Applied mathematical problem solving, modelling, applications, and links to other subjects

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning (applied) problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.

The problem of the graphic artist

'The problem of the graphic artist' is a small example of applying elementary mathematics (divisibility of natural numbers) to a real problem which we ourselves have actually experienced. It deals with the possibilities for partitioning a sheet of paper into strips. In this contribution we report on a teaching unit in grade 6 as well as on informal tests with students in school and university. Finally we analyse this example methodologically, summarise our observations with pupils and students, and draw some didactical conclusions.

Identifying the component structure of job satisfaction by principal components analysis among extension officers in North West Province, South Africa

The component structure of a 34-item scale measuring different aspects of job satisfaction was investigated among extension officers in North West Province, South Africa. A simple random sampling technique was used to select 40 extension officers from which data were collected. A structured questionnaire consisting of 34 job satisfaction and 10 personal characteristic items was administered to the extension officers. Items on job satisfaction were measured at interval level and analyzedwith Principal ComponentAnalysis. Most of the respondents (82.5%) weremales, between 40 to 45 years, 85% were married and 87.5% had a diploma as their educational qualification. Furthermore, 54% of the households size between 4 to 6 persons, whereas 75% were Christians. The majority of the extension officers lived in their job area (82.5), while 80% covered at least 3 communities and 3 farmer groups. In terms of number of farmers covered, only 40% of the extension officers covered more than 500 farmers and 45% travelled more than 40 km to reach their farmers. From the job satisfaction items 9 components were extracted to show areas for job satisfaction among extension officers. These were in-service training, research policies, communicating recommended practices, financial support for self and family, quality of technical help, opportunity to advance education, management and control of operations, rewarding system and sanctions. The results have several implications for motivating extension officers for high job performance especially with large number of clients and small number of extension agents.

Cleanliness versus cow comfort – an insolvable problem?

Cubicle should provide good resting comfort as well as clean udders. Dairy cows in cubicle houses often face a restrictive environment with regard to resting behaviour, whereas cleanliness may still be impaired. This study aimed to determine reliable behavioural measures regarding resting comfort applicable in on-farm welfare assessments. Furthermore, relationships between cubicle design, cow sizes, management factors and udder cleanliness (namely teats and teat tips) were investigated. Altogether 15 resting measures were examined in terms of feasibility, inter-observer reliability (IOR) and consistency of results per farm over time. They were recorded during three farm visits on farms in Germany and Austria with cubicle, deep litter and tie stall systems. Seven measures occurred to infrequently to allow reliable recording within a limited observation time. IOR was generally acceptable to excellent except for 'collisions during lying down', which only showed good IOR after improvement of the definition. Only three measures were acceptably repeatable over time: 'duration of lying down', 'percentage of collisions during lying down' and 'percentage of cows lying partly or completely outside lying area'. These measures were evaluated as suitable animal based welfare measures regarding resting behaviour in the framework of an on-farm welfare assessment protocol. The second part of the thesis comprises a cross-sectional study on resting comfort and cow cleanliness including 23 Holstein Friesian dairy herds with very low within-farm variation in cubicle measures. Height at withers, shoulder width and diagonal body length were measured in 79-100 % of the cows (herd size 30 to115 cows). Based on the 25 % largest animals, compliance with recommendations for cubicle measures was calculated. Cleanliness of different body parts, the udder, teats and teat tips was assessed for each cow in the herd prior to morning milking. No significant correlation was found between udder soiling and teat or teat tip soiling on herd level. The final model of a stepwise regression regarding the percentage of dirty teats per farm explained 58.5 % the variance and contained four factors. Teat dipping after milking which might be associated with an overall clean and accurate management style, deep bedded cubicles, increasing cubicle maintenance times and decreasing compliance concerning total cubicle length predicted lower teat soiling. The final model concerning teat tip soiling explained 46.0 % of the variance and contained three factors. Increasing litter height in the rear part of the cubicle and increased alley soiling which is difficult to explain, predicted for less soiled teat tips, whereas increasing compliance concerning resting length was associated with higher percentages of dirty teat tips. The dependent variable ‘duration of lying down’ was analysed using again stepwise regression. The final model explained 54.8 % of the total variance. Lying down duration was significantly shorter in deep bedded cubicles. Further explanatory though not significant factors in the model were neck-rail height, deep bedding or comfort mattresses versus concrete floor or rubber mats and clearance height of side partitions. In the attempt to create a more comprehensive lying down measure, another analysis was carried out with percentage of ‘impaired lying down’ (i.e. events exceeding 6.3 seconds, with collisions or being interrupted) as dependent variable. The explanatory value of this final model was 41.3 %. An increase in partition length, in compliance concerning cubicle width and the presence of straw within bedding predicted a lower proportion of impaired lying down. The effect of partition length is difficult to interpret, but partition length and height were positively correlated on the study farms, possibly leading to a bigger zone of clear space for pelvis freedom. No associations could be found between impaired lying down and teat or teat tip soiling. Altogether, in agreement with earlier studies it was found that cubicle dimensions in practice are often inadequate with regard to the body dimensions of the cows, leading to high proportions of impaired lying down behaviour, whereas teat cleanliness is still unsatisfactory. Connections between cleanliness and cow comfort are far from simplistic. Especially the relationship between cubicle characteristics and lying down behaviour apparently is very complex, so that it is difficult to identify single influential factors that are valid for all farm situations. However, based on the results of the present study the use of deep bedded cubicles can be recommended as well as improved management with special regard to cubicle and litter maintenance in order to achieve both better resting comfort and teat cleanliness.

