INFLUENCE OF
TEACHER, PUPIL FACTORS AND THEIR KNOWLEDGE OF STATISTICS ON PUPILS’ ACHIEVEMENT
IN MATHEMATICS IN OSUN STATE, NIGERIA
Prince Mensah
OSIESI,^{1}^{ }Monica Ngozi
ODINKO^{2}
^{1} Department of Educational Management,
Faculty of Education, Federal University of OyeEkiti,
Ekiti State, Nigeria Email: princeosiesi@yahoo.com
^{2} Institute of Education,
University of Ibadan, Ibadan, Oyo State, Nigeria
Email: moniquengozi@yahoo.com


ABSTRACT 
Keywords: Statistics; curriculum; Teacher;
factors; Nigeria 

The study investigated the
influence of teachers’ and pupils’ factors and their knowledge of statistics
on pupils’ achievement in mathematics in Osun
State, Nigeria. The study adopted the survey design. The input, process and
output evaluation model was used. The multistage sampling procedure was used
to select 43 public primary schools, 43 primary five teachers and 689 primary
5 pupils. Four instruments, namely Classroom Teaching Observation Scale(r =
0.73), Pupils’ Mathematics Achievement Test (r = 0.89), Pupils’ Statistics
Achievement Test (r = 0.82) and Teachers’ Content Knowledge of Statistics
questionnaire (r = 0.78) were used. The data were collected from June to
July, 2016. Data were analysed using correlation
coefficient and multiple regression at p<0.05. Findings revealed that
pupils statistical knowledge [β = .390, t _{688 }= 1.655,
p<.05], Parents qualification [β = 4.386, t _{688 }= 2.174,
p< .05], classroom management [β = .292, t _{688 }= 2.043,
p <.05] and lesson preparation [β = 2.695, t _{688 }= 2,481,
p<.05] were most influential in predicting pupils’ mathematics
achievement. Thus, to improve mathematics achievement, teachers and pupils’
statistics knowledge and education should be intensified. Publisher All rights reserved. 
INTRODUCTION
Mathematics and
statistics play a fundamental role in almost every field of human activity.
Over the years, the teaching of statistics at the primary level of education
has been incorporated into the mathematics curriculum which is to be executed
by teachers who may or may not be specifically trained to teach statistics.
There is an increasing recognition that statistics though related to
mathematics is a distinct discipline and not a subfield of mathematics. It is
imperative that both teachers and learners see statistics and mathematics in
the correct perspective to differentiate the features of their logic. Studies
on the evaluation of the effectiveness of the primary school mathematics
curriculum (statistics inclusive) were mostly in terms of teaching methods
employed by the teacher, instructional delivery, enrolment and dropout rates
without consideration for both the teachers’ and pupils’ content knowledge of
statistics as embedded in the curriculum.
Mathematics is a tool with which learners
obtain knowledge and experience about life. It directs learners’ knowledge into
real life problems and how to deal with them by improving their ability in
logical thinking and reasoning thereby preparing them for their future endeavours. It is well thoughtout as the mother of all
learning in both arts and sciences and is a prerequisite in pursuing a
profession in these disciplines. This perspective on mathematics has gained
more attention with the rapid advances in information and communication
technology. Mathematics seems not to involve only computation but also is a
tool for understanding structures, relationships and patterns to produce
solutions for complex real life problems. This makes it necessary for people of
all ages to be successful in life.
Statistics has an
important role in determining the existing positions of education, per capita
income, unemployment, population growth rate, housing in any country; to
mention but a few. Statistics are sets of mathematical equations that are used
to analyze what is happening in the world around us. When used correctly,
statistics tell us any trend in what happened in the past and can be useful in
predicting what may happen in the future (eMathZone.com, 2015). Leavy (2010) submitted that the teaching of statistics, as
compared to mathematics, has additional considerations when taking into account
the type of knowledge needed for teaching it. The knowledge needed to carry out
the ‘work of statistics’ extends beyond concepts, terms, and representations.
Statistics did not originate within mathematics and as a result, many of the
core statistical ideas are not mathematical in nature. Moore (2004) went
further to assert that “statistics, while being a mathematical science, is not
a subfield of mathematics”.
