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The Influence of Students` Perceptions on Mathematics Performance. A Case of a Selected High School in South Africa

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This study investigates the influence of students’ perceptions on mathematics performance at a selected South African secondary school. The influence of factors such as strength and weaknesses in mathematics, teacher support/learning material, family background and support, interest in mathematics, difficulties or challenges in doing mathematics, self-confidence and myths and beliefs about mathematics were identified as constructs of perceptions that influence students’ performance. Five of the seven constructs were found to be influential on students’ performance in mathematics. Quantitative methods were used to analyse the data collected from a questionnaire which was administered to randomly selected secondary school students (n=124) in Polokwane, South Africa. From the regression analysis of the data, the following hierarchy of themes emerged as components of students’ perceptions of mathematics. These were (i) weaknesses in mathematics (ii) family background and support, (iii) interests in mathematics, (iv) self-confidence in mathematics, (v) myths and beliefs about mathematics (vi) teacher /learning material support, (vii) difficulties in learning mathematics. Results from t-tests, Anova and suggest that there were significant differences in the perceptions and beliefs about mathematics between males and females, between mature and juvenile students and among students from different language backgrounds respectively. Correlation analysis results showed strong positive relationships between performance and perception constructs such as self-confidence, interests in mathematics, teacher and learning support material as well as myths and beliefs .The respondents tend to view lack of proficiency in mathematics as a challenge, and attribute success in mathematics to effort and perseverance. Students also perceive difficulty in mathematics as an obstacle, and attribute failure to their own lack of inherited mathematical ability. These findings suggest that differences in (i) myths and beliefs about mathematics success, ( (ii) motivation given by mathematics teachers and parents, (iii) mathematics teachers' teaching styles and learning materials and (iv) self confidence in mathematics may lead to differences in perceptions about mathematics. These in turn may lead to differences in attitudes towards mathematics and learning mathematics which have a bearing on performance. DOI: 10.5901/mjss.2014.v5n3p431
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The Influence of Students` Perceptions on Mathematics Performance.
A Case of a Selected High School in South Africa
Paul Mutodi
Department of Maths, Science and Technology, University of Limpopo (Turfloop Campus)
E-mail: paul.mutodi@ul.ac.za
Hlanganipai Ngirande
Department of Business Management, University of Limpopo (Turfloop Campus)
E-mail: hlanganipai.ngirande@ul.ac.za
Doi:10.5901/mjss.2014.v5n3p431
Abstract
This study investigates the influence of students’ perceptions on mathematics performance at a selected South African
secondary school. The influence of factors such as strength and weaknesses in mathematics, teacher support/learning
material, family background and support, interest in mathematics, difficulties or challenges in doing mathematics, self-
confidence and myths and beliefs about mathematics were identified as constructs of perceptions that influence students’
performance. Five of the seven constructs were found to be influential on students’ performance in mathematics. Quantitative
methods were used to analyse the data collected from a questionnaire which was administered to randomly selected
secondary school students (n=124) in Polokwane, South Africa. From the regression analysis of the data, the following
hierarchy of themes emerged as components of students’ perceptions of mathematics. These were (i) weaknesses in
mathematics (ii) family background and support, (iii) interests in mathematics, (iv) self-confidence in mathematics, (v) myths
and beliefs about mathematics (vi) teacher /learning material support, (vii) difficulties in learning mathematics. Results from t-
tests, Anova and suggest that there were significant differences in the perceptions and beliefs about mathematics between
males and females, between mature and juvenile students and among students from different language backgrounds
respectively. Correlation analysis results showed strong positive relationships between performance and perception constructs
such as self-confidence, interests in mathematics, teacher and learning support material as well as myths and beliefs .The
respondents tend to view lack of proficiency in mathematics as a challenge, and attribute success in mathematics to effort and
perseverance. Students also perceive difficulty in mathematics as an obstacle, and attribute failure to their own lack of
inherited mathematical ability. These findings suggest that differences in (i) myths and beliefs about mathematics success, ( (ii)
motivation given by mathematics teachers and parents, (iii) mathematics teachers' teaching styles and learning materials and
(iv) self confidence in mathematics may lead to differences in perceptions about mathematics. These in turn may lead to
differences in attitudes towards mathematics and learning mathematics which have a bearing on performance.
Keywords: Perceptions, Mathematics Achievement, Attitudes, Beliefs, secondary school students
1. Introduction
This study explores the influence of students’ perceptions on mathematics achievement at a selected secondary school
in Polokwane, South Africa. Seven perceptual variables which influence students’ achievement were identified.
Mathematical perceptions considered for this study include individual constructs that are generated by individual
experiences (student characteristics), home and societal context of the student and those emanating from classroom
experiences (Hannula, 2007). Studies generally have found boys to hold a more positive attitude towards mathematics
(e.g. Kaasila, Hannula, Laine & Pehkonen, 2006). In this study, the term ‘perceptions of mathematics’ is conceptualised
as a mental representation or view of mathematics, apparently constructed as a result of social experiences, mediated
through interactions at school, or the influence of parents, teachers, peers or mass media. It also refers to some kind of
mental representation of something, originated from past experience as well as associated beliefs, attitudes and
conceptions. There are several studies that focus on investigating the perceptions that students have about mathematics
itself (Picker & Berry, 2000; Rensaa 2006; Aguilar, 2012; Moreau, Mendick & Epstein, 2010). Despite this large body of
research, there is a lack of research on views and beliefs held by South Africa secondary school students.
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In South Africa mathematics is a perceived as a difficult subject, accessible only to the few. Adults frequently claim
dislike or incompetence towards the subject, while many students choose not to pursue mathematics post-compulsory
education. Recent studies (e.g. Sterling, 2004, de Villiers, 2010) indicate that there is a critical shortage of people
qualified in mathematics in South Africa. Mathematics achievement in South Africa is abnormally poor (Spaull, 2012). In
addition; there is the recent decline in recruitment into higher education courses in mathematics, science, technology and
engineering noted in South Africa where negative views of mathematics (and science) are often cited as contributory
factors(Fry,2006).Many theories have been advocated to explain the overall poor performance at all grade levels.
Students who perform well in mathematics are treated as “nerds”. Many people generally dislike mathematics. It is seen
as a subject reserved for the selected few. It often evokes feelings of stress; anxiety and fear (Atallah, Bryant and Dada,
2009). Furthermore, it is seen as a filter that hinders students from pursuing their career aspirations mathematics and
science –related fields (Fisher, 2008).
Perceptions and beliefs about mathematics originate from past experiences; comprising both cognitive and
affective dimensions Aguilar, Rosas and Juan Zavaleta (2012). From a cognitive point of view it relates to a person’s
knowledge, beliefs, and other cognitive representations while from an affective domain it refers to a person’s attitudes,
feelings and emotions about mathematics. The term is also understood broadly to include all visual, verbal
representations, metaphorical images and associations, beliefs, attitudes and feelings related to mathematics and
mathematics learning experiences. Therefore, the main aim of this study is to explore and identify the range of
perceptions, beliefs and attitudes towards mathematics as it is perceived by the secondary school students.
It is widely claimed that, negative perceptions and myths of mathematics are widespread among the students,
especially in the developed countries (e.g., Mtetwa & Garofalo, 1989; Ernest, 1996; & Gadanidis, 2012). Sam (2002)
claimed that many students are scared of mathematics and feel powerless in the presence of mathematical ideas. They
regarded Mathematics as "difficult, cold, abstract, and in many cultures, largely masculine" (Ernest, 1996, p.802). Buxton,
cited by Sam (2002) viewed mathematics as "fixed, immutable, external, intractable and uncreative" or "a timed-
test"(p.115). Even scientists and engineers whose jobs are related to mathematics "often harbour an image of
mathematics as a well-stocked warehouse from which to select ready-to-use formulae, theorems, and results to advance
their own theories"(Peterson, 1996).
