Designing professional learning tasks for mathematics learning trajectories

Resumen basado en el de la publicaci??n

A kockázat megjelenése a származtatott pénzügyi termékekben (The risk appearing in financial derivatives)

A pénzügyi kockázatok szerepe, modellezése, kezelése az utóbbi évtizedekben vált egyre hangsúlyosabbá az elméletben és a gyakorlatban egyaránt. A 2007-ben kezdődő pénzügyi válság egyik kiváltó oka a kockázatok nem megfelelő felmérése volt. A válság egyik tanulsága, hogy bár a matematika és a fizika hozzájárulása rendkívül mély módszertani apparátust biztosított a kockázatok számszerűsítésére, ezen eredmények pénzügyi alkalmazása csak akkor sikeres, ha pontosan értjük a modellek feltételeit és korlátait. Jelen cikk a pénzügyi derivatívák értékelésének alapelveit, valamint a származtatott ügyletekben megjelenő kockázatokat tekinti át, illetve bemutatja azokat a bizonytalansági tényezőket, amelyek megkérdőjelezik az értékelés objektivitását. / === / The modeling and management of financial risks became one of the most important topics of the last decade both in theory and fi nancial practice. The mismanagement of fi nancial risks can be mentioned among the reasons contributing to the eruption of the recent crisis. In order to use successfully the methodology of mathematics and physics in pricing of derivatives, we have to consider the assumptions and limits of the models. This paper introduces the main concepts – no arbitrage pricing and risk neutral valuation – in derivatives’ pricing, then presents and quantifies the risk of some derivative products. I am arguing that the assumptions of the Black–Scholes and Merton model are injured at several points, so the pricing can not be perfectly cleared from all the risk preferences. All those risks, deriving from the difference of the reality and the model are priced in the volatility parameter in the practice.

The promotion and assessment of generic skills from interdisciplinary teaching teams

The paper explains a teaching project financed by the University of Barcelona (UB). It focuses on ageneric skill of the University of Barcelona, which is defined as "the learning capability andresponsibility”, and in which analytical and synthesis skills are included. It follows a multidisciplinaryapproach including teachers of Mathematics, World Economics and Economic History. All of us sharethe same students during the first and the second course of the grade in Economics at the Faculty ofEconomics and Business. The project has been developed in three stages. The first one has beendone during the first semester of the course 2012/13, being applied to first year students on thesubjects of Mathematics and Economic History. The second phase is being to be done during thesecond semester only on the Economic History subject. A third stage is going to be done next course2013/14 to second year students on the subject of World Economics. Each different teaching teamhas developed specific materials and assessment tools for each one of the subjects included in theproject. The project emphasizes two teaching dimensions: the elaboration of teaching materials topromote the acquisition of generic skills from an interdisciplinary point of view, and the design ofspecific tools to assess such skills. The first results of the first phase of the project shows cleardeficiencies in the analytical skill regarding to first year students.

The promotion and assessment of generic skills from interdisciplinary teaching teams

The paper explains a teaching project financed by the University of Barcelona (UB). It focuses on ageneric skill of the University of Barcelona, which is defined as "the learning capability andresponsibility”, and in which analytical and synthesis skills are included. It follows a multidisciplinaryapproach including teachers of Mathematics, World Economics and Economic History. All of us sharethe same students during the first and the second course of the grade in Economics at the Faculty ofEconomics and Business. The project has been developed in three stages. The first one has beendone during the first semester of the course 2012/13, being applied to first year students on thesubjects of Mathematics and Economic History. The second phase is being to be done during thesecond semester only on the Economic History subject. A third stage is going to be done next course2013/14 to second year students on the subject of World Economics. Each different teaching teamhas developed specific materials and assessment tools for each one of the subjects included in theproject. The project emphasizes two teaching dimensions: the elaboration of teaching materials topromote the acquisition of generic skills from an interdisciplinary point of view, and the design ofspecific tools to assess such skills. The first results of the first phase of the project shows cleardeficiencies in the analytical skill regarding to first year students.

