The longitudinal variation of equatorial waves due to propagation on a varying zonal flow

The general 1-D theory of waves propagating on a zonally varying flow is developed from basic wave theory, and equations are derived for the variation of wavenumber and energy along ray paths. Different categories of behaviour are found, depending on the sign of the group velocity (cg) and a wave property, B. For B positive the wave energy and the wave number vary in the same sense, with maxima in relative easterlies or westerlies, depending on the sign of cg. Also the wave accumulation of Webster and Chang (1988) occurs where cg goes to zero. However for B negative they behave in opposite senses and wave accumulation does not occur. The zonal propagation of the gravest equatorial waves is analysed in detail using the theory. For non-dispersive Kelvin waves, B reduces to 2, and analytic solution is possible. B is positive for all the waves considered, except for the westward moving mixed Rossby-gravity (WMRG) wave which can have negative as well as positive B. Comparison is made between the observed climatologies of the individual equatorial waves and the result of pure propagation on the climatological upper tropospheric flow. The Kelvin wave distribution is in remarkable agreement, considering the approximations made. Some aspects of the WMRG and Rossby wave distributions are also in qualitative agreement. However the observed maxima in these waves in the winter westerlies in the eastern Pacific and Atlantic are not consistent with the theory. This is consistent with the importance of the sources of equatorial waves in these westerly duct regions due to higher latitude wave activity.

Breaking the double-edged sword of effort/trying hard: developmental equilibrium and Longitudinal relations among effort, achievement, and academic self-concept

Ever since the classic research of Nicholls (1976) and others, effort has been recognized as a double-edged sword: whilst it might enhance achievement, it undermines academic self-concept (ASC). However, there has not been a thorough evaluation of the longitudinal reciprocal effects of effort, ASC and achievement,in the context of modern self-concept theory and statistical methodology. Nor have there been developmental equilibrium tests of whether these effects are consistent across the potentially volatile early-to-middle adolescence. Hence, focusing on mathematics, we evaluate reciprocal effects models over the first four years of secondary school, relating effort, achievement (test scores and school grades), ASC, and ASCxEffort interactions for a representative sample of 3,421 German students (Mn age = 11.75 years at Wave 1). ASC, effort and achievement were positively correlated at each wave, and there was a clear pattern of positive reciprocal positive effects among ASC, test scores and school grades—each contributing to the other, after controlling for the prior effects of all others. There was an asymmetrical pattern of effects for effort that is consistent with the double-edged sword premise: prior school grades had positive effects on subsequent effort, but prior effort had non-significant or negative effects on subsequent grades and ASC. However, on the basis of a synergistic application of new theory and methodology, we predicted and found a significant ASC-by-effort interaction, such that prior effort had more positive effects on subsequent ASC and school grades when prior ASC was high—thus providing a key to breaking the double-edged sword.

Long-term positive effects of repeating a year in school: Six-year longitudinal study of self-beliefs, anxiety, social relations, school grades, and test scores

Consistently with a priori predictions, school retention (repeating a year in school) had largely positive effects for a diverse range of 10 outcomes (e.g., math self-concept, self-efficacy, anxiety, relations with teachers, parents and peers, school grades, and standardized achievement test scores). The design, based on a large, representative sample of German students (N = 1,325, M age = 11.75 years) measured each year during the first five years of secondary school, was particularly strong. It featured four independent retention groups (different groups of students, each repeating one of the four first years of secondary school, total N = 103), with multiple post-test waves to evaluate short- and long-term effects, controlling for covariates (gender, age, SES, primary school grades, IQ) and one or more sets of 10 outcomes realised prior to retention. Tests of developmental invariance demonstrated that the effects of retention (controlling for covariates and pre-retention outcomes) were highly consistent across this potentially volatile early-to-middle adolescent period; largely positive effects in the first year following retention were maintained in subsequent school years following retention. Particularly considering that these results are contrary to at least some of the accepted wisdom about school retention, the findings have important implications for educational researchers, policymakers and parents.