Learning in Mathematics: Difficulties and Perceptions of Students

Journal of Educational Research, Dept. of Education, IUB, Pakistan (Vol. 21 No.
1) 2018
Learning in Mathematics: Difficulties and Perceptions of Students
Nasrin Akhter*
Nasreen Akhter**
Abstract
Many students find their studies in mathematics to be difficult and
unrewarding. There is a tendency for students to opt out of studying
mathematics as soon as possible. However, mathematics is usually seen to
be important and holds a central place in the curricula in most countries.
Mathematical ideas find application in numerous areas of life and in many
careers. Thus, negative attitudes among students may have important
ramifications for career choices and contributions in wider society. This
study considered a sample of students (N = 647) from Punjab, Pakistan
and collated their perceptions in relation to their learning in mathematic.
The tools of data collection of this study were questionnaire. The findings
indicate that students show positive attitude and grasp of mathematics
content at grade 9th and 10th in mathematics. This was noticed that there
were differences in attitude in what is required by the students and what is
occurred in classroom where the learners are taught Mathematics. This
study suggests the solutions about the competencies of students to work
through mathematical difficulties.
Keywords: Learning in Mathematics, Difficulties, Perceptions, Field Dependency
Introduction
In looking at mathematics education, Brown et al. (2008) noted the widespread
opinion among learners that mathematics is difficult, with students opting out whenever
possible. By contrast in the neighboring country (Scotland), mathematics is a highly
popular subject at all levels in school and university (Scottish Qualifications Authority,
undated). This illustrates that, while mathematics is seen as difficult and unattractive in
some countries, this observation does not apply in all. Sadly, there is a lack of research
that explores learning in mathematics to see whether the factors underpinning the
differences can be observed.
One of the problems in mathematics arises from its very nature. When learning
mathematics, one goal is that students can conduct procedures in order to obtain correct
answers. In seeking to achieve this goal, the students are encouraged to practice the
*
Assistant Professor, Faculty of Education, University of Okara, Okara, Email:
nasrin_cs2005@hotmail.com
**
Assistant Professor, Department of Education, Faculty of Education, the Islamia University of
Bahawalpur
147
Journal of Educational Research, Dept. of Education, IUB, Pakistan (Vol. 21 No. 1) 2018
procedures. Thus, the procedures are memorized and then automated in the minds of
learners (Alenezi, 2008). While this can generate confidence, it often ignores an
emphasis that students should understand what they are doing and why they are doing
it. In this way, mathematics can be reduced to a process of practicing procedures until
they are memorized, with little opportunity to understand what the procedures mean or
how they might be applied wider life. In an interesting study, using factor analysis,
Almadani et al. (2012) confirmed that examination successes in mathematics depended
on recall skills, this broad picture applying to all school subjects. While facts may be
memorized in some subject areas, in mathematics it was the procedures that were being
memorized.
By its very nature, mathematics makes high conceptual demands on students. It
involves procedures that may appear to be abstract and unrelated to life. It has been
shown again and again that this places high demands on the limited working memory
capacity in learners (Reid, 2009). Working memory is part of brain that helps learners
in thinking, comprehension and problem solving skills. It has limited capacity for
individuals and help to control comprehension.
This study also seeks to explore the extent of field dependency in learning in
mathematics in high school students. Witkin and Goodenough (1981) described that
field dependent is a person that cannot detach an item from its context. Field-Dependent
individuals can unsatisfactorily separate an item from its background and willingly
accept the dominating field. Field-Independent individuals can easily ‘break up’ an
systematized perceptual field and separate willingly an item from its context. Very
often, experienced teachers of mathematics hear learners say that, when faced with a
mathematics problem they state they are uncertain where to start. This is a classic sign
of information overload related to working memory limitations and that is where an
understanding of the learner characteristic known as field dependency is central. Field
dependency is the extent to which a person can focus on what is essential for a task in
hand and instead of; ignoring what is peripheral for that task (Tinajero & Paramo,
1998). This has been considered in detail in the study of mathematics and this learner
characteristic is very important in being able to undertake mathematical problems of the
sort used in schools (Onwumere & Reid, 2009).
Mathematics is an integral part of the curriculum in almost all the countries of
the world. In Pakistan, mathematics is considered a key subject for many fields. Khan
(2012) noted that mathematics is not usually a popular subject and is a subject where
students face many problems, with many opting out as they are allowed. Ali (2011)
considers that, in Pakistan, it is poorly taught. However, teachers can only teach what
is mandated for them. Very often, teachers are forced to follow the ways prescribed by
textbooks. Procedures are memorized, practiced and then tested in formal examinations,
credit being given for the correct conduct of procedures leading to correct answers
148
(Mohammad, 2002; Amirali & Halai, 2010). One study conducted in Pakistan has
shown very clearly that a rigorous curriculum designed by school teachers was much
more successful than the curriculum imposed from outside and designed by those
outside the classroom (Ali & Reid, 2012). Thus, part of the problem in mathematics
education may well be in an inappropriate curriculum.
In Pakistan, the curriculum for secondary grades is arranged under five broad
themes and goals: (1) Numbers and Operations, (2) Measurements and geometry, (3)
Algebra (4), Information handling, (5) Logical thinking and reasoning. However, if the
examinations give the rewards to candidates for the correct conduct of taught
procedures, then practicing procedures will become the focus for both teachers and
learners. Many studies have considered areas of difficulty in mathematics. For example,
Barmby and Harries (2007) investigated the significance of representations in
understanding of multiplication. Harrie and Patrick (2006) carried out investigation on
the array representation in learning multiplication calculations. They used an innovative
approach for recording learners work on computer. Matthews and Pepper (2005)
examined that the main reasons for giving up mathematics include lack of satisfaction
coupled with boredom along with perceived irrelevance. Nardi and Steward (2003)
argue that, at age of 12-15, enjoyment is an important feature for learners when seeking
understanding.
In a wider sense, research shows consistently that learners naturally want to
make sense of what they are being taught. This observation stems right back to the
work of Piaget (Wadsworth, 1979) and was very evident in the study of Skryabina
when she looked at what attracted learners into studying physics (Reid & Skryabina,
2000). The principle led to the idea of the applications-led curriculum where the themes
being studied were determined by an analysis of the needs of the learners in the context
of their age, culture and lifestyle (Reid, 2000). Alenezi (2008) considered the place of
applications in the teaching and learning of mathematics and noted that this presented
very specific difficulties in that the incited capacity of working memory could not cope
with the mastering of a mathematical procedure, understanding what that procedures
meant and seeing how it could be applied?
In considering any mathematical task, the learner has to cope with the
procedure to be followed and any mathematical representation being used. The working
memory may be able to cope with this but has little or no capacity left to consider any
understanding of the concepts underpinning the procedure or situations where the
procedure might be applied. The evidence shows clearly that difficulties in
mathematics can largely be explained in terms of the limitations of working memory
capacity. In this context, Alenezi (2008) observed that the best way forward is to
concentrate on practicing the procedures until these are automated. Automated
procedures take up very little working memory space, leaving capacity for the learner to
149
consider understanding and applications. However, if the examination procedures

