Utilising student profiles in mathematics course arrangements

This thesis develops a method for identifying students struggling in their mathematical studies at an early stage. It helps in directing support to students needing and benefiting from it the most. Thus, frustration felt by weaker students may decrease and therefore, hopefully, also drop outs of potential engineering students. The research concentrates on a combination of personality and intelligence aspects. Personality aspects gave information on conation and motivation for learning. This part was studied from the perspective of motivation and self-regulation. Intelligence aspects gave information on declarative and procedural knowledge: what had been taught and what was actually mastered. Students answered surveys on motivation and self-regulation in 2010 and 2011. Based on their answers, background information, results in the proficiency test, and grades in the first mathematics course, profiles describing the students were formed. In the following years, the profiles were updated with new information obtained each year. The profiles used to identify struggling students combine personality (motivation, selfregulation, and self-efficacy) and intelligence (declarative and procedural knowledge) aspects at the beginning of their studies. Identifying students in need of extra support is a good start, but methods for providing support must be found. This thesis also studies how this support could be taken into account in course arrangements. The methods used include, for example, languaging and scaffolding, and continuous feedback. The analysis revealed that allocating resources based on the predicted progress does not increase costs or lower the results of better students. Instead, it will help weaker students obtain passing grades.

Studies on integrating kinematic design method with mechanical systems simulation techniques

Theultimate goal of any research in the mechanism/kinematic/design area may be called predictive design, ie the optimisation of mechanism proportions in the design stage without requiring extensive life and wear testing. This is an ambitious goal and can be realised through development and refinement of numerical (computational) technology in order to facilitate the design analysis and optimisation of complex mechanisms, mechanical components and systems. As a part of the systematic design methodology this thesis concentrates on kinematic synthesis (kinematic design and analysis) methods in the mechanism synthesis process. The main task of kinematic design is to find all possible solutions in the form of structural parameters to accomplish the desired requirements of motion. Main formulations of kinematic design can be broadly divided to exact synthesis and approximate synthesis formulations. The exact synthesis formulation is based in solving n linear or nonlinear equations in n variables and the solutions for the problem areget by adopting closed form classical or modern algebraic solution methods or using numerical solution methods based on the polynomial continuation or homotopy. The approximate synthesis formulations is based on minimising the approximation error by direct optimisation The main drawbacks of exact synthesis formulationare: (ia) limitations of number of design specifications and (iia) failure in handling design constraints- especially inequality constraints. The main drawbacks of approximate synthesis formulations are: (ib) it is difficult to choose a proper initial linkage and (iib) it is hard to find more than one solution. Recentformulations in solving the approximate synthesis problem adopts polynomial continuation providing several solutions, but it can not handle inequality const-raints. Based on the practical design needs the mixed exact-approximate position synthesis with two exact and an unlimited number of approximate positions has also been developed. The solutions space is presented as a ground pivot map but thepole between the exact positions cannot be selected as a ground pivot. In this thesis the exact synthesis problem of planar mechanism is solved by generating all possible solutions for the optimisation process ¿ including solutions in positive dimensional solution sets - within inequality constraints of structural parameters. Through the literature research it is first shown that the algebraic and numerical solution methods ¿ used in the research area of computational kinematics ¿ are capable of solving non-parametric algebraic systems of n equations inn variables and cannot handle the singularities associated with positive-dimensional solution sets. In this thesis the problem of positive-dimensional solutionsets is solved adopting the main principles from mathematical research area of algebraic geometry in solving parametric ( in the mathematical sense that all parameter values are considered ¿ including the degenerate cases ¿ for which the system is solvable ) algebraic systems of n equations and at least n+1 variables.Adopting the developed solution method in solving the dyadic equations in direct polynomial form in two- to three-precision-points it has been algebraically proved and numerically demonstrated that the map of the ground pivots is ambiguousand that the singularities associated with positive-dimensional solution sets can be solved. The positive-dimensional solution sets associated with the poles might contain physically meaningful solutions in the form of optimal defectfree mechanisms. Traditionally the mechanism optimisation of hydraulically driven boommechanisms is done at early state of the design process. This will result in optimal component design rather than optimal system level design. Modern mechanismoptimisation at system level demands integration of kinematic design methods with mechanical system simulation techniques. In this thesis a new kinematic design method for hydraulically driven boom mechanism is developed and integrated in mechanical system simulation techniques. The developed kinematic design method is based on the combinations of two-precision-point formulation and on optimisation ( with mathematical programming techniques or adopting optimisation methods based on probability and statistics ) of substructures using calculated criteria from the system level response of multidegree-of-freedom mechanisms. Eg. by adopting the mixed exact-approximate position synthesis in direct optimisation (using mathematical programming techniques) with two exact positions and an unlimitednumber of approximate positions the drawbacks of (ia)-(iib) has been cancelled.The design principles of the developed method are based on the design-tree -approach of the mechanical systems and the design method ¿ in principle ¿ is capable of capturing the interrelationship between kinematic and dynamic synthesis simultaneously when the developed kinematic design method is integrated with the mechanical system simulation techniques.

