Tals del-helhetsrelationer : Elevers sätt att urskilja del-helhetsrelationer i öppna utsagor.

På vilket sätt kan vi hjälpa alla elever att bli förtrogna med matematikens uttrycksformer? Ett sätt är att bygga en stadig aritmetisk grund för eleverna där de befäster talens innehåll. Det är vad den här uppsatsen handlar om. Uppsatsen beskriver vad som skiljer användandet av del-helhetsrelationer från andra sätt att lösa öppna utsagor på. Uppsatsen beskriver även vilka kritiska aspekter om öppna utsagor som kan förekomma hos elever i årskurs 1 och 2. Uppsat-sen är skriven ur en fenomenografisk ansats med variationsteoretiska inslag eftersom de två teorierna är nära besläktade. Studien genomfördes genom filmade intervjuer med 11 elever som valdes ut genom en munt-lig och en skriftlig diagnos samt ett skriftligt arbetsblad. Resultatet visar att elever som använ-der automatiserade del-helhetsrelationer har en fördel när de löser öppna utsagor jämfört med elever som använder andra lösningsmetoder. Skillnaderna syns tydligt när det gäller lösandet av öppna subtraktionsutsagor där helheten saknas. En väg till den abstrakta förståelsen för tals del-helhetsrelationer går via fingertalen. Min slutsats är att eleverna redan tidigt i skolan måste få undervisning om fingertalen samt talens del-helhetsrelationer för att undvika att de utvecklar matematiksvårigheter.

Chinese young children’s strategies on basic addition facts

Kindergartens in China offer structured full-day programs for children aged 3-6. Although formal schooling does not commence until age 7, the mathematics program in kindergartens is specifically focused on developing young children’s facility with simple addition and subtraction. This study explored young Chinese children’s strategies for solving basic addition facts as well as their intuitive understanding of addition via interview methods. Results indicate a strong impact that teacher-directed teaching methods have on young children’s cognitions in relation to addition.

A problem-posing intervention in the development of problem-solving competence of underachieving, middle-year students

This study reported on the issues surrounding the acquisition of problem-solving competence of middle-year students who had been ascertained as above average in intelligence, but underachieving in problem-solving competence. In particular, it looked at the possible links between problem-posing skills development and improvements in problem-solving competence. A cohort of Year 7 students at a private, non-denominational, co-educational school was chosen as participants for the study, as they undertook a series of problem-posing sessions each week throughout a school term. The lessons were facilitated by the researcher in the students’ school setting. Two criteria were chosen to identify participants for this study. Firstly, each participant scored above the 60th percentile in the standardized Middle Years Ability Test (MYAT) (Australian Council for Educational Research, 2005) and secondly, the participants all scored below the cohort average for Criterion B (Problem-solving Criterion) in their school mathematics tests during the first semester of Year 7. Two mutually exclusive groups of participants were investigated with one constituting the Comparison Group and the other constituting the Intervention Group. The Comparison Group was chosen from a Year 7 cohort for whom no problem-posing intervention had occurred, while the Intervention Group was chosen from the Year 7 cohort of the following year. This second group received the problem-posing intervention in the form of a teaching experiment. That is, the Comparison Group were only pre-tested and post-tested, while the Intervention Group was involved in the teaching experiment and received the pre-testing and post-testing at the same time of the year, but in the following year, when the Comparison Group have moved on to the secondary part of the school. The groups were chosen from consecutive Year 7 cohorts to avoid cross-contamination of the data. A constructionist framework was adopted for this study that allowed the researcher to gain an “authentic understanding” of the changes that occurred in the development of problem-solving competence of the participants in the context of a classroom setting (Richardson, 1999). Qualitative and quantitative data were collected through a combination of methods including researcher observation and journal writing, video taping, student workbooks, informal student interviews, student surveys, and pre-testing and post-testing. This combination of methods was required to increase the validity of the study’s findings through triangulation of the data. The study findings showed that participation in problem-posing activities can facilitate the re-engagement of disengaged, middle-year mathematics students. In addition, participation in these activities can result in improved problem-solving competence and associated developmental learning changes. Some of the changes that were evident as a result of this study included improvements in self-regulation, increased integration of prior knowledge with new knowledge and increased and contextualised socialisation.

Solving tri-diagonal linear systems using field programmable gate arrays

In this paper, we present the outcomes of a project on the exploration of the use of Field Programmable Gate Arrays(FPGAs) as co-processors for scientific computation. We designed a custom circuit for the pipelined solving of multiple tri-diagonal linear systems. The design is well suited for applications that require many independent tri diagonal system solves, such as finite difference methods for solving PDEs or applications utilising cubic spline interpolation. The selected solver algorithm was the Tri Diagonal Matrix Algorithm (TDMA or Thomas Algorithm). Our solver supports user specified precision thought the use of a custom floating point VHDL library supporting addition, subtraction, multiplication and division. The variable precision TDMA solver was tested for correctness in simulation mode. The TDMA pipeline was tested successfully in hardware using a simplified solver model. The details of implementation, the limitations, and future work are also discussed.