reward the correct conduct of procedures and the curriculum is overloaded, there is no
time or motive for the hard-pressed teacher to consider either understanding or
applications, leaving the learner dissatisfied.
Statement of the Problem
While mathematics is logical in nature, it is also somewhat abstract and that,
while it applies widely in life, it is difficult to make these applications real and tangible
to young learners. The present study was regarding “Attitude in Learning Mathematics:
High School Students’ Perceptions, Difficulties and Field Dependency in their
Mathematics studies”. Objectives of the study were to explore:
1. The high school students’ perceptions and attitudes towards mathematics.
2. The challenges and difficulties related to mathematics performance.
3. The relationship between mathematics achievements and age with the field
dependency.
Research Questions
This study targeted to answer following questions
1. What are the high school students’ perceptions towards mathematics learning
and experiences in the classroom?
2. What are the difficulties the students encounter in their mathematics
experiences?
3. What is the relationship between mathematics achievements and age with the
field dependency of students?
Significance of the Study
The study anticipates shedding light on the solution of the conceptual
mathematics difficulties students usually face in secondary classrooms in Pakistan. This
study will help students to gain command over subject content at secondary level in
mathematics. There seems to be a huge difference between; what is required by the
students and what happens in the classroom where students learn Mathematics? This
study may recommend about the in competencies of students to work through
mathematical difficulties by majority of students in secondary mathematics. This study
also anticipates exploring the reasons of the lack of critical thinking and problem
solving in Pakistani students and search out; why students fail to apply their knowledge
of mathematics to the novel situations.
Research Methods and Sample
A quantitative investigation using a questionnaire of 45 items was made to
examine high school students’ attitude and difficulties in mathematics learning and
experiences in the classroom. The questionnaire was developed by the researcher by
150
look at the themes from the literature to examine high school students’ attitude and
difficulties in mathematics learning and experiences in the classroom. Internal
consistency of 45 items was measured by Cronbach’s Alpha statistic that was 0.94.
Moreover, Johnston Figure test (1976) Field dependency (a standardized test) was used
to explore the level of field dependency of students. Six hundred and forty seven
students from science group, aged approximately 14-16 were selected from 4 districts in
Punjab, Pakistan. The sample contained; 43% male and 57% female; 65% urban and
35% rural; 35% public and 65% private school; 58% 9th class and 42% 10th class
students. Data was collected during school hours and analyzed through percentage and
chi-square test.
Findings of the Study
The overall picture gained by considering the response data is now presented.
The responses regarding perceptions, attitudes, and difficulties are presented in the form
of percentage.
Perceptions of Students in Mathematics Learning
Table 1 from the first section of the questionnaire explore how do the students
perceive about their learning in mathematics?
Table 1
Perceptions of students in mathematics learning
Statements SA A N DA SDA
I entirely comprehend my lessons. 44 46 6 3 1
I like teaching method of my teachers 53 36 5 4 2
I truly comprehend the procedures in class. 33 48 11 5 3
I do not like doing too much class work daily. 28 28 15 17 12
I dislike home task because I can’t do it independently. 19 18 15 24 24
There is sufficient revision at school to help me
37 41 7 10 5
comprehend well.
I think tuition is necessary to get good marks in
41 27 9 14 9
mathematics.
I tend to panic near the exam. 16 30 19 19 16
I find it problematic to revise the entire year syllabus in the
17 34 11 25 13
annual examinations.
I do not like short questions because I cannot express all
10 16 11 35 28
that I know.
151
I like multiple choice questions in mathematics exam. 53 28 6 7 6

