CHAPTER I
INTRODUCTION
1.1. Background of the Study
Mathematics has been a struggle for those students or even any other person who hates it,
or to those persons who doesn’t put their interest in it, and of course, for the passive learners. “I
hate Math’’, “Mathematics is very difficult”, “I don’t know how to deal with it”, “I don’t like
Math”. These are some of those statements that we can hear from students whenever they are
asked about their Math subject. They are having hard times in dealing with this, especially in
problem solving, understanding word problems, and remembering mathematical methodologies.
Mathematics has been a part of our lives and will continues to be a part. It is important to
understand and literate every aspect in this subject. According to Hill (2008)“Mathematics is
seen as a language” which means, like a language, it was used in our daily lives.
Math requires deductive reasoning, and passive learners often struggle with this kind of
active problem solving. Students with memory and attention problems also may struggle since
both skills are necessary for Mathematical aptitude(Maria Ocadiz, 2008).
Mathematics is the science of numbers and their operation, measurement,
transformations, generalizations, quantities and even shapes. Having a difficulty even one of
Math’s branches is a very hard problem.
Mathematics problem solving is not a topic but a process that underline the whole
mathematics programs which contextually helped concepts and skills to be learned. Many
students struggled to accomplish mathematics especially in problem solving however, they still
need to learn mathematics because of its importance in daily life. (Ibrahim, 2001).
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According to Hill (2008), they must be able to solve problem because problem solving is
important for the development of human competencies. In real life, students need to solve
problems because that is a basic way to survive in our daily lives and mathematics is seen as the
language. The primary and secondary mathematics curriculum emphasized on arithmetic,
problem solving, communication, mantic-thinking, connection building and technology
application skills. Mathematics skills such as language number fact, information and arithmetic
are vital in problem solving. Deficiency in any of these skills could cause difficulties in
mathematics skills among students.
It was therefore this study was conducted to know the difficulties experienced by the
Senior High School Students of Ave Maria College in Mathematics and what made this subject a
struggle to them. And to determine the possible ways of how they can somehow lessen their
difficulties experienced. The researchers’ observation is based on their subjects, the General
Math, Business Math and Pre-Calculus in the first semester as well as the “Statistics and
Probability” in second semester for the Grade-11 Students. They have seen and observed that
majority of the students are having a hard time in performing mathematical activity.
The study focused on Grade-11 Students of Ave Maria College. The researchers’ interest
brought them to study about the factors and difficulties of the students in learning the subject and
how it can be assessed by the students themselves and by their instructors help.
1.2. Statement of the problem
The study aimed to analyze the difficulties of Grade-11 Students at Ave Maria College in
learning Mathematics.
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This study was conducted to find answers to the following specific questions:
1. What are the common difficulties encountered by the students in learning Mathematics as
revealed by:
1.1 Student-respondents?
1.2 Teacher-respondents?
2. What are the reasons students give why learning Mathematics is difficult?
3. What measures undertaken by the students and teachersto overcome the difficulties of the
students in learning the subject?
4. What measures need to be taken by the students and teachers in order to make the
learning of Mathematics easily and fun?
1.3. Objectives of the Study
The study aimed to determine the difficulties of the randomly selected Grade-11 Students
at Ave Maria College in Mathematics.
The purposes of this research are the following:
1. To identify the difficulties encountered by the said students.
2. To know what were the reasons that the students give why learning Mathematics is
difficult.
3. To determine the measures undertaken by students and teachers in order to overcome
those difficulties experienced by the students in learning the subject.
4. To assess the measures needed to be taken by the students and teachers in order to make
the learning of Mathematics easily and fun.
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1.4. Significance of the Study
This research can help the students who are having their difficulties in Mathematics
specifically the Grade-11 students of Ave Maria College, especially in understanding word
problems, problem solving, computing, and other difficulties that students are facing. Also for
the teachers who are handling Math subject, they can use this as their guide for teaching for this
can be their basis of how they will instruct and teach the students as well as giving the problems
properly to the students so that they can understand and can solve without any struggle.
1.5. Scope and Delimitations of the Study
This study involves the randomly selected Grade-11 Students who are officially enrolled
at Ave Maria College in the school year 2018-19. The researchers conducted their research at
Ave Maria College, Vallesville-Fatima, Liloy Zamboanga del Norte. That determines the
difficulties of the student-respondents which are the randomly selectedGrade-11 Students of Ave
Maria College in learning mathematics.
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It covers the Difficulties in Mathematics and what made it difficult for them, it identified
what are their actions undertaken, and determined the measures need to be undertaken both by
the students themselves and the teachers to make these difficulties easy and fun. The interviews
results sees the struggles of the selected student in learning the subject and determined the
measures need to be taken to overcome the difficulties experienced by the students.
1.6. Definition of Key Terms

Passive learner- is someone who is not engaged in the learning process.

Mathematics skills- a skill of an individual related to computing numbers, and
understanding mathematics terminologies.

Cognitive skills-is a term referring to an individual’s ability to process to (thoughts) that
should not deplete on a large scale in healthy individuals. It is defined as "the ability of
an individual to perform the various mental activities most closely associated with
learning in problem solving.