Solving tri-diagonal linear systems using field programmable gate arrays

In this paper, we present the outcomes of a project on the exploration of the use of Field Programmable Gate Arrays (FPGAs) as co-processors for scientific computation. We designed a custom circuit for the pipelined solving of multiple tri-diagonal linear systems. The design is well suited for applications that require many independent tri-diagonal system solves, such as finite difference methods for solving PDEs or applications utilising cubic spline interpolation. The selected solver algorithm was the Tri-Diagonal Matrix Algorithm (TDMA or Thomas Algorithm). Our solver supports user specified precision thought the use of a custom floating point VHDL library supporting addition, subtraction, multiplication and division. The variable precision TDMA solver was tested for correctness in simulation mode. The TDMA pipeline was tested successfully in hardware using a simplified solver model. The details of implementation, the limitations, and future work are also discussed.

Motivations for eWOM exchanges in an online community : self-development, problem solving support, relaxation

Electronic word-of-mouth (eWOM) has gained significant attention from academics and practitioners since it has become an important source of consumers’ product information, which can influence consumer purchase intentions (Cheung & Lee, 2012). eWOM exchanges exist in two types of online communities: online communities of practice and online communities of interest. A few prior studies in online communities of interest have examined members’ motivations for product knowledge exchange (Hung & Li, 2007; Ma & Agarwal, 2007). However, there is a lack of understanding of member motivations for exchanging social bonds and enjoyment in addition to exchanging knowledge pertaining to products in the community. It is important to have an initial comprehension of motivation as an antecedent of these three eWOM exchanges so as to be able to determine the driving factors that lead members to generate eWOM communication. Thus, the research problem "What are the driving factors for members to exchange eWOM in an online community?" was justified for investigation. The purpose of this study was to examine different member motivations for exchanging three types of eWOM. Resource exchange theory and theory on consumer motivation and behavior were applied to develop a conceptual framework for this study. This study focused on an online beauty community since there is an increasing trend of consumers turning to online beauty resources so as to exchange useful beauty product information (SheSpot, 2011). As this study examined consumer motivation in an online beauty community, a web-based survey was the most effective and efficient way to gain responses from beauty community members and these members were appropriate samples from which to draw a conclusion about the whole population. Multiple regression analysis was used to test the relationships between member motivations and eWOM exchanges. It was found that members have different motivations for exchanging knowledge, social bonds, and enjoyment related to products: self-development, problem solving support, and relaxation, respectively. This study makes three theoretical contributions. First, this study identifies the influence of self-development motivation on knowledge exchange in an online community of interest, just as this motivation has previously been found in online communities of practice. This study highlights that members of the two different types of online communities share similar goals of knowledge exchange, despite the two communities evincing different attributes (e.g., member characteristics and tasks’ objectives). Further, this study will assist researchers to understand other motivations identified by prior research in online communities of practice since such motivations may be applicable to online communities of interest. Second, this study offers a new perspective on member motivation for social bonding. This study indicates that in addition to social support from friends and family, consumers are motivated to build social bonds with members in an online community of interest since they are an important source of problem solving support in regard to products. Finally, this study extends the body of knowledge pertaining to member motivation for enjoyment exchange. This study provides a basis for researchers to understand that members in an online community of interest value experiential aspects of enjoyable consumption activities, and thus based on group norms, members have a mutual desire for relaxation from enjoyment exchange. The major practical contribution is that this study provides an important guideline for marketing managers to develop different marketing strategies based on member motivations for exchanging three types of eWOM in an online community of interest, such as an online beauty community. This will potentially help marketing managers increase online traffic and revenue, and thus bring success to the community. Although, this study contributes to the literature by highlighting three distinctive member motivations for eWOM exchanges in an online community of interest, there are some possible research limitations. First, this study was conducted in an online beauty community in Australia. Hence, further research should replicate this study in other industries and nations so as to give the findings greater generalisability. Next, online beauty community members are female skewed. Thus, future research should examine whether similar patterns of motivations would emerge in other online communities that tend to be populated by males (e.g., communities focused on football). Further, a web-based survey has its limitations in terms of self-selection and self-reporting (Bhatnagar & Ghose, 2004). Therefore, further studies should test the framework by employing different research methods in order to overcome these weaknesses.

