Knowledge accelerator by transversal competences and multivariate adaptive regression splines

Transversal competences constitute a set of the knowledge, skills, and attitudes required for various positions and in different professions. Such competences include: entrepreneurship, teamwork, creativity, and communicativeness; they are increasingly listed by employers in different countries as the key requirements in the labor market. The article presents the model of accelerating the process of acquiring transversal competences, developed based on the analysis of data collected in four countries of the European Union: Poland, Finland, Slovakia, and Slovenia. In the analysis, multivariate additive regression spline method was used, along with artificial neural networks, in order to create the best model describing the influence of different variables on the acceleration of acquiring transversal competences. Herewith, we demonstrated that by accelerating the acquisition of the transversal competence of entrepreneurship is influenced by the following factors: rank of the training method in the developed matrix, student numbers and the weighted average of the pace of acceleration regarding the acquisition of the remaining transversal competences, i.e., teamwork, communicativeness and creativity by the given student. The results validate our new method of the acceleration of acquiring transversal competences by students. Students may be from various higher education institutions in different countries. Developed results may be used in the course of education within the framework of the already planned vocational courses and for developing the skills required by employers for various positions and in different professions.

     

Mathematics-related teaching competence of Taiwanese primary future teachers: evidence from TEDS-M

This paper draws on data from the international TEDS-M study, organized by the IEA, and utilizes a conceptual framework describing the Taiwanese perspective of mathematics and mathematics teaching competences (MTCs) with regard to investigating the uniqueness and patterns of Taiwanese future primary teacher performance in the international context. The framework includes content-oriented and thought-oriented categories of mathematics competence. The latter category contains subcategories adopted and revised from (3rd Mediterranean conference on mathematical education. Hellenic Mathematical Society, Athens, 2003) the competence approach by Niss. Hsieh’s (Research on the development of the professional ability for teaching mathematics in the secondary school level (3/3). Taiwan: National Science Council, 2009) model is also adopted and revised to serve as an analytical framework, including four categories relating to MTCs, representations, language, and misconceptions or error procedures. This paper shows that in thought-oriented mathematics competences Taiwan and Singapore share a unique pattern of higher percent correct in competences related to formalization, abstraction, and operations in mathematics than in those related to the way of thinking, modelling and reasoning in and with mathematics. The paper also addresses weak teaching competences claimed in domestic studies, which conflict with the TEDS-M results. Namely, in contrary to the international trend, Taiwanese future primary teachers are weak at judging mathematics competences required by students to learn mathematical concepts or solve problems, and superior at diagnosing and dealing with student misconceptions and error procedures.     

Using an ANP performance management framework to manage the development of transversal competences in University degrees

Organisations are concerned about measuring the performance of the product/service they deliver to their customers. In all types of organisations, if a proper performance assessment is to be developed, it should be measured in different dimensions. At University, the new study programs include the development and assessment of transversal competences due to their importance in enhancing the abilities and improving the employability of students. The achievement of transversal competences can be assessed in different levels/stages; for example, the 1st and 2nd years of a Bachelor’s degree; the 3rd and 4th years of a Bachelor’s degree and at Master’s level. The purpose of this paper is to integrate the research into performance management in organisations to develop an approach consisting of four components (a methodology, a solid and integrated performance management framework, graphical diagrams and quantitative techniques) to assess and manage the achievement of transversal competences through the different levels of study using a consolidated approach. The proposal uses the Analytic Network Process (ANP) to model dependences and feedback among the elements of the competences.

     

A model of professional competences in mathematics to update mathematical and didactic knowledge of teachers

This paper describes part of a research and development project carried out in public elementary schools. Its objective was to update the mathematical and didactic knowledge of teachers in two consecutive levels in urban and rural public schools of Region de Los Lagos and Region de Los Rios of southern Chile. To that effect, and by means of an advanced training project based on a professional competences model, didactic interventions based on types of problems and types of mathematical competences with analysis of contents and learning assessment were designed. The teachers’ competence regarding the didactic strategy used and its results, as well as the students’ learning achievements are specified. The project made possible to validate a strategy of lifelong improvement in mathematics, based on the professional competences of teachers and their didactic transposition in the classroom, as an alternative to consolidate learning in areas considered vulnerable in two regions of the country.     