I realize that the allowable time for mathematics paper is
30 31 11 18 10
insufficient.
If I have problem in understanding something new, I seek
46 37 6 7 4
help from my teacher.
If I have problem in understanding something new, I seek
35 31 10 17 7
help from my tutor.
When the mathematics marks of student improve, it is due
51 28 9 6 6
to his own hard work.
I feel difficulty in learning a topic because I did not
17 32 16 25 10
understand previous ideas.
Teacher question in class helps my understanding. 54 34 4 4 4
Only those units of textbook are taught that are important
23 20 10 23 24
to pass the examination.
From Table 1, many positive features are evident but, in most cases, significant
minorities do not share the general views. This is parallel to the findings of Alhmali
(2007) where he found marked polarization of views related to mathematics in his study
in Libya. Overall, the majority of participants were agreed that they understand their
mathematics lessons. They are satisfied with teaching methods used for teaching
mathematics and understand the techniques of solving math questions. The data also
shows that the majority of participants were agreed that they like the multiple-choice
questions in mathematics tests. However, there are areas where students express
uneasiness. Inevitably, students do not wish to work too hard and tend to become
anxious as examinations approach while they do not enjoy revising in mathematics
tests.
Attitude of Students in Mathematics
Table 2 from the 2nd section of the questionnaire presents what is the students’
attitude towards their learning in mathematics?
152
Table 2
Attitude of students in mathematics
Statements High Medium Low