Difficulty- a problem or degree of difficulty
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CHAPTER II
REVIEW OF RELATED LITERATURE AND STUDIES
2.1.Review of Related Literature
2.1.1. Computational Weaknesses
Students might experience computational weaknesses in the course of their math
assignments and exams. Examples of computational weaknesses include carrying the wrong
number during multiplication or division, transporting the wrong number when writing down the
final answer, writing numbers in the wrong column during long division or even misreading
signs and symbols. Math teachers award marks for each question for applying the right formula,
showing the correct workings and coming up with the right answer. Students who commit
computational errors lose marks on the workings and answers. Incomplete mastery of basic
number facts, such as the multiplication tables, simple addition and subtraction, is a common
problem for math students. Number facts are the building blocks for learning math and are
necessary for understanding more complex concepts. For example, algebra requires students first
to sort out basic equations before finding the value of the letter.
2.1.2. Inattentiveness
Students need to be highly attentive during class and when completing assignments and
exams to excel in mathematics. Students who fall to pay proper attention to detail and double
checked their work before submission often score poorly. Memorizing instead of understanding
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mathematical principles also causes difficulties for students, especially when they are unable to
remember the exact steps used to solve a problem. As a result, students who regularly practice
answering math problems are better off than those who do not questions accurately and
methodically
2.1.3. Memory Ability
Some students lack well-developed mental strategies for remembering how to complete
algorithmic procedures and combinations of basic facts. However, strategies to improve
capacities for remembering facts, formulas, or procedures can be taught. Repetition games such
as calling out fact combinations and having students solve them and then repeat those that were
called before their turn can help. For example, the teacher would call out “3 X 5 = 15 and a
student would respond with “15.” That student would then ask a number question such as “7 - 5"
of the group. The responder would reply, “3 X 5 = 15 and 7- 5 = 2.” The game continues as each
player calls out a new fact and each responder answers with all the previous combinations and
the new answer. Students’ ability to organize their thinking and use it to recall data will affect
success throughout the curriculum.
2.1.4. Attention Span
Students may be mentally distracted and have difficulty focusing on multistep problems
and procedures. Dealing with long-term projects or a number of variables or pieces of
information at one time can interfere with achievement. Effective teachers should use attention
getters such as drawings and learning aids. Students who work in pairs can help each other stay
on task.
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2.1.5. Understanding the Language of Mathematics
Students are confused by words that also have special mathematical meaning, such as
“volume,” “yard,” “power,” and “area.” Lack of understanding of mathematical terms such as
“divisor,” “factor,” “multiple,” and “denominator” seriously hampers students’ abilities to focus
on and understand terms and operations for algorithms and problem solving. Memorizing these
terms without meaning and context is not productive.
2.1.6. Environmental Factors
When the Mathematics content being taught is unconnected to student’s ability level and
experiences, serious achievement gaps may result. This situation may occur if students are absent
frequently or transfer to another school during the academic year. A student may find the
mathematics curriculum to be more advanced or paced differently than what was being taught in
the previous school. Without intervention strategies, students could remain “lost” for the duration
of their education. To few life experiences, such as trips to neighborhood stores or opportunities
to communicate with others about numbers through practical life examples, can make math
irrelevant for students. Gaps exist, therefore, not only in the curriculum but between the learner
and perceived usefulness of the subject matter.
2.1.7. Learning Disabilities
Learning disabilities are common source of difficulty in understanding mathematics.
Students who suffer from dyscalculia, for example, generally have a problem with numbers and
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arithmetic. They usually have problems recognizing numbers and matching them with amounts,
comparing numbers and mastering number relationships, comprehending sequences and even
making accurate estimations. Such students might also have difficulties understanding math
vocabulary and are unable to process word problems in mathematics.
2.1.8.Personal or Individualized Factors
Some students believe that their mathematical achievement is mainly attributable to factors
beyond their control, such as luck. These students think that if they scored well on a mathematics
assignment, they did so only because the content happened to be easy. These students do not
attribute their success to understanding or hard work. Their locus is external because they believe
achievement is due to factors beyond their control and do not acknowledge that diligence and a
positive attitude play a significant role in accomplishment. Students might also believe that
failure is related to either the lack of innate mathematical inability or level of intelligence. They
view their achievement as accidental and poor progress as inevitable. In doing so, they limit their
capacity to study and move ahead (Beck, 2000; Phillips & Gully, 2007).
2.1.9. Dyscalculia Factors
According to the “LDA of California and UC Davis M.I.N.D. Institute “Q.U.I.L.T.S.”
(2001-2002), individuals with this kind of Learning Disability may also have poor
comprehensions of math symbols, may struggle with memorizing and organizing numbers, have
difficulty telling time, or have trouble with counting. This can be identified in a person if
symptoms are recognized , there are such: Shows Difficulty understanding concepts of place
value, and quantity, number lines, positive and negative value, carrying and borrowing. Has
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difficulty understanding and doing word problems. Has difficulty sequencing information or
events, exhibits difficulty using steps involved in math operations, shows difficulty
understanding fractions, is challenged making changes and handling money, displays difficulty
recognizing patterns when adding, subtracting, multiplying, or dividing, has difficulty
understanding concepts related to time such as days, weeks, months, seasons, quarters and etc.
and exhibits difficulty organizing problems on the page, keeping numbers lined up, following
through on long division problems.
2.1.10. Making Connection
Some students have difficulty making meaningful connections within and across
mathematical experiences. For instance, a student may not readily comprehend the relation
between numbers and the quantities they represent. If this kind of connection is not made, math
skills may be not anchored in any meaningful or relevant manner. This makes them harder to
recall and apply in new situations.
2.1.11. Difficulty Comprehending the Visual and Spatial Aspects and
Perceptual Difficulties
A far less common problem and probably the most severe is the inability to effectively
visualize math concepts. Students who have this problem may be unable to judge the relative size
among three dissimilar objects. This disorder has obvious disadvantages, as it requires that a
student rely almost entirely on rote memorization of verbal or written descriptions of math
concepts that most people take for granted. Some mathematical problems also require students to
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combine higher-order cognition with perceptual skills, for instance, to determine what shape will
result when a complex 3-D figure is rotated.
2.1.12. Incomplete Understanding of the Language of Math
For some students, a math disability is driven by problems with language. These children
may also experience difficulty with reading, writing, and speaking. In math, however, their
language problem is confounded by the inherently difficult terminology, some of which they
hear nowhere outside of the math classroom. These students have difficulty understanding
written or verbal directions or explanations, and find word problems especially difficult to
translate.
2.1.13.Difficulty Transferring Knowledge
One fairly common difficulty experienced by people with math problems is the inability
to easily connect the abstract or conceptual aspects of math with reality. Understanding what
symbols represent in the physical world is important to how well and how easily a child will
remember a concept. Holding and inspecting an equilateral triangle, for example, will be much
more meaningful to a child than simply being told that the triangle is equilateral because it has
three equal sides. And yet children with this problem find connections such as these painstaking
at best.
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2.2. Related Foreign Studies
Buan (1997) tested other variables possibly related to mathematics achievement and
attitude. It was aimed to compare the effects of cooperative and individualistic instructions on
student's achievement in mathematics and their attitude towards the subject. It was found that
there is a significant difference in the pre-test and posttest scores of the cooperative group in the
achievement test and attitude scale. In the individualistic group there is a significant difference in
the pre-test and post-test achievement scores only but there is no significant change in attitude
scores. Angay's (1998) research work on pupils' difficulties in basic operations involving fraction
concluded that the pupils performed poorly in the four fundamental operations of fractions.
Moreover, the finding showed that there is a significant difference between the pupils'
achievement and their parents' educational attainment. According to Lucero (1999), parental
involvement was significantly correlated with both pupils' mathematics achievement and
attitudes. Mathematics achievement was significantly correlated with both father's education and
mathematics attitudes; while mathematics attitude was significantly correlated with parents'
monthly income. Bigornia (2000) determined the factors affecting the mathematical proficiency
level of Grade VI pupils. Teacher competence, pupils' background and communication skills
were found to have highly significant relationship with pupils' mathematics achievement.
According to the study of H.J. Sherman and Y.J. Yard, students fall below their expected
level of mathematics achievement for a variety of reasons. When asked why they were not as
successful in learning mathematics, many people reply that they “never understood math,” or
“never liked it because it was too abstract and did not relate to them.” These reasons and others
can be categorized, in general, as environmental, personal or individualized factors.
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A major component of the child-centered, systematic teaching approach is content. The
discipline of mathematics presents many challenges to dissimilar learners. Mathematics has often
been termed the "gatekeeper" of success or failure for high school graduation or career success.
It is essential that "mathematics become a pump rather than filter in the pipeline of American
education". A lack of sufficient mathematical skill and understanding affects one's ability to
make critically important educational, life, and career decisions.
2.2.1. Curricular Materials
Spiraling the curriculum provides opportunities for learners to deal with content
developmentally over time. Concepts can be built upon and related to previous learning
throughout the curriculum as students become more proficient and experienced in mathematics.
However, it is critical that the same content not be taught year after year, in almost the same
manner of delivery. Students who do not "get it" the first time are not likely to "get it" the next
several times it is taught in the usual manner. Moreover, underachieving students are frequently
assigned repetitious and uninteresting skill-and-drill work each year in order to teach them "the
