Learning Analytics: Issues on the Pupil-Teacher Ratio in Public Primary Schools in Nigeria

Pupil-teacher ratio (PTR) is one of the key measurements of quality education. This article presents the pupil-teacher ratio for 133 public primary schools in a local government area (LGA) of Ogun State, Nigeria. The data were obtained from a complete enumeration of the records of each school. It was discovered that the average PTR obtained from the data analysis is higher than the national average. Using PTR equals 35 as a benchmark of Nigeria, only 25 (19%) schools out of the 133 schools considered have an acceptable PTR (below 35), 52 (39%) schools have a moderate PTR (between 35 and 50) and 56 (42%) schools have unacceptable and high PTR (above 50). This article shows that there is high pupil-teacher ratio in the country’s public primary schools. This research will be helpful in the following; educational evaluation and assessment, audit and quality assurance, decision makers in the Ministry of Education in gap analysis for recruitment purposes, assessing the level of implementation of policies on education and monitoring of the progress made in attaining development sustainable goals (SDG) as it relates to access to quality education. Keywords—Education, Learning analytics, Pupil-teacher ratio, Smart campus, Statistics, Teacher, Nigeria


Introduction
The pupil-teacher ratio is the total number of pupils in a particular school divided by the total number of qualified teachers. The format for computation of PTR used in this article is the same used by the UNESCO [1]. PTR is often confused with "class size" even though; they are different but similar metrics in educational evaluation. PTR is a key indicator in measuring quality and equity in public primary education. Other indicators as listed by [2] include, but not limited to: educational qualification of the teacher, health condition and intellectual quotient of the pupil, psychological variables such as externalizing or internalizing behavior [3], motivation of the teachers [4], the quality of teaching and teaching aids [5], school-home distance, quality of curriculum and educational policies [6][7][8][9], social and environmental factors.
Several authors who have presented similar research papers showed that smaller PTR is desirable for effective learning to take place, citing that higher number of pupils in a class reduces the attention given to each pupil by the teacher, which consequently affect the academic performance, especially at practical classes. Historically, education in general has not received the necessary and adequate funding from governments in Nigeria and that have resulted in its falling standard. One of the manifestations is the prevalence of high PTR of which this article portrays. The official PTR in Nigeria, according to [2] is 35 which are often higher in urban areas. The high PTR in the urban areas can be attributed to economic migration from the rural to urban areas.
PTR is a widely researched concept in educational evaluation, audit and management. Stakeholders such as parents [10], voters [11], researchers [12], economists [13] believe that low PTR is good for their wards. Privately owned or funded schools seem to have a low PTR [14][15] and often times, policies are formulated and implemented by government to reduce PTR of public primary schools by increasing space allocation [16], building more schools to boost school enrolment [17], subsidy strategies [18], resource expansion and improved budgetary allocations [19][20], progressive pedagogy [21], class-size reduction and staffing. The strategies are necessary to address the issue of fading productivity of schooling [22] and encourage early childhood education [23].
This work presents an analysis of data of the number of teachers and the pupils in government funded primary schools across the LGA considered. Low or high PTR is just one of the concerns of primary education, others can be seen in [24][25][26][27][28].