Educators attempt to explain this phenomenon through the widespread beliefs or mathematical myths that
"learning mathematics is a question more of ability than effort"(McLeod, 1992, p.575) or "there is an inherent natural
ability for mathematics"(Fitz Simons et al., 1996, p. 768). Many people hold the view that mathematics is only for the
clever ones, or only for those who have 'inherited mathematical ability'. Another widely held belief is that mathematics is
a male dominant subject. One other stereotyped image is that boys are better in mathematics than girls (Ernest, 2001).
Thus, many adults accept this lack of accomplishment in mathematics as a permanent state over which they have little
control. Parents and significance others have a strong influence on students’ beliefs and attitudes towards mathematics
(McLeod, 1989). Students’ mathematics learning outcomes are strongly related to their beliefs and attitudes towards
mathematics (Furinghetti & Pehkonen, 2000; Leder, Pehkonen, & Törner, 2002; Pehkonen, 2003). According Sam (2002)
parents’ views about mathematics have strong effect on the way they teach their children. This often creates tension
between the parents and teachers if they share contrasting images of mathematics.
One origin of different student perceptions is the individual life histories that each student brings to mathematics
learning. These life histories influence the way the students position themselves in the classroom, the way they engage
with mathematics, teacher and peers and the way they interpret mathematical experiences. On the other hand, there are
contextual factors that students of the same class share with each other. These are, for example, the personality of the
teacher, quality of teaching and learning support material, interests in mathematics, self –confidence and general
proficiency in the subject. These influence all students in a class and are the origin of shared experiences. Moreover,
also students’ individual experiences are partly shaped by the shared events in the classroom. This is illustrated with an
arrow from classroom context to individual experiences.
2. Objectives of the Study
The objectives of this study are:
1. To identify the range of student's perceptions towards mathematics held by South African students.
2. To examine whether there is a relationship between the identified perception constructs and student
performance in mathematics.
3. To examine whether gender, age and language background have an effect on the way students perceive
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mathematics and how these perceptions influence performance.
4. To give recommendations to authorities on strategies that can be employed to enhance positive perceptions
towards mathematics.
3. Research Questions of the Study
The research question that guides this study is:
1. Which of the identified perception constructs have a direct influence on students’ performance?
4. Research Hypotheses
H1: There is a significant relationship between students’ perceptions and mathematics performance.
H2: There is a significant difference between the perceptions of male and female students towards mathematics
performance
5. Significance of the Study
By examining the different images, attitudes, belief and myths of mathematics that students hold, there is a potential for
such images, attitudes, beliefs to be challenged, promoted or discouraged. The information obtained will enhance better
strategies and measures for promoting student understanding and participation in mathematics related fields. The results
of this study might inform the extent of the influences of parents and teachers in shaping students' perceptions of
mathematics. This information can be used to promote positive influence while attempting to avoid the negative
influences of these sources. It will help to understand better the roles of parents and teachers in the shaping of students'
images of mathematics. The findings will reflect possible implication for mathematics education and mathematics teacher
education. Knowing how students perceive mathematics learning experiences in school and how this could influence
their images of mathematics will help us to understand better how mathematics should be presented in the classroom.
This knowledge may also help to enhance better curriculum planning and teacher development programmes. Students’
views of mathematics are important as they can shape the way in which they learn mathematics. Such views and
perceptions may have more influence than knowledge in determining how individuals organise and define tasks.
Perceptions of what mathematics is and is not, may affect attitudes, performance, confidence and perceived usefulness
of mathematics.
6. Literature Review and Theoretical Orientations
To find a well-developed, well-defined theoretical framework in the study of beliefs and attitudes is a challenge and the
endeavour to develop one coherent framework for this area has been unfruitful for many researchers. According to
Hannula (2004) there are on-going debates on the theoretical frameworks used in the conceptualisation of affect in
mathematics education. Currently there is no precise, shared language for describing the affective domain, within a
theoretical framework that permits its systematic study. Thus, this study is guided by different notions and discusses the
relationship between their conceptions. The constructs, beliefs and attitudes, images, views, perspectives and opinions
are not directly observable and have to be inferred, and because of their closeness it is problematic to have a common
definition of these notions (Leder & Forgasz, 2002). Efforts by researchers to isolate these concepts yield no acceptable
results. Kislenko, Grevholm, and Lepik (2005) explained the interplay among thinking, feeling, opinions, beliefs, views
and perspectives. They argued that beliefs are a part of persons’ knowledge that is highly subjective and on the other
hand the conceptions feelings and beliefs are often overlapping and cannot be distinguished. Some researchers consider
beliefs to be part of knowledge (e.g. Furinghetti, 2003; Renzi, 2005, Brown, 2006), some think beliefs are part of attitudes
(e.g. Pehkonen and Pietilä, 2004), and some consider them as part of conceptions (e.g. Thompson, 1992).
Ignacio, Nieto and Barona (2006) used the term mathematics self-concept to refer to personal beliefs relating to
the world of mathematics, what is to the set of ideas, judgements, beliefs, and attributions that the person has steadily
built up during his or her process of learning in the school environment. Personal beliefs affect the person’s interest in
mathematics, efficiency in performing mathematics tasks, motivation and pleasure with mathematics, attribution of
causes to academic success or failure, and self-concept as belonging to a certain social group. Hannula (2006) pointed
out that a mathematics learner’s liking or disliking of mathematics derives from his/her belief structure. People’s beliefs
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and attitudes towards mathematics are shaped by individual personal characteristics and experiences related to their
academic self-image. An individual’s view of mathematics is a compound of knowledge, beliefs, conceptions, attitudes,
and feelings. Literature suggests that attitudes and beliefs are interlinked. Kayander and Lovric (2005) claims that
attitudes may influence the formation of new beliefs.
Beliefs might be thought of as lenses through which one looks when interpreting the world (Philipp, 2006).
Research shows that the beliefs and feelings adults experienced as learners carry forward to their adult lives, and these
feelings are important factors in the ways they relate to the new generation of learners. There is a lack of interest in
mathematics or a relatively higher tendency of mathematics avoidance among many of the South African students. Most
students hold the belief or myth that being good in mathematics is mainly due to ability than effort (McLeod, 1992). Many
students admit this lack of achievement in mathematics as a permanent state over which they have little control.
According to Tobias (2003), millions of adults are blocked from professional and personal opportunities because they
fear or perform poorly in mathematics, for many these negative experiences remain throughout their lives.
Moscucci (2008) discussed 'a meta-belief systems activity' on the basis of learning experimentation, where the
importance of making learners aware of their belief systems regarding mathematics became apparent. Many of a
teacher’s beliefs and views seem to originate in and be shaped by experiences” (Thompson, 1992, p. 139).Pajares
asserts that whereas beliefs that are formed from experiences appear to be more resistant, “learning and inquiries are
dependent on prior beliefs”.
There is need for teachers to learn about their students from the students themselves. Pedagogy that is intended
to improve students’ academic achievement needs to be informed by the students themselves. Insight into the
perceptions of the learners with regard to their mathematical experiences can prove beneficial in developing effective
pedagogy for improved mathematics achievement. South African students, in particular, are in need of effective
pedagogy that will improve their school mathematics performance. The purpose of this study is to provide insights into
the perceptions of South African students with respect to their experiences inside and outside classrooms, with or without
their teachers. Implications of these perceptions may inform pedagogical considerations in improving the mathematics
achievement of South African tertiary students.