basics." This type of work often represents a narrow view of mathematical foundations and a low
level of expectation of students' abilities. It limits opportunities to reason and problem solve.
2.2.2. The Gap between Learner and Subject Matter
When Mathematics’ content being taught is unconnected to students' ability level and/or
experiences, serious achievement gaps result. This situation may occur if students are absent
frequently or transfer to another school during the academic year. A student may find the
mathematics curriculum to be more advanced or paced differently than what was being taught in
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the previous school. Without interventions strategies, students could remain "lost" for the
duration of their education.
Too few life experiences, such as trips to neighborhood stores or opportunities to
communicate with others about numbers through practical life examples, can make math
irrelevant for students. Gaps exist, therefore, not only in the curriculum but between the learner
and perceived usefulness of the subject matter.
Lack of understanding of mathematical terms such as "divisor," "factor," "multiple," and
"denominator" seriously hampers students' abilities to focus on and understand terms and
operations for algorithms and problem solving. Memorizing these terms without meaning and
context is not productive.
According to S.P. Gurganus -Pearson Allyn Bacon Prentice Hall, Development of
Cognitive Structures Related to Mathematics. As children develop cognitively from pre-lingual
and pre-symbolic stages to the use of language and symbols to manipulate concepts, their
abilities related to later mathematics learning are also developing. Some of the most critical
cognitive abilities for mathematics learning are memory, language skills, and the ability to make
mental representations of number and space.
2.2.3.Assessments in Mathematics Classroom
Assessment that enhances mathematics learning becomes a routine part of ongoing
classroom activity rather than an interruption. Assessment does not simply mark the end of a
learning cycle. Rather, it is an integral part of instruction that encourages and supports further
learning. Opportunities for informal assessment occur naturally in every lesson. They include
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listening to students, observing them, and making sense of what they say and do. Especially with
very young children, the observation of students' work can reveal qualities of thinking not tapped
by written or oral activities. In planning lessons and making instructional decisions, teachers
identify opportunities for a variety of assessments. Questions like the following become a regular
part of the teacher's planning: "What questions will I ask?" "What will I observe?" "What
activities are likely to provide me with information about students' learning?" Preparation for a
formal assessment does not mean stopping regular instruction and teaching to the test. Instead,
for students, ongoing instruction is the best preparation for assessment. Similarly, for teachers,
ongoing assessment is the best foundation for instruction.
Assessment that enhances mathematics learning incorporates activities that are consistent
with, and sometimes the same as, the activities used in instruction. For example, if students are
learning by communicating their mathematical ideas in writing, their knowledge of mathematics
is assessed, in part, by having them write about their mathematical ideas. If they are learning in
groups, they may be assessed in groups. If graphing calculators are used in instruction, they are
to be available for use in assessment.
Students' classroom work, along with projects and other out-of-class work, is a rich
source of assessment data for making inferences about students' learning. Many products of
classroom activity are indicators of mathematics learning: oral comments, written papers, journal
entries, drawings, computer-generated models, and other means of representing knowledge.
Students and teachers use this evidence, along with information from more formal assessment
activities, to determine next steps in learning. Evidence of mathematics learning can be found in
activities that range from draft work, through work that reflects students' use of feedback and
15
helpful criticism, to a polished end product. Continuous assessment of students' work not only
facilitates their learning of mathematics but also enhances their confidence in what they
understand and can communicate. Moreover, external assessments support instruction most
strongly when classroom work is included. When classroom work, the teacher's judgments, and
students' reflections are valued parts of an external assessment, they enhance students'
mathematics learning by increasing the fit between instructional goals and assessment.
2.2.4. Difficulties in Mathematics Skills and Problem-solving
Lack of many mathematics skills caused difficulties in solving problem. Students are
required to apply and integrate many mathematical concepts and skills during the process of
making decision and problem-solving. Garderen (2006) stated deficiency in visual-spatial skill
might cause difficulty in differentiating, relating and organizing information meaningfully.
However, the lacked of mathematics skills among students are varied (Hill 2008; Kaufman 2008;
Berch & Mazzocco 2007; Garderen 2006; Osmon et al. 2006; Garnett 1998; Nathan et al. 2002).
This study looked into five types of mathematics skills. i) number fact skill (proficiency of
number facts, tables and mathematics principal); 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 the expertise to transfer
information and transform problems into mathematical sentence); 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, inefficiency to transfer knowledge, difficulty to make meaningful connection among
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information, incompetency to transform information mathematically, incomplete mastery of
mathematical terms, incomplete understanding of mathematical language and difficulty in
comprehend and visualizing mathematical concept might result in difficulties (Garnett 1998;
Nathan et al. 2002). These could lead to making various errors and confusion in the process of
problem-solving. Conceptual understanding and procedural knowledge are essential to skills in
problem solving (Geary 2004). These skills should be supported by cognitive systems that
control focus and interference in information processing. Apart from that, language and visualspatial skills are also important to interpret and to manipulate information effectively in the
working memory. Any obstacle at any levels could lead to difficulties in the process of problemsolving. The difficulties could become cumulative with time. Although, theoretically the age of
eleven years old and upwards is the age of formal-operational phase but it varies according to the
cognitive maturity. This could influence the degree of difficulties in spite of pedagogical,
affective, physiology and psychosocial factors (Dacey & Travers 2006; Carnine 1997).
Theoretically, based on Geary (2004) and Garnett (1998), lacked in mathematics skills that could
cause difficulties in mathematics especially in problem-solving might be due to interference in
cognitive abilities. Below is the theoretical framework of the study
2.2.5. Problem Solving
Problem-solving is categorized into two aspects; i) how the problems are deliveredlinguistic (using words) or nonlinguistic (using graphic or problem based); and ii) the
illumination of the problem structure – information, objective and action-plan (Zhining et al.
1995). According to Ibrahim (1997), there are two main procedural steps in problemsolving: i)
transforming the problem into mathematical sentences; and ii) computation of the operational
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involved in the mathematical sentences. 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. The three phase problem solving process consists of; i)
reading and understanding problem ii) organizing strategy and solving problem iii) confirmation
of the answer and process. Each phase involved a different combination of mathematical skills
and different cognitive abilities. In this study, cognitive abilities of learning were limited to the
ability to focus, to make perceptions, to use logic, to memorize and to recall. According to
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. Cognitive and psychological factors could
affected the ability to use mathematics skills and thinking in problem-solving. 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 by visual and auditory, memorizing simple things and understanding language. As a
result, students might struggle in different phases in the process of problem-solving. According
to Goldin (1998), support systems such as verbal-syntax, imaging, mathematics notation,
planning, organizing & controlling and affective systems are critical aspects in problem-solving.
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2.2.6. Working Memory and Field Dependency
It is commonly agreed that learning with understanding is more desirable than learning
by rote. Understanding is described in terms of the way information is represented and structured
in the memory. A mathematical idea or procedure or fact is understood if it is a part of an
internal network, and the degree of understanding is determined by the number and the strength
of the connections between ideas. When a student learns a piece of mathematical knowledge
without making connections with items in his or her existing networks of internal knowledge, he
or she is learning without understanding. Learning with understanding has progressively been
elevated to one of the most important goals for all learners in all subjects. However, the
realisation of this goal has been problematic, especially in the domain of mathematics where
there are marked difficulties in learning and understanding. The experience of working with
learners who do not do well in mathematics suggests that much of the problem is that learners
are required to spend so much time in mathematics lessons engaged in tasks which seek to give
them competence in mathematical procedures. This leaves inadequate time for gaining
understanding or seeking how the procedures can be applied in life. Much of the satisfaction
inherent in learning is that of understanding: making connections, relating the symbols of
mathematics to real situations, seeing how things fit together, and articulating the patterns and
relationships which are fundamental to our number system and number operations. Other factors
include attitudes towards mathematics, working memory capacity, extent of field dependency,
curriculum approaches, the classroom climate and assessment. In this study, attitudes, working
memory capacity and extent of field dependency will be considered. The work will be
underpinned by an information processing model for learning. A mathematics curriculum
framework released by the US National Council of Teachers of Mathematics (NCTM, 2000)
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offers a research-based description of what is involved for students to learn mathematics with
understanding. The approach is based on “how learners learn, not on “how to teach”, and it
should enable mathematics teachers to see mathematics from the standpoint of the learner as he
progresses through the various stages of cognitive development. The focus in the present study is
to try to find out what aspects of the process of teaching and learning seem to be important in
enabling students to grow, develop and achieve. The attention here is on the learner and the
nature of the learning process. What is known about learning and memory is reviewed while the
literature on specific areas of difficulty in learning mathematics is summarised. Some likely
explanations for these difficulties are discussed. Attitudes and how they are measured are then
discussed and there is a brief section of learner characteristics, with special emphasis on field
dependency as this characteristic seems to be of importance in learning mathematics. The study
is set in schools in Nigeria and England but the aim is not to make comparisons. Several types of
measurement are made with students: working memory capacity and extent of field dependency
are measured using well-established tests (digit span backward test and the hidden figure test).
Performance in mathematics is obtained from tests and examinations used in the various schools,
standardized as appropriate. Surveys and interviews are also used to probe perceptions, attitudes