The promotion and assessment of generic skills from interdisciplinary teaching teams

The paper explains a teaching project financed by the University of Barcelona (UB). It focuses on ageneric skill of the University of Barcelona, which is defined as "the learning capability andresponsibility”, and in which analytical and synthesis skills are included. It follows a multidisciplinaryapproach including teachers of Mathematics, World Economics and Economic History. All of us sharethe same students during the first and the second course of the grade in Economics at the Faculty ofEconomics and Business. The project has been developed in three stages. The first one has beendone during the first semester of the course 2012/13, being applied to first year students on thesubjects of Mathematics and Economic History. The second phase is being to be done during thesecond semester only on the Economic History subject. A third stage is going to be done next course2013/14 to second year students on the subject of World Economics. Each different teaching teamhas developed specific materials and assessment tools for each one of the subjects included in theproject. The project emphasizes two teaching dimensions: the elaboration of teaching materials topromote the acquisition of generic skills from an interdisciplinary point of view, and the design ofspecific tools to assess such skills. The first results of the first phase of the project shows cleardeficiencies in the analytical skill regarding to first year students.

The association of faculty's teaching philosophy and teaching behaviour, and critical thinking and self- direction in learning

The intent in this study was to investigate in what ways teachers· beliefs about education and teaching are expressed in the specific teaching behaviours they employ, and whether teaching behaviours, as perceived by their students, are correlated with students· critical thinking and self-directed learning. To this end the relationships studied were: among faCUlty members· philosophy of teaching, locus of control orientation, psychological type, and observed teaching behaviour; and among students· psychological type, perceptions of teaching behaviour, self-directed learning readiness, and critical thinking. The overall purpose of the study was to investigate whether the implicit goals of higher education, critical thinking and self-direction, were actually accounted for in the university classroom. The research was set within the context of path-goal theory, adapted from the leadership literature. Within this framework, Mezirow·s work on transformative learning, including the influences of Habermas· writings, was integrated to develop a theoretical perspective upon which to base the research methodology. Both qualitative and quantitative methodologies were incorporated. Four faCUlty and a total of 142 students participated in the study. Philosophy of teaching was described through faCUlty interviews and completion of a repertory grid. Faculty completed a descriptive locus of control scale, and a psychological type test. Observations of their teaching behaviour were conducted. Students completed a Teaching Behaviour Assessment Scale, the Self-Directed Learning Readiness Scale, a psychological type test, and the Watson-Glaser Critical Thinking Appraisal. A small sample of students were interviewed. Follow-up discussions with faculty were used to validate the interview, observation, teaching behaviour, and repertory grid data. Results indicated that some discrepancies existed between faculty's espoused philosophy of teaching and their observed teaching behaviour. Instructors' teaching behaviour, however, was a function of their personal theory of practice. Relationships were found between perceived teaching behaviour and students· self-directed learning and critical thinking, but these varied across situations, as would be predicted from path-goal theory. Psychological type of students and instructor also accounted for some of the variability in the relationships studied. Student psychological type could be shown as a partial predictor of self-directed learning readiness. The results were discussed in terms of theory development and implications for further research and practice.

Learning to manage in knowledge-based organizations: the role of learning logs or portfolios

Paper presented at the 8th European Conference on Knowledge Management, Barcelona, 6-7 Sep. 2008 URL: http://www.academic-conferences.org/eckm/eckm2007/eckm07-home.htm

An electronic portfolio for quantitative assessment of surgical skills in undergraduate medical education.

