices that the teacher’s employ in teaching mathematical word problems? 6. What are the strategies used by the students in solving mathematical word problems? 3

Hypothesis of the Study Ho 1: There is no significant difference in the extent of causes in solving problems when the respondents are grouped according to their profile variables.

Significance of the Study The result of this study will be very beneficial to school administrators, teachers, students, parents, researchers and to the researcher herself. To the school administrators, the findings can give them insights to find some measures to improve or enhance teacher’s competence other than themselves. To the teachers, the findings can guide them in determining strategies for the development of their skills in problem solving to be taught/ learned by the students. To the students, the results of this study are their guide to acquire more skills in problem-solving. To the researchers, the result of this study may serve as tool or guide in their research studies. To the parents, this study will serve as a guide to help their children become expose in different world problems to eliminate fears in facing it.

Scope of the Study 4

The research will be conducted to the selected secondary institutions in the Municipality of Siquijor. Particularly the researcher will get ten percent (10%) of the total population of the student-respondents and one hundred percent (100%) of the total population of the teacher-respondents both in the selected public and private secondary education in the Municipality of Siquijor.

Theoretical Framework This study is guided by the Situated Learning Theory of Jean Lave and Etienne Wenger (1990) which is learning in the same context in which concepts and theories are applied.It hinges on the belief that learning is embedded in or connected to the context in which knowledge and skills are developed (Santrock 2004). Snowman and Biehler (2006) maintain that learning is made meaningful when it is anchored on a realistic context because learning cannot be separated from daily routine that keep on acquiring new information every day in life.

According to Aquino (2015), the perspective of situated learning theory is anchored on the idea that knowledge acquisition is focused on problem-solving skills. Situated learning engages students in tasks that are related to real world situations. It stresses the context and application of knowledge instead of memorizing facts and ideas. In addition, Piaget’s foremost contributions was to enhance the understanding of mental development. This would lead to the activities that involve thinking, perceiving and problem-solving. 5

Constructivist approach views learning as a process of constructing meaning which is greatly influenced by the learners’ experiences and understanding. Therefore, constructivist teacher should make the learners construct their own knowledge by connecting lesson to their past experiences

Conceptual Paradigm

INPUT 

Student’s Profile



Teacher’s Profile



Test result in problem

PROCESS



Student’s Strategies in Solving Mathematical

Administration of Test and Questionnaire

solving 

OUTPUT



Tallying



Treatment of Data

 Intervention Program

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Definition of Terms

Figure 1 Conceptual Framework of the Study

Definition of Terms The following terms are defined as the researcher uses it in the study: Difficulties Refers to the obstacles that cause error or mistakes made by students when dealing with mathematical word problems. Mathematical Word Problem

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Refers to mathematical exercises that present relevant information on a problem as text, rather than in the form of mathematical notation Mathematical Skill Refers to the ability to solve mathematical problems Lack Refers to the insufficient skills in solving mathematical problems Average Refers to the normal skills of students in solving mathematical word problems

CHAPTER II RELATED LITERATURE AND STUDIES

Problem-solving is the ability to identify and solve problems by applying appropriate

skills

systematically

(Jabberwocky).

It

provides

students

with

opportunities to use their newly acquired knowledge in meaningful, real-life activities and assists them in working at higher levels of thinking.

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Problem solving has been and will be a necessary skill not only in Mathematics but in everyday living. Part and parcel of problem solving is to translate word problems into mathematical equation. However, students especially in grade school have difficulties in analyzing and interpreting word problems. Students most especially in grade school can easily perform an indicated operation but when this is given verbal forms, students need to first identify what operation is involved by translating this into a mathematical sentence before actually performing the operation and arriving at the correct answer (Dela Cruz and Lapinid, 2014).

Problem solving requires two distinct types of mental skill, analytical and creative. Analytical or logical thinking includes skills such as ordering, comparing, contrasting, evaluating and selecting. It provides a logical framework for problem solving and helps to select the best alternative from those available by narrowing down the range of possibilities (a convergent process). Analytical thinking often predominates in solving closed problems, where the many possible causes have to be identified and analyzed to find the real cause. Lack of mathematical skills caused difficulties in solving problem. Students are required to apply and integrate many mathematical concepts and skills during the process of making decisions and problem-solving. The lacked of mathematical skills among students are varied (Hill 2008).

These mathematical skills are:

i) number fact skill (proficiency of number facts, tables and mathematics principal);

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ii) arithmetic skill (accuracy and logarithm in computational and mathematical working-procedure);

iii) information skill (expertise to connect information to a concept, operational, and experience as well as the expertise to transfer information and transform problems into mathematical sentences.);

iv) language skill (proficiency of terms and relevance of mathematical information);

v) visual spatial skill (skill to visualize mathematical concepts, manipulate geometrical shape and space meaningfully.)