Identification of Problem-based learning components and their effects on graduates' competencies

This study investigated the relationship between higher education and the requirement of the world of work with an emphasis on the effect of problem-based learning (PBL) on graduates' competencies. The implementation of full PBL method is costly (Albanese & Mitchell, 1993; Berkson, 1993; Finucane, Shannon, & McGrath, 2009). However, the implementation of PBL in a less than curriculum-wide mode is more achievable in a broader context (Albanese, 2000). This means higher education institutions implement only a few PBL components in the curriculum. Or a teacher implements a few PBL components at the courses level. For this kind of implementation there is a need to identify PBL components and their effects on particular educational outputs (Hmelo-Silver, 2004; Newman, 2003). So far, however there has been little research about this topic. The main aims of this study were: (1) to identify each of PBL components which were manifested in the development of a valid and reliable PBL implementation questionnaire and (2) to determine the effect of each identified PBL component to specific graduates' competencies. The analysis was based on quantitative data collected in the survey of medicine graduates of Gadjah Mada University, Indonesia. A total of 225 graduates responded to the survey. The result of confirmatory factor analysis (CFA) showed that all individual constructs of PBL and graduates' competencies had acceptable GOFs (Goodness-of-fit). Additionally, the values of the factor loadings (standardize loading estimates), the AVEs (average variance extracted), CRs (construct reliability), and ASVs (average shared squared variance) showed the proof of convergent and discriminant validity. All values indicated valid and reliable measurements. The investigation of the effects of PBL showed that each PBL component had specific effects on graduates' competencies. Interpersonal competencies were affected by Student-centred learning (β = .137; p < .05) and Small group components (β = .078; p < .05). Problem as stimulus affected Leadership (β = .182; p < .01). Real-world problems affected Personal and organisational competencies (β = .140; p < .01) and Interpersonal competencies (β = .114; p < .05). Teacher as facilitator affected Leadership (β = 142; p < .05). Self-directed learning affected Field-related competencies (β = .080; p < .05). These results can help higher education institution and educator to have informed choice about the implementation of PBL components. With this information higher education institutions and educators could fulfil their educational goals and in the same time meet their limited resources. This study seeks to improve prior studies' research method in four major ways: (1) by indentifying PBL components based on theory and empirical data; (2) by using latent variables in the structural equation modelling instead of using a variable as a proxy of a construct; (3) by using CFA to validate the latent structure of the measurement, thus providing better evidence of validity; and (4) by using graduate survey data which is suitable for analysing PBL effects in the frame work of the relationship between higher education and the world of work.

The relationships of character strengths with coping, work-related stress, and job satisfaction

Personality traits have often been highlighted to relate to how people cope with stressful events. The present paper focuses on character strengths as positive personality traits and examines two basic assumptions that were derived from a core characteristic of character strengths (i.e., to determine how individuals deal with adversities): (1) character strengths correlate with coping and (2) buffer the effects of work-related stress on job satisfaction. Two different samples (i.e., a mixed sample representing various occupations [N = 214] and a nurses sample [N = 175]) filled in measures for character strengths, coping, work-related stress, and job satisfaction. As expected, intellectual, emotional, and interpersonal strengths were related to coping. Interpersonal strengths played a greater role for coping among nurses, as interactions with others are an essential part of their workday. Furthermore, intellectual strengths partially mediated the negative effect of work-related stress on job satisfaction. These findings open a new field for research on the role of personality in coping with work-related stress. Character strengths are trainable personal characteristics, and therefore valuable resources to improve coping with work-related stress and to decrease the negative effects of stress. Further research is needed to investigate this assumed causality.