BACKGROUND We evaluated a newly designed electronic portfolio (e-Portfolio) that provided quantitative evaluation of surgical skills. Medical students at the University of Seville used the e-Portfolio on a voluntary basis for evaluation of their performance in undergraduate surgical subjects. METHODS Our new web-based e-Portfolio was designed to evaluate surgical practical knowledge and skills targets. Students recorded each activity on a form, attached evidence, and added their reflections. Students self-assessed their practical knowledge using qualitative criteria (yes/no), and graded their skills according to complexity (basic/advanced) and participation (observer/assistant/independent). A numerical value was assigned to each activity, and the values of all activities were summated to obtain the total score. The application automatically displayed quantitative feedback. We performed qualitative evaluation of the perceived usefulness of the e-Portfolio and quantitative evaluation of the targets achieved. RESULTS Thirty-seven of 112 students (33%) used the e-Portfolio, of which 87% reported that they understood the methodology of the portfolio. All students reported an improved understanding of their learning objectives resulting from the numerical visualization of progress, all students reported that the quantitative feedback encouraged their learning, and 79% of students felt that their teachers were more available because they were using the e-Portfolio. Only 51.3% of students reported that the reflective aspects of learning were useful. Individual students achieved a maximum of 65% of the total targets and 87% of the skills targets. The mean total score was 345 ± 38 points. For basic skills, 92% of students achieved the maximum score for participation as an independent operator, and all achieved the maximum scores for participation as an observer and assistant. For complex skills, 62% of students achieved the maximum score for participation as an independent operator, and 98% achieved the maximum scores for participation as an observer or assistant. CONCLUSIONS Medical students reported that use of an electronic portfolio that provided quantitative feedback on their progress was useful when the number and complexity of targets were appropriate, but not when the portfolio offered only formative evaluations based on reflection. Students felt that use of the e-Portfolio guided their learning process by indicating knowledge gaps to themselves and teachers.

An electronic portfolio for quantitative assessment of surgical skills in undergraduate medical education.

BACKGROUND We evaluated a newly designed electronic portfolio (e-Portfolio) that provided quantitative evaluation of surgical skills. Medical students at the University of Seville used the e-Portfolio on a voluntary basis for evaluation of their performance in undergraduate surgical subjects. METHODS Our new web-based e-Portfolio was designed to evaluate surgical practical knowledge and skills targets. Students recorded each activity on a form, attached evidence, and added their reflections. Students self-assessed their practical knowledge using qualitative criteria (yes/no), and graded their skills according to complexity (basic/advanced) and participation (observer/assistant/independent). A numerical value was assigned to each activity, and the values of all activities were summated to obtain the total score. The application automatically displayed quantitative feedback. We performed qualitative evaluation of the perceived usefulness of the e-Portfolio and quantitative evaluation of the targets achieved. RESULTS Thirty-seven of 112 students (33%) used the e-Portfolio, of which 87% reported that they understood the methodology of the portfolio. All students reported an improved understanding of their learning objectives resulting from the numerical visualization of progress, all students reported that the quantitative feedback encouraged their learning, and 79% of students felt that their teachers were more available because they were using the e-Portfolio. Only 51.3% of students reported that the reflective aspects of learning were useful. Individual students achieved a maximum of 65% of the total targets and 87% of the skills targets. The mean total score was 345 ± 38 points. For basic skills, 92% of students achieved the maximum score for participation as an independent operator, and all achieved the maximum scores for participation as an observer and assistant. For complex skills, 62% of students achieved the maximum score for participation as an independent operator, and 98% achieved the maximum scores for participation as an observer or assistant. CONCLUSIONS Medical students reported that use of an electronic portfolio that provided quantitative feedback on their progress was useful when the number and complexity of targets were appropriate, but not when the portfolio offered only formative evaluations based on reflection. Students felt that use of the e-Portfolio guided their learning process by indicating knowledge gaps to themselves and teachers.

Promotion of learning skills in the study of economics. pilot project in the subject area of