Smooth DMS-FEM: A new approach to solving nearly incompressible nonlinear elasto-static problems

The DMS-FEM, which enables functional approximations with C(1) or still higher inter-element continuity within an FEM-based meshing of the domain, has recently been proposed by Sunilkumar and Roy [39,40]. Through numerical explorations on linear elasto-static problems, the method was found to have conspicuously superior convergence characteristics as well as higher numerical stability against locking. These observations motivate the present study, which aims at extending and exploring the DMS-FEM to (geometrically) nonlinear elasto-static problems of interest in solid mechanics and assessing its numerical performance vis-a-vis the FEM. In particular, the DMS-FEM is shown to vastly outperform the FEM (presently implemented through the commercial software ANSYS (R)) as the former requires fewer linearization and load steps to achieve convergence. In addition, in the context of nearly incompressible nonlinear systems prone to volumetric locking and with no special numerical artefacts (e.g. stabilized or mixed weak forms) employed to arrest locking, the DMS-FEM is shown to approach the incompressibility limit much more closely and with significantly fewer iterations than the FEM. The numerical findings are suggestive of the important role that higher order (uniform) continuity of the approximated field variables play in overcoming volumetric locking and the great promise that the method holds for a range of other numerically ill-conditioned problems of interest in computational structural mechanics. (C) 2011 Elsevier Ltd. All rights reserved.

Optimal H2 order-one reduction by solving eigenproblems for polynomial equations

A method is given for solving an optimal H2 approximation problem for SISO linear time-invariant stable systems. The method, based on constructive algebra, guarantees that the global optimum is found; it does not involve any gradient-based search, and hence avoids the usual problems of local minima. We examine mostly the case when the model order is reduced by one, and when the original system has distinct poles. This case exhibits special structure which allows us to provide a complete solution. The problem is converted into linear algebra by exhibiting a finite-dimensional basis for a certain space, and can then be solved by eigenvalue calculations, following the methods developed by Stetter and Moeller. The use of Buchberger's algorithm is avoided by writing the first-order optimality conditions in a special form, from which a Groebner basis is immediately available. Compared with our previous work the method presented here has much smaller time and memory requirements, and can therefore be applied to systems of significantly higher McMillan degree. In addition, some hypotheses which were required in the previous work have been removed. Some examples are included.

A Hybrid Imperialist Approach in Solving University Timetabling Problems. Information Sciences. Vol. 283, 1-21

Generating timetables for an institution is a challenging and time consuming task due to different demands on the overall structure of the timetable. In this paper, a new hybrid method which is a combination of a great deluge and artificial bee colony algorithm (INMGD-ABC) is proposed to address the university timetabling problem. Artificial bee colony algorithm (ABC) is a population based method that has been introduced in recent years and has proven successful in solving various optimization problems effectively. However, as with many search based approaches, there exist weaknesses in the exploration and exploitation abilities which tend to induce slow convergence of the overall search process. Therefore, hybridization is proposed to compensate for the identified weaknesses of the ABC. Also, inspired from imperialist competitive algorithms, an assimilation policy is implemented in order to improve the global exploration ability of the ABC algorithm. In addition, Nelder–Mead simplex search method is incorporated within the great deluge algorithm (NMGD) with the aim of enhancing the exploitation ability of the hybrid method in fine-tuning the problem search region. The proposed method is tested on two differing benchmark datasets i.e. examination and course timetabling datasets. A statistical analysis t-test has been conducted and shows the performance of the proposed approach as significantly better than basic ABC algorithm. Finally, the experimental results are compared against state-of-the art methods in the literature, with results obtained that are competitive and in certain cases achieving some of the current best results to those in the literature.

An implicit technique for solving 3D low Reynolds number moving free surface flows

This paper describes the development of an implicit finite difference method for solving transient three-dimensional incompressible free surface flows. To reduce the CPU time of explicit low-Reynolds number calculations, we have combined a projection method with an implicit technique for treating the pressure on the free surface. The projection method is employed to uncouple the velocity and the pressure fields, allowing each variable to be solved separately. We employ the normal stress condition on the free surface to derive an implicit technique for calculating the pressure at the free surface. Numerical results demonstrate that this modification is essential for the construction of methods that are more stable than those provided by discretizing the free surface explicitly. In addition, we show that the proposed method can be applied to viscoelastic fluids. Numerical results include the simulation of jet buckling and extrudate swell for Reynolds numbers in the range [0.01, 0.5]. (C) 2008 Elsevier Inc. All rights reserved.