Incomplete mastery of number facts, weakness in computational, inability to connect conceptual aspects of math, in efficiency to transfer knowledge, difficulty to make meaningful connection among information, incompetency to transform information mathematically, incomplete mastery of mathematical terms, incomplete mastery of mathematical language and difficulty to comprehend and visualizing mathematical concept might results to difficulties (Nathan et al. 2002). In addition, lack of commitment to solving problem, misinterpreting the problem, lack of knowledge of the techniques and processes involved in problem solving, inability to use techniques ineffectively, using a method inappropriate to the particular problem and insufficient or inaccurate information lead to the difficulties in solving mathematical word problem and making various errors and confusion in the process of problem-solving.

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Difficulties faced among students were more noticeable during the first procedural step in solving problem compared to the other. Polya (1981) stated that problem-solving is a process starting from the minute students is faced with the problem until the end when the problem is solved. There are many problem solving models.

Problem-solving models Polya (1981)

Krulick&Rudnick (1996)

Zalina (2005)

4- hierarchy phase

5-hierarchy phase

3- hierarchy phase

i) understanding problem;

i) reading and thinking;

i) understanding problem;

ii) planning;

ii) analyze and planning;

iii) performing the plan;

iii) organizing strategy; iii) stating the answer;

iv) confirmation of the

iv) getting the answer;

answer

ii) solving the problem;

v) confirmation of the answer

Each phase involved a different combination of mathematical skills and different cognitive abilities. Stendall (2009), the abilities to give good concentration, to make meaningful perceptions, to think logically and to use memory effectively are important factors in learning skills and solving problems. These abilities vary among students.

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According to Dendane (2009), mathematical problem solving related to counting and daily transactions of commerce has been present from the earliest days of human experience. On the other hand, geometry was also widely used in land measurement [1] Mathematics is now used to quantify numerically and spatially natural as well as man-made situations. It is used to solve problems and with the advent of the computer technology, it has helped in making social, economical and technological advances that few decades ago would have been unthinkable.

Learning mathematical facts and contents is important but is not enough. Students should learn how to use these facts to develop their thinking skills and solve problems. Mathematics educators have accepted the idea that the development of problem solving ability deserves special attention [2] and that one of the most important components in any mathematics curriculum or program is genuine mathematical problem solving. If well facilitated, mathematical problem may help students:

1. develop and improve the generic ability to solve real life problems, 2. develop critical thinking skills and reasoning, 3. gain deep understanding of concepts, 4. work in groups, interact with and help each other.

Mathematical problem solving is a process that involves a set of factors and tasks to achieve a defined goal.

It depends on many skills and factors which

therefore makes it challenging both to learn and to teach.

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Mathematical application is no longer an intellectual exercise for the new nor limited to scientist alone.

It has become an essential part of man’s working

equipment, which provides the best hope for coping effectively with problems in everyday area of life (Parami, et. al., 2016).

According to Uthai in Phonapichat, et. al. (2013), difficulties affecting mathematical problem solving can be classified as: 1) students cannot understand the whole or some parts of the problem due to the lack of imagination and experience needed to consider the problem. 2) Students have difficulties in reading and comprehension, unable to understand what important information is in a problem and organize it accordingly. Thus they cannot invert the text into mathematical symbols. (3) Students lack interest in solving mathematical problems due to the length and complexity of the problems, which is demotivating. 4. Teachers do not present daily life matters as a problems very often.

5) Teachers are likely to make students

memorize “keywords” in the problems to use in formulae. 6) Teachers focus on following examples given in textbooks rather than teaching the principles behind each problem. 7) Teachers teach without concern with thinking process orders.

Related Studies Foreign Studies Meese (2001) said that teachers need to understand students’ potential, problems and learning difficulties in order to implement effective teaching strategy and to produce meaningful learning among students. If learning approaches and teaching strategies applied did not fulfil the intellectual needs of the students these 13

could lead to students’ difficulties in learning mathematics. Aside from that, weakness in understanding concepts, logic-thinking and lacking of strategic knowledge caused errors in problem-solving (Tay Lay Heong 2005). Phonapichat, et. al. (2013) asserts that mathematics teaching is to enable students to solve problems in daily life. It reflects that students have difficulties in comprehending mathematical problems affecting the process of problem-solving. Therefore, in order to allow teachers to establish a proper teaching plan suitable for students’ learning process.

This study aimed to analyze the difficulties in

mathematical problem solving among elementary school students.