This communication is part of a larger teaching innovation project financed by the University ofBarcelona, whose objective is to develop and evaluate transversal competences of the UB, learningability and responsibility. The competence is divided into several sub-competencies being the ability toanalyze and synthesis the most intensely worked in the first year. The work presented here part fromthe results obtained in phase 1 and 2 previously implemented in other subjects (Mathematics andHistory) in the first year of the degree of Business Administration Degree. In these subjects’ previousexperiences there were deficiencies in the acquisition of learning skills by the students. The work inthe subject of Mathematics facilitated that students become aware of the deficit. The work on thesubject of History insisted on developing readings schemes and with the practical exercises wassought to go deeply in the development of this competence.The third phase presented here is developed in the framework of the second year degree, in the WorldEconomy subject. The objective of this phase is the development and evaluation of the same crosscompetence of the previous phases, from a practice that includes both, quantitative analysis andcritical reflection. Specifically the practice focuses on the study of the dynamic relationship betweeneconomic growth and the dynamics in the distribution of wealth. The activity design as well as theselection of materials to make it, has been directed to address gaps in the ability to analyze andsynthesize detected in the subjects of the first year in the previous phases of the project.The realization of the practical case is considered adequate methodology to improve the acquisition ofcompetence of the students, then it is also proposed how to evaluate the acquisition of suchcompetence. The practice is evaluated based on a rubric developed in the framework of the projectobjectives. Thus at the end of phase 3 we can analyze the process that have followed the students,detect where they have had major difficulties and identify those aspects of teaching that can help toimprove the acquisition of skills by the students. The interest of this phase resides in the possibility tovalue whether tracing of learning through competences, organized in a collaborative way, is a goodtool to develop the acquisition of these skills and facilitate their evaluation.

Science learning and graphic symbols: an exploration of early years teachers’ views and use of graphic symbols when teaching science

The study investigated early years teachers’ understanding and use of graphic symbols, defined as the visual representation(s) used to communicate one or more “linguistic” concepts, which can be used to facilitate science learning. The study was conducted in Cyprus where six early years teachers were observed and interviewed. The results indicate that the teachers had a good understanding of the role of symbols, but demonstrated a lack of understanding in regards to graphic symbols specifically. None of the teachers employed them in their observed science lesson, although some of them claimed that they did so. Findings suggest a gap in participants’ acquaintance with the terminology regarding different types of symbols and a lack of awareness about the use and availability of graphic symbols for the support of learning. There is a need to inform and train early years teachers about graphic symbols and their potential applications in supporting children’s learning.

Mathematics teaching life histories in the study of teachers' perceptions of change

The aim of this paper is to discuss teachers' perceptions of change in their thought and/or practice over time and their perceptions of what kind of experiences or challenges might have influenced those changes. Two mathematics teaching life histories of Brazilian teachers are examined, considering a context of curriculum development in the state of São Paulo, Brazil. Reflection on teachers' thought and practice and interest in their own development, including interest in their own learning of mathematics, seemed to be the most important internal aspects influencing change and development. Close support seemed to be the most important external aspect. The retrospective analysis put a good face on personal change and development. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

Assessment of Competences in the Physical Chemistry Area: Use of the Department Teaching Portfolio

Competences have become a standard learning outcome in present university education within the European Higher Education Area (EHEA). In this regard, updated tools for their assessment have turned out essential in this new teaching-learning paradigm. Among them, one of the most promising tools is the “learner´s portfolio”, which is based on the gathering and evaluation of a range of evidences from the student, which provides a wider and more realistic view of his/her competence acquisition. Its appropriate use as a formative (continuous) assessment instrument allows a deeper appraisal of student´s learning, provided it does not end up as another summative (final) evaluation tool. In this contribution we propose the use of the portfolio as a unifying assessment tool within a university department (Physical Chemistry), exemplifying how the portfolio could yield both personalized student reports and averaged area reports on competence acquisition. A proposed stepwise protocol is given to organize the individual competence reports and estimate the global competence level following a bottom-up approach (i.e. ranging from the class group, subject, grade, and academic course).

Learning mathematics in a classroom community of inquiry

This article considers the question of what specific actions a teacher might take to create a culture of inquiry in a secondary school mathematics classroom. Sociocultural theories of learning provide the framework for examining teaching and learning practices in a single classroom over a two-year period. The notion of the zone of proximal development (ZPD) is invoked as a fundamental framework for explaining learning as increasing participation in a community of practice characterized by mathematical inquiry. The analysis draws on classroom observation and interviews with students and the teacher to show how the teacher established norms and practices that