ABSTRACT Public views on assigning students mathematics homework have been controversial. Although homework is designed for students to complete during non-school hours (Cooper, 1989), many see homework as excessive pressure on students. Most research placed their focus on the influence of the time spent on homework or the amount of homework on student achievement. Few studies have addressed the impact of types of mathematics homework. The purpose of this study is to examine the role of homework types in influencing opportunity to learn (OTL) on student achievement. This quantitative study used subsets of a large existing dataset collected by University of Chicago School Mathematics Project (UCSMP) in Pre-Transition Mathematics, Transition Mathematics, and Algebra. The findings showed that OTL measured by lesson coverage and by teachers’ reported posttest OTL have significant impact. Each type of homework as a mediator might have significant, positive or negative mediating effects or no mediating effects at all. The findings from having OTL measured by lesson coverage as the independent variable were more consistent with each mathematics course. The differences of the mediating effects of types of homework on the impact of OTL measured by lesson coverage on student mathematics achievement and on the impact of teachers’ reported posttest OTL on students’ mathematics achievement may be explained through the nature of the types of homework as well as through limitations of the study. Recommendations for future research and implications of the study were presented in the discussion part of the study.

This thesis is focused on the mechanisms for corrosion andhydriding of Zircaloy. Special attention is paid tomicrostructural characterisation by cross sectionaltransmission electron microscopy of the oxide layer formed.Three main topics have been treated in this work: (i)Pre-transition oxides were investigated with the purpose ofevaluating if it is possible to predict post-transitionbehaviour of different alloys. (ii) The reason for the commonlyobserved accelerated corrosion of Zircaloy in the presence oflithium hydroxide was investigated by studying the phasetransformation of differently stabilised zirconium oxides andby corrosion studies. (iii) Pre-hydrided Zircaloy-2 was studiedto investigate the influence of hydrogen on the oxidationbehaviour. Characterisation of pre-transition oxides formed onzirconium alloys, has been accomplished with the aim ofdetermining if there are any differences in the properties(morphology, pores, cracks and phases) of the oxide layersformed which might explain the differences in corrosionbehaviour later in life. Four Zircaloy-2 versions and oneZircaloy-4 version were tested in an autoclave at 288° Cfor 20h and 168h and at 360˚C for 96h. Based on thecharacterisation of pre-transition oxide layers only small orno differences were found between the different alloycompositions, thus it is not possible to predict long-timecorrosion behaviour by studying pre-transition oxides. However,large differences were found between the two test temperatures.The higher oxidation temperature results in increased oxidationrates and larger oxide grains, the columnar grains are a factorof 3-4 longer, and the equiaxed grains have an almost doubledmaximum diameter. The fraction of columnar grains andtetragonal phase also increases with temperature. The reasonfor the difference in morphology between the two temperaturesis not fully understood, but the results show that acceleratedtesting at elevated temperatures may be a questionableapproach. One of the Zircaloy-2 samples was also anodicallyoxidised. The oxide layer formed only contains equiaxed grainsand phase analysis shows both monoclinic and tetragonal phasesare present. Oxidation tests of Zircaloy-2 and Zircaloy-4 in water andlithiated water at 360 ° C show that the pre-transitionoxidation rate is not affected by the presence of LiOH, but thetransition occurs earlier and the post-transition oxidationrate is increased. The oxidation rate correlates with thedensity of cracks in the oxide layer and the morphology of theoxide grains. The oxides formed have a layered structure andfor samples oxidised in LiOH solution the inner protectivelayer is thin. The effect of LiOH is suggested to be the resultof partial dissolution of the oxide and subsequentincorporation of lithium ions during adissolution-precipitation process. Newly formed oxide isprobably more hydrous, and the grain boundaries areparticularly liable to dissolution. The increased concentrationof LiOH within cracks and pores could reach the detrimentallevels necessary for dissolution. This is supported by theinsensitivity in the pre-transition region to both thecompositions of the alloy and to the environment. The alloycomposition influences the microstructure of the oxide layer,and thereby the resistance to accelerated corrosion rate inlithiated water. The hydrogen pickup ratio follows the weightgain, not the oxidation rate, up to the second transition. Whenthe protective oxide layer is degraded the hydrogen pickupratio increases markedly. To evaluate if hydrogen is a cause for or a consequence ofaccelerated corrosion, pre-transition oxidation tests ofZircaloy-2 have been performed with hydrogen present in threedifferent states: i) Hydrogen in solid solution in thezirconium alloy, corresponding to the initial oxidation priorto precipitation of hydrides. ii) Uniformly distributedhydrides simulating a situation in whish hydrides starts toprecipitate and iii) Massive surface hydride claimed to be themain cause of accelerated oxidation. Based on the resultsobtained, it is concluded that the oxidation of massivezirconium hydride resembles the oxidation of zirconium metal.This fact clearly shows that accelerated oxidation of zirconiumalloys cannot be due solely to the presence of a massivehydride layer, but also requires a combined effect offorexample interfacial roughness and hydride precipitation. <b>Keywords:</b>Zircaloy, Zirconium alloys, Oxidation, Oxidelayer, Pre-Transition, Hydriding, Pre-Hydrided, Hydrides,Lithium Hydroxide (LiOH), Lithiated Water, Dissolution, CrossSectional TEM