and aspects of difficulties. Throughout, large samples were employed in the data collection with
the overall aim of obtaining a clear picture about the nature and the influence of attitudes,
working memory capacity and extent of field dependency in relation to learning, and to see how
this was related to mathematics achievement as measured by formal examination. The study
starts by focussing on gaining an overview of the nature of the problems and relating these to
student perception and attitudes as well as working memory capacity. At that stage, the focus
moves more towards extent of field dependency, seen as one way by which the fixed and limited
20
working memory capacity can be used more efficiently. Data analysis was in form of comparison
and correlation although there are also much descriptive data. Some very clear patterns and
trends were observable. Students are consistently positive towards the more cognitive elements
of attitude to mathematics (mathematics is important; lessons are essential). However, they are
more negative towards the more affective elements like enjoyment, satisfaction and interest.
Thus, they are very realistic about the value of mathematics but find their experiences of learning
it much more daunting. Attitudes towards the learning of mathematics change with age. As
students grow older, the belief that mathematics is interesting and relevant to them is weakened,
although many still think positively about the importance of mathematics. Loss of interest in
mathematics may well be related to an inability to grasp what is required and the oft-stated
problem that it is difficult trying to take in too much information and selecting what is important.
These and other features probably relate to working memory overload, with field dependency
skills area being important. The study identified clearly the topics which were perceived as most
difficult at various ages. These topics involved ideas and concepts where many things had to be
handled cognitively at the same time, thus placing high demands on the limited working memory
capacity. As expected, working memory capacity and mathematics achievement relate strongly
while extent of field dependency also relates strongly to performance. Performance in
mathematics is best for those who are more field-independent. It was found that extent of field
dependency grew with age. Thus, as students grow older (at least between 12 and about 17), they
tend to become more field-independent. It was also found that girls tend to be more fieldindependent than boys, perhaps reflecting maturity or their greater commitment and attention to
details to undertake their work with care during the years of adolescence. The outcomes of the
findings are interpreted in terms of an information processing model. It is argued that curriculum
21
design, teaching approaches and assessment which are consistent with the known limitations of
the working memory must be considered during the learning process. There is also discussion of
the importance of learning for understanding and the problem of seeking to achieve this while
gaining mastery in procedural skills in the light of limited working memory capacity. It is also
argued that positive attitudes towards the learning in mathematics must not only be related to the
problem of limited working memory capacity but also to ways to develop increased field
independence as well as seeing mathematics as a subject to be understood and capable of being
applied usefully.
2.3. Related Local Studies
A study conducted in Lanao del Norte by Caliao (2000) aimed to determine the factors
associated with the pupils' ability to solve problems in mathematics by associating pupils'
mathematics achievement with the following factors: home environment, quality of mathematics
instruction received by the pupils, pupils' attitude towards mathematics, mental ability, and
reading comprehension ability. The factors identified to be significantly associated with the
pupils' mathematics achievement were the following: fathers' education, neighbours, friends and
relatives who took care of the child, buying things of educational value, teachers' profile such as
number of math seminars attended, number of years in teaching math, number of awards
received, lesson plan preparation, teachers' activity like conducting review classes, coaching
during math competitions, encouraging and supporting pupils to participate in math competitions
and the number of skills taught, mothers' hours spent at home and at work, mental ability, and
reading comprehension.
Montecalvo (2000) assessed the problem solving skills and attitude in Mathematics of
Grade Six pupils in Linamon District, Division of Lanao del Norte during the school year 199922
2000. Results show that majority of the pupils had average performance in problem solving skills
along fractions, decimals, and percentage. Likewise, they had a fair attitude level towards
mathematics and perceived that mathematics is useful for problems in everyday life.
Furthermore, significant relationship existed between pupils' performance in problem solving
skills test and type of school as well as pupils' average grade in Mathematics. Finally, no
significant relationship existed between pupil’s performance in problem solving skills test and
the following pupil-related factors, namely: family income, size of family, and attitudes toward
mathematics.
Cañete's (2002) study determined the teacher and pupil factors affecting problem solving
difficulties in mathematics. It concluded that pupils had satisfactory performance in basic skills
test and fair attitude toward Mathematics but low performance in Problem solving achievement
test. A significant relationship existed between pupils' problem solving skills in Mathematics and
some teacher factors, namely, educational qualification, and possession of master's units/degree,
specialized training, performance rating and strategies in teaching math. No sufficient evidence
was seen to show significant relationship between pupils' skills in Mathematics and the pupil
factors, mothers’ educational attainment and family annual income.
Silva et al (2006) investigated the factors associated with non-performing Filipino
students in mathematics in selected accredited schools in the Philippines (private and public
institutions from Metro Manila and provinces). Results showed that, though the students have
average mental ability, they encounter difficulties attributed to reading deficiencies and learning
styles.
Lee-Chua (2006) discussed efforts spearheaded by various groups to develop a successful
problem-solving culture. “We have learned to focus on certain critical variables”. According to
23
the researcher, these variables include: extensive parental support, early exposure, mental
toughness, excellent master teachers, and good textbooks.
Alvaera, Bayan, & Martinez (2009) of De LaSalle University, Manila, conducted study
intended to determine whether parental involvement and autonomy (mothers and fathers), and
teaching approach can predict public school students’ achievement as measured by the general
average grades of students. In determining which variable has a significant relationship with
student achievement, it showed that mother involvement was significantly related with the
students' academic achievement.Of all the predictors of achievement used by the researchers, it
was only mother involvement that had significantly predicted student achievement. This does not
mean that teaching approach, father involvement, father autonomy and mother autonomy does
not contribute in predicting achievement. This simply implies that their contribution in the
achievement of the students is not as significant as compared to the contribution of mothers'
involvement. The current study focuses on academic achievement as measured by the general
average grade of the student from the previous grading period. It has been well established how
academic achievement is influenced by a particular factor. Parents' involvement in the child's
schooling like assisting the child's in making their assignments explains much the grade of the
child. It was concluded in the study that only mother involvement can predict students'
achievement.
Rondez (1997) studied grade six pupils in Iligan City wherein she attempted to associate
high achievement in mathematics with the following factors: home environment, quality and
quantity of math instruction received by pupils, and pupils' attitude towards math. The factors
significantly associated with high achievement in math are the following: pupil respondents'
father's educational attainment, number of influencing household member, seminars attended and
24
math awards received by the teacher respondents, and pupils' attitude towards math. This
indicated that pupils' academic achievement not only in Mathematics but also with other subjects
is greatly influenced by other factors not only pupil and parent factors.
25
CHAPTER III
RESEARCH DESIGN AND METHODOLOGY
This chapter presents the methodology used and the overall design in the study.
Including the research method, research design, locale, research respondents, data gathering
procedure, research instruments, validity and reliability of data, and statistical tools and analysis.
3.1. Research Design
A combination of Qualitative and Quantitative approach was used to have better
understanding. A Qualitative Research was used in order to give more explanation in the valid
data through the use of words. Also with the Quantitative Research that was used to tally the
possible responses of all the respondents, to get their number and their corresponding frequency.
The data was gathered through answering the questionnaire that weregiven to the 2 types of
respondents.
3.2. Research Locale
The research focuses about the difficulties of students in learning Mathematics and was
only conducted at Ave Maria College, Vallesville, Fatima, Liloy, Zamboanga del Norte.
3.3. Research Respondents
The target respondents of the study werethe two Math Teachers and the 50% randomly selected
Senior High Students of Ave Maria College. The researchers only choose the grade-11 students
because Mathematic related subjects are already out taught in Grade-12.
26
i. Students
Table 1 presents the student-respondents or the study.
Table 1: Student Respondents
G-11
Students
N=
Male
Female
Total
f=
%
f=
%=
f=
%=
15
24%
48
76%
63
100%
ii. Teachers
Table 2 presents the 2 teacher respondents of the study.
Table 2: Teacher Respondents
Math
Teachers
N=
Male
Female
Total
f=
%
f=
%=
f=
%=
2
100%
0
0%
2
100%
3.4.Data Gathering Procedure
Theresearchers used a survey questionnaire of the past researcher called ‘Difficulties in
Mathematics’ byJR Smith as their data gathering technique. They distributed few pages for every
27
student respondents that was composed of 2 the parts, the part 1 contains the personal
information of the student-respondent and part 2 contains the responses of the questions that
were provided to them.After accomplishing the instrument, the questionnaires were collected for
checking and for analysis. All the responses of the student-respondents were properly tallied,
analyzed, and interpreted. Meanwhile,the researchers had an interview to the other respondents,
the teacher-respondents of the study in the purpose of identifying the difficulties experienced by
their students in mathematics according to their observation and to identify their ways of
overcoming those difficulties.
3.5. Research Instrument
In order to know the difficulties of students in Mathematics, a survey questionnaire
wasdistributed to the student respondents of the study. In where, it was credited from the past
researcher of “Difficulties in Mathematics” named “JR Smith”. The research instrument that was
used was composedof two parts. The part 1 was all about the personal information (name, age,
address, grade, and strand) and the part 2 has three tables that contained the questions. A
questionnaire were also provided to the teacher respondents that are especially made to know the
observation of the Math teachers at Ave Maria College about the difficulties of their student in
the subject, and to know the actions they have implied to overcome those difficulties.
3.6.Validation of Instrument
Before the instruments were given to the student-respondents of the study, these were
subjected for validation in order to determine the suitability, appropriateness and relevance of the
28
items in the questionnaire to the research questions. The questionnaire was submitted to the
research adviser for corrections and approval. The valid gathered data were from our studentrespondents who are the randomly selected Grade-11 Students and 2 Math teachers of Ave Maria