The conceptions, attitudes, and expectations of the students regarding mathematics and mathematics teaching
have been considered to be very significant factor underlying their school experience and achievement (Borasi, 1990;
Schoenfeld, 2008). These conceptions determine the way students approach mathematics tasks, in many cases leading
them into non-productive paths. Students have been found to hold a strong procedural and rule- oriented view of
mathematics and to assume that mathematical questions should be quickly solvable in just a few steps, the goal just
being to get “right answers”. For them, the role of the student is to receive mathematical knowledge and to be able to
demonstrate so; the role of the teacher is to transmit this knowledge and to ascertain that students acquired it (Borasi,
1990). Such conceptions may prevent the students from understanding that there are alternative strategies and
approaches to many mathematical problems, different ways of defining concepts, and even different constructions due to
different starting points. They may approach the tasks in the mathematical class with a very narrow frame of mind that
keeps them from developing personal methods and build confidence in dealing with mathematical ideas.
Crawford et al. (1993) found that the majority of students perceived mathematics as “numbers, rules and formulae”
(p. 213). For some students awareness of mathematics involves simply the recall of facts and the use of formal
procedures. These views were associated with what he calls a “surface approach” to learning mathematics, that is, “the
reproduction of knowledge and procedures”( p. 212). Research revealed that many students relate mathematics mainly
with computations (Iddo & Ginsburg, 1994). Many students tend to identify mathematics with arithmetic. Doing
mathematics is normally associated with calculations. It is widely maintained in the literature that negative images and
myths of mathematics are widespread among the students. Many students view mathematics as a difficult, cold and
abstract subject. It is perceived by many students as an exclusive discipline Buhagiar (2013). From epistemological and
pedagogical perspectives, it is perceived as a subject that involves a lot of work. The subject is seen as an obstacle,
often dreaded and as hard work. Mathematics is also viewed as a static and objective discipline, available for discovery
by mathematicians, in turn to be transmitted by teachers and received by the students.
Many students seem to concentrate on computations as the essence of mathematics. Many believe that
mathematical activity includes procedures that are divorced from real life, from discovery and from problem solving. The
fact that mathematics is usually presented as a body of absolute truths which exists independently of the learners and
taught in a hierarchical, linear and prescriptive fashion reinforces the view that mathematics is a difficult subject. There is
also a claim that mathematics is only for the clever ones, or only for those who have inherited mathematical ability
(Kimball & Smith, 2013). Being mathematically knowledgeable is often treated as an indicator of general intelligence, as
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evidenced by the widespread use of mathematics in entrance tests. This view causes many people to believe that
learning mathematics is a question of ability rather than effort and that there is an inherent natural ability for mathematics.
This perception leads students to accept their lack of accomplishment in mathematics as a permanent state over which
they have little control.
Figure 1: Mathematical Perceptions development model
7. Methodology
A quantitative research approach was used. The researchers used a quantitative approach because, as noted by
Kabungaidze, Mahlatsana and Ngirande (2013), quantitative research design allows the researcher to answer questions
about the relationships between measured variables with the purpose of explaining, predicting and controlling certain
phenomena. The study population consisted of both male and female grade 10 students from a selected high school in
Limpopo province of South Africa. The total size of the population was 150(N=150). Using the RaoSoft sample size
calculator, a minimum recommended sample size of 124 respondents was obtained. The respondents were selected
using a simple random sampling method.
A 57-item self-administered questionnaire divided into seven categories of perceptions was designed using
existing instruments as well as information which emerged from the literature. The questionnaire consisted of three
sections, namely the Biographical and occupational data questionnaire, the perceptions section and the performance
section. The biographical and occupational data questionnaire was constructed by the researchers to tap information
relating to certain key biographical and occupational variables relating to the respondents such as gender, age and
home. This information was used mainly for a description of the sample.
Perceptions and performance variables were identified from literature and a 5-point likert scale was designed by
the researchers. Responses to each of the items were rated with anchors labelled: 1 = strongly disagree, 2 = disagree, 3
= neither agree nor disagree, 4 = agree, 5= strongly agree. The reliability was tested using the Cronbach Alpha
coefficient and a coefficient of 0.910 was achieved, hence the reliability of the instrument can be accepted based on
Cooper and Schindler (2008)’s argument that any coefficient above 0.70 implies reliability of the instrument. The
Cronbach’s alpha coefficients for the sub-categories of the identified perceptions were also calculated and the results are
shown in the table 1 below.
Table 1: Reliability Statistics
Description Cronbach's Alpha Number of items
Mathematics Performance .695 4
Strength and weaknesses in mathematics .699 4
Teacher /learning material support .868 10
Family background and support .701 4
Interests in mathematics .713 8
Difficulties or challenges in learning mathematics .738 8
Self confidence inmathematics .648 9
Myths and beliefs about mathematics .789 10
Overall Questionnaire reliability .910 57
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To observe content validity, the questionnaire was adopted and structured so that the questions posed were clearly
articulated and directed. All statements were formulated to eliminate the possibility of misinterpretations. This was
followed by a pre-tested administered to 87 students who were excluded from the participants in the main study. The
identified amendments were made to ensure the simplicity and clarity of some questions, making it fully understandable
to the participants (Masitsa, 2011).
In administering the questionnaire, the following procedure was followed:
The researchers personally requested the school principal permission to distribute the copies of the
questionnaire. Questionnaire distribution was done in such a way as to cause no disturbance to student’s
classes.
The researchers distributed the questionnaire to the respondents during breaks (e.g. lunch time) and also ask
the respondents to deposit completed questionnaires in a locked box located in the school administration
building where they will be collected after three days. A covering letter assuring the prospective respondents
of anonymity and confidentiality was accompanying the questionnaire. This covering letter also informs the
prospective respondent what the study was about and ask him/her to respond to the questionnaire voluntarily.
The returned questionnaires were inspected to determine their level of acceptability. They were coded. The data
was transferred to an Excel sheet. A statistical computer package, Statistics Package for Social Sciences (SPSS) version
20.0, was used to process the results. Descriptive statistics (e.g. means and standard deviations) were used to describe
the data in summary form. Pearson product-moment correlation coefficient was used to measure the relationships
between the variables (i.e. myths and beliefs, strengths and weaknesses in mathematics, self confidence in
mathematics, family background and support as well as interests in mathematics) and the dependent variable
(mathematics proficiency). Standard multiple regression analysis was also carried out to assess the relative contribution
of the independent variables to the variability of the dependent variable. To test the demographic mean differences,
Analysis of Variance (ANOVA) and t-test were used.
8. Results
8.1 Response rate
A follow up of the questionnaires showed a good response rate from the research participants. At the end of the data
collection phase, the total number of the completed questionnaires was 124. Given that the sample size of the study was
150, this represented a response rate of 82.7%. Many observers presumed that higher response rates assure more
accurate survey results (Holbrook, Krosnick, & Pfent, 2008). Response rates (60 - 70%) are considered as ideal for this
type of study (Babbie, 2013).
8.2 Subjects
The sample consisted of 124 secondary school students. Table 1 presents demographical data of the study sample.
Table 2: Demographic variables
Variable Frequency Percentages
Gende
r
Male 51 41
Female 73 59
Age
16-20 years 78 63
21 years and above 46 37
Home language
Sepedi 90 72.5
Shangane 64.8
Venda 13 10.5
Swati 10 8.1
Othe
r
5 4.1
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Demographic data about the respondents shows that 73 (59%) were females and 51(41%) were males. The majority
78(63%) of the participants were in the 16-20 years category. Sepedi dominated the home languages 90(72.5%) while
Venda 13(10.5%) was also notable. The other languages were insignificantly represented. The school is dominated
Sepedi speaking students.
8.3 Perception constructs Summary descriptive statistics
Data collected were analysed in an effort to explore the perceptions of students regarding mathematics. In particular, the
identified perceptions focused on eight (8) constructs: (i) mathematics performance, (ii) difficulties or challenges in
learning mathematics, (iii) myths and beliefs about mathematics, (iv) family background and support, (v) self confidence
in mathematics, (vi) teacher /learning material support, (vii) interests in mathematics, (viii) weaknesses in mathematics.