I like Mathematics 43 37 20
I find mathematics beneficial in my daily life 54 31 15
I find mathematics an interesting subject 62 26 12
I wish to study mathematics because I like it 65 22 13
I feel mathematics is easy to understand 61 28 11
Knowing mathematics will help me in my career 63 26 11
Mathematics allows me to create ideas 49 30 21
Understanding mathematics is important to me 64 25 11
Mathematics rules can never be proved wrong 64 25 11
On the whole, it is evident from Table 2 that learners feel confident regarding
mathematics learning. The majority of the participants in this study expressed positive
views regarding mathematics with most expressing that they feel happy to learn
mathematics. Their optimism was slightly over-confident when they consider that
mathematics rules can never be proved wrong. Using the method pioneered by
Johnstone et al. (1971) and employed by many (Ali & Reid, 2013), students were asked
to rate the topics studied in the following way:
Easy I understand the topic first time
Moderate I did not understand it first time
Difficult I have never have understood the topic
Not taught Topic not studied
Students Difficulties in Learning in Mathematics
Table 3 presents the answer of questions exploring what are the students
difficulties in learning of mathematics. The topics about difficulties in mathematics are
given in Table 3 and 4.
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Table 3
Grade 9th students difficulties in learning in mathematics
Grade 9, N = 375 Easy Moderate Difficult Not Taught
Matrices and determinants 50 20 20 10
Real and complex numbers 50 30 10 10
Logarithms 32 30 28 10
Algebraic expressions and algebraic
40 35 15 10
formulas
Factorization 50 30 10 10
Algebraic manipulation 40 30 20 10
Linear equations and inequalities 40 30 20 10
Linear graph and its applications 40 30 20 10
Introduction to coordinate geometry 40 25 25 10
Congruent triangles 40 30 20 10
Parallelograms and triangles 35 30 25 10
Line bisectors and angle bisectors 45 35 10 10
Sides and angles of a triangle 50 20 20 10
Average score 42 29 19 10
Table 4
Grade 10th students difficulties in learning mathematics
Grade 10, N = 272 Easy Moderate Difficult Not Taught
Quadratic equations 45 30 20 5
Theory of quadratic equations 50 30 10 10
Variations 45 35 15 5
Partial equations 50 35 10 5
Sets and functions 45 40 10 5
Basic statistics 55 15 20 10
Trigonometry 45 30 10 15
Projection of a side of a triangle 45 35 15 5
Chords of a circle 50 20 20 10
Tangent to a circle 45 25 20 10
Chords and arcs 70 20 5 5
154
Angle in a segment of a circle 60 20 10 10

Practical geometry 55 20 13 12
Average score 51 27 14 8
From the tables above, the student responses appear to find most topics are easy
and little difficult. But a logarithm is most difficult for students. In addition, the
responses showed that, introduction to coordinate geometry and Parallelograms and
triangles are difficult for students. This is similar to the findings of Ali and Reid (2013).
Compared to the 9th class, the proportions selecting ‘difficult’ are much higher. This
pattern is very similar to that obtained by Ali and Reid (2012).
By evaluating the results applying chi-square statistic, data of male and female
students was compared. Results are given in Table 5. Data exhibits that majority of
participants were agreed that they understand their mathematics lessons. They also
expressed that they do not like to do homework because they do not have enough ability
to do it on their own. The outcome here reflects the fact that there are limited
opportunities to develop increased field independence in the educational culture in
Pakistan. In the overall data, two groups appeared to show higher levels of confidence
in mathematics learning: boys and those for urban schools. This was checked using chi-
square as a contingency test and it was found that the differences were often significant.
155
Table 5
Gender differences in their attitude to school mathematics
Statements Gender SD D N A SA χ2 df p
I understand my lessons Female 0 1 15 129 131