The reasons for teaching
statistics in schools may include the following: it is useful for daily life,
has an instrumental role in other disciplines and is important in developing
critical reasoning. At the primary
school level, statistics is often reduced to frequency counts and bar graphs
with rules for calculating mean, median, mode and range added later at the
higher classes. Indeed, the mathematics
curriculum itself does not give strong and specific emphasis to interpreting,
reading, critiquing and questioning data on statistics. It is imperative that
learners see statistics and mathematics in a correct perspective to enable them
understand the different features of their logic. Pupils of primary schools
especially need to acquire statistical skills and knowledge to be able to
describe and interpret the world around them. Research has revealed that while
pupils are able to perform some statistical calculations, they do not have the
ability to inspect them critically (PerelliD’Argenzio
et al, 1998).
Academic
achievement is usually used in schools to ascertain learners’ success in the
learning of a given subject curriculum content. According to Adediwura and Tayo (2007),
academic achievement is denoted by examination or test scores assigned by
subject teachers. Academic achievement remains a burning issue to teachers,
pupils, parents or guardians and other educational stakeholders. Poor academic
achievement has been a recurrent issue in most school subjects especially
mathematics among learners in primary schools (Adesemowo,
2005). Aremu (2000) stated that learners’ poor
achievement can be wearisome to pupils, teachers and parents, and pupils’ are
often blamed for their poor achievement (Aremu & Sokan, 2003). The persistent poor achievement of pupils’ in
the subject as observed from their first school leaving certificate examination
results has been cause for concern, yet the way out to this downward trend has
become a mirage. This may have been due to many factors among which could be comprehending the statistics component in the mathematics
curriculum.
At the primary
school level, statistics is usually taught within the mathematics curriculum by
teachers who may or may not be specifically trained to teach statistics. Most
teachers acknowledge the practical importance of statistics and are willing to
give more relevance to the teaching it (Alieme & Osiesi, 2015). However, many mathematics teachers do not
consider themselves well prepared to teach statistics nor face their learners’
difficulties. Statistics is not just a set of techniques; it is an attitude of
mind in approaching data. It enables people to make decisions in the face of
uncertainty. The mathematics curriculum should reflect the needs of children to
understand their world. Much
scientific work deals with gathering, interpreting and predicting from data.
This is the essence of statistics. Therefore, statistics education in the 21st
century has become increasingly important (Lionel, 2006). There is the need to
develop an appreciation of statistics through its applications to the pupils’
world. However, the relationship and distinction between statistics and
mathematics seems difficult to establish. It is important for teachers to
inculcate the differences outlined by Moore (2004) in children, while teaching
statistics at the primary school level.
Teachers play
crucial roles in the educational attainment of learners because the teacher is
responsible for the translation and implementation of educational policies,
curriculum contents, instructional materials as well as assessment of pupils’
learning outcomes (Afe, 2003). Teacher qualification
include a range of variables affecting teacher quality: type of teaching
certification, undergraduate major or minor, advanced degree(s), type of
preparatory programme and years of teaching
experience. Abe and Adu (2013) restated that teaching
qualification is one of a number of academic and professional degrees that
enables a person to become a registered teacher in primary or secondary school.
DarlingHammond (2001) reported that teachers with higher educational
qualifications tended to promote teaching effectiveness more than those with
lower qualifications. Researchers argued that assigning experienced and
qualified teachers to low performing schools and learners’ is likely to pay off
with better performance gaps (Adegbile & Adeyemi, 2008). The above strongly shows that subject
matter knowledge (competence), teacher qualification, teachers’
years of teaching experience, teacher teaching method, teacher instructional
strategy and classroom behaviour are strong variables
that could affect learners’ achievement.
Marzano (2003) stated that the major independent
impact on learners’ achievement is instructional strategies and how
instructions are delivered. Instructional strategy or learning strategy may be
a process by which an instruction module or an entire course is delivered. It
takes the form of conference, demonstration, discussion and lecture. In
planning instruction for a course, a unit or a lesson, teachers carry out a
series of actions based on informed decisions.
According to McLeod, Fisher and Hoover (2003), teachers have a sole
responsibility to decide how to utilize their resources and choose strategies
that will advance their learners to the appropriate level of achievement.