Table 3: Summary descriptive statistics
Item Description Mean Std. Deviation Rank
1 Mathematics Performance 3.5181 1.4993 1
2 Difficulties in learning mathematics 3.1431 .56863 2
3 Myths and Beliefs about mathematics 3.1379 . 4657 3
4 Family background and Support. 3.1126 .61158 4
5 Self confidence in mathematics 3.0789 .524595 5
6 Teacher /Learning material support 3.0570 .5755 6
7 Interests mathematics 2.9969 .61989 7
8 Weaknesses in Mathematics 2.8347 .74687 8
The overall mean for each construct were analysed and are shown in table 3 above. The results showed that students
perceive mathematics proficiency (overall mean (M) =3.5181, with a standard deviation (SD =1.4993) as the main
contributing factor to their success in Mathematics. Students perceive that it is worthwhile for one to ask himself/herself:
“What does he wants us to do? They also confirmed that the more the time spend studying mathematics the better the
results in tests and assignments. They also revealed the contributions of effort and endurance when solving a problem,
usually lead to correct results. To solve math problems accurately and efficiently, students confirmed that one needs to
develop flexibility and to learn multiple strategies.
Difficulties in learning mathematics were also perceived as another form obstacle that affects some sections of
students. Difficulty in learning mathematics also presents itself as a difficulty in applying formulae, using measurements,
writing out phases of calculations, writing numbers, and spatial perception. Students who struggle with mathematics
perceive that the amount of material in any mathematics is so overwhelming making it difficult to absorb. Students also
perceive mathematics as a huddle one has to cross in order to progress to the next grade level. Students also indicated
their academic progress is hampered by low scores in mathematics even if they are performing well in other subjects.
Myths and Beliefs about mathematics were also ranked highly (mean=3.1379, SD=. 4657) in terms of its
contribution to students’ liking and disliking of mathematics. Myths in relation to gender and maths are not the only ones
that have the potential to have a negative impact on students’ learning in maths. Maths is valued because it is considered
by the community to be an indicator of intelligence. Students’ feelings of lack of control could stem from the idea that
maths is “difficult” or that you have to have a “maths brain” in order to succeed in the subject. Feelings of lack of control
can be due to cultural norms, such as negative stereotypes about image and gender. Women are often too ready to
admit inadequacy and say, "I just can't do math.". The idea that math ability is mostly genetic is one dark facet of a larger
fallacy that intelligence is mostly genetic. The results revealed that student’ beliefs about what mathematics is and what it
is not has an effect on their overall performance.
Weaknesses in mathematics was least ranked (mean=2.8347 and SD =0 .74687). Thus most students do not
perceive that their weaknesses or strength in tackling mathematics problems has an effect on their performance.
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Table 4: Gender and Age mean differences
One-Sample Test
Test Value = 0
t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference
Lower Upper
Gende
r
31.809 123 .000 1.4113 1.323 1.499
Age 77.393 123 .000 3.3710 3.285 3.457
A t-test was conducted to test whether there was a significant difference between male and female students’
mathematics perceptions. It must be recalled that the study hypothesised that there is a significant difference between
male and female students’ mathematics perceptions. The results for the test are shown in table 4 above (df = 123, t =
31.809, p=0.00). The null hypothesis was rejected since the p-value is less than 0.05. Therefore we conclude that there
is a significant difference in the way mathematics is perceived between males and females. This is consistent with
findings by Hoang (2008) who showed that male consistently reported slightly more positive perceptions and attitudes
than females. However a research carried out by Mohamed and Waheed (2011) showed that the students’ positive
attitude towards mathematics is medium and there is no gender difference in their attitudes.
A t-test was also conducted to test whether there was a significant difference in views and attitudes towards
mathematics between the two age cohorts of students. The results for the test are shown in table 4 above (df=123, t
=77.393, p=0.00). The null hypothesis was rejected since the p-value is less than 0.05. Therefore we conclude that there
is a significant difference in views and attitudes towards mathematics between the two age cohorts of students.
To test if there are significant differences in perceptions among students from different language backgrounds, an
Analysis of Variance (ANOVA) test was conducted to test the following hypothesis.
H0 : There is no significant difference in math perceptions among students from different language backgrounds.
H1 : There is a significant difference in math perceptions among students from different language backgrounds.
The results of the test in table 6 below show that (df = 1, df =122, F= 0.160, p=0.690).Therefore, we do not reject
the null hypothesis since p>0.05 and conclude that there are no significant differences in mathematics perceptions
among students from different language backgrounds.
Table 6: ANOVA (Home language and perception mean differences)
Sum of Squares d
f
Mean Square F Sig.
Home language
Between Groups .427 1.427 .160 .690
Within Groups 325.444 122 2.668
Total 325.871 123
Mathematics performance Between Groups .087 1.087 .154 .696
Within Groups 68.810 122 .564
Total 68.897 123
Weaknesses in mathematics Between Groups .514 1.514 .920 .339
Within Groups 68.097 122 .558
Total 68.611 123
Teacher /learning material support Between Groups .148 1.148 .443 .507
Within Groups 40.596 122 .333
Total 40.743 123
Family support Between Groups .159 1.159 .423 .517
Within Groups 45.848 122 .376
Total 46.007 123
Interests in mathematics
Between Groups .288 1.288 .749 .388
Within Groups 46.976 122 .385
Total 47.264 123
Difficulties in mathematics Between Groups .007 1.007 .025 .875
Within Groups 32.380 122 .265
Total 32.387 123
Myths and beliefs
Between Groups .098 1.098 .448 .504
Within Groups 26.578 122 .218
Total 26.676 123
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Further tests on the different constructs identified showed that there are no perception differences as all the p-values are
all greater than 0.05.This means that there are no significant differences in the ways students perceive weaknesses in
mathematics, teacher support/learning material, family background and support, interests in mathematics, difficulties in
doing mathematics, self-confidence and myths and beliefs about mathematics. The seven constructs seem to have the
same contribution to the students’ performance.
Table 7: Correlation Analysis: The strength and direction of the relationship between independent variables (myths and
beliefs, weaknesses in mathematics, self confidence in mathematics, family background and support as well as interests
in mathematics) and the dependent variable (mathematics performance)
Correlations
Maths
performance Weaknesses in
mathematics Teacher /learning
material support Family
support Interests in
mathematics
Difficulties in
mathematics Self
confidence Myths and
beliefs
Mathematics
performance
Pearson
Correlation 1.000 .407** .756** .652** .797** .688** .826** .713**
Sig. (2-
tailed) . .000 .000 .000 .000 .000 .000 .000
N 124 124 124 124 124 124 124 124
Weaknesses in
mathematics
Pearson
Correlation .407** 1.000 .792** .607** .732** .771** .485** .541**
Sig. (2-
tailed) .000 . .000 .000 .000 .000 .000 .000
N 124 124 124 124 124 124 124 124
Teacher /learning
material support
Pearson
Correlation .756** .792** 1.000 .794** .906** .782** .741** .725**
Sig. (2-
tailed) .000 .000 . .000 .000 .000 .000 .000
N 124 124 124 124 124 124 124 124
Family support
Pearson
Correlation .652** .607** .794** 1.000 .722** .589** .685** .582**
Sig. (2-
tailed) .000 .000 .000 . .000 .000 .000 .000
N 124 124 124 124 124 124 124 124
Interests in
mathematics
Pearson
Correlation .797** .732** .906** .722** 1.000 .720** .713** .725**
Sig. (2-
tailed) .000 .000 .000 .000 . .000 .000 .000
N 124 124 124 124 124 124 124 124
Difficulties in
mathematics
Pearson
Correlation .688** .771** .782** .589** .720** 1.000 .743** .776**
Sig. (2-
tailed) .000 .000 .000 .000 .000 . .000 .000
N 124 124 124 124 124 124 124 124
Self confidence
Pearson
Correlation .826** .485** .741** .685** .713** .743** 1.000 .590**
Sig. (2-
tailed) .000 .000 .000 .000 .000 .000 . .000
N 124 124 124 124 124 124 124 124
Myths and beliefs
Pearson
Correlation .713** .541** .725** .582** .725** .776** .590** 1.000
Sig. (2-
tailed) .000 .000 .000 .000 .000 .000 .000 .
