Implementing the OPTIMAL model : the impact on students' motivation in an elementary school games environment

Optimal challenge occurs when an individual perceives the challenge of the task to be equaled or matched by his or her own skill level (Csikszentmihalyi, 1990). The purpose of this study was to test the impact of the OPTIMAL model on physical education students' motivation and perceptions of optimal challenge across four games categories (i. e. target, batting/fielding, net/wall, invasion). Enjoyment, competence, student goal orientation and activity level were examined in relation to the OPTIMAL model. A total of 22 (17 M; 5 F) students and their parents provided informed consent to take part in the study and were taught four OPTIMAL lessons and four non-OPTIMAL lessons ranging across the four different games categories by their own teacher. All students completed the Task and Ego in Sport Questionnaire (TEOSQ; Duda & Whitehead, 1998), the Intrinsic Motivation Inventory (IMI; McAuley, Duncan, & Tanmien, 1987) and the Children's Perception of Optimal Challenge Instrument (CPOCI; Mandigo, 2001). Sixteen students (two each lesson) were observed by using the System for Observing Fitness Instruction Time tool (SOFTT; McKenzie, 2002). As well, they participated in a structured interview which took place after each lesson was completed. Quantitative results concluded that no overall significant difference was found in motivational outcomes when comparing OPTIMAL and non-OPTIMAL lessons. However, when the lessons were broken down into games categories, significant differences emerged. Levels of perceived competence were found to be higher in non-OPTIMAL batting/fielding lessons compared to OPTIMAL lessons, whereas levels of enjoyment and perceived competence were found to be higher in OPTIMAL invasion lessons in comparison to non-OPTIMAL invasion lessons. Qualitative results revealed significance in feehngs of skill/challenge balance, enjoyment and competence in the OPTIMAL lessons. Moreover, a significance of practically twice the active movement time percentage was found in OPTIMAL lessons in comparison to non-OPTIMAL lessons.

On the formulation and the calculation of the harmonic contributions to the Debye-Waller factor in metals (sodium)

The algebraic expressions for the anharmonic contributions to the Debye-Waller factor up to 0(A ) and 0 L% ) £ where ^ is the scattering wave-vector] have been derived in a form suitable for cubic metals with small ion cores where the interatomic potential extends to many neighbours. This has been achieved in terms of various wave-vector dependent tensors, following the work of Shukla and Taylor (1974) on the cubic anharmonic Helmholtz free energy. The contribution to the various wave-vector dependent tensors from the coulomb and the electron-ion terms in the interatomic metallic potential has been obtained by the Ewald procedure. All the restricted multiple whole B r i l l o u i n zone (B.Z.) sums are reduced to single whole B.Z. sums by using the plane wave representation of the delta function. These single whole B.Z. sums are further reduced to the •%?? portion of the B.Z. following Shukla and Wilk (1974) and Shukla and Taylor (1974). Numerical calculations have been performed for sodium where the Born-Mayer term in the interatomic potential has been neglected because i t is small £ Vosko (1964)3 • *n o^er to compare our calculated results with the experimental results of Dawton (1937), we have also calculated the r a t io of the intensities at different temperatures for the lowest five reflections (110), (200), (220), (310) and (400) . Our calculated quasi-harmonic results agree reasonably well with the experimental results at temperatures (T) of the order of the Debye temperature ( 0 ). For T » © ^ 9 our calculated anharmonic results are found to be in good agreement with the experimental results.The anomalous terms in the Debye-Waller factor are found not to be negligible for certain reflections even for T ^ ©^ . At temperature T yy Op 9 where the temperature is of the order of the melting temperature (Xm) » "the anomalous terms are found to be important almost for all the f i ve reflections.

On the path integral formulation and the evaluation of quantum statistical averages

Four problems of physical interest have been solved in this thesis using the path integral formalism. Using the trigonometric expansion method of Burton and de Borde (1955), we found the kernel for two interacting one dimensional oscillators• The result is the same as one would obtain using a normal coordinate transformation, We next introduced the method of Papadopolous (1969), which is a systematic perturbation type method specifically geared to finding the partition function Z, or equivalently, the Helmholtz free energy F, of a system of interacting oscillators. We applied this method to the next three problems considered• First, by summing the perturbation expansion, we found F for a system of N interacting Einstein oscillators^ The result obtained is the same as the usual result obtained by Shukla and Muller (1972) • Next, we found F to 0(Xi)f where A is the usual Tan Hove ordering parameter* The results obtained are the same as those of Shukla and Oowley (1971), who have used a diagrammatic procedure, and did the necessary sums in Fourier space* We performed the work in temperature space• Finally, slightly modifying the method of Papadopolous, we found the finite temperature expressions for the Debyecaller factor in Bravais lattices, to 0(AZ) and u(/K/ j,where K is the scattering vector* The high temperature limit of the expressions obtained here, are in complete agreement with the classical results of Maradudin and Flinn (1963) .

Optimal and Robust Designs of Step-stress Accelerated Life Testing Experiments for Proportional Hazards Models

Accelerated life testing (ALT) is widely used to obtain reliability information about a product within a limited time frame. The Cox s proportional hazards (PH) model is often utilized for reliability prediction. My master thesis research focuses on designing accelerated life testing experiments for reliability estimation. We consider multiple step-stress ALT plans with censoring. The optimal stress levels and times of changing the stress levels are investigated. We discuss the optimal designs under three optimality criteria. They are D-, A- and Q-optimal designs. We note that the classical designs are optimal only if the model assumed is correct. Due to the nature of prediction made from ALT experimental data, attained under the stress levels higher than the normal condition, extrapolation is encountered. In such case, the assumed model cannot be tested. Therefore, for possible imprecision in the assumed PH model, the method of construction for robust designs is also explored.