Selective catalytic reduction of nitrogen oxides with ammonia in forced unsteady state reactors - Case based reasoning and mathematical model simulation reasoning

The application of forced unsteady-state reactors in case of selective catalytic reduction of nitrogen oxides (NOx) with ammonia (NH3) is sustained by the fact that favorable temperature and composition distributions which cannot be achieved in any steady-state regime can be obtained by means of unsteady-state operations. In a normal way of operation the low exothermicity of the selective catalytic reduction (SCR) reaction (usually carried out in the range of 280-350°C) is not enough to maintain by itself the chemical reaction. A normal mode of operation usually requires supply of supplementary heat increasing in this way the overall process operation cost. Through forced unsteady-state operation, the main advantage that can be obtained when exothermic reactions take place is the possibility of trapping, beside the ammonia, the moving heat wave inside the catalytic bed. The unsteady state-operation enables the exploitation of the thermal storage capacity of the catalyticbed. The catalytic bed acts as a regenerative heat exchanger allowing auto-thermal behaviour when the adiabatic temperature rise is low. Finding the optimum reactor configuration, employing the most suitable operation model and identifying the reactor behavior are highly important steps in order to configure a proper device for industrial applications. The Reverse Flow Reactor (RFR) - a forced unsteady state reactor - corresponds to the above mentioned characteristics and may be employed as an efficient device for the treatment of dilute pollutant mixtures. As a main disadvantage, beside its advantages, the RFR presents the 'wash out' phenomena. This phenomenon represents emissions of unconverted reactants at every switch of the flow direction. As a consequence our attention was focused on finding an alternative reactor configuration for RFR which is not affected by the incontrollable emissions of unconverted reactants. In this respect the Reactor Network (RN) was investigated. Its configuration consists of several reactors connected in a closed sequence, simulating a moving bed by changing the reactants feeding position. In the RN the flow direction is maintained in the same way ensuring uniformcatalyst exploitation and in the same time the 'wash out' phenomena is annulated. The simulated moving bed (SMB) can operate in transient mode giving practically constant exit concentration and high conversion levels. The main advantage of the reactor network operation is emphasizedby the possibility to obtain auto-thermal behavior with nearly uniformcatalyst utilization. However, the reactor network presents only a small range of switching times which allow to reach and to maintain an ignited state. Even so a proper study of the complex behavior of the RN may give the necessary information to overcome all the difficulties that can appear in the RN operation. The unsteady-state reactors complexity arises from the fact that these reactor types are characterized by short contact times and complex interaction between heat and mass transportphenomena. Such complex interactions can give rise to a remarkable complex dynamic behavior characterized by a set of spatial-temporal patterns, chaotic changes in concentration and traveling waves of heat or chemical reactivity. The main efforts of the current research studies concern the improvement of contact modalities between reactants, the possibility of thermal wave storage inside the reactor and the improvement of the kinetic activity of the catalyst used. Paying attention to the above mentioned aspects is important when higher activity even at low feeding temperatures and low emissions of unconverted reactants are the main operation concerns. Also, the prediction of the reactor pseudo or steady-state performance (regarding the conversion, selectivity and thermal behavior) and the dynamicreactor response during exploitation are important aspects in finding the optimal control strategy for the forced unsteady state catalytic tubular reactors. The design of an adapted reactor requires knowledge about the influence of its operating conditions on the overall process performance and a precise evaluation of the operating parameters rage for which a sustained dynamic behavior is obtained. An apriori estimation