The results

suggest that there are several difficulties in problem solving, namely 1) students have difficulties in understanding the keyword appearing in problems, thus cannot interpret them in mathematical sentences. 2) Students are unable to figure out what to assume and what information from the problem is necessary to solving it, 3) whenever students do not understand the problem, they tend to guess the answer without any thinking process; 4) Students are impatient and do not like to read mathematical problems, and 5) Students do not like to read long problems. Therefore, the results found in this research will lead to the creation and the development of mathematical problem solving diagnostic tests for teachers, in order to improve students’ mathematical problem solving skills. Angateeah (2017) conducted a study where it explored the cognitive processes undergone by Mauritian students who have difficulties in solving word problems.

Based on the findings, all students could read the problems.

Achievers (HA) are wrong due to careless errors.

High

While HA demonstrate good 14

problem solving skills, some exhibit overconfidence. Average Achievers suffer from procedural errors while Low Achievers face difficulties mainly in visualizing and representing the problem.

Tambychika, Subahan and Meerah (2010) asserts that problem solving is one of major aspect in mathematics curriculum which required students to apply and to integrate many mathematical concepts and skills as well as making decision.

The findings showed that respondents lacked in many mathematical skills such as number-fact, visual-spatial and information skills. Information skill was the most critical. The deficiency of these mathematics skills and also of cognitive abilities in learning inhibits the mathematics problem-solving. This understanding on how the deficits influenced the problem-solving is expected to give effective guide lines in preparing diagnostic instruments and learning modules in order to develop the mathematics skills.

Local Studies Miranda (2006) stated that children might experience difficulties in thinking and learning when they demonstrated difficulty in giving attention, describing orientation of shape and space, making perception and understanding mathematical language. As a result, students struggle in different phases in the process of problem-solving.

Dela Cruz and Lapinid (2014) examined the students’ difficulties and level of performance in translating worded problems into mathematical symbols. A 20-item 15

problem solving test involving the four fundamental operations was given during the third quarter of the school year 2012-2013 to 2014 Grade 5 students. Scores in this test measured their performance level in translating worded problems while interpretation of their mistakes identified their difficulties in translating word problems. Results indicate that 40% of the respondents are below the satisfactory level in translating worded problems. Carelessness, lack of comprehension, interchanging values, and unfamiliar words are some of the common difficulties encountered by the respondents in translating word problems.

Ganal and Guiab (2014) focused on the problems and difficulties encountered by Bachelor of Elementary Education sophomore students towards mastering learning competencies in mathematics. The problems and difficulties are categorized into personal problems, emotional problems, problems on teacher’s instruction, problems with school adjustment, problems in adjusting to classmates and boardmates, and problems arising from over-extended schedule/workloads for practice in different competitions. The study reveals the findings that in general, the respondents encountered personal problems relating to school expenses, lack of interest and negative attitude towards the subject.

The emotional problems

encountered are excessive stress in doing academic tasks and low self-esteem or not believing in one’s capabilities.

On problems relating to teacher’s instruction, there

are no effective motivation and introduction, and not creative enough to adapt his/her method to the learner’s capability. As to problems with school adjustment, the most frequent are difficulty in adjusting to life/role of a college student, and not doing the tasks well.

The problems in adjusting to classmates/boardmates are how to be 16

accepted by classmates and boardmates, and working effectively with different kinds of

classmates.

With

regard

to

problems

arising

from

over-extended

schedule/workloads for practice in different competitions, the most common problems are too many academic tasks and project assigned, and studying and reviewing too many subjects everyday. Ambut, et. al. (2008) conducted a study on reading and mathematics tutorial based on intervention. The findings show that the respondents were performing very low in reading. After the intervention, out of 26, 6 or 23.1 percent were on frustration level, 13 or 50 percent were on instructional level and 7 or 26.9 percent were on independent level. CHAPTER III RESEARCH METHODOLOGY

This chapter presents the description of the research design, research respondents, and data gathering procedure, validation of questionnaires, research instruments, and statistical tools.

Research Design This research will utilize the descriptive-quantitative method. This study will utilize the descriptive method to know the difficulties of the students in solving mathematical word problems. The descriptive research involves describing, analyzing, and interpreting data. The quantitative method is utilized to measure to

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what extent causes of the difficulties of the students in solving mathematical word problem. Research Locale The research will be conducted to the selected private and public schools in the Municipality of Siquijor. The researcher will get ten percent (10%) of the total population of the student-respondents in the selected private and public secondary institutions in the Municipality of Siquijor and one hundred percent (100%)of the total population of the Mathematics teacher-respondents in the selected private and public secondary institution in the Municipality of Siquijor.

