In the marine ecosystem, the time delay or lag may occur in the predator response function, which measures the rate of capture of prey by a predator. This is because, when the growth of the prey population is null at the time delay period, the predator’s growth is affected by its population and prey population densities only after the time delay period. Therefore, the generalized Gause type predator-prey fishery models with a selective proportional harvesting rate of fish and time lag in the Holling type II predator response function are proposed to simulate and solve the population dynamical problem. From the mathematical analysis of the models, a certain dimension of time delays in the predator response or reaction function can change originally stable non-trivial critical points to unstable ones. This is due to the existence of the Hopf bifurcation that measures the critical values of the time lag, which will affect the stabilities of the non-trivial critical points of the models. Therefore, the effects of increasing and decreasing the values of selective proportional harvesting rate terms of prey and predator on the stabilities of the non-trivial critical points of the fishery models were analysed. Results have shown that, by increasing the values of the total proportion of prey and predator harvesting denoted by qx Ex and qy Ey respectively, within the range 0.3102 ≤ qx Ex ≤ 0.9984 and 0.5049 ≤ qy Ey ≤ 0.5363, the originally unstable non-trivial critical points of the fishery models can be stable.

Perceived self-efficacy refers to the people’s beliefs in their capabilities to exert control over their own functioning and over events that affect their live. Accessing student self-efficacy can provide educator with additional insight of students’ subsequent performance. Hence, this study examined the relationship between self-efficacy and mathematics performance among Applied Science university students. The sample consisted of first year Applied Science university students from two different backgrounds; matriculation and diploma. Students were given two sets of survey questionnaire which were developed by the authors to measure the students’ self-efficacy and their ability to solve the integral calculus questions. The questions were divided into four domains namely concept of calculus, translation from concept to formula, techniques of integration and recognition of functions. The findings from this study did not fully provide evidence to support the view that positive self-efficacy beliefs in mathematics increase mathematics performance since there was no significant impact on what the students perceived and what they actually scored. However, this study found out that if the aspects of self-efficacy were to be examined individually to see if there was any significant impact towards mathematics performance, it can be seen that Techniques of integration (r = 0.243, p < 0.05) and Recognition of function (r = 0.205, p < 0.05) were significant and positively related to mathematics performance to some extent. The study also showed that self–efficacy is correlated with all of the aspects of performance which the correlations values are as follows: Concept in Calculus (r = 0.730, p < 0.01), Translation from Concept to Formula (r = 0.705, p < 0.01), Techniques of integration (r = 0.852, p < 0.01) and Recognition of function (r = 0.773, p < 0.01). The results of this study can help the educators to evaluate and improve the effectiveness of the current mathematics teaching.

From the constructivist paradigm, knowing misconceptions of students regarding a particular concept is deemed vital in designing effective instruction. Ausubel (1968) commented that 'The most important single factor influencing learning is what the learner already knows; ascertain this and teach him accordingly'. The symbiosis between science and mathematics is a profound one. Science views mathematics as a significant branch. Science likes to refer mathematics as the Queen, as mathematics nurtures the growth of science especially in the areas such as scientific prediction and manipulation. On the other hand, many concepts of mathematics are invented for the purpose of science such Proportion and Calculus to name a few. Two major ideas in Proportion are the Direct and the Inverse. A good grasp of these mathematical ideas is paramount for students in understanding the fundamental nature of science in its quantitative form. This paper offers a comprehensive description of seven hundred and fifty nine science based students (385 female and 374 male) from a local university in their developmental understanding of this mathematical idea of Inverse Proportion from the six domains i.e., Definition of Inverse Proportion, Graphical Representation of Inverse Proportion, Mathematical Representation of Inverse Proportion, Data Characteristic of Inverse Proportion, Relational Understanding of Inverse Proportion, and Problem Solving in Inverse Proportion. It discusses these six domains from two perspectives i.e., Academic Ability and Gender. The paper is based on a study by Beh et al (2008) anchoring on Constructivism. Among the major findings are: Students irrespective of high or low academic ability generally performed poorly in domains requiring conceptual understanding but showed relatively higher competency for the domain requiring procedural skills. Students of higher level academic ability demonstrate a significant in dept understanding of Inverse Proportion than students of lower level of academic ability; and Male students overall understanding of Inverse is significantly higher than their female counterparts at the 5% level. Since the study is based on Constructivism, it also highlights students' alternative frameworks. Implications for teaching and learning will be discussed.

Loligo Duvauceli, is known as squid in the local name. Squid is a species of high value and a good source of protein besides fish. In this paper, a logistic growth model with constant and periodic harvesting are used to find the optimum sustainable population of Loligo Duvauceli in order to preserve the resource. The data used for this study was obtained from Department of Fisheries. The aims of this study are to estimate to determine the stability of the equilibrium point. Then, the effect of the constant and the periodic harvesting on the population of squids analysed. Finally, to compare the results obtained between the two strategies. The best harvesting selected squids is periodic harvesting.