of the system parameters result in diminution of the computational efforts. Usually the convergence of unsteady state reactor systems requires integration over hundreds of cycles depending on the initial guess of the parameter values. The investigation of various operation models and thermal transfer strategies give reliable means to obtain recuperative and regenerative devices which are capable to maintain an auto-thermal behavior in case of low exothermic reactions. In the present research work a gradual analysis of the SCR of NOx with ammonia process in forced unsteady-state reactors was realized. The investigation covers the presentationof the general problematic related to the effect of noxious emissions in the environment, the analysis of the suitable catalysts types for the process, the mathematical analysis approach for modeling and finding the system solutions and the experimental investigation of the device found to be more suitable for the present process. In order to gain information about the forced unsteady state reactor design, operation, important system parameters and their values, mathematical description, mathematicalmethod for solving systems of partial differential equations and other specific aspects, in a fast and easy way, and a case based reasoning (CBR) approach has been used. This approach, using the experience of past similarproblems and their adapted solutions, may provide a method for gaining informations and solutions for new problems related to the forced unsteady state reactors technology. As a consequence a CBR system was implemented and a corresponding tool was developed. Further on, grooving up the hypothesis of isothermal operation, the investigation by means of numerical simulation of the feasibility of the SCR of NOx with ammonia in the RFRand in the RN with variable feeding position was realized. The hypothesis of non-isothermal operation was taken into account because in our opinion ifa commercial catalyst is considered, is not possible to modify the chemical activity and its adsorptive capacity to improve the operation butis possible to change the operation regime. In order to identify the most suitable device for the unsteady state reduction of NOx with ammonia, considering the perspective of recuperative and regenerative devices, a comparative analysis of the above mentioned two devices performance was realized. The assumption of isothermal conditions in the beginningof the forced unsteadystate investigation allowed the simplification of the analysis enabling to focus on the impact of the conditions and mode of operation on the dynamic features caused by the trapping of one reactant in the reactor, without considering the impact of thermal effect on overall reactor performance. The non-isothermal system approach has been investigated in order to point out the important influence of the thermal effect on overall reactor performance, studying the possibility of RFR and RN utilization as recuperative and regenerative devices and the possibility of achieving a sustained auto-thermal behavior in case of lowexothermic reaction of SCR of NOx with ammonia and low temperature gasfeeding. Beside the influence of the thermal effect, the influence of the principal operating parameters, as switching time, inlet flow rate and initial catalyst temperature have been stressed. This analysis is important not only because it allows a comparison between the two devices and optimisation of the operation, but also the switching time is the main operating parameter. An appropriate choice of this parameter enables the fulfilment of the process constraints. The level of the conversions achieved, the more uniform temperature profiles, the uniformity ofcatalyst exploitation and the much simpler mode of operation imposed the RN as a much more suitable device for SCR of NOx with ammonia, in usual operation and also in the perspective of control strategy implementation. Theoretical simplified models have also been proposed in order to describe the forced unsteady state reactors performance and to estimate their internal temperature and concentration profiles. The general idea was to extend the study of catalytic reactor dynamics taking into account the perspectives that haven't been analyzed yet. The experimental investigation ofRN revealed a good agreement between the data obtained by model simulation and the ones obtained experimentally.