Literature Review
There are diverse views on the impact of PTR on academic performance, human capital development, economy, after school life and so on. Coincidentally, some of the views about the effect of PTR have proven to be insignificant on the educational, sociological and psychological variables. A survey of literature is done to outline the perceived relationship, independence and associations of PTR and some studied variables.
Generally, researchers have found out that PTR and other factors are significant predictors of learning or educational attainment of pupils. These are presented in Table 1. It should be noted that the perceived significant relationship may not account for hidden or unexplained variables that were not pictured in by the various researchers.
In addition, it has been observed that the following have a significant effect on PTR; expansion of charter schools [38], infant mortality [39] and skill-biased technological changes [40]. [29] Age, socioeconomic background and PTR [30] Expenditure per student, PTR, and families' background [31] School management, teaching and learning resources, PTR and syllabus coverage [32] Sanitation facilities in school, enrolment ratio, environment, drinking water, spacestudent ratio, PTR and dropout and repetition rates [33] Educational expenditure and PTR [34] PTR [35][36][37] 2.1 Pupil-teacher ratio as a significant positive predictor PTR has been found to have a positive correlation or a link or association with some educational, sociodemographic, psychological, socioeconomic, pedagogical and environmental variables. A look at previous works in the literature showed that the association is often studied simultaneously with other identified variable or school input. In the developing countries, free education inevitably increases the PTR [41] because of increased access and subscription, and high enrolment rate while in the developed countries, free education reduces the PTR because of calculated efforts are done to increase the carrying capacity of schools and recruitment of more qualified teachers.
Five broad areas were identified here, which are: • Effect of PTR on teachers • Educational attainment • Cognitive abilities • Life after school • Drop-out

Effect of PTR on teachers:
The educational qualification and wages were identified to be positively correlated with PTR [42]. Highly skilled teachers are normally assigned to big classes for the purposes of maximum impact and return on investment. Ordinarily, high wages are paid as compensation. On the other hand, high PTR often leads to high incidence of teachers' sickness absenteeism [43], voice disorders [44] and burn outs [45].
Effect of PTR on educational attainment: PTR has been found to be less significant positively correlated with educational attainment of the pupils [46][47], although, parental education [48], strong pedagogical strategies [49] and ICT adoption [50] have more impact.
Effect of PTR on cognitive ability: PTR has been found to be positively related to the ability of pupils to perform well on cognitive tests. It has been identified to be true in mathematics [51] and language proficiency [52] tests.
Effect of PTR on life after school: PTR has been found to be positively correlated with labor, employment and some aspects of life after school. These come in the form of larger capital to labor ratio [53], higher enumeration and job satisfaction [54], benefit from less intergenerational mobility [55], decreased probability of being unemployed after school [56] and health lifestyle [57].
Effect of PTR on pupil dropout: Pupils are more likely to drop out of school (early school-leaving) if the school they attend is associated with a higher PTR or lower expenditure per pupil [58][59]. These are predominant features in developing countries, where teacher pupil interaction and advising is very minimal because of high PTR.

2.2
Teacher-pupil ratio as significant negative predictor PTR has been found to have a negative correlation or association with some educational, sociodemographic, psychological, socioeconomic, pedagogical and environmental variables. That is the high PTR leads to a reduction of the effects of the studied variable or school input and vice versa.
Low PTR has been identified to lead to high returns on education [60], which readily reflects on the cognitive performance of the pupils [61]. High level of monetary investments in education measured as expenditure per pupil leads to lower PTR [62][63]. The consequences of such spending are restriction of access [64][65] and engagement of inexperienced teachers and a reduction of teachers' remuneration [66]. On the other hand, a reduction in the educational facilities leads to high PTR [67][68]. This scenario is readily found in the developing countries where government reduces the school fees without investing in the infrastructure that will cater for the increased number of pupils anticipated as a result of the fee reduction. The increased enrollment rate will inevitably snowballed into high PTR. The geographical size is also related to PTR as increasing district sizes reduce the PTR [69][70].
The quality of education has been found to be negatively correlated with PTR [71], as the perceived quality [72] and examination pass rates [73] erode with increasing PTR. Although the trend can be reversed by recruitment of additional teachers [74]. The teachers, on the other hand, often demand for high incentives in order to deliver efficiently [75], which leads to low PTR, increasing pupil-teacher interaction [76] and enhancing job satisfaction [77].