College. Interviews were recorded and transcribed. Data finding was analyzed descriptively. The
researchers also get some of their other information from the books they’ve read, some are from
the thesis they consulted, and some are from the internet.
3.7. Treatment of Data
All the responses taken from the given questionnaires were tabulated in table form using frequency and
percentage to be able to interpret and analyzed the gathered data from the respondents. (N)=number, (f)=frequency
f/N x 100 = %
And the study also useddescriptive analysis in explaining the gathered data furthermore in the purpose of
better understanding.
29
CHAPTER IV
PRESENTATION, ANALYSIS AND INTERPRETATION OF DATA
This chapter presents the data, the analysis, and interpretation of results following the order of
specific questions that were raised in the first Chapter.
4.1. Difficulties encountered by students in Learning Mathematics
Based on the survey conducted the difficulties of students encountered in learning mathematics
can be classified into two aspects as revealed by the Students and the Teachers. The student’s
perspective is summed in five aspects and the teacher’s perspective was revealed word by word
based on their observations. These are presented intables 3 and 4 below.
4.1.1. Students’ Perspective
Table 3 presents the difficulties encountered by the students in learning Mathematics.
Table 3:
Difficulties Encountered by Students in Learning Mathematics.
Difficulties
Frequency (f)
Percentage
Computational weaknesses
14
20%
Instructional disability
1
1%
30
Memory Gap
28
41%
Attention Span
6
9%
Lack of Understanding Math
20
29%
terms
It can be gleaned in Table 3 that majority of the students are having difficulties in
mathematics because of their Memory Gap, garnering 41% of the overall percentage. This means
that these students are struggling remembering the lessons that was discussed by their instructors,
they often forgot how a particular mathematical solution was done, and they don’t have welldeveloped mental strategies for remembering how to complete algorithmic procedures and
combinations of basic facts.Having difficulty in remembering things can be a really serious
problem in learning mathematics. But there are still some ways to overcome these difficulties.
However, 29% of the students stated that they are having Lack of Understanding in
Mathematical Terminologies, which means these students do not understand mathematical terms,
“plane” for example, students tend to interpret this as a literal plane, a tool for smoothing or
sharping a wood surface, whereas in mathematical term, it is a flat two dimensional surface with
infinite width and length, zero thickness and zero curvature. In the meantime, 20% of the
students said that they struggled in mathematics because they are having a Computational
weakness, which means this separate group of the student-respondents of the study is having
difficulty calculating numbers which will always lead to the wrong answer of the student in
his/her solution. Meanwhile 9% of the student-respondents are having difficulties in mathematics
because of their poor attention span, which means these students can be distracted easily; they
don’t have the ability to focus and sustain attention on their mathematical task which will also
31
lead to misinterpretations of numbers and can lead to wrong answers. And there is only 1% of
the student-respondents stated that they do have an Instructional disabilities. This small
percentage of students are having problem in acquainting, organizing, using, and understanding
verbal or nonverbal information. Having this problem will affect the learning of a student or an
individual, especially in mathematics where good attention span is definitely required.
4.1.2. Teacher’s Perspective and Observation
Below are the difficulties of students in learning mathematics revealed by the teachers as
they have answered the question “What problems or difficulties did your students encountered in
learning the subject?”
Teacher 1 said that “Majority of the students have difficulties in terms of Comprehension.
And they hate numbers and variables.” This simply means that their students cannot easily
understand the lesson that they have discussed. It may be because some of the mathematical
terms that they are used are new to the students and they cannot comprehend what it could be,
and what can it do to their topic. This can be related to the identified difficulties in the studentrespondent’s questionnaire, the “Lack of Understanding in Math Terms”.
Meanwhile, Teacher 2 stated that “Most of the learners are not equipped with the
necessary mathematical skills for Math in SHS and it resulted the classroom instruction flow be
slow to provide bridging session to provide the learners with necessary skills for particular
topic.” Teacher 2 tried to interpret that students are not ready for the new curriculum particularly
the Senior High School Program which has new version of learning for the students. It is
observed that some of the subjects of the senior high school are also taught in college. Senior
32
High School Students should be trained and taught with those skills in order for them to deal
with those advanced topics in Mathematics at senior high school.
The teachers revealed difficulties of their students in learning mathematics do not
coincide to the statements of the students itself. In where in the student’s perspective, majority of
them said that they are more likely having difficulties in mathematics because of their poor
memory gap or they are having hard times in remembering things that are taught in their math
class, like mathematical formulas and procedures of solving.But poor memory gap can be
resulted because of the poor attention span the student exerted during the discussion, where
having poor attention span can also lead to poor comprehension which the instructors have
observed to students.
33
4.2. Reasons of Students’ Difficulty in Math
Table 5 presents the reasons given by the student-respondents on why they are having
difficulties in learning mathematics.
TABLE 4
What are the reasons students give why learning Mathematics is difficult?
Statements
Very true
Little bit
Not true of
of me
true of me
me
Total
F
%
F
%
F
%
F
%
1. I like learning math.
11
17
20
32
32
51
63
100
2. Math is boring.
26
41
28
44
9
15
63
100
3. I like to come up with new
26
41
34
54
3
5
63
100
22
35
38
60
3
5
63
100
18
29
33
52
15
24
63
100
ways to solve math problem.
4. Learning new things in math is
for fun me.
5.Math is unpredictable and
cannot be understood easily.
34
6. I believe there is an easy way
44
70
17
27
1
3
63
100
147
39
170
44
63
17
378
100
to solve math problems.
Total
As shown in the table 5, only 17% of students said that they really love learning math,
which means, the remaining 83% of them do not like to learn math for some reasons. And not
having your interest in this subject can lead the students to incline themselves not to listen to the
discussion. And 41% of the students says that math is boring, they did not find math as a fun
subject, they do not see math as fun as they wanted and expected it to be. This may be caused by
the teachers’ wrong strategy used in introducing the math topics to their students or any other
possible reasons that caused the students to have this reason of their difficulty. And also 41% of
the students love to come up with new things in math, which is a positive indication that these
students still wanted to learn the subject despite of the difficulties they have experienced.
Meanwhile, 33% of the studentssay that learning new things in math is fun, this is a another
positive indication that these students still wanted to learn new things about math as shown by
the good percentage it garnered. In the meantime, 29% of the students said that math is
unpredictable and not easy to understand, this means that, even these students still wanted to
learn things in math, they really see math as a difficult subject. But as discussed, they may be
having this difficulty because of their poor attention span. And lastly 44% of students said that
they believe that there is an easy way in arriving to the answer, this simply means that these
identified students wanted their instructors to teach them the easiest possible way of defining and
solving mathematical problems.
35
4.3. Measures Undertaken to Overcome the Difficulties
4.3.1. Student’s Actions Undertaken
Table 6 presents the partial actions undertaken by the students and teachers to overcome the
difficulties in mathematics
TABLE 5
What actions were undertaken to overcome these difficulties?
Statements
Always
Most of
Once in
almost
the time
a While
F
1. In my math classes we
%
21
F
%
F
%
Never
F
%
Total
F
%
33
31
49
10
16
1
2
63
100
12
23
36
24
38
9
14
63
100
14
34
54
17
27
3
5
63
100
practice solving over and
over again until we get it.
2. My teacher asks me
7
to explain how I got my
answers to math problems.
3. I work on math problems
9
during class time with other
students in my class.
36
4. My teacher tries to
16
25
20
32
23
36
4
7
63
100
5. We copy notes
37
59
14
22
10
16
2
3
63
100
6. We have quizzes or tests
43
68
19
30
1
2
0
0
63
100
7. We do projects that are
27
43
6
10
19
30
11
17
63
100
21
33
32
51
10
16
0
0
63
100
14
22
30
48
15
24
4
6
63
100
38
60
20
32
5
8
0
0
63
100
11
18
29
46
19
30
4
6
63
100
244
35
258
37
153
22
38
6
693
100
understand my way of doing
math problems.
graded.
8. In math class, my teacher
gives us worksheets that
have many short math
problems.
9. In math class, we work on
one big math problem for a
long time.
10. My teacher shows us
how to solve math problems
and then we practice.
11. I do self study at least
one hour per day.
Total
37
Table 6 shows the actions undertaken by the students and teachers to lessen the
difficulties experienced by the students in learning Mathematics. The researchers have given the
statements in our questionnaire and has the (always almost, most of the time, once in awhile, and
never) to shows how often they make their assignments, they solve their math problems and what
are their ways to make it easy.33%of the students stated that they practice more often their math
problem solving, these students have done solving mathematical problems on their own as their
way of lessening the difficulties they have experienced in learning mathematics. 14% of the
students said that they work their math problem in class; this simply tells that this group of
students prefers to do their mathematical works like assignments in class, maybe because they
can still freshly remember the steps on doing such procedure of defining the answer of a
particular mathematical problem. 59% says they copy notes from the board, by doing this, they
can have their reviewer whenever they wanted to remember how a mathematical solution was
done comprehensively. 30 % says they often have a quizzes or tests, this is done by the teachers
to test the student’s progress in learning such mathematical solution, and so they can assess the
significant things the students need to execute to lessen the difficulties if ever there will be. And
68% of the students said that they study atleast per day, they find this as their way of lessening
the difficulties they are experiencing, reading and recalling the topics that were taught by their
instructor, and practicing solving such on their own. Meanwhile12% of the students said that
their teacher ask them to explain how they got their answers to the math problems. This is a way
of the instructor to know if their students really understand the topic and to know if that
particular student really knows how to come up with the answers correctly by following the
methods they have used. In the meantime, 25% of the students said that their teacher tries to
understand their way of doing math problems. This is to test the knowledge of the students in a
38
particular topic. By this, instructors can identify where and what need to be improved by a
particular student in solving mathematical problem. And 33% of the students said that their
teacher gave them a worksheet that has many short math problems. 60% of the students stated
that their teacher shows them how to solve math problems and then they practice similar
problems. Students practice on their own on solving the particular solution that was taught by
their instructors. This is a way of the students to master a particular mathematical solution and to
test their independency on solving such.
4.3.2. Measures Undertaken
For the question number 3 “What measures did you undertake to overcome your
difficulties in learning the subject?” in the part 2 of the student-respondent’s questionnaire,
Students stated that they have done:

Watch tutorials online (Watch videos online on how a particular mathematical problem is
solved or done )

Listen to the instructors carefully (Listen to the instructor whenever he/she is discussing a
particular mathematical topic)

Self-study (Review the notes you have copied and try to practice solving on your own)

Group-study (Review the topic discussed with peers or classmates)
39
Table 6 presents the measures undertaken by the students alone as their way of lessening the
difficulties they have experienced in learning mathematics
Table 6
Measures undertaken by the students
Statements
F
%
Watch video tutorials online
23
37%
Listen to the instructors carefully
16
25%
Self study
6
10%
Group study
18
28%
Total
63
100%
As seen in table above, majority of the students prefer to watch video tutorials online as
their way of lessening the difficulties they had experienced in learning such Mathematical
problems, which garners the 37% of the frequency. These students used the help of technology to
lessen their learning difficulties in math. Some prefer to have a group study as their way of
lessening the difficulties that garnered 28% of the overall frequency. These students find that
studying together with their peers as an alternative way of easing the understanding of a
particular topic, this is maybe because when you enjoy doing something you can really
appreciate what you are doing and you can really understand it rather than doing something in
lone, it is so boring and students would tend to refuse on receiving ideas and knowledge.
40
Butthere are still students who still preferred doing self-study of course in mathematics as their
own way of easing the understanding in a particular topic. Though it is boring to do a task alone,
these particular students can deal with this, they can still learn on their own provided that the
topic will be introduced by the instructors fluently with the procedures of doing such. A large
percentage of the students see that listening to the teachers as they discussed is a way that helped
them in overcoming the difficulties they have encountered in learning the subject. This is very
true, because based on the findings of this study as revealed by the instructor; students are more
likely having difficulties in mathematics because of their poor comprehension. And having poor
attention while the teacher discussed a topic can lead to poor comprehension of the lesson.
4.3.3. Instructor’s Actions Undertaken
Below are the presented actions undertaken by the teachers to overcome the difficulties
encountered by their students in learning mathematics as they have answered the question “What
measures did you undertake to overcome the difficulties encountered by your students in
learning the subject?”
Teacher 1 revealed that he sometimes translates the statements into vernacular and Filipino. And
also, he introduced some methodologies that are related and useful to the particular topic. This
math instructor sees that using vernacular language in discussing a topic would be helpful for the
better understanding of their students in such topic. Maybe because, using English language can
cause confusion to the part of the students. That can lead to problems in terms of their
comprehension. He also introduced some easy methodologies on solving a particular
41
mathematical problem to somehow convince the students that there are still some ways on
defining answer on such mathematical problem on a much easier way but still will come up with
the same correct answer.
Teacher 2 stated that he provide the learners with bridging topics to equip them with
necessary/required mathematical skills before introducing the topics identified in Curriculum
Guide. Since, Mathematical proficiency levels for the learners are not the same, he required
himself to prepare different worksheet for them to improve the skills. As a way of lessening the
difficulties of his students in learning mathematics, he first introduced some topics that are
related to the topics that were identified in the curriculum guide, where students can use this for
them to systematically correctly solve the problem that was given in the topic identified in the
curriculum guide. He also provides worksheet whenever he introduced such topics for the
students can have exercises to develop their knowledge about the topic, but in different level.
Because, not all students had the same level of learning proficiency in mathematics. This can
help the students in overcoming their difficulties in the course.
4.4. Measures need to be taken to overcome the Difficulties
4.4.1. Student’s Suggestions
For the question number 4 “What can you suggest to lessen the difficulties and make the
learning of Mathematics fun?” in the part 2 of the student-respondent’s questionnaire,students
suggested as follows:
42