Wet oxidation of recalcitrant lignin waters: Experimental and kinetic studies

The dissertation is based on four articles dealing with recalcitrant lignin water purification. Lignin, a complicated substance and recalcitrant to most treatment technologies, inhibits seriously pulp and paper industry waste management. Therefore, lignin is studied, using WO as a process method for its degradation. A special attention is paid to the improvement in biodegradability and the reduction of lignin content, since they have special importance for any following biological treatment. In most cases wet oxidation is not used as a complete ' mineralization method but as a pre treatment in order to eliminate toxic components and to reduce the high level of organics produced. The combination of wet oxidation with a biological treatment can be a good option due to its effectiveness and its relatively low technology cost. The literature part gives an overview of Advanced Oxidation Processes (AOPs). A hot oxidation process, wet oxidation (WO), is investigated in detail and is the AOP process used in the research. The background and main principles of wet oxidation, its industrial applications, the combination of wet oxidation with other water treatment technologies, principal reactions in WO, and key aspects of modelling and reaction kinetics are presented. There is also given a wood composition and lignin characterization (chemical composition, structure and origin), lignin containing waters, lignin degradation and reuse possibilities, and purification practices for lignin containing waters. The aim of the research was to investigate the effect of the operating conditions of WO, such as temperature, partial pressure of oxygen, pH and initial concentration of wastewater, on the efficiency, and to enhance the process and estimate optimal conditions for WO of recalcitrant lignin waters. Two different waters are studied (a lignin water model solution and debarking water from paper industry) to give as appropriate conditions as possible. Due to the great importance of re using and minimizing the residues of industries, further research is carried out using residual ash of an Estonian power plant as a catalyst in wet oxidation of lignin-containing water. Developing a kinetic model that includes in the prediction such parameters as TOC gives the opportunity to estimate the amount of emerging inorganic substances (degradation rate of waste) and not only the decrease of COD and BOD. The degradation target compound, lignin is included into the model through its COD value (CODligning). Such a kinetic model can be valuable in developing WO treatment processes for lignin containing waters, or other wastewaters containing one or more target compounds. In the first article, wet oxidation of "pure" lignin water was investigated as a model case with the aim of degrading lignin and enhancing water biodegradability. The experiments were performed at various temperatures (110 -190°C), partial oxygen pressures (0.5 -1.5 MPa) and pH (5, 9 and 12). The experiments showed that increasing the temperature notably improved the processes efficiency. 75% lignin reduction was detected at the lowest temperature tested and lignin removal improved to 100% at 190°C. The effect of temperature on the COD removal rate was lower, but clearly detectable. 53% of organics were oxidized at 190°C. The effect of pH occurred mostly on lignin removal. Increasing the pH enhanced the lignin removal efficiency from 60% to nearly 100%. A good biodegradability ratio (over 0.5) was generally achieved. The aim of the second article was to develop a mathematical model for "pure" lignin wet oxidation using lumped characteristics of water (COD, BOD, TOC) and lignin concentration. The model agreed well with the experimental data (R2 = 0.93 at pH 5 and 12) and concentration changes during wet oxidation followed adequately the experimental results. The model also showed correctly the trend of biodegradability (BOD/COD) changes. In the third article, the purpose of the research was to estimate optimal conditions for wet oxidation (WO) of debarking water from the paper industry. The WO experiments were' performed at various temperatures, partial oxygen pressures and pH. The experiments showed that lignin degradation and organics removal are affected remarkably by temperature and pH. 78-97% lignin reduction was detected at different WO conditions. Initial pH 12 caused faster removal of tannins/lignin content; but initial pH 5 was more effective for removal of total organics, represented by COD and TOC. Most of the decrease in organic substances concentrations occurred in the first 60 minutes. The aim of the fourth article was to compare the behaviour of two reaction kinetic models, based on experiments of wet oxidation of industrial debarking water under different conditions. The simpler model took into account only the changes in COD, BOD and TOC; the advanced model was similar to the model used in the second article. Comparing the results of the models, the second model was found to be more suitable for describing the kinetics of wet oxidation of debarking water. The significance of the reactions involved was compared on the basis of the model: for instance, lignin degraded first to other chemically oxidizable compounds rather than directly to biodegradable products. Catalytic wet oxidation of lignin containing waters is briefly presented at the end of the dissertation. Two completely different catalysts were used: a commercial Pt catalyst and waste power plant ash. CWO showed good performance using 1 g/L of residual ash gave lignin removal of 86% and COD removal of 39% at 150°C (a lower temperature and pressure than with WO). It was noted that the ash catalyst caused a remarkable removal rate for lignin degradation already during the pre heating for `zero' time, 58% of lignin was degraded. In general, wet oxidation is not recommended for use as a complete mineralization method, but as a pre treatment phase to eliminate toxic or difficultly biodegradable components and to reduce the high level of organics. Biological treatment is an appropriate post treatment method since easily biodegradable organic matter remains after the WO process. The combination of wet oxidation with subsequent biological treatment can be an effective option for the treatment of lignin containing waters.