Robust competence assessment for job assignment

Allocating the right person to a task or job is a key issue for improving quality and performance of achievements, usually addressed using the concept of “competences”. Nevertheless, providing an accurate assessment of the competences of an individual may be in practice a difficult task. We suggest in this paper to model the uncertainty on the competences possessed by a person using a possibility distribution, and the imprecision on the competences required for a task using a fuzzy constraint, taking into account the possible interactions between competences using a Choquet integral. As a difference with comparable approaches, we then suggest to perform the allocation of persons to jobs using a robust optimisation approach, allowing to minimise the risk taken by the decision maker. We first apply this framework to the problem of selecting a candidate within n for a job, then extend the method to the problem of selecting c candidates for j jobs (c ? j) using the leximin criterion.     

On the nature of OR: taking stock

This paper argues that OR, having reached its maturity, must now play to its strengths. In strategic terms this means competing in those areas where OR's core competences can be brought to bear. Using a competence model it is suggested that OR's core products are (i) the development and implementation of the quantitative, algorithmic ‘smart bits’ and (ii) the ‘helpful ways’ of managing intervention processes. These core products are supported and sustained by three core competences labelled process, analytic, and context. Individuals and small groups of practitioners develop ‘strands of practice’ and larger groups ‘webs of practice’ on the basis of their core competences. It is argued that this is giving rise to the emergence of three archetypes of OR service, namely the OR technical consultancy, the OR process consultancy, and the full service OR consultancy. Both the technical and process consulting are built around ‘strands of practice’ of individuals and find their natural home in small service providers. The full service OR consulting practice, in the past located in internal OR groups, will in the future be located within the large management consultancies, which are capable of managing ‘webs of practice’. The implications for the worlds of OR practice and academia are examined.     

数学建模对高中生构建数学底层思维的作用及其教学实施建议

数学底层思维即用数学的眼光观察世界、用数学的思维分析世界以及用数学的语言表达世界,是人们面对自然和社会中纷繁多样的现象和问题时,所展现的自发的、不依赖监督的、融汇数学学科核心素养的思维方式.作为国家高中新课程标准中数学六大核心素养之一的数学建模,是培养学生数学底层思维的良好载体,对人才培养和社会发展均起到良好的促进作用.本文主要阐述了数学建模对高中生构建数学底层思维的作用,并结合教学实例给出教学实施建议.     

Influences of CAS and GC in early algebra

In the last years, several studies have investigated the role of technology in teaching and learning mathematics. However, the specific role of computer algebra systems (CAS) in early algebra in contrast to graphic calculators (GC) is still unclear. The CAYEN project is researching this field by comparing 13-year-old pupils—one GC class and two CAS classes have been observed while acquiring elementary algebraic competences with nearly the same teaching sequence. The field of algebraic competences is split into syntactic abilities and symbol sense. The results of this explorative case study show that the development of symbol sense is influenced by the adoption of CAS in the learning process. Especially when transitioning from arithmetic to algebra, the pupils’ views of algebra as well as their conceptions of algebraic objects seem to be affected by the availability of CAS.     

Cost estimation algorithm and decision-making model for curriculum modification in educational organization

The decision about curriculum modification usually takes place at the knowledge level, mainly with consideration of individual academic staff competences and qualifications. However, traditional approaches to cost estimation of curriculum modification are focused on material resources only. In this paper we present a cost estimation method and decision model for curriculum modification in educational organizations. The proposed method works at the knowledge level and employs competence sets as knowledge representation models in educational organizations. Authors used the theory of hierarchical, multilevel systems in order to define the model of the decision-making process of curriculum modification and its dimension. Basing on this and also using a fuzzy competence model the cost estimation algorithm in the form of a group competences expansion algorithm is proposed. The algorithm focuses on the cost of staff competence expansion caused by the knowledge development process.     

The simplified updating rule in the formalization of digital educational games

Competence-based Knowledge Space Theory (CbKST) has been proven to be a very well-fitting basis for realizing personalization in technology-enhanced learning. Especially in the area of game-based learning, however, some extensions and improvements are needed.Personalization in a serious game cannot be regarded simply as the selection of game assets according to the individual learner's current competences but it must also pay heed to the up-keeping of a storyline, it must be ensured that no part of the story is omitted that may be necessary to understand a later part. Therefore, a CbKST-compatible Markovian model for storytelling is proposed.A second issue is the ongoing, non-invasive assessment of the learner's current competences during the game. Every action of the learner within the game should be taken into account for the competence assessment, and the assessment must be done in real-time, i.e. there must not be any delay caused by the assessment which would interrupt the flow of the game. A simplified update procedure for competence assessment within CbKST is suggested which can solve this issue, and simulation results are presented comparing the new procedure with the classical one.     