Spatial thinking processes employed by primary school students engaged in mathematical problem solving

This thesis describes changes in the spatial thinking of Year 2 and Year 4 students who participated in a six-week long spatio-mathematical program. The main investigation, which contained quantitative and qualitative components, was designed to answer questions which were identified in a comprehensive review of pertinent literatures dealing with (a) young children's development of spatial concepts and skills, (b) how students solve problems and learn in different types of classrooms, and (c) the special roles of visual imagery, equipment, and classroom discourse in spatial problem solving. The quantitative investigation into the effects of a two-dimensional spatial program used a matched-group experimental design. Parallel forms of a specially developed spatio-mathematical group test were administered on three occasions—before, immediately after, and six to eight weeks after the spatial program. The test contained items requiring spatial thinking about two-dimensional space and other items requiring transfer to thinking about three-dimensional space. The results of the experimental group were compared with those of a ‘control’ group who were involved in number problem-solving activities. The investigation took into account gender and year at school. In addition, the effects of different classroom organisations on spatial thinking were investigated~one group worked mainly individually and the other group in small cooperative groups. The study found that improvements in scores on the delayed posttest of two-dimensional spatial thinking by students who were engaged in the spatial learning experiences were statistically significantly greater than those of the control group when pretest scores were used as covariates. Gender was the only variable to show an effect on the three-dimensional delayed posttest. The study also attempted to explain how improvements in, spatial thinking occurred. The qualitative component of the study involved students in different contexts. Students were video-taped as they worked, and much observational and interview data were obtained and analysed to develop categories which were described and inter-related in a model of children's responsiveness to spatial problem-solving experiences. The model and the details of children's thinking were related to literatures on visual imagery, selective attention, representation, and concept construction.

C programs for solving the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Influence of the addition of calcium hydroxide powder on some physical and chemical properties of the sealer MTA fillapex

Objective: This study evaluated the flow, pH and calcium release of MTA Fillapex (G1) or Fillapex plus 10% in weight of calcium hydroxide powder (G2), compared to AH Plus (G3) and Sealapex (G4). Materials and methods:The flow test was performed according to ISO 6876:2001 requirements. The sealers were placed into plastic tubes and immersed in deionized water. After 24 hours, 7, 14 and 28 days, the water of each tube was removed and tested to evaluate the pH values and the level of released calcium. Calcium release values were analyzed statistically by Kruskal Wallis and Dunn tests and pH values analyzed by ANOVA and Tukey tests (? = 5%). Results:G1 presented higher flow among all sealers. The addition of 10% calcium hydroxide into MTA Fillapex reduced the flow (p < 0.05) but, in a level, that is lower than the one recommended for ISO norms. G2 and G4 presented pH values and calcium release higher than G3 (p < 0.05) in all periods. G1 presented pH value higher than G3 (p < 0.05), except in 7 days period (p > 0.05). G4 presented higher pH values than G1 and G2, but the calcium release was similar for all periods (p > 0.05). G3 presented lower calcium release among all groups (p < 0.05). Conclusion: The addition of 10% calcium hydroxide in MTA Fillapex caused reduction in flow and no negative interference in pH and/or calcium release. However, the obtained flow is different from ISO requirements. Clinical relevance: MTA Fillapex presents levels of flow above the ISO norms. The addition of calcium hydroxide is a suggestion for solving this problem, but the impact of these procedures should be carefully evaluated.

Student Problem Solving

The purpose of this study is to determine if students solve math problems using addition, subtraction, multiplication, and division consistently and whether students transfer these skills to other mathematical situations and solutions. In this action research study, a classroom of 6th grade mathematics students was used to investigate how students solve word problems and how they determine which mathematical approach to use to solve a problem. It was discovered that many of the students read and re-read a question before they try to find an answer. Most students will check their answer to determine if it is correct and makes sense. Most students agree that mastering basic math facts is very important for problem solving and prefer mathematics that does not focus on problem solving. As a result of this research, it will be emphasized to the building principal and staff the need for a unified and focused curriculum with a scope and sequence for delivery that is consistently followed. The importance of managing basic math skills and making sure each student is challenged to be a mathematical thinker will be stressed.

Review of: Solving the Mysteries of the Dead Sea Scrolls: New Light on the Bible, by Edward M. Cook

Edward M. Cook's new book makes an excellent addition to the growing list of "introductions" to the Dead Sea Scrolls. Aimed primarily at a Christian lay and clerical audience, it succeeds admirably in leading its readers through the labyrinthine world of Scroll scholarship and controversy. The book divides itself into two uneven parts. In the first part, chapters 1-4, Cook deals with the discovery of the Scrolls in 1947 and the subsequent history of their decipherment and (often delayed) publication. Cook's treatment of this controversial topic is the most fair and evenhanded I have ever read; he has done meticulous research, reading many accounts of the Scrolls, from Edmund Wilson's in the 1950's to the latest journal articles from 1993. The result is a highly readable account of the finding and purchase of the Scrolls, the appointment of an international team of scholars to decipher and publish them, the delays in publication (including the results of the Six Day War in 1967, when most of the Scroll fragments fell into Israeli hands), and the controversy surrounding then editor-in-chief John Strugnell and the release of the photographs in the late 1980's and early 1990's. Cook is objective and fair throughout, but particularly striking is his sympathetic portrayal of the original seven member editorial team.