A teacher who has
prepared his instructional materials, and established efficient routines should
do a “careful analysis of goal and selection of appropriate content for
learners” (Eggen & Kauchak,
2001). For planning to be effective during teaching and learning, teachers are
expected to incorporate effective classroom management as a process through
which they create and maintain an environment conducive for productive
learning. This includes teachers’ actions that aim at managing learners’ behaviour and conducting the business of the classroom,
which includes administering corrective measures to students’ behaviour and developing ways of preventing occurrence of
problems (Taylor, 2009). Effective teaching and learning cannot take place in a
classroom that lacks order, hence classroom management and organisation
is important because they enhance productive learning (Marzano
et al, 2003; Asiyai, 2011). Teachers are expected to take time at the
beginning of the academic year, especially on the first day of the school
session, to establish classroom management, routines and expectations for the
regulation of learners’ behaviour. This will enable
the teacher prevent behavioural problems even before
they occur and increase instructional time by reducing the time spent on
classroom management (Marzano et al, 2003, Marzano, 2010). If proper classroom management is not
enhanced, disruptive behaviour by some learners can
jeopardize learning as it does not just affect only learners who are
noncompliant but other learners’ in the classroom.
Pupils’ gender can
predict pupils’ achievement. Boys are likely to be more interested in subjects
associated with numbers and are trained to tackle difficult problems unlike
their female counterparts. Although boys are generally seen to be stronger
physically than girls and so can handle difficult jobs, recent developments
have changed such notions since girls are also delving into activities which
were previously believed to be for boys, especially in the field of engineering
and mechanical works. Unfortunately, gender inequality in education has
remained a perennial global problem (Bordo, 2001;
UNESCO, 2003; Reid, 2003). The same is true for teachers’ gender as pupils seem
more open and flexible with teachers of a particular gender, teaching a
particular subject at a given time.
The relationship
between the socioeconomic status (SES) of learners and their academic
achievement is well established in sociological research works (Aikens & Barbarin, 2008;
Hamid, 2011; Palardy, 2008; Shittu,
2004). According to American Psychological Association (APA), socioeconomic
status is commonly conceptualized as the social standing or class of an
individual or group and often measured as a combination of education, income
and occupation. Parent’s educational status, occupation and family size are the
socioeconomic factors been considered in the study. While there is
disagreement over how best to measure SES, most studies indicate that children
from low SES families do not perform well as they potentially could have
performed when compared with children from high SES families (Considine & Zappala, 2002).
The quality of parents and home background of a student also go a long way in
predicting their achievement in a subject (Shittu,
2004). Moreover, where the family size is large, parents might find it
difficult to provide all the necessary support to the child. The size of the
family thus; plays a significant role as regard discipline, provision of
necessary materials and emotional support needed by pupils for effective
learning. Family size in this context refers to the total number of children in
the learners’ family in addition to the learner himself. Increase in family
size would alter the availability of time and material resources needed by the
children of such families. Family size and the position a child occupies in a
family may contribute positively or negatively to pupil’s academic achievement Oginni (2018). Children may as a result of their birth
position, perform more or less in academics (Booth & Kee,
2006). In the same vein, parental occupation may have a positive or negative
effect on the general wellbeing and academic achievement of children.
STATEMENT OF THE PROBLEM
The seeming
decline in the achievement of pupils in mathematics has raised concerns for
stakeholders. The implementation of the curriculum for primary school
mathematics with statistics imbedded in it, may have been contributing to poor
learners’ low achievement in the subject. Consequently, this study evaluated
the extent to which pupil and teacher knowledge of statistics hampers pupils’
achievement in mathematics.
RESEARCH QUESTIONS
1. To what extent
would pupil factors (pupils’ statistical knowledge, gender, parents’ occupation, parents’
qualification, family size and pupils’ position in the family) and teacher
factors (teachers’ statistical knowledge, lesson preparation, classroom management, instructional delivery,
qualification and years of teaching experience) influence pupils’ achievement
in mathematics?
2. Is there any significant
relationship in the performance of pupils in statistics and mathematics
achievement tests?
METHODOLOGY
The study is a non experimental design of the survey research type. The
research type was employed because the researcher had no direct control of the
dependent and the independent variables as they had already occurred.
The population for
the study comprised of all primary five pupils in public schools in Iwo and Ikire local government areas of Osun
State, Nigeria. The public primary schools were chosen to ensure homogeneity of
the sample with respect to curriculum content used and school type. Multistage
sampling technique was used in selecting the required number of respondents for
the study. First, two educational zones
were purposively selected from the six educational zones in Osun
State. Two local government areas of the state were also purposively selected
from the educational zone; to ensure that the selected local government areas
were not clustered within a zone and prevent contamination. Purposive sampling
was used to select forty three public primary schools from the study areas.
This is to ensure that schools are far apart in terms of distance in order to
avoid undue interaction among the participants of one school and the
other. In each school selected, simple
random sampling was used to select Primary 5 intact classes. Where only one arm
existed, the affected arm was automatically adopted. The class teacher of any
class selected and the pupils therein automatically qualified to participate.