A multicriteria accreditation system for information technology skills and qualifications

Employees must acquire new competences and qualifications throughout their lives, in order to be able to deal with the multiple changes in the labour market. The specific knowledge and competences, acquired either formally or non-formally, must be recognized so that they can be transferred and utilized. The existing titles of studies and accreditation mechanisms do not generally cover this need. This paper aims to propose an integrated approach for the evaluation of information technology knowledge and skills, regardless of where and how they have been acquired, so as to apply a continuous education and training policy. The proposed multicriteria methodology for the evaluation of qualifications and skills concerns candidates wishing to be accredited in an information technology specialization or profession. The methodology refers to the evaluation of the professional experience, studies and vocational training of the candidates for accreditation. It contains the analysis and modelling of the qualitative criteria as well as the implementation of multicriteria aggregation–disaggregation techniques attributing value to each criterion. Then, the candidates are classified in categories of professionals using the Electre Tri method, accepting as input data the multicriteria assessments on each criterion. The proposed evaluation approach has been adapted to the Greek educational system and is applied to a specific example of candidate.     

Fächerübergreifender und fächerverbindender Unterricht in der gymnasialen Lehrerausbildung in Baden-Württemberg

One example each is discussed of a project and a smaller teaching unit, in order to show the difference between these two forms of cross-curricular teaching. Several concrete lessons and project concepts are then presented and explained, which have been elaborated at teacher training seminars together with or by student teachers. The paper examines and points out the advantages of cross-curricular teaching as well as Problems involved. Advantages observed for instance are new approaches for motivation, or a wider range of opportunities to further development of social competences, whereas the Problems encountered had to do with materials acquisition and didactics, questions remaining open, uncertainty, organisational aspects, and design and preparation of tests.     

Solving an integrated job-shop problem with human resource constraints

We propose two exact methods to solve an integrated employee-timetable and job-shop-scheduling problem. The problem is to find a minimum cost employee-timetable, where employees have different competences and work during shifts, so that the production, that corresponds to a job-shop with resource availability constraints, can be achieved. We introduce two new exact procedures: (1) a decomposition and cut generation approach and (2) a hybridization of a cut generation process with a branch and bound strategy. We also propose initial cuts that strongly improve these methods as well as a standard MIP approach. The computational performances of those methods on benchmark instances are compared to that of other methods from the literature.     

Impacts of supplier knowledge sharing competences and production capacities on radical innovative product sourcing

An effective sourcing strategy leads to cost savings and value added collaborations. For radical innovative product sourcing (RIPS), the exact nature and demand of products are highly uncertain. As such, knowledge sharing competences and production capacities of potential suppliers are prerequisite capabilities. The main aim is to investigate the impacts of these considerations on sourcing strategies through the development of two optimization models. Under the assumptions of single product sourcing, single period time window, uncertain demand and stochastic supply, KKT conditions are used to solve a simplified nonlinear optimization model analytically. The model is then expanded and particle swarm optimization is used to solve numerically the number of suppliers, order quantities and the level of relationship investments that maximize the value of sourcing. Through extensive scenario and sensitivity analyses, we provide some key insights.     

What is it that Cognitive Abilities are Abilities to Do?

This article outlines a conception of perceptual-recognitional abilities. These include abilities to recognize certain things from their appearance to some sensory modality, as being of some kind, or as possessing some property. An assumption of the article is that these abilities are crucial for an adequate understanding of perceptual knowledge. The specific aim here is to contrast those abilities with abilities or competences as conceived in the virtue-theoretic literature, with particular reference to views of Ernest Sosa and John Greco. In the course of the discussion, it is emphasized that the notion of exercising a perceptual-recognitional ability is a success notion: exercising such an ability is nothing less than acquiring knowledge. Even so, the view can make sense of our fallibility. It can also be defended in the face of an objection stemming from consideration of what are here called success-rate abilities.     