Memorize mathematical formulas (memorize mathematical formulas that will tell the
pattern of how a solution will be done or how a solution was done)

Listen attentively to the instructor (listen to the instructors thoughtfully as they are
discussing a topic to)

Do a self-study (help yourself by reviewing the topic that has been taught in the class
whenever you are free)

Instructors should add some fun challenges (instructors should add some fun challenges
in discussing a topic such as games)

Instructors should discuss the topic repeatedly (teachers should confer the topic to the
students repeatedly until the will get the topic)

Think math as an easy subject (one should never see math as a hard course)

Instructors should provide visual aids (teachers should provide visual aids in discussing a
topic to catch the attention of the students)

Well organized presentation from the instructor (instructors should present their topics
orderly to avoid confusions of the students)
Table 7 presents the suggestions that were given by the student-respondents to lessen the
difficulties in mathematics and make it easy and fun.
43
Table 7
Suggestions of the students to lessen the difficulties
Statements
F
%
Memorize mathematical formulas
7
11%
Listen attentively to the instructor
16
25%
Do a Self-study
8
13%
Instructors should add some fun
6
10%
8
13%
Think math as an easy subject
2
3%
Instructors should provide visual aids
9
14%
Well organized presentation from the
7
11%
63
100%
challenges
Instructors should discuss the topic
repeatedly
instructor
Total
As presented in the table 9, students provided several suggestions to lessen the difficulties that
they commonly encountered in the subject. Thus, most of the students suggested that one should
listen to the instructor attentively in order to lessen the difficulties in learning mathematical
44
topicin which it garnered 25% of the overall percentage. This is to improve their comprehension
about the topic that is being discussed, student would gather enough knowledge, the will really
know how a particular solution was done only if they will just listen to the discussion of their
teacher. But, their suggestion does not only focus on to their part alone, they have also suggested
that the instructors should also take scheme to the said problems of the students. As suggested or
said by the 10% of students,Instructors should add some fun challenges in discussing a topic in
which it reaped of,in order to make the discussion or topic more interesting and tempts the
students to participate in the class. In that way students will be able to learn. Meanwhile 13% of
the students said thatInstructors should discuss the topic repeatedly until their student will get the
topic because some of the students are slow learners that they need a time of learning.
However11% of the students aforesaid that Instructor should provide visual aids and Instructors
should also providea well-organizedpresentation of a topic, considering the fact that some
students cannot facilelyunderstand the topic without such visual aids and other educational
helping materials, so that students can grasp the discussion or topic thoroughly. Otherwise 11%
of the students said that there is a need to memorize all mathematical formulas because they can
easily solve such mathematical problems. As recommended by the 13% of the students they
suggested that students should do a self-study because some of the students might find very hard
to learn from somebody so they tend to do a self-education. On the other hand 3% of the students
suggested that think math as an easy subject because in that way they cannot sense any pressure
also they tend to go with the flow of the subject so that they can easily deal with such
mathematical problems.
45
CHAPTER V
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
This section presents the synthesis of the study. It draws conclusion based on findings
and propose substantial recommendations.
5.1. Summary
This research output found out that among students difficulties in learning mathematics
defined by HJ. Sherman SYJ. Y that student fallsin their expected level of mathematics
achievement for a variety of reasons.
Majority of the Grade-11 students of Ave Maria College who are having difficulties in
Mathematics are from the strands of HUMSS and HE & ICT. This is according to the findings
that were observed by the researchers on the answers that were given to them by the studentrespondents.
Memory Gap is the dominant difficulties among grade-11 students from Ave College
followed by the lack of understanding in mathematics terms. It is better that students have a
concrete understanding about the terminologies that their subject has.
Computational weakness is the next difficulties faced by the students, followed by
Attention Span and Instructional Disability.This is according to their answers given in the
questionnaires that were provided to them. But, it was revealed by their instructors that these
students are having difficulties in terms of their comprehensions and most of them hate numbers
and variables. Also, most of the learners are not equipped with the necessary mathematical skills
for Math in SHS.Our research also found out that students have more action undertaken to lessen
46
this difficulty. These are the spending time on watching video tutorials in YouTube about the
topic that they have tackled in their math discussions in the class to gain more understanding and
lessen the difficulties they have experienced, listen to the instructors fluently when discussing
will also help, do a self-study about the lesson that was discussed by the instructor, or do it with
a group can also help students to lessen the difficulties. In the meantime, instructors of the said
students also exerted effort to lessen the difficulties of their students. Sometimes, they translate
the statements into vernacular and Filipino for better understanding and interactions. Also, they
introduce some methodologies that are related and useful to the particular topic. And, teachers
provide their students with bridging topics to equip them with necessary/required mathematical
skills before they will be introduced to the topics identified in Curriculum Guide. Since,
Mathematical proficiency level for the learners are not the same, teachers were required to
prepare different worksheet for them to improve the skills.
The result of this research will give benefits not just to the studentsin Ave Maria College,
but also the other reader of this book and the teachers that either handling mathematics or
planning to teach mathematics.This will be served as their tool and this can be used as their basis
if how they will instruct the students as well as giving the problem properly to the students so
that they can understand and can solve without any hesitation. Not only that, this will be serve as
a guide for all the students who really having hard times in dealing math subject on how can they
somehow lessen the difficulties they are experiencing in the particular subject.
47
5.3. Conclusion
This study conclude that out of the 63 student-respondents, 41% of the students were
having difficulties in terms of their Memory Gap, which is the dominant difficulties experienced
by the said students and others are lacking of understanding in mathematics terminologies,
attention span and other mentioned difficulties on the previous chapter. It was also revealed by
the teacher-respondents of the study that these students also having hard time on dealing with
comprehensions.But despite of the facts that were previously recognized in the relation of the
student’s difficulties in mathematics, students can really learn such if there will be a double
effort that will be exerted by both of the students themselves and the teachers. There is nothing
hard for a person who loves what he is doing.
The researchers would also like to conclude that the academic performances of majority
of the students are above the average, this is because of the courage, eagerness, and willingness
of the students in learning the subject have overcome their difficulties, it’s therefore they still
have the average academic performance despite of the challenges they have encountered in the
subject.
Also teachers have already found their own ways to somehow help their students with
their difficulties in the particular subject. However, based on the recommendation that was
derived from this study, these can help them furthermore in helping their students in overcoming
the difficulties they have experienced in learning math and make it easy and fun.
48
5.4. Recommendation
5.4.1. Recommendation for the Learners and Instructors
In learning, especially in school, it is the responsibility of both the students and teachers
to enhance the capability of one’s student in Mathematics. Students have to listen to the teachers
whenever they are discussing the topic, meanwhile, the teacher is tasked to teach their students
fluently, they should convince the students that Math is easy and it is fun opposite to what the
students are thinking, and teachers should understand the difficulties of the students, what made
it difficult for them, what is the reason of their difficulties and why is it difficult for them. In
learning, there should be a harmony between the student and the teacher, so, Students and
Instructors should always have a good relationship inside the class.
Teachers are the person who can tell best what the situation of their students is in the
class, possibly, they know what the reasons are and the nature of their difficulties in a particular
subject, if there are really is. This can be used as their guide on where to adjust and can tell them
what to do best in delivering and discussing a topic in a particular subject.
Among the common difficulties of the students in the relation to mathematics that were
identified in the previous chapter, these recommendations can be used by the learners and and
the teachers in overcoming the difficulties in mathematics particularly.
5.4.1.1. Recommendation for the Difficulties

For computational weaknesses in order to make it easy for computing, teachers should
introduce some easy methodologies in solving such problems. Teachers should discuss
the lesson repeatedly until there students get it. And for the part of the students, they
49
should do their own study about the topic, maybe do some research, or study with your
peers so that it would be fun and it can help you to understand the problem easy.