In all, 43 Primary Five class teachers in the selected schools and 689 pupils
constituted the study sample.
Instrumentation
Four instruments were developed by the researchers and adopted in
collecting data for the study: Classroom Teaching Observation Scale
(CTOS) with Scot’s Pi reliability coefficient index of 0.73, Pupils’
Mathematics Achievement Test (PMAT) with KudarRichardson
KR20 reliability coefficient of 0.89, Pupils’ Statistics Achievement Test
(PSAT) with KudarRichardson KR20 reliability
coefficient of 0.82, Teachers’ Content Knowledge of Statistics Questionnaire
(TCKOSQ) with Cronbach Alpha reliability coefficient
index of 0.78. The instruments were all developed, pilot tested and validated
by the researchers.
The Classroom
Teaching Observation Scale (CTOS) consisted of twelve items. The contents of CTOS consist of pedagogical
skills displayed by the teacher, teacher classroom organisation
and teacher/pupils relationship during teaching. This was placed on 4 point Likert Scale of Poor (1), Fair (2), Good (3) and Excellent
(4). The Mathematics Achievement Test (MAT) contained two sections (A & B).
Section A was used to capture the demographic data of the respondents with
respect to class, age and gender, position in the family, family size. Section
B contained questions designed to test the cognitive level of achievement of
the learners’ mathematics. It consisted of 20 multiple choice test items with
four options lettered A to D. Correct
response to each of the items attracted a score of 5 while an incorrect
response attracted a score of 0. The Statistics Achievement Test (SAT)
contained two sections (A & B). Section A was used to capture the biodata
of the respondents with respect to class, age and gender. Section B contained
questions on statistics achievement test which was used to test the cognitive
level of achievement of the learners. It consisted of 20 multiple choice test
items with four option letters A to D.
Correct response to each of the items attracts a score of 5 while an
incorrect response attracts a score of 0. Teachers’ Content Knowledge of
Statistics Questionnaire (TCKOSQ) was administered to participating
headteachers of the selected primary schools.
It consisted of two sections A and B. Section A
solicited information on respondents’ personal data such as gender, name of
school, qualification and years of teaching experience. Section B contained the
questions on the statistics achievement test which was used to test the
statistics content knowledge of the teachers. It contained twenty (20) multiple
choice test items with four option letters A to D. Correct response to each of the items will
attract a score of 5 while an incorrect response will attract a score of 0.
Three postgraduate students were trained within three days as research
assistants. The researchers and the research assistants administered the
instruments to the pupils and teachers in the sampled schools. The classroom
observation was carried out by the researchers. Data were collected for six
weeks. The data collected were analysed using
inferential statistics (multiple linear regression and correlation) at 0.5%
level of significance.
RESULTS AND DISCUSSION
Table 1 gives the summary of the intercorrelation matrix of the independent
variables (pupils’ statistical knowledge, teachers’ statistical knowledge,
teacher factors and pupil factors) and the dependent variables (pupils achievement in mathematics) under study. The intercorrelation matrix of Pearsonmoment correlation coefficients
that indicates the correlation among the predictor variables in predicting the
dependent variable (pupils mathematics achievement). Adegoke (2012) emphasised that an
intercorrelation matrix is a descriptive statistics table that shows the import
of the predictor variables in predicting the dependent variable (also called
the criterion variable) along with their means and standard deviations. The
essence of the intercorrelation matrix is to determine the degree of tolerance
(that is to determine the coefficient of measuring the multicollinearity)
among the independent variable in a study. Multicollinearity
is detected by examining the tolerance for each independent variable. Tolerance
is the amount of variability in one independent variable that is not explained
by the other independent variables. This is because none of the values of the
correlation coefficients are highly correlated with each other (i.e. r >
0.75). The implication of this is that all the predictor variables in the study
are good enough to be part of the model in predicting achievement in
mathematics. There is a clear indication of nonviolation of the major
assumptions required for running a regression analysis. Therefore, it is
observed from Table 1, that at p < 0.5, there is no multicollinearity
between or among the variables of study. This concurs with Tabachnick
and Fidell (2007) which affirmed that multicollinearity amongst the variables of interest must be
resolved before proceeding with regression analysis.