7.3 4 p < 0.05
completely Male 9 15 20 171 156
I like the way my teacher Female 5 2 11 88 170

18.3 3 p < 0.001
explains the methods Male 9 21 21 146 174
I actually understand the Female 2 4 26 146 97

16.6 4 p < 0.01
procedures in class Male 17 29 46 166 114
Female 36 55 27 68 90
I think tuition is necessary to
get good marks in 28.5 4 p < 0.001
mathematics Male 21 38 33 109 170
Female 24 52 51 95 53
I tend to panic near the exam 21.0 4 p < 0.001
Male 78 72 72 98 53
I think that the allowed time Female 29 37 45 74 89
19.9 4 p < 0.001
limit is very short in Male 34 84 29 124 102
mathematics paper Female 6 8 16 102 144
If I have a problem in
understanding something new, 19.0 3 p < 0.001
I seek help from my teacher Male 20 36 25 137 153
I feel difficulty in learning a Female 32 75 57 75 37

topic because I did not 14.0 4 p < 0.01
understand previous ideas Male 36 86 47 130 72
Teacher question in class Female 4 7 4 96 165

24.1 2 p < 0.001
helps my understanding Male 24 21 23 121 182
Only those units of textbook Female 91 51 32 44 58

30.3 4 p < 0.001
are taught that are important to Male 61 99 31 88 92
pass the examination
Mathematics rules can never Female 18 24 37 84 111
19.1 4 p < 0.001
be proved wrong Male 43 55 45 75 155
In several of the comparisons, the differences between males and females

reflect the generally higher male confidence in relation to studies. Thus, the males tend
to be more confident when it comes to feeling that they understand and in seeking help.
156
Table 6
Grade differences in their attitude to the school mathematics learning
Statements Class SD D N A SA χ2 df p
th
I hate homework because I 9 75 73 64 78 87
31.3 4 p < 0.001
cannot do it on my own 10 th
80 84 35 41 30
th
I think tuition is necessary to get 9 24 37 20 123 173
52.1 4 p < 0.001
good marks in mathematics 10th 33 56 40 54 87
I do not like short questions 9th 87 133 44 76 37
because I cannot express all that 21.1 4 p < 0.001
I know 10th 94 101 24 25 26
I think that the allowed time limit 9th 37 83 39 126 91
is very short in mathematics 20.6 4 p < 0.001
paper 10th 26 39 35 72 100
I feel difficulty in learning a 9th 36 86 53 144 58
topic because I did not 17.7 4 p < 0.01
understand previous ideas 10th 32 75 51 62 50
Teacher question in class helps 9th 25 19 13 138 182