<p>This thesis is focused on the mechanisms for corrosion andhydriding of Zircaloy. Special attention is paid tomicrostructural characterisation by cross sectionaltransmission electron microscopy of the oxide layer formed.Three main topics have been treated in this work: (i)Pre-transition oxides were investigated with the purpose ofevaluating if it is possible to predict post-transitionbehaviour of different alloys. (ii) The reason for the commonlyobserved accelerated corrosion of Zircaloy in the presence oflithium hydroxide was investigated by studying the phasetransformation of differently stabilised zirconium oxides andby corrosion studies. (iii) Pre-hydrided Zircaloy-2 was studiedto investigate the influence of hydrogen on the oxidationbehaviour.</p><p>Characterisation of pre-transition oxides formed onzirconium alloys, has been accomplished with the aim ofdetermining if there are any differences in the properties(morphology, pores, cracks and phases) of the oxide layersformed which might explain the differences in corrosionbehaviour later in life. Four Zircaloy-2 versions and oneZircaloy-4 version were tested in an autoclave at 288° Cfor 20h and 168h and at 360˚C for 96h. Based on thecharacterisation of pre-transition oxide layers only small orno differences were found between the different alloycompositions, thus it is not possible to predict long-timecorrosion behaviour by studying pre-transition oxides. However,large differences were found between the two test temperatures.The higher oxidation temperature results in increased oxidationrates and larger oxide grains, the columnar grains are a factorof 3-4 longer, and the equiaxed grains have an almost doubledmaximum diameter. The fraction of columnar grains andtetragonal phase also increases with temperature. The reasonfor the difference in morphology between the two temperaturesis not fully understood, but the results show that acceleratedtesting at elevated temperatures may be a questionableapproach. One of the Zircaloy-2 samples was also anodicallyoxidised. The oxide layer formed only contains equiaxed grainsand phase analysis shows both monoclinic and tetragonal phasesare present.</p><p>Oxidation tests of Zircaloy-2 and Zircaloy-4 in water andlithiated water at 360 ° C show that the pre-transitionoxidation rate is not affected by the presence of LiOH, but thetransition occurs earlier and the post-transition oxidationrate is increased. The oxidation rate correlates with thedensity of cracks in the oxide layer and the morphology of theoxide grains. The oxides formed have a layered structure andfor samples oxidised in LiOH solution the inner protectivelayer is thin. The effect of LiOH is suggested to be the resultof partial dissolution of the oxide and subsequentincorporation of lithium ions during adissolution-precipitation process. Newly formed oxide isprobably more hydrous, and the grain boundaries areparticularly liable to dissolution. The increased concentrationof LiOH within cracks and pores could reach the detrimentallevels necessary for dissolution. This is supported by theinsensitivity in the pre-transition region to both thecompositions of the alloy and to the environment. The alloycomposition influences the microstructure of the oxide layer,and thereby the resistance to accelerated corrosion rate inlithiated water. The hydrogen pickup ratio follows the weightgain, not the oxidation rate, up to the second transition. Whenthe protective oxide layer is degraded the hydrogen pickupratio increases markedly.</p><p>To evaluate if hydrogen is a cause for or a consequence ofaccelerated corrosion, pre-transition oxidation tests ofZircaloy-2 have been performed with hydrogen present in threedifferent states: i) Hydrogen in solid solution in thezirconium alloy, corresponding to the initial oxidation priorto precipitation of hydrides. ii) Uniformly distributedhydrides simulating a situation in whish hydrides starts toprecipitate and iii) Massive surface hydride claimed to be themain cause of accelerated oxidation. Based on the resultsobtained, it is concluded that the oxidation of massivezirconium hydride resembles the oxidation of zirconium metal.This fact clearly shows that accelerated oxidation of zirconiumalloys cannot be due solely to the presence of a massivehydride layer, but also requires a combined effect offorexample interfacial roughness and hydride precipitation.</p><p><b>Keywords:</b>Zircaloy, Zirconium alloys, Oxidation, Oxidelayer, Pre-Transition, Hydriding, Pre-Hydrided, Hydrides,Lithium Hydroxide (LiOH), Lithiated Water, Dissolution, CrossSectional TEM</p>