N 124 124 124 124 124 124 124 124
**. Correlation is significant at the 0.01 level (2-tailed).
Pearson Correlation analysis was used to determine the strength and direction of the relationships. Correlation is a
technique for investigating the relationship between two quantitative variables, for example, teacher/learning support
material and mathematics performance. Pearson's correlation coefficient (r) is a measure of the strength of the
association between the two variables. Table 3 shows that there is a weak positive relationship between weaknesses in
mathematics and mathematics performance (r=0.407, p=0.000). This means that the more the challenges a student
encounters in mathematics, the less the performance. The results are compatible with Zacharia and Barton ( 2004)
findings which revealed that a student’s weaknesses in mathematics have a negative effect on performance.
The results of the study also yields a statistically significant positive correlations with teacher /learning material
support and mathematics performance (r=0.756, p=0.000). This means that the more a student gets enough support
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from his/her teacher, the more he/she is likely to become more proficient in mathematics. These findings are consistent
with Hammond (2000) who indicates that measures of teacher quality and support strongly correlates with student
achievement in mathematics.
Family background and support showed statistically significant positive correlations with mathematics
performance (r=0.652; p=0.000); interests in mathematics and mathematics performance (r=0.797, p=0.000) meaning
the more a student is interested in mathematics, the more chances of becoming proficient in the subject. In supported of
these findings, Kupari & Nissinen (2013) in their study concluded that students’ mathematics achievement is positively
correlated to family background and support.
Self-confidence showed statistically significant positive correlations with mathematics performance (r=0.826,
p=0.000). Chick & Vincent (2005) found self-confidence to be positively correlated to achievement, with highly self-
regulated students being more motivated to use planning, organizational, and self-monitoring strategies to achieve good
performance in mathematics.
Statistically significant positive correlations were also found between difficulties in mathematics, myths and beliefs
and performance (r=0.688, p=0.000); (r=0.713, p =0.000) respectively. Kane and Mertz (2012) also revealed that myths
and beliefs about mathematics have a strong influence on student performance.
It will be recalled that the purpose of this study was to investigate the relationship between student`s perceptions
and mathematics performance and it was hypothesized that there is a significant positive relationship between students’
perceptions and mathematics performance. Since the p-values of all the relationships in table 3 are less than 0.05, it
therefore means that we reject the null hypothesis and conclude that there is a significant positive relationship between
students’ perceptions and mathematics performance.
Table 8: Regression Analysis
Model Summaryb
Model R R Square Adjusted R
Square Std. Error of the
Estimate
Change Statistics Durbin-
Watson
R Square
Change F Change df1 df2 Sig. F
Change
1 .925a .856 .850 .28957 .856 140.726 5118 .000 2.073
a. Predictors: (Constant), Myths and beliefs, Strengths and Weaknesses in mathematics, Self confidence in mathematics,
Family background and support, Interests in mathematics.
b. Dependent Variable: Mathematics Performance
Coefficientsa
Model Unstandardized CoefficientsStandardized Coefficients t Sig. Collinearity Statistics
BStd. Error Beta Tolerance VIF
1
(Constant) -.636 .194 -3.282.001
Strengths and Weaknesses in
mathematics -.374 .053 -.374 -7.108.000 .440 2.271
Family background and support .003 .066 .003 .051 .959 .418 2.392
Interests in mathematics .709 .089 .587 7.943 .000 .223 4.492
Self confidence in mathematics .692 .077 .485 9.003 .000 .419 2.385
Myths and beliefs .303 .082 .188 3.698 .000 .469 2.130
a. Dependent Variable: Mathematics Performance
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Collinearity Diagnosticsa
ModelDimension Eigenvalue Condition
Index
Variance Proportions
(Constant) Strengths and
weaknesses in
mathematics
Family
background
and support
Interests in
mathematics Self confidence
in mathematics
Myths and
beliefs about
mathematics
1
1 5.918 1.000 .00 .00 .00 .00 .00 .00
2 .038 12.546 .14 .43 .00 .01 .01 .02
3 .017 18.430 .35 .32 .24 .04 .08 .01
4 .012 22.290 .12 .04 .59 .17 .03 .17
5 .009 25.214 .01 .05 .16 .02 .74 .29
6 .006 32.268 .38 .15 .01 .77 .15 .52
a. Dependent Variable: Mathematics Performance
Residuals Statisticsa
Minimum Maximum Mean Std. Deviation N
Predicted Value 1.6909 4.8030 3.5181 .69260 124
Residual -.84335 .95863 .00000 .28363 124
Std. Predicted Value -2.638 1.855 .000 1.000 124
Std. Residual -2.912 3.310 .000 .979 124
a. Dependent Variable: Mathematics Performance
Ordinary least squares regression (OLS) of the perception variables were used to determine the magnitude and direction
of effects of these variables on performance. The intercept regression model was used in this analysis because some of
the predictors have a possibility of being equal to zero so much that the intercept would have a meaningful interpretation.
The results of that analysis are shown in Table 8. The model indicates that 85.6%% (R-Square=0.856) variation in
student performance is explained by five (5) of the predictor variables, which are self-confidence, interest in mathematics,
family background and support, weaknesses in mathematics, and myths and beliefs about mathematics. Teacher
support, learning material and difficulties in doing mathematics were insignificant. The Durbin-Watson indicates that the
assumption of independent error is tenable since for these data the figure is 2.073 and is close to 2 (Durbin & Watson,
1951). No incidences of multi-collinearity were observed in the model since none of the variance inflation factors (VIF)
are close to or greater than 5. The analysis of variance table shows that the variables in the model have a statistically
significant effect on performance outcomes (F=140.726; Sig. =0.000).
A regression model was built in the form of an equation where the dependent variable is equal to the weighted
combination of the independent variables:
From the regression results presented in Table 8, it can be noted that not all variables have a statistically significant
effect on student performance. Statistically significant effects are observed on weaknesses in mathematics (t=-7.108, sig.
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=0 .000); family background and support (t=0.051, sig. = 0.959); interest in mathematics (t=7.743, Sig. = 0 .000); self-
confidence (t=9.003, sig. =0.000) and myths and beliefs about mathematics (t=3.6989, sig. =0.000). Four of the five
variables (family background and support (0.003), interest in mathematics (0.587), self-confidence (0.485), myths and
beliefs about mathematics (0.188)) yield positive Beta coefficients indicating that they result in increases in student
performance. Therefore, at Į=0.05 level of significance, the study conclude that traits such as family background and
support, interest in mathematics, , self-confidence and myths and beliefs about mathematics have a positive effect on
students performance while strengths and weaknesses in mathematics seem to have a negative influence on students’
performance. Teacher support, teaching and learning support material and difficulties or challenges in doing mathematics
were considered insignificant in the regression model.
9. Discussion of Results
It can be recalled that the purpose of this study was to explore the students’ self-perceptions on mathematics and the
influence of these perceptions on achievement. The effects of demographic factors, which are gender, age and home
language, were also envisaged. It was also hypothesized highly that males perceive math more positively than females.
9.1 Gender and Perceptions
This study found that there was a significant difference in the way mathematics is perceived between males and females.
This is consistent with findings by Hoang (2008) who showed that male consistently reported slightly more positive
perceptions and attitudes than females. However a research carried out by Mohamed and Waheed (2011) showed that
the students’ positive attitude towards mathematics is medium and there is no gender difference in their attitudes.