PTR is not a significant predictor
The last case is the instances where the PTR has no significant effect on the studied variable or educational input presented by the various authors. That is, neither no link exists between PTR and the variables and factors, nor does PTR contribute to their significance. Some of such instances of zero correlation are listed.
PTR was found neither to be related to geographical boundaries [85] nor contributes to bullying behaviors [86]. Furthermore, PTR is not associated with matriculation pass rate [87], career choice of pupils after school [88], educational qualifications or remuneration [89][90] and greenness performance [91]. Finally, authors have reported that there seem to be no link between PTR and educational attainment [92][93] or cognitive performance of pupils [94][95].

Materials and Methods
The details on how the data was obtained from the study area and the statistical methodology are presented.

Study area and data
The data were obtained from the records of 133 public primary schools in a local government area (LGA) in Ogun State, Nigeria. The records were collected from the official school and staff registers at the various schools with the condition that the data should be used for academic and scholarly purposes only. Privately funded and special primary schools were not considered. The raw data contains the number of teachers and the pupils in government funded primary schools across the LGA considered.

Computation of PTR
The PTR can be calculated using the formula;

Statistical analysis
Descriptive statistics and ranking were used to present information obtained from the analysis of the data. Similar analysis has been performed on some related educational data [96][97][98][99][100].

4
Results and Discussion

PTR Computation and descriptive statistics
The pupil-teacher ratio was computed for each of the schools and presented in Table 2. Thereafter, the results of the descriptive statistics of the number of students and the teachers are presented. The distribution of the population of teachers, male and female students are shown in Figures 1, 2 and 3. The descriptive statistics on the variables; teacher, number of male pupils and number of female pupils is presented in Table 3.

PTR Ranking
It is clear to all the PTR is not the same for all the schools considered as seen in Table 2. It is then necessary to know the schools with high PTR (PTR of more than say 35). The ranks of the schools considered based on their pupil-teacher ratio is presented in Table 4. The PTR was arranged from the highest to the lowest values. The ranking yielded three non-overlapping groups which are distinctly colored. The current PTR in Nigeria is 35, that is, 35 pupils to a teacher. 56 schools with red color have high PTR and requires more teachers to reduce the value of the PTR, which is PTR of 50 and above. However, those with yellow color are adjudged to be acceptable (25 schools), which is PTR of 35 and below. The acceptability is subject to interpretation from the Nigerian context, because the survey area is one of the educational developed states in Nigeria and, ordinarily, it is expected that the PTR should be small. However, this article points to the contrary. Moreover, it is expected that PTR should be high in education less developed states of the country which are the northern and the Niger Delta area of the country.

Conclusion
The research had led to the following conclusions: • Only 25 (19%) schools out of the 133 schools considered have an acceptable PTR (below 35). • 52 (39%) schools out of the 133 schools considered have a moderate PTR (between 35 and 50).
• 56 (42%) schools out of the 133 schools considered have unacceptable and high PTR (above 50). • More qualified teachers are urgently needed in these schools in order to ensure effective teaching and learning are taking place • Adequate funding should be provided by the government to sustain these schools and to ensure that these pupils are not deprived of their basic rights.
This research will be helpful in educational evaluation and assessment, audit and quality assurance, to decision makers in the Ministry of Education in gap analysis for recruitment purposes, assessing the level of implementation of policies on education and to monitor the progress made in attaining development sustainable goals (SDG) as it relates to access to quality education.  (2) decades in both public and private schools. She has supervised over ten (10) undergraduate students and currently supervising two (2) post graduate students. She has also served as examiner to several PhD thesis and a reviewer to some journals. She is a Mathematician with research interest in quantum stochastic differential equations, stochastic differential equations, ordinary differential equations, Mathematical Statistics. Some of her research activities in differential equations cover both qualitative and quantitative analysis of solutions. She also has interest in Mathematics education and Mathematical Physics.
Opeyemi P Ogundile received his B.Sc from Covenant University in Nigeria and proceeded to the prestigious university of Ibadan, Nigeria for his Master's in Mathematics. He is currently a faculty member at Covenant university, Nigeria and his areas of interest are Financial Mathematics, Mathematical Modeling, Stochastic (numerical) Differential Equation and Statistics.