Spontaneous Focusing on Numerosity in the Development of Early Mathematical Skills

The aim of the present set of longitudinal studies was to explore 3-7-year-old children.s Spontaneous FOcusing on Numerosity (SFON) and its relation to early mathematical development. The specific goals were to capture in method and theory the distinct process by which children focus on numerosity as a part of their activities involving exact number recognition, and individual differences in this process that may be informative in the development of more complex number skills. Over the course of conducting the five studies, fifteen novel tasks were progressively developed for the SFON assessments. In the tasks, confounding effects of insufficient number recognition, verbal comprehension, other procedural skills as well as working memory capacity were aimed to be controlled. Furthermore, how children.s individual differences in SFON are related to their development of number sequence, subitizing-based enumeration, object counting and basic arithmetic skills was explored. The effect of social interaction on SFON was tested. Study I captured the first phase of the 3-year longitudinal study with 39 children. It was investigated whether there were differences in 3-year-old children.s tendency to focus on numerosity, and whether these differences were related to the children.s development of cardinality recognition skills from the age of 3 to 4 years. It was found that the two groups of children formed on the basis of their amount of SFON tendency at the age of 3 years differed in their development of recognising and producing small numbers. The children whose SFON tendency was very predominant developed faster in cardinality related skills from the age of 3 to 4 years than the children whose SFON tendency was not as predominant. Thus, children.s development in cardinality recognition skills is related to their SFON tendency. Studies II and III were conducted to investigate, firstly, children.s individual differences in SFON, and, secondly, whether children.s SFON is related to their counting development. Altogether nine tasks were designed for the assessments of spontaneous and guided focusing on numerosity. The longitudinal data of 39 children in Study II from the age of 3.5 to 6 years showed individual differences in SFON at the ages of 4, 5 and 6 years, as well as stability in children.s SFON across tasks used at different ages. The counting skills were assessed at the ages of 3.5, 5 and 6 years. Path analyses indicated a reciprocal tendency in the relationship between SFON and counting development. In Study III, these results on the individual differences in SFON tendency, the stability of SFON across different tasks and the relationship of SFON and mathematical skills were confirmed by a larger-scale cross-sectional study of 183 on average 6.5-year-old children (range 6;0-7;0 years). The significant amount of unique variance that SFON accounted for number sequence elaboration, object counting and basic arithmetic skills stayed statistically significant (partial correlations varying from .27 to .37) when the effects of non-verbal IQ and verbal comprehension were controlled. In addition, to confirm that the SFON tasks assess SFON tendency independently from enumeration skills, guided focusing tasks were used for children who had failed in SFON tasks. It was explored whether these children were able to proceed in similar tasks to SFON tasks once they were guided to focus on number. The results showed that these children.s poor performance in the SFON tasks was not caused by their deficiency in executing the tasks but on lacking focusing on numerosity. The longitudinal Study IV of 39 children aimed at increasing the knowledge of associations between children.s long-term SFON tendency, subitizing-based enumeration and verbal counting skills. Children were tested twice at the age of 4-5 years on their SFON, and once at the age of 5 on their subitizing-based enumeration, number sequence production, as well as on their skills for counting of objects. Results showed considerable stability in SFON tendency measured at different ages, and that there is a positive direct association between SFON and number sequence production. The association between SFON and object counting skills was significantly mediated by subitizing-based enumeration. These results indicate that the associations between the child.s SFON and sub-skills of verbal counting may differ on the basis of how significant a role understanding the cardinal meanings of number words plays in learning these skills. The specific goal of Study V was to investigate whether it is possible to enhance 3-year old children.s SFON tendency, and thus start children.s deliberate practice in early mathematical skills. Participants were 3-year-old children in Finnish day care. The SFON scores and cardinality-related skills of the experimental group of 17 children were compared to the corresponding results of the 17 children in the control group. The results show an experimental effect on SFON tendency and subsequent development in cardinality-related skills during the 6-month period from pretest to delayed posttest in the children with some initial SFON tendency in the experimental group. Social interaction has an effect on children.s SFON tendency. The results of the five studies assert that within a child.s existing mathematical competence, it is possible to distinguish a separate process, which refers to the child.s tendency to spontaneously focus on numerosity. Moreover, there are significant individual differences in children.s SFON at the age of 3-7 years. Moderate stability was found in this tendency across different tasks assessed both at the same and at different ages. Furthermore, SFON tendency is related to the development of early mathematical skills. Educational implications of the findings emphasise, first, the importance of regarding focusing on numerosity as a separate, essential process in the assessments of young children.s mathematical skills. Second, the substantial individual differences in SFON tendency during the childhood years suggest that uncovering and modeling this kind of mathematically meaningful perceiving of the surroundings and tasks could be an efficient tool for promoting young children.s mathematical development, and thus prevent later failures in learning mathematical skills. It is proposed to consider focusing on numerosity as one potential sub-process of activities involving exact number recognition in future studies.