Forgasz and Murimo (2011) also found gender differences in favour of male students' perceptions. Isiksal and Cakiroghi
(2010) also claim that boys are perceived to be better at mathematics than girls. Research shows that girls have lower
self-esteem than boys (Kleinfeld, 2006). Female students suffer a severe drop in self-esteem at adolescence while males
gain in self-assurance as they age while girls lose the vitality and sense of self they displayed in the lower grades.
9.2 Age and Perceptions
This study found that there was a significant difference in views and attitudes towards mathematics between the two age
cohorts of students. Descriptive statistics indicated that 16-20 year old students perceive mathematics differently than
older students. This is consistent with findings by Martinot and Désert (2007) which revealed that age was not statistically
significant in explaining perception levels the different age groups.
9.3 Language and Perceptions of Mathematics
This study found that there was a significant difference in perceptions of mathematics across different language cohorts.
Analysis of variance confirmed that language factors have no effect students’ perceptions of mathematics. South Africa is
a multi-cultural and multi-lingual country, students from different language backgrounds tent to perceive mathematics
differently. Students use language to communicate and to understand mathematics concepts. Language influences
students’ thought by moulding perceptions and structuring ideas Nordin (2005). This may be due to the lack of ability in
understanding of the subject matter and the instructional language. Language effects and perceptions of mathematics
have been extensively studied and results are inconsistent, with a number of studies revealing that the knowledge and
skills are new, unfamiliar and different from the language used in everyday life (Marissa, 2009).This may cause a
problem in the understanding of the mathematics concepts. Many researchers recommended that emphasis should be
given more on building up students’ proficiency in English before they could learn mathematics effectively.
9.4 Relationships between perception constructs and performance
The results emanating from the research also indicate that there is a statistically significant positive relationship between
teacher and learning materials supports a, family background and support, self-confidence, myths and beliefs, difficulties
in mathematics and performance in mathematics. From the above analysis one can assert that teacher/learning material
support, family background and support, self-confidence, myths and beliefs as well as difficulties in mathematics can
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predict performance in mathematics. However, there was a statistically significant positive weak relationship between
weaknesses in mathematics and performance among the sample of students selected to participate in the research.
Since the p-values were less than 0.05 it therefore means that we reject the null hypothesis and conclude that the
identified constructs can predict performance.
Several relationships observed in this study were similar to findings of previous researchers. For example, student
beliefs were significantly related to several types of academic outcomes. Lynch (2002) found that students’ self-
perceptions of their reading ability were significantly associated with achievement whereas self-confidence beliefs were
associated with good performance in examinations.
In general, students who attributed their academic success to factors such as self-confidence, interest in
mathematics as well as family background and support tended to show higher achievement levels than students who
attribute their academic outcomes to natural talent or to good luck. In support of this claim, Wentzel and Wigfield (1998)
shared the same sentiments.
10. Conclusion and Recommendations
This study investigated the range of perception constructs towards mathematics performance shared by students at a
selected South African secondary school. Results from regression analysis revealed that five of the seven factors were
found to be influential on students’ performance in mathematics. The influence of factors such as weaknesses in
mathematics, teacher support/learning material, family background and support, interest in mathematics, difficulties in
doing mathematics, self-confidence and myths and beliefs about mathematics were identified as the major causes of
such perceptions. Results reveal that gender-related factors have an influence in the way students perceive
mathematics. It also revealed that age has an effect on students’ perceptions of mathematics. Language-related effects
were also found to significantly affect students’ performance.
This study has implications for all stakeholders, including teachers, schools and parents. The research reveals
that’s students who believe that their efforts will improve their performance are likely to enhance their achievement.
Therefore this study recommends that parents and teachers should play a significant role in shaping students’
perceptions and attitudes towards mathematics. It also recommends that students should not be discouraged by past
experiences in lower grades that convince them that they cannot do well in mathematics.
Additionally, higher maths ability is often believed to go hand-in-hand with greater levels of general intelligence.
Many students tend to subscribe to this attitude towards maths. However the study recommends that students should not
hold on to such myths and beliefs about mathematical intelligence that can affect their performance. If they believe that
intelligence in mathematics is a fixed quantity, something they have or do not have, but not something they acquire over
time, and they may not see the point of extra effort. Finally, if students attribute their success to their innate talents rather
than effort, they may not be motivated to work.
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Updating mathematics teachers’ pedagogical skills and content knowledge is inevitable as the trend of students’ performance in Tanzania is alarming. Currently, social media have been one of the strategies for elevating mathematics teachers’ professional competencies through online learning communities. The study aimed at examining how mathematics teachers use Informal WhatsApp Groups (IWGs) as one of the social media for Continued Professional Development (CPD). Key study questions are what are the perceptions of mathematics teachers on the benefits of IWGs in CPD? How do mathematics teachers use IWGs for CPD-related activities? What are the challenges they encounter? And what Mathematics teachers recommend for better use of IWGs for CPD? Two IWGs were involved with a total of 54 mathematics teachers who are currently teaching in secondary schools. The open-ended questionnaire was shared in the IWGs, and members accepted to fill it. Ten members including those who have been in the IWGs for a longer period, those who frequently posted or asked questions, and group leaders were invited for interviews. The findings show that the IWGs have contributed to teachers developing their pedagogical skills and content knowledge through sharing experience, and materials and demonstrating teaching practices in video clips. The challenges include the problem of internet accessibility, inactiveness of members, and lack of effective criteria for evaluating the validity and reliability of information shared. The recommendation is for the authorities to set supportive policies and practices that will create enabling environments for mathematics teachers on CPD.
... Matematik Öğretmenine İlişkin Algılar Yapılan araştırmalar matematik öğretmenine yönelik algıların öğrencilerin matematik başarısı üzerinde önemli bir rolü olduğunu vurgulamıştır (Mutadi ve Ngirande, 2014;Yalçın, 2012). Aynı zamanda öğrencilerin matematik öğretmeni algıları, çaba, öz-yeterlik, akademik duygular, tutumlar, motivasyonlar ve matematiğin yararlı ve değerli olduğuna ilişkin algılar gibi matematik başarısı ile yakından ilgili olan değişkenler üzerinde de rol oynadığını göstermektedir (Bawuah, Sare ve Kumah, 2014;den Brok, Fisher ve Scott, 2005;den Brok, van Tartwijk, Wubbels ve Veldman, 2010;Federici ve Skaalvick, 2014a, 2014bJang, Reeve ve Deci, 2010;Putwain ve Symes, 2011;Reddy, Rhodes ve Mulhall, 2003;Sakiz vd., 2012). ...
... Yalçın'ın araştırma sonuçlarına göre öğrencilerin matematiği öğrenmeyi zorlayıcı bir süreç olarak algılama düzeyleri matematik başarıları ile olumsuz ilişkilidir (Yalçın, 2012). Öğrencilerin matematiğe ilişkin zorluk algıları üzerine yapılan diğer araştırmalarda da öğrencilerin matematiğe ilişkin zorluk algılarının matematikte çaba gösterme ve matematikte başarılı olma algıları ile negatif yönde ilişkili olduğunu göstermiştir (Hannula ve Laakso, 2011;Ma, 1997;Mutadi ve Ngirande, 2014). ...