Language-related learning of mathematics: a comparison of kindergarten and primary school as places of learning

The study described in this paper presents research results from two separate projects, as well as two theoretical pillars that form the foundation of these projects. The first of these pillars focuses on the interactional relationship between mathematical and linguistic learning; the second defines an understanding of learning as a process that unfolds through institutions, whereby the most important element in the education of a child is the child him/herself rather than the specific place of learning. That is, for the purposes of this paper, the same linguistic issues arise independently of whether the child is in primary school or kindergarten. The results of both projects are used in the reconstruction of linguistic conditions of the learning of mathematics. These analyses can lead us to conclude that improvement in children’s linguistic competences should be only a secondary goal; the real key to the more effective promotion of children’s education in terms of subject-related learning seems to lie in the improved education and further education of teaching staff. The results should thus form a theoretical basis for the development of unified support and training concepts for children and educators.     

Conservation science and technology identity instrument: Empirically measuring STEM identities in informal science learning programs

Our research centered on developing the Conservation Science and Technology Identity (CSTI) instruments as an empirical way to measure STEM identities and the intersection of identity constructs such as competence, performance, recognition, and ways of seeing and being. The surveys were used in a large funded multi-year project for teens and adults learning geospatial technologies and conservation science to use in intergenerational community conservation projects. We investigated whether an informal STEM learning program was developing new STEM identities or advancing well-developed identities. The instruments’ content validity was determined through a vetting process from national STEM identity research experts. Reliability was estimated with Cronbach coefficient alpha. Mann-Whitney and Wilcoxon Signed Rank tests were used to determine participants’ STEM identities and the workshop’s effect on specific identity constructs. We found teens and adults had historically similar STEM identities, with stronger conservation science than technology. Both science and technology competences, as well as technology ways of seeing and being, significantly increased, suggesting CSTI can be a valuable instrument in empirically assessing STEM identities.     

Student Competence in Understanding the Matter Concept and Its Implications for Science Curriculum Standards

Using the US national sample from the 1995 Third International Mathematics and Science Study (TIMSS), this study examined students' competence levels in understanding the matter concept at grades 3, 4, 7, 8 and high school graduation, and compared them to the expectations in the US national science education standards. It was found that third‐grade students were developing understanding on mixtures, and fourth‐grade students were developing understanding on separating mixtures; seventh‐ and eighth‐grade students were only at the beginning level of differentiating chemical properties from physical properties; they were not ready for the particulate model of chemical change. High school physical science specialization students were still at the developing level of understanding kinetic and atomic models of chemical and physical changes; they may not be able to master those theories. The findings suggest that the Benchmarks for Science Literacy and Atlas for Science Literacy may have overestimated the competences of elementary, middle school, and high school students.     

TDmat–mathematics diagnosis evaluation test for engineering sciences students

Since 1989, the Mathematics Education Project (PmatE–Projecto Matemática Ensino) has developed several strategies to improve the success of students in Mathematics. The most important of these are mathematical games for all grades above primary school. The online evaluation of Mathematics subjects is one of PmatE's goals. The implementation of an on-line diagnosis test–TDmat (Teste Diagnóstico de Matemática), mandatory for all students enrolling for the first time in Science and Engineering courses at the University of Aveiro, was the approach chosen to evaluate the mathematical competences of these students. TDmat is a computer test with automatic evaluation in which the analysis of results is done automatically. This paper describes how it is conceived as well as the main results and conclusions drawn from evaluations of the school years 2003/2004 and 2004/2005.     

CAS in general mathematics education

A rational discussion of the use of Computer algebra systems (CAS) in mathematics teaching in general education needs an explicit image of (general) mathematics education, an explication of global perspectives and goals on mathematics teaching focusing on general education (chapter 1). The conception of general education according to the «ability of communication with experts» described in chapter 2 can be such an orientation for analysing, considering, classifying and assessing the didactical possibilities of using CAS. CAS are materialised mathematics allowing for more or less exhaustive outsourcing of operative (also symbolically) knowledge and skills to the machine. This frees up space of time as well as mental space for the development of those competences being in our view relevant for general mathematics education. In chapter 3 the idea of outsourcing and the role of CAS for it is discussed more detailed as well as consequences being possible for the CAS-supported teaching of mathematics. Beyond, CAS can be didactically used and reflected as a model of communication between (mathematical) experts and lay-persons (chapter 4). Chapter 5 outlines some research perspectives.