Surface studies of limestones and dolostones : characterisation using various techniques and batch dissolution experiments with hydrochloric acid solutions

In this thesis, stepwise titration with hydrochloric acid was used to obtain chemical reactivities and dissolution rates of ground limestones and dolostones of varying geological backgrounds (sedimentary, metamorphic or magmatic). Two different ways of conducting the calculations were used: 1) a first order mathematical model was used to calculate extrapolated initial reactivities (and dissolution rates) at pH 4, and 2) a second order mathematical model was used to acquire integrated mean specific chemical reaction constants (and dissolution rates) at pH 5. The calculations of the reactivities and dissolution rates were based on rate of change of pH and particle size distributions of the sample powders obtained by laser diffraction. The initial dissolution rates at pH 4 were repeatedly higher than previously reported literature values, whereas the dissolution rates at pH 5 were consistent with former observations. Reactivities and dissolution rates varied substantially for dolostones, whereas for limestones and calcareous rocks, the variation can be primarily explained by relatively large sample standard deviations. A list of the dolostone samples in a decreasing order of initial reactivity at pH 4 is: 1) metamorphic dolostones with calcite/dolomite ratio higher than about 6% 2) sedimentary dolostones without calcite 3) metamorphic dolostones with calcite/dolomite ratio lower than about 6% The reactivities and dissolution rates were accompanied by a wide range of experimental techniques to characterise the samples, to reveal how different rocks changed during the dissolution process, and to find out which factors had an influence on their chemical reactivities. An emphasis was put on chemical and morphological changes taking place at the surfaces of the particles via X-ray Photoelectron Spectroscopy (XPS) and Scanning Electron Microscopy (SEM). Supporting chemical information was obtained with X-Ray Fluorescence (XRF) measurements of the samples, and Inductively Coupled Plasma-Mass Spectrometry (ICP-MS) and Inductively Coupled Plasma-Optical Emission Spectrometry (ICP-OES) measurements of the solutions used in the reactivity experiments. Information on mineral (modal) compositions and their occurrence was provided by X-Ray Diffraction (XRD), Energy Dispersive X-ray analysis (EDX) and studying thin sections with a petrographic microscope. BET (Brunauer, Emmet, Teller) surface areas were determined from nitrogen physisorption data. Factors increasing chemical reactivity of dolostones and calcareous rocks were found to be sedimentary origin, higher calcite concentration and smaller quartz concentration. Also, it is assumed that finer grain size and larger BET surface areas increase the reactivity although no certain correlation was found in this thesis. Atomic concentrations did not correlate with the reactivities. Sedimentary dolostones, unlike metamorphic ones, were found to have porous surface structures after dissolution. In addition, conventional (XPS) and synchrotron based (HRXPS) X-ray Photoelectron Spectroscopy were used to study bonding environments on calcite and dolomite surfaces. Both samples are insulators, which is why neutralisation measures such as electron flood gun and a conductive mask were used. Surface core level shifts of 0.7 ± 0.1 eV for Ca 2p spectrum of calcite and 0.75 ± 0.05 eV for Mg 2p and Ca 3s spectra of dolomite were obtained. Some satellite features of Ca 2p, C 1s and O 1s spectra have been suggested to be bulk plasmons. The origin of carbide bonds was suggested to be beam assisted interaction with hydrocarbons found on the surface. The results presented in this thesis are of particular importance for choosing raw materials for wet Flue Gas Desulphurisation (FGD) and construction industry. Wet FGD benefits from high reactivity, whereas construction industry can take advantage of slow reactivity of carbonate rocks often used in the facades of fine buildings. Information on chemical bonding environments may help to create more accurate models for water-rock interactions of carbonates.