... Matematikle ilgili zorluk duygusunun matematik başarısı (Ma, 1997;Yalçın, 2012), motivasyon (O'Brien ve Crandall, 2003) ve matematikte çaba (Hannula ve Laakso, 2011) ile negatif yönde ilişkili olduğu düşünüldüğünde, matematik öğrenmeyi zorlu bir süreç olarak algılayan öğrencilerin neden daha düşük matematik başarısına sahip oldukları daha iyi anlaşılabilir. Böyle bir bulgu, matematiği öğrenmeyi zorlayıcı bir süreç olarak algılayan öğrenciler ile matematiği çaba gerektiren bir süreç olarak algılayan öğrencilerin neden farklı profillerde sınıflandırıldığını da açıklayabilir (Hannula ve Laakso, 2011;Ma, 1997;Mutadi ve Ngirande, 2014;Yalçın, 2012). İnsan davranışı esas olarak algıya dayalıdır (Segal, 1998) ve bu bulgular, olumsuz algıların düşük matematik başarısına neden olabileceğini göstermektedir. ...
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Bu çalışmanın temel amacı, ortaokul öğrencilerinin matematik öğretmenine yönelik algıları, matematik öğrenmeye yönelik algıları ve matematiksel yılmazlık düzeylerinin öğrencileri benzer profillere sahip kümelere ayırmada kullanılıp kullanılamayacağını incelemektir. Çalışma grubu yaşları 11 ile 15 arasında değişen ortaokul öğrencilerinden oluşmaktadır. Profil grupları oluşturmak için iki aşamalı küme analizi kullanılmıştır. Kümeleme analizi sonucunda iki farklı profil ortaya çıkmıştır. Bulgular, bu çalışmada oluşturulan kümelerin öğrencilerin matematik öğretmenine yönelik algılarına, matematik öğrenmeye yönelik algılarına, matematiksel yılmazlıklarına ve matematik başarılarına göre farklılaştığını göstermiştir. Sonuçlar 1. kümedeki öğrencilerin, 2. kümedeki öğrencilere nazaran, matematik başarılarının daha yüksek olduğunu, matematiğe daha çok değer verdiklerini, matematik öğretmenlerini bilgili ve destekleyici kişiler olarak, matematik öğrenmeyi ise eğlenceli ve çaba gerektiren bir süreç olarak algıladıklarını göstermektedir. 2. kümedeki öğrenciler daha düşük matematik başarısına sahiptir. Matematik öğretmenlerini kaygı kaynağı ve matematiği öğrenme sürecini ise zor bir süreç olarak algılamaktadırlar. Ayrıca matematik yeteneğinin geliştirilebileceğine dair inanç düzeyleri 1. kümeyle karşılaştırıldığında anlamlı bir şekilde daha düşüktür.
... Previous studies emphasized that students' perceptions of mathematics teachers have an important role in mathematics achievement (Mutadi & Ngirande, 2014;Yalçın, 2012). Previous studies also showed that students' perceptions of mathematics teachers also have a role in the variables closely related to their mathematics achievements, such as effort, self-efficacy, academic emotions, attitudes, motivations, and perceptions that mathematics is useful and valuable (Bawuah, Sare, & Kumah, 2014;den Brok, Fisher, & Scott, 2005;den Brok, van Tartwijk, Wubbels, & Veldman, 2010;Federici & Skaalvick, 2014a, 2014bJang, Reeve, & Deci, 2010;Putwain & Symes, 2011;Reddy, Rhodes, & Mulhall, 2003;Sakiz et al., 2012). ...
... According to Yalçın's research results, students' perception level that mathematics learning as a challenging process is negatively related to their mathematics achievement (Yalçın, 2012). In also other studies on students' perception of difficulty related to mathematics, results showed that the students' perceptions related to mathematics are negatively associated with the effort in mathematics and perceptions about being successful in mathematics (Hannula & Laakso, 2011;Ma, 1997;Mutadi & Ngirande, 2014;Yalçın, 2012). ...
... Given that the feeling of difficulty regarding mathematics negatively correlates with mathematics achievement (Ma, 1997;Yalçın, 2012), motivation (O'Brien & Crandall, 2003), and effort in mathematics (Hannula & Laakso, 2011;Yalçın, 2012), it can be better understood why students who perceive mathematics learning as a challenging process tend to have lower mathematics achievement. Such a finding can also explain why the students who perceive mathematics learning as a challenging process and those who perceive mathematics learning as a process requiring effort are classified into different profiles (Hannula & Laakso, 2011;Ma, 1997;Mutadi & Ngirande, 2014;Yalçın, 2012). Human behavior is mainly perception-driven (Segal, 1998), and these findings show that negative perceptions might cause low mathematics achievement. ...
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The primary purpose of the present study was to examine whether Turkish middle school students' perceptions of mathematics teachers, perceptions of mathematics learning, and their mathematical resilience can be used to divide students into clusters with similar profiles. The sample consisted of middle school students with ages ranging from 11 to 15. Two-step cluster analysis was used to create profile groups. As a result of cluster analysis, two distinct profiles were revealed. The results showed that clusters -formed in the present study differentiated according to students’ perceptions of mathematics teachers, learning mathematics, their mathematical resilience, and their mathematics achievement. Students in cluster 1 have higher mathematics achievement, value mathematics, perceive mathematics teachers as knowledgeable and supportive people, perceive learning mathematics as a fun process requiring effort. Students in cluster 2 have lower mathematics achievement. They perceive mathematics teachers as the source of anxiety and learning mathematics as a difficult process. They also have low belief levels that mathematics ability can be improved in comparison to cluster 1.
... Therefore, this section of the research seeks to investigate whether students' insight about mathematics will affect the achievement in this subject, and thus reflect in their overall academic achievement. According to Mutodi and Ngirande (2014), students' achievement in certain subjects greatly relies on their attitude towards the subject. ...
... This value shows that student with good perception and insight of mathematics tends to achieve better in mathematics and vice versa. According to Mutodi and Ngirande (2014), how students perform in certain subjects depends on their perception towards the subject. A clear insight towards the subjects will motivates a person perform better in a subject. ...
... Beliefs stem from the experiences (Mutodi & Ngirande, 2014) and it is difficult and slow to change beliefs (Ambrose, 2004;Kaiser & Maaß, 2007;Viholainen, Asikainen & Hirvonen 2014). When the possible connections between beliefs and learning processes are considered, the search for methods to change beliefs is an unsolved problem (Kaiser & Maaß, 2007); and the question of how beliefs of teachers in teaching and learning mathematics are related with applications is an active research area (Ärlebäck, 2009). ...
... So, it can be said that the starting point of changing students' mathematical beliefs is teachers' beliefs (Mason & Scrivani, 2004). However, teachers' beliefs are shaped through the experiences in learning mathematics during their student years, and the experiences in teacher education process during their university years; in other words, it depends on their history and their experiences (Handal, 2003;Mutodi & Ngirande, 2014;Philipp, 2007;Ramirez, 2017). Thus, the beliefs of pre-service mathematics teachers in mathematics and modelling may affect their teaching activities when they become teachers in the future. ...
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The aim of this study is to investigate pre-service mathematics teachers' beliefs towards mathematics and modelling in mathematical modelling processes. To achieve this aim, a phenomenology design was utilized. The study was conducted with 30 elementary level pre-service mathematics teachers receiving mathematical modelling courses. A semi-structured interview form was used to explore teachers' beliefs. At the end of the study, it was seen that mathematical modelling applications caused an increase of application-oriented beliefs. It was also observed that pre-service teachers who had schema and formalism-oriented beliefs evaluated mathematical modelling practices as time consuming and incomprehensible. Findings imply that modelling applications should be included in all levels of mathematics instructional curricula, in addition to the undergraduate curriculum.
... According to Daudu, et al. (2016), the way students perceive a subject determines their success or failure in that subject. Mutodi and Ngirande (2014) found that the perceptions shared by the students in South Africa about Mathematics performance are due to one's selfconfidence, family background, teaching strategy, learning materials, interest in Mathematics, traditions, and beliefs. According to Daso, et al. (2021), different people perceive Mathematics differently; minority of the people view Mathematics as a simple, fallible and interesting subject while majority of the people perceived Mathematics as dreaded, bored, difficult, unfriendly, absolute and very abstract. ...
