An Appraisal of the Degree of School Effectiveness among Secondary Schools of Zamfara State, Nigeria

This study was conducted purposely to assess the degree of school effectiveness among public secondary schools of Zamfara State, Nigeria. In order to achieve this fundamental objective, one research question was formulated. A descriptive survey research design was adopted in the study. Population of the study comprised the entire 2361 classroom teachers deployed in the 158 public secondary schools of Zamfara State-Nigeria. From the population of the study, a sample size of 266 teachers was extracted using a ‘Multistage Random Sampling Technique’. A semi-structured questionnaire developed by Lezzote and Snyder (2011) on a five Likert type scale instrument with 21 items was employed as an instrument for data collection. The instrument composite reliability was computed using Cronbach’s alpha method and obtained the value of .949. All data covered in the study were collected through a field survey approach. Analytically, the current study discovered that, the degree of school effectiveness was at a high extent with mean score (M=3.68, SD=0.15). Based on this finding, the paper recommends that, stakeholders in educational sector comprising government’s ministries, departments and agencies, policymakers, secondary schools’ principals, instructional teachers as well as the learners and their parents/guardians should reciprocally work together in the process of appropriate perpetration and advancement of effective school system and its practices.

Stanley Depth and Sequentially Cohen- Macaulay Lexsegment Ideals

In the first chapter we give some basic definitions from commutative algebra. We give some results obtained in recent years for the Stanley depth of multigraded S-modules, where S = K[x1 , . . . , xn ] is a polynomial ring in n indeteminantes with coefficients in a field K. We also give some results regarding the progress towards the Stanley’s conjecture. In the second chapter, we show that if I ⊂ J be monomial ideals of a polynomial algebra S over a field. Then the Stanley depth of J/I is smaller or equal to the √ √ Stanley depth of J/ I. We give also an upper bound for the Stanley depth of the intersection of two primary monomial ideals Q, Q , which is reached if Q, Q √ √ are irreducible, ht(Q + Q ) is odd and Q, Q have no common variables. These results are proved in my paper [23]. In the third chapter, we give different bounds for the Stanley depth of a monomial ideal I of a polynomial algebra S over a field K. For example we show that the Stanley depth of I is less than or equal to the Stanley depth of any prime ideal associated to S/I. Also we show that the Stanley’s conjecture holds for I and S/I when the associated prime ideals of S/I are generated by disjoint sets of variables. These results are proved in my paper [24]. In the forth chapter, we give an upper bound for the Stanley depth of the edge ideal I of a k-partite complete graph and show that Stanley’s conjecture holds for I. Also we give an upper bound for the Stanley depth of the edge ideal of an s-uniform complete bipartite hypergraph. In this chapter we also give an upper bound for the Stanley depth of the edge ideal of a complete k-partite hypergraph and as an application we give an upper bound for the Stanley depth of a monomial ideal in a polynomial ring S. We give a lower and an upper bound for the cyclic module S/I associated to the complete k-partite hypergraph. These results are proved in our papers [26] and [27]. In the fifth chapter, the associated primes of an arbitrary lexsegment ideal I ⊂ S are determined. As application it is shown that S/I is a pretty clean module, therefore, S/I is sequentially Cohen-Macaulay and satisfies the Stanley’s conjecture. These results are proved in my paper [25].