11.1 2 p < 0.01
my understanding 10 th
3 9 14 79 165
Only those units of textbook are 9th 95 98 23 70 91
taught that are important to pass 18.3 4 p < 0.01
the examination 10th 57 52 40 62 59
9th 46 35 54 154 88
I like mathematics 41.8 4 p < 0.001
10th 19 23 18 85 125
th
I find mathematics an interesting 9 58 63 49 96 111
22.1 4 p < 0.001
subject 10th 26 24 27 74 119
I want to learn mathematics 9th 67 60 49 76 125
15.4 4 p < 0.01
because I enjoy it 10 th
29 28 32 66 115
I feel mathematics is easy to 9th 62 68 35 100 112
17.4 4 p < 0.01
understand 10 th
27 26 29 84 104
The data shows that as compared to the 9th class, the proportions selecting
“demanding” are much higher. The chi square analysis helps in exploring the difference
between opinions of male and female students. Also the results show that majority of
students from urban areas have positive perceptions. The outcome here may well reflect
the fact that there are limited opportunities to develop increased field independence in
the educational culture in Pakistan.
157
Table 7
Area of school differences in the school mathematics learning
Items D N A SA χ2
Area SD df p
I understand my lessons Urban 8
14 27 207 162 p<
18.5 2
completely Rural 1 2 8 93 125 0.001
I do not like short questions Urban 130 159 45 47 37 p<
because I cannot express all that I Rural 51 75 23 54 26 20.7 4
0.001
know
Teacher question in class helps Urban 21 17 24 153 203
12.7 2 p < 0.01
my understanding Rural 7 11 3 64 144
Chi square results of mathematics learning regarding area difference show that
majority of students from urban areas have positive perceptions. The majority of
students from urban areas expressed that they understand their lessons of mathematics
completely.
Table 8
School type differences in the school mathematics
Statements School SD D N A SA χ2 df p
I do not like doing too much Public 37 60 16 69 42 p<
class work daily
47.6 4
Private 40 52 78 115 138 0.001
I think that the allowed time Public 12 45 21 95 51 p<
limit is very short in 22.9 3
mathematics paper Private 51 73 53 106 140 0.001
When the mathematics marks Public 16 14 18 87 89 p<
of student improve, it is due 85.4 3
to his own hard work Private 26 27 39 97 234 0.001
Only those units of textbook Public 24 64 13 72 51 p<
are taught that are important 56.7 4
to pass the examination Private 128 86 50 60 99 0.001
Public 13 10 35 93 73 p<
I like mathematics 21.2 4
Private 52 46 37 146 142 0.001
I find mathematics useful in Public 9 10 32 86 87 p<
my daily life
16.5 3
Private 46 34 66 115 162 0.001
I find mathematics an Public 24 23 38 68 71 p<
interesting subject
15.5 4
Private 60 64 38 102 159 0.001
158
The table 8 showed that the Public and private schools draw very different
student populations and, therefore, large differences are to be expected. The proportion
of girls exceeded that of boys, mainly because of the current patterns in education at the
moment. In one other study, there was a marked development of independency with age
over the range from 12-17 (Onwumere & Reid, 2014). Indeed, there is considerable
circumstantial evidence that the extent of field independence can grow with age but this
seems to depend of experiences and has cultural implications. The outcome reflects the
fact that there are the limited opportunities to develop increased field independence in
the educational culture in Pakistan. When the results for the measured field dependency
were correlated with mathematics marks, significant correlation values were obtained.
This is in accordance with the literature. The positive correlation values (0.3 at 0.05
level of significance) between field dependency and age of students show that field
dependency makes an effect on learners’ performance as well as achievement in
relation to age. The students who are field independent perform better in mathematics
than the others who are field dependent.
Discussions
This study was intended to explore students’ perceptions of the mathematic
learning and difficulties. The finding shows that the students belonging to the private
sector and urban areas differ in their views as compared to the public schools and rural
areas. This is the pattern of education system Pakistan, especially in the public schools.
The students in the public schools of Pakistan are generally belonging to the middle or
the lower class of the society, with lesser incomes. They do not have several modern
facilities and they have to learn with old and traditional limited resources. In Pakistani
schools, there is a recommended textbook of mathematics for all classes. The
examination is totally based on this prescribed textbook. In the current teaching
methodology, much of the focus is given on just to solve these exercises instead of
instilling in the pupils a perfect knowledge of the basic concepts of mathematics. Thus,
at present the teaching practices of the subject mathematics make students the rote
learners of textbooks.
This study shows that the majority expressed positive views regarding
mathematics; with most expressing that they feel happy to learn mathematics. The
students well perceived their learning in mathematics. Students generally find
mathematics a boring and difficult course and this finding is little contrasting to (Brown
et al, 2008). The majority of the students showed that they seem a little importance of
using student centered approaches mathematics curriculum as curriculum do not stress
to solve problems in classroom. Simply, the students are not encouraged and rewarded
in their mathematics performance. The deficiency of programs of development and
resources causes problems to the students as well as teachers (Memon, 2007; Halai,
1998). Particularly from the rural areas schools, the students pointed out the difficulties
159
in their mathematics learning experiences because of inexperienced staff and