Research Question 1: To what
extent would pupil factors (pupils’ statistical knowledge, gender, parents’ occupation, parents’
qualification, family size and pupils’ position in the family) and teacher
factors (teachers’ statistical knowledge, lesson preparation, classroom
management, instructional delivery, qualification and years of teaching
experience) influence pupils’ achievement in mathematics?
Table 2 shows that
pupils achievement in mathematics, based on teachers and pupils statistical
knowledge and other variables considered in the study, yielded a coefficient of
multiple regression (R) = 0.70, a coefficient of determination (R^{2})
= 0.49 and adjusted R square (R_{adj}) =
0.29.This reveals that the predictor variables jointly explained about 29% of
the variance in pupils’ achievement in mathematics. Likewise, Table 3
shows that teachers’ classroom management skill, teachers’ lesson preparation style, pupils’
statistical knowledge and parents qualification had a significant influence on
pupils’ achievement in mathematics, F _{(12, 30)} = 2.425; p<0.05.
Going by the
findings of this study, learners’ achievement in mathematics and statistics is
related. This implies that learners’ knowledge and achievement in mathematics
can go a long way in determining his or her knowledge and achievement in
statistics. This is in consonance with the Moore (2004); Alieme
and Osiesi (2015), who asserts that statistics, while
closely related to mathematics, is a distinct discipline. Therefore, a pupil
who performs well in statistics will likely have high achievement in
mathematics. Teachers’ classroom management skill, teachers’ lesson preparation
style, pupils’ statistical knowledge and parents’ qualification significantly
influence pupils’ achievements in mathematics. This finding is in line with the
findings of Eggen & Kauchak
(2001) who restated the import of lesson preparation by the teacher as a factor
that could foster classroom management, learners’ attitude to learning and
their overall academic outcomes. The finding of the study also buttresses
assertions by Asiyai (2011), Charles (2011), Daly
(2005), Marzano et al, (2003), Marzano
(2010) and Sowell (2013) that classroom management enhances effective teaching
and learning, which in turn gives rise to productive learning outcome.
Research question 2: Is there any significant relationship in the performance of pupils’ in
statistics and mathematics achievement tests?
Table 4 shows that
there is a significant relationship between pupils’ achievement in statistics
and mathematics achievement tests with a correlation value of r = 0.002. The
finding is in tandem with studies conducted by Moore (2004), Leavy (2010), Alieme and Osiesi (2015) which restated the relationship that exists
between knowledge of statistics and mathematics achievement among learners.
However, the finding negates the findings of Ndukwu
(2002) and Adeola (2011) which stated that teachers’
qualification significantly influences pupils’ intellectual development. It
also contradicts Marzano (2003) who found that
teachers’ instructional delivery has a major independent impact on learners’
achievement and opposes claims by Ghanbarzadeh
(2001), Scott (2001), Bowen and Richman (2000); that learners’ attitude towards
a subject is a predictor of their achievement in such a subject. The finding
does not give credence to the findings of Popham
(2005) and Goodykonntz (2011); that learners’ poor
attitude towards mathematics could lead to their poor performance in
mathematics and statistics. The study shows that parents’ qualification has a
significant influence on pupils’ achievement in mathematics by supporting
Phillips (1998) that parental qualification and social economic status have an
impact on pupils’ achievement. Furthermore, this study revealed that pupils’
gender, family size and position in the family do not influence their
achievement in mathematics. This is in consonance with Abiam
and Odok (2006), Howes
(2002) and Sinnes (2005), who noted that there is no
significant relationship between gender and mathematics achievement.
CONCLUSION AND RECOMMENDATIONS
This study sought
to evaluate the extent to which teachers’ and pupils’ statistical knowledge,
pupil and teacher factors influence pupils’ achievement in mathematics in Osun State, Nigeria. Findings show that teachers’ classroom
management skill, lesson preparation style, pupils’ statistical knowledge and
parents’ qualification significantly influence pupils’ achievement in
mathematics. Furthermore, the findings show that there is a significant
relationship between pupils’ achievement in statistics and mathematics.
Therefore, efforts geared at improving mathematics achievement, especially at
the primary level, should include statistics knowledge and education in order
to enhance pupils’ achievement in mathematics. Hence, it is recommended that if
Osun State government intends to vigorously improve
mathematics achievement among learners, particularly primary school pupils, she
should do the following: enlighten parents on the need for a higher educational
qualifications and to ensure that pupils view statistics and mathematics in the
proper perspective and that teachers are well enlightened on the need for
statistics knowledge in mathematics teaching and learning and on the
distinction between statistics and mathematics.
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