Das Jahr 2000 Problem - Sorgen mit der Zeit?

Vortrag beim Treffen Lions Club Kassel Brüder Grimm am 20. August 1999. In der Zeit vor der Jahrtausendwende gab es Bedenken, dass größere Probleme durch die übliche Darstellung der Jahresangabe mit nur zwei Ziffern entstehen würden, weil Rechner nicht zwischen 1900 und 2000 unterscheiden könnten. Als Beispiel genannt wurden Fahrstühle, die seit 100 Jahren nicht mehr gewartet wurden und daher stehenbleiben. Tatsächlich ist dann sehr wenig passiert, ob wegen der lebhaften Diskussion vorher oder nicht, ist umstritten. Der Vortrag betrachtet sehr gründlich die technischen Probleme, die sich mit der Zeitdarstellung auf Rechnern ergeben.

Problem??tica de la formaci??n profesional espec??fica

Se presenta experiencia educativa que propone la creaci??n de un grupo de trabajo para analizar la problem??tica de la formaci??n profesional y proponer mejoras. Se realiza en el IES Padre P??veda en Guadix, Granada. Los objetivos son: seguimiento del cat??logo nacional de las cualificaciones profesionales y de los nuevos t??tulos de formaci??n profesional que afecta directamente a nuestro alumnado; estudiar la necesidad de implantar nuevos ciclos formativos en nuestra comunidad relacionados con la demanda de alumnado; estudiar el equilibrio o desequilibrio entre los distintos subsistemas de formaci??n profesional, e intentar evitar un estancamiento en la formaci??n profesional espec??fica; impulsar el establecimiento de los centros integrados en Andaluc??a; estudiar y analizar la legislaci??n vigente, difundi??ndola a toda nuestra comunidad escolar; analizar el plan Andaluz de formaci??n profesional; elaborar informes donde se reflejen los resultados de nuestro trabajo y darle la mayor difusi??n posible.

Stereo-Based Head Pose Tracking Using Iterative Closest Point and Normal Flow Constraint

In this text, we present two stereo-based head tracking techniques along with a fast 3D model acquisition system. The first tracking technique is a robust implementation of stereo-based head tracking designed for interactive environments with uncontrolled lighting. We integrate fast face detection and drift reduction algorithms with a gradient-based stereo rigid motion tracking technique. Our system can automatically segment and track a user's head under large rotation and illumination variations. Precision and usability of this approach are compared with previous tracking methods for cursor control and target selection in both desktop and interactive room environments. The second tracking technique is designed to improve the robustness of head pose tracking for fast movements. Our iterative hybrid tracker combines constraints from the ICP (Iterative Closest Point) algorithm and normal flow constraint. This new technique is more precise for small movements and noisy depth than ICP alone, and more robust for large movements than the normal flow constraint alone. We present experiments which test the accuracy of our approach on sequences of real and synthetic stereo images. The 3D model acquisition system we present quickly aligns intensity and depth images, and reconstructs a textured 3D mesh. 3D views are registered with shape alignment based on our iterative hybrid tracker. We reconstruct the 3D model using a new Cubic Ray Projection merging algorithm which takes advantage of a novel data structure: the linked voxel space. We present experiments to test the accuracy of our approach on 3D face modelling using real-time stereo images.

The Logical Problem of Language Change

This paper considers the problem of language change. Linguists must explain not only how languages are learned but also how and why they have evolved along certain trajectories and not others. While the language learning problem has focused on the behavior of individuals and how they acquire a particular grammar from a class of grammars ${cal G}$, here we consider a population of such learners and investigate the emergent, global population characteristics of linguistic communities over several generations. We argue that language change follows logically from specific assumptions about grammatical theories and learning paradigms. In particular, we are able to transform parameterized theories and memoryless acquisition algorithms into grammatical dynamical systems, whose evolution depicts a population's evolving linguistic composition. We investigate the linguistic and computational consequences of this model, showing that the formalization allows one to ask questions about diachronic that one otherwise could not ask, such as the effect of varying initial conditions on the resulting diachronic trajectories. From a more programmatic perspective, we give an example of how the dynamical system model for language change can serve as a way to distinguish among alternative grammatical theories, introducing a formal diachronic adequacy criterion for linguistic theories.