The paper provides five tests of data normality at different sample sizes. The tests are the Shapiro-Wilk (SW) test, Anderson-Darling (AD) test, Kolmogorov-Smirnov (KS) test, Ryan-Joiner (RJ) test, and Jarque-Bera (JB) test. These tests were used to test for normality for two secondary data sets with sample size (155) for large and (40) for small; and then test the simulated scenario with standard normal “N(0,1)” data sets; where the large samples of sizes (150, 140, 130, 130, 110 and 100) and small samples of sizes (40. 35, 30, 25, 20, 15 and 10) are considered at two levels of significance (5% and 10%). However, the aim of this paper is to detect and compare the performance of the different normality tests considered. The normality test results shows Kolmogorov-Smirnov (KS) test is a most powerful test than other tests since it detect the simulated large sample data sets do not follow a normal distribution at 5%, while for small sample sizes at 5% level of significance; the results showed the Jarque-Bera (JB) test is a most powerful test than other tests since it detects that the simulated small sample data do not follow a normal distribution at 5%. This paper recommended JB test for normality test when the sample size is small and KS test when the sample size is large at 5% level of significance.
This study was a quasi-experimental design aimed at exploring the effect of Teaching forUnderstanding (TfU)
This study investigated the efficacy of metacognitive instructional strategy in the improvement of the knowledge of cognition among junior secondary students with Mathematics Disability (MD) in everyday arithmetic in Port Harcourt Local Government Area (LGA) of Rivers State, Nigeria. Pre-test, post-test quasi-experimental design was used. A total of 60 Junior Secondary Class 3 (JSC3) students with MD participated in the study. A diagnostic instrument, teacher judgment, and the internal examination results were used as criteria for the identification and selection of JSC3 students with MD for participation. Three instruments were used for data collection, viz: Everyday Arithmetic Problem-Solving Achievement Test (EAPSAT), Mathematics Disability Diagnostic Test (M2DT), and Metacognitive Strategy Assessment (MSA). The instruments were respectively used to measure everyday arithmetic achievement, diagnosis and metacognitive knowledge of cognition. The Cronbach alpha was used to determine the reliability of each section of MSA (declarative knowledge, α =0.81, conditional knowledge, α =0.84, procedural knowledge α =0.78). The test-retest method was used to determine the reliability of EAPSAT and M2DT to obtain indices of 0.83 and 0.80 respectively. The research questions were answered using mean and standard deviation whereas the hypotheses were tested using Analysis of Covariance (ANCOVA). The findings among others established that the metacognitive knowledge of students improved over time; there were significant main effects of metacognitive strategy on student procedural, declarative and conditional knowledge respectively. A recommendation of the study is that teachers should adopt the metacognitive strategy while teaching everyday arithmetic.
Fitting nonlinear models is not a single-step procedure but it involved a process that requires careful examination of each individual step. Depending on the objective and the application domain, different priorities are set when fitting nonlinear models; these include obtaining acceptable parameter estimates and a good model fit while meeting standard assumptions of statistical models. We propose steps in fitting nonlinear models in this research work. Two reciprocal power regression models were considered with a non-linear data set. Then, the following steps are considered (i) fit the models to the data collected using iterative steps, (ii) to develop a linear model to estimate the parameter β1 and β2 when the initial value (or growth rate β3) lies between -1.0 ≤ β3 ≤1.0 ); using the transform models of the reciprocal power regression model (iii) to find the “best” model between the two models using R2, AIC and BIC. The results show Model B is better than Model A, using the model selection criteria.
This study is an exploration of the effectiveness of Design-Based Learning (DBL) model in the improvement of senior secondary students’ achievement in solid geometry in Emohua Local Government Area of Rivers State. The quasi-experimental design was adopted. A sample of 59 Senior Secondary School I (SSSI) students took part in the study. Solid Geometry Achievement Test (SGAT) was the instrument used for data collection. The Kuder-Richardson KR-21 method was used to establish the reliability of SGAT to obtain an index of 0.84. Two research questions and two null hypotheses guided the study. The research questions were answered using mean and standard deviation while the hypotheses were tested using Analysis of Covariance (ANCOVA) at .05 level of significance. The findings established that DBL model was superior to Problem-based Learning (PbL) model in advancing the learning achievement of students in solid geometry. The students of both groups improved in learning over time with higher learning gain among students in the experimental group. The male and the female students in the experimental group outperformed their counterparts in the control group over SGAT scores. The male and the female students taught using the DBL and PbL respectively did not significantly differ over SGAT scores. It was recommended among others that mathematics teacher should apply the DBL in teaching solid geometry in the senior secondary schools in Nigeria because when effectively utilized, this instructional model is capable of advancing the learning achievement of students in mathematics irrespective of their locations and gender
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