... Daso, et al. (2021) also revealed that students' perception about Mathematics determines their attitudes towards learning it. Mutodi and Ngirande (2014) confirmed that students, who accredited their success to their interest, self-confidence, as well as good family background, have a chance to come up with higher achievements than those who point their academic success to chance and natural talent. ...
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This study investigated student and lecturer perception of difficult Mathematics courses in tertiary institutions in Rivers State. The analytical survey research design was adopted for the study with all undergraduate Mathematics students from the seven tertiary institutions in Rivers State constituting the population of the study. A sample of 100 respondents constituting 63 students (23 male; 40 female) and 37 lecturers from three tertiary institutions were selected by simple random sampling. Student and Lecturer Perception of Difficult Mathematics Courses (SLPDMC) was the instrument used for data collection. SLPDMC which was validated by three experts in Mathematics Education with reliability index of 0.87 obtained by test and re-test method contained four sections and 64 items. The criterion cutoff point of 2.50 was used for decision making. The six research questions were answered with mean and standard deviation while the two hypotheses were tested using independent sample t-test at 0.05 level of significance. The study identified some students and lecturers perceived difficult Mathematics courses, their causes and possible remedies. Findings of the study also showed that the differences between the male and the female students and students and lecturers perceptions of difficult Mathematics courses in tertiary institutions were not significant. The study recommended the use of qualified lecturers and active and innovative instructional strategies that enhances students' learning interest and study habit, provision of adequate learning facilities and materials, covering of course contents during instruction and attending conferences and workshops to remediate perceived difficulties in teaching and learning of some Mathematics courses in tertiary institution.
... The present study is supported by Mutodi and Ngirande (2014). Their study on learners' perception of mathematics performance resulted in a significant difference in perception and beliefs about mathematics. ...
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The benefits of differentiated scaffolding strategies on boosting academic performance and confidence in Mathematics learners were studied in this paper. Quasi-experimental research was conducted at a state university’s Secondary School Laboratory in the Philippines. It involved sixty Grade 8 learners, 30 from the control group and 30 from the experimental group. A panel of specialists assessed developed lessons on triangle congruence topics and the academic performance test and confidence scale. The developed lesson, test, and scale were improved after the panel of experts’ comments and suggestions were considered. The instruments were pilot tested and came out reliable; the academic performance test had a Cronbach alpha of 0.807, while the confidence scale in Mathematics had a Cronbach alpha of 0.810. In addition, the mean, standard deviation, One-way Analysis of Covariance (ANCOVA), and Pearson Product Moment Correlation were used to analyze the data. The findings demonstrated that when learners were taught using differentiated scaffolding strategies, their academic performance significantly increased at the Fairly Satisfactory level. However, when they were taught using conventional teaching strategies, their academic performance remained at Did Not Meet Expectations. The performance outcomes of both groups were significantly different. Also, there was no significant difference in learners’ confidence between the two groups when compared. Furthermore, there was a significant link between academic performance and confidence in Mathematics among students taught using differentiated scaffolding methodologies. Thus, concerns about increasing learners’ mathematical literacy may be addressed with differentiated scaffolding strategies.
... Students' positive perceptions of mathematics lessons and self-confidence in their abilities correlated positively with the mathematics literacy they achieved. Positive perceptions of mathematics can be developed if students are aware of the role of mathematics in life (Kaya & Aydın, 2016;Mutodi & Ngirande, 2014). ...
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This study aims to analyze student mathematical literacy ability from the perspective of students' Mathematical Ability. This research is a descriptive study with a qualitative approach. The research subjects were three students of XI IPA 1 MAN 1 Padang with different mathematical abilities: low, medium, and high. Data were collected through documentation, tests, and interviews. The results of the analysis show that students with high abilities can solve routine problems, interpret problems and solve them with formulas, carry out procedures well, can deal with complex situations, use their reasoning in solving problems, can work effectively and interpret different representations and then relate them to the real world. Students with moderate abilities can solve routine problems, interpret problems and solve them with formulas, and carry out procedures properly. Meanwhile, students with low abilities are only able to solve routine questions. Based on these results, it is necessary to look for strategies in the mathematics learning process, which enable the improvement of students' mathematical literacy skills.
... The results showed that students' attitudes towards mathematics were positive and many of them believed that mathematics teaching is a worthwhile and necessary subject which could help them in their future career. In South Africa, Mutodi and Ngirande (2014) in their study on the influence of students` perceptions on mathematics performance in selected high schools reported that weaknesses in mathematics, family background and support, interests in mathematics, self-confidence in mathematics, myths and beliefs about mathematics and learning materials influenced students' attitude towards the subject. ...
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Safety needs to be a visceral element of construction processes in order for them to succeed. In that context, the United Arab Emirates (UAE) makes use of Estidama as a tool for building design so as to measure practices relating to sustainable building via its Pearl Rating System. To that end, in essence, it shares some similarities with UK BREEAM measures. Against this backdrop, the current research will evaluate the potential for using Estidama as a tool for implementing systems with a view to track construction workers’ health and safety (H&S). It has been pointed out that there needs to be greater appraisal when it comes to these systems within GCC nations and, on a larger level, draw linkages between cultural, socioeconomic, institutional, environments, political, and safety-related elements across construction sites owing to poor levels of understanding. Notably, meaningful comparisons of H&S statistical data could help drive enhanced performance; however, greater degrees of transparency must be ensured and the ability to secure valid information. A systematic literature forms the cornerstone of this research, and exploratory interviews are then undertaken with UAE-based construction professional staff. According to the findings, a lot of work needs to be done in order to enhance H&S performance. Governments need to demonstrate greater commitment towards enforcement, whereas the perception of legislation leaves a lot to be desired. Put simply, the prospect of implementing tools such as Estidama is not impervious to challenge. In a similar vein, questions must be asked about implementing H&S regulations with building green …
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Research on the effectiveness of educational inputs, particularly research on teacher effectiveness, typically overlooks teachers’ potential impact on behavioral outcomes, such as student attendance. Using longitudinal data on teachers and students in North Carolina I estimate teacher effects on primary school student absences in a value-added framework. The analysis yields two main findings: First, teachers have arguably causal, statistically significant effects on student absences that persist over time. Second, teachers who improve test scores do not necessarily improve student attendance, suggesting that effective teaching is multidimensional and teachers who are effective in one domain are not necessarily effective in others.
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Abstract. In this chapter we consider beliefs and the related concepts of conceptions and knowledge. From a review of the literature in different fields we observe that there is a diversity of views and approaches in research on these subjects. We report on a small research project of our own attempting to clarify the understanding of beliefs among specialists in mathematics education. A panel of 18 mathematics educators participated in a panel that we termed “virtual”, since the participants communicated with us only by e-mail. We sent nine characterizations related to beliefs, selected from the literature, to the panelists, asked them to express their agreement or disagreement with the statements, and also asked each to give their own characterization of the term. The answers were analyzed, searching for the elements around which the concept of beliefs has developed along the years. We discuss issues on which there was agreement and disagreement and conjecture what lies behind the differences. As a final step we make some suggestions relating to characterization of the term belief and ways of dealing with it in future research.
Book
The twenty chapters in this book all focus on aspects of mathematical beliefs, from a variety of different perspectives. Current knowledge of the field is synthesized and existing boundaries are extended. The book is divided into three, partly overlapping, sections. The first concentrates on conceptualizations and measurement of beliefs, the second on research about teachers' beliefs, and the third on facets of students' beliefs about mathematics. A diversity of instruments is used for data collection, including surveys, interviews, observations, and essay writing, as well as more innovative approaches. The volume is intended for researchers in the fleld, as well as for mathematics educators teaching the next generation of students. The book is also useful for those working in other subject disciplines, since many of the themes explored have relevance well beyond mathematics education.