For lack of understanding in math terminologies, teachers are required to define and
explain farther the terminologies before proceeding to the main topic; they can use
vernacular language in explaining to interpret it more. For the part of the students, again,
they should do their own research. Enough understanding about mathematical
terminologies can really help students in understanding the whole topic.

For attention span, the teachers should prepare attractive tools that are necessary
indiscussing a particular topic. They can maybe provide colorful visual aid in the purpose
of catching the student’s attention, or they can have games that could be related to the
topic just to make every student to participate because they can see it fun and interesting.
But students should also have to play their part that they should always listen attentively
to the discussion because it is very disrespectful for the teacher’spart that they are
exerting too much effort just for benefits of the students, but it just turn out to just be
wasted.

For the Memory Gap, it is the responsibility of the students that they should always study
their lesson if they aimed tomaster such algorithmic procedures. Therefore, students
should always study the lesson that was discussed in order to overcome the struggle in
Memory Gap. But teachers are also require to help the students, Maybe they should have
a weekly test about the topic that were discussed covered in the whole week, in this way,
students will be forced to study the lesson and forced them to recall the topic
discussed.Some students lack well-developed mental strategies for remembering how to
complete algorithmic procedures and combinations of basic facts. However, strategies to
50
improve capacities for remembering facts, formulas, or procedures can be taught.
Repetition games such as calling out fact combinations and having students solve them
and then repeat those that were called before their turn can help.
51
LIST OF REFERENCES
A. Internet Sources
Alvaera, Bayan, & Martinez (2009), Parental Involvement and Autonomy and Teaching
Approach Factors in Learning Math, pg 24
Angay's (1998), Pupils' Difficulties in Basic Operations Involving Fraction, pg 12.
Berch (2007), the lacked of mathematics skills among students pg, 16
Beck, Philips & Gully (2000).Representational system learning and problem solving in
Mathematics, Journal of Mathematics factor, pg 22.
Bigornia (2000), Factors Affecting the Mathematical Proficiency Level of Grade VI Pupils, pg
12.
Buan (1997), Effects of Cooperative and Individualistic Instructions on Student's Achievement
in Mathematics
Caliao (2000), Determined Factors of Students in Math Problem Solving, pg 22
Cañete's (2002), Factors Affecting Problem Solving Difficulties in Mathematics pg, 23.
Dacey & Travers (2006),
Garnett (1998), The Deficiency in Visual-spatial Skills pg, 16
Garderen (2006),The Deficiency in Visual-spatial Skill pg, 16
Geary (2004), Conceptual Understanding and Procedural Knowledge in Problem Solving pg, 17
H.J. Sherman and Y.J. Yard, Students fall below their expected level of mathematics
achievement pg, 12
Kaufman (2008), the lacked of mathematics skills among students pg, 16
Lucero (1999), Parental involvement both pupils' mathematics achievement. pg,12
Mazzocco (2007), the lacked of mathematics skills among students pg, 16
52
Maria Ocadiz, Maria (2008). International Mathematics Report 2008
Miranda, F (2006) How can you tell your child have math difficulties
Montecalvo (2000), Mathematics of Grade Six Pupils in Linamon District, Divison of Lanao del
Norte, 22-23.
Nathan et al. (2002), the lacked of mathematics skills among students pg, 16
Osmon et al. (2006), The deficiency in visual-spatial skill pg, 16
Rondez (1997), Factors Affecting the Grade-6 Students in Learning Mathematics, 24-25
S.P. Gurganus -Pearson Allyn Bacon Prentice Hall, Development of Cognitive Structures
Related to Mathematics. Pg, 14
Silva et al (2006), Filipino Students in Mathematics, pg 23.
Lee-Chua (2006), Efforts Spearheaded by Various Groups to Develop a Successful Problemsolving Culture. PG 23-24
Hill, (2008), Cognitive Skills and Mathematics Skills., 21st Century Skill.
Ibrahim Ismail (2001), Academic Journal in Mathematics.
B.Resource Locator

http://www.MATHEMATICS_skilss.com/fileadmin/download/problemsolving/22008/08_Tirri.pdf (ThambySubahan, 2008).

http://www.comweaknesses.com

https://www.Jr Smith;;difficulties in math subject.com//

International Conference on Mathematics Education Research 2010 (ICMER 2010) link/
http://www.pbs.org/wnet/gperf/education/ed_mi_overview.html

http //www. Idoline.
53

www.thirteen.org./edonline/concepts2class/mi.com

https://ac.els-cdn.com/S1877042810021257/1-s2.0-S1877042810021257main.pdf?_tid=8695293e-12d1-48aa-8484861b21d9c776&acdnat=1535537901_43b4df1f9c19461a8b4e59f6d298bd50

https://www.pbs.org/wgbh/misunderstoodminds/mathdiffs.html

http://theses.gla.ac.uk/1278/
54
APPENDICES
Appendix A: Respondents of the Study
I. Student Respondents
G-11
Students
N=
Male
Female
Total
f=
%
f=
%=
f=
%=
15
24%
48
76%
63
100%
II. Teacher Respondents
Math
Teachers
N=
Male
Female
Total
f=
%
f=
%=
f=
%=
2
100%
0
0%
2
100%
55
Appendix B: Research Tools
I. Teacher-Respondents’ Questionnaire
Survey Questionnaire
(TEACHER)
Part I: Personal Information
Direction: Please fill up the information accordingly.
Name: ________________________________________ Strand:______________
Age: ______
Sex: __________
Address: ___________________
Part II:Responds
Direction: Please answer the questions provided below.
1. What problems or difficulties did your students encountered in learning the subject?
__________________________________________________________________
________________________________________________________________________
_______________________________________________________________________
2. What measures did you undertake to overcome the difficulties encountered by your
students in learning the subject?
__________________________________________________________________
_____________________________________________________________________
56
II. Student-Respondents Questionnaire
Survey Questionnaire of JR Smith
(Students)
Part I: Personal Information
Direction: Please fill up the information accordingly.
Name: ________________________________________ Strand:______________
Age: ______
Sex: __________
Address: ___________________
Part II:Responds
Direction: Below are questions related to Difficulties in Learning Math Check ( √ ) the
column and box that describes you the most:
1.) What are your difficulties in Math subject?
(
) Computational Weakness
(
) Instructional Disability
(
) Memory Gap
(
) Attention Span
(
) Lack of understanding Mathematics terminologies
57
2.) Rate the following statements according to your experience
This is very
This is a little
This is not at
true of me
bit true of me
all true of me
(1)
(2)
(3)
Statements
1. I like learning math
2. Math is boring
3. I like to come up with new ways to
solve math problem
4. Learning new things in math is fun for
me
5. Math is unpredictable and cannot be
understood easily
6. I believe there is an easy way to solve
math problems.
58
Statements
7. In my math classes we practice solving
over and over again until we get it
8. My teacher asks me to explain how I
got my answers to math problems
9. I work on math problems during class
time with other students in my class
10. My teacher tries to understand my way
of doing math problems.
11. We copy notes from the board.
12. We have quizzes or tests
13. We do projects that are graded
14. In math class, my teacher gives us
worksheets that have many short math
problems
59
Almost
Most of
Once in a
always
the time
while
Never
15. In math class, we work on one big
math problem for a long time
16. My teacher shows us how to solve
math problems and then we practice
similar problems.
17. I do self-study at least one hour per
day
3.What measures did you undertake to overcome your difficulties in learning the subject?
______________________________________________________________________________
______________________________________________________________________________
4. What can you suggest to lessen the difficulties and make the learning of Mathematics fun?
______________________________________________________________________________
60
Appendix C: Spot Map
61