insufficient resources (Memon, 2007; Anderson et al., 2005). Overall correlation of
mathematics marks (standardized) and extent of field dependency is moderate.
Likewise, Onwumere (2009) showed that extent of field dependency was highly
correlated with mathematics performance for each age group. Moreover, these results
were consistent with the findings of Al-Enezi (2006) and (Onwumere, 2009). Thus, the
standardized mathematics examination scores reflect that there is a general ability in
students in mathematics, and then this ability correlates with the measured extent of
field dependency.
Conclusions and Recommendations
It is found from the study that the students are enthusiastic in their learning in
mathematics. They found mathematics interesting and valuable. Although very few
found studying mathematics boring and tough. The students of the 9th and 10th class in
this study were of the view that mathematics is an interesting, useful and analytical
power generating subject. The Figure 2was generated on the basis of Findings, the key
problems and recommendations from the study which were detailed below the figure. .
160
Change buying
policies
Teach what this means
Lack of
Build all educational Comprehension
Re-design course to courses with formative
exploit the new assessment
technologies
Positively Disposed Lack of

to Mathematics Understanding in
Learning Mathematical
Concepts
Change buying
policies
Mathem-
atics Lack of Curriculum
Percepti- Support
ons And
Difficult
-ies
Seeking for Lack of Knowledge

Understanding and of the Wide Range of
Range of Wider Assessment
Skills Give students
focused
experience
Change assessment and Introduce students to Lack of Experience

no recall the wide range of and Appropriate
Assessments Training
Figure 1. The key problems and recommendations from the study

In the figure above, the boxes and circles show the findings and key problems
and outer text shows the recommendations from the study. The above figure
2summarizes the key findings as there were some problems identified by the students,
particularly, difficult with large classes, demanding in time in preparing lessons.
Furthermore, they perceived that their learning in mathematics is not matched properly
with curriculum that gives more focus recalling skills and relies more on book and the
current assessment system is over-loaded and its focus on just more and more formal
examinations. Moreover, the correlation values between field dependency and age of
students show that field dependency makes an effect on learners’ performance as well
as achievement in relation to age. Furthermore, the above diagram shows that the
important implications for understanding of the realities that exist in secondary
161
mathematics classrooms in Pakistan. This is recommended from this study that the
teachers should be supported and given the time and resources to develop better ways
for the future. Moreover, there should be a broader opportunity to develop increased
field independence in the educational culture in Pakistan.
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163

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Journal of Educational Research, Dept. of Education, IUB, Pakistan (Vol. 21 No.

Learning in Mathematics: Difficulties and Perceptions of Students

consider understanding and applications. However, if the examination procedures

I like multiple choice questions in mathematics exam. 53 28 6 7 6

Statements High Medium Low

Angle in a segment of a circle 60 20 10 10

I understand my lessons Female 0 1 15 129 131

I like the way my teacher Female 5 2 11 88 170

I actually understand the Female 2 4 26 146 97

I feel difficulty in learning a Female 32 75 57 75 37

Teacher question in class Female 4 7 4 96 165

Only those units of textbook Female 91 51 32 44 58

In several of the comparisons, the differences between males and females

Teacher question in class helps 9th 25 19 13 138 182

in their mathematics learning experiences because of inexperienced staff and

Positively Disposed Lack of

Seeking for Lack of Knowledge

Change assessment and Introduce students to Lack of Experience

Figure 1. The key problems and recommendations from the study

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