Data Gathering Procedure The researcher will write a letter to the Superintendent in the Division of Siquijor, and the School Director of the Catholic Schools asking permission to conduct a survey about one hundred (100%) of the total population of the Mathematics teacher-respondents in the selected basic education institutions in the Municipality of Siquijor and ten percent (10%) of the total population of the studentrespondents in both selected private and public schools in the Municipality of Siquijor. The researcher herself will conduct the survey and retrieve the questionnaires, tabulate, compute, analyze, and interpret the data.

Validation of Questionnaires

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Research questions will be formulated by the researcher based on the 21st Century Mathematics, by Henry N. Adorna, et.al., Math Power

(Intermediate

Algebra) by A.O. Reyes and Next Century Mathematics Geometry by Jesus P. Mercado, et.al.,(2008). The research questions validated by the experts in the field like the adviser of the researcher. The research questions were checked and were revised. To achieve content-related validity, the researcher will show the research instruments for comments and improvements to experts. The researcher hopes that the comments of the experts will be very helpful for the improvement of the research instruments.

Research Instruments The survey questionnaires have two (2) parts. The first part is on the demographic profile of the student-respondents (which include age, gender, and year level) and teacher-respondents (which include age, gender, highest educational attainment, civil status, length of service, and teaching position). The second part is the survey questionnaire proper. It composed of students’ survey questionnaire and teachers’ survey questionnaire. Statistical Tool The following statistical tools will be applied in the presentation, analysis, and interpretation of the data gathered. 19

1. Percentage The researcher will use the percentage formula (P=

∑𝒇 𝒏

X 100) in getting the

percentage of the demographic profile of the respondents where P= Percentage ∑= Summation f= Frequency n= Total number of respondents 𝑻𝑺

The researcher will use the percentage(P= 𝑻𝑰 X100) in getting the percentage of the scores of the respondents in the questionnaires where: P= Percentage TS= Total score TI= Total number of Items To measure the students’ difficulties when solving mathematical word problems, numerical scaling is provided below.

Scale

Verbal Description

Meaning

96-100

Excellent

Students show excellent skills in solving mathematical word problem starting problem,

from

understanding using

the

appropriate

20

strategies/methods,

visualizing

the

problem, familiarizing problem context, computational skill and the ability to identify the formula to be used to solve the problem. (Score of 5/5) 90-95

Very Good

Students show a very good skills in solving mathematical word problem starting

from

problem,

understanding using

strategies/methods, problem,

the

appropriate visualizing

familiarizing

the

problem

context/computational skill to solve the problem. (Score of 4/5) 85-89

Average

Students

showaverage

skills

in

solving mathematical word problem, using appropriate strategies/methods, visualizing the problem, familiarizing the

problem

content

and

computational skill. (Score of 3/5) 80-84

Good

Students

show

understanding appropriate

good

the

skills

problem,

in

using

strategies/methods,

visualizing the problem, familiarizing 21

problem context, and has a good computational

skill

to

solve

the

problem. (2/5) 75-79

Lack of Understanding

Students show lack in understanding the

problem,

using

strategies/methods,

appropriate

visualizing

the

problem, familiarizing problem context, and lack in computational skill to solve the problem. (Score of 1/5) Below 74

Poor

Students are poor in understanding the

problem,

using

strategies/methods, problem,

appropriate

visualizing

familiarizing

the

problem

contexts and poor in computational skill to solve the problem. (Score 0/5)

2. Weighted Mean The researcher will use weightedmean formula (𝑋𝑤 =

∑𝒇𝒙 𝒏

) in getting the

mean of the extent causes of students’ difficulties in solving mathematical word problem to both students and teachers where Xw = Weighted mean ∑ = Summation 22

f = Frequency x = Weights n = Total number of respondents Likert Scaling The researcher will use Likert Scaling in identifying the extent causes of students’ difficulties in solving mathematical word problems will be rated in the scale of 1 to 5, where 1 is the lowest and 5 is the highest with accompanying verbal description of 5 as strongly agree, 4 as agree, 3 as doubtful, 2 as disagree and 1 as strongly disagree.

3. Chi-square The researcher will use chi-square formula (𝒙𝟐 = ∑

(𝑶−𝑬)𝟐 𝑬

) in getting the

significant relationship between the integration of concepts on history and philosophy by the teachers and their profile where O = Observed frequency E = Expected frequency ∑ = Summation 𝑥 2 = Chi-aquare Formula for E is given below: 𝐸=

𝑆𝑢𝑏𝑡𝑜𝑡𝑎𝑙 𝐴(𝐵) 𝐺𝑇

23

Where GT= Grand Total

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Presented during DLSU

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Problems

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students.

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An analysis of

school students’ difficulties in mathematical problem solving.

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World

Conference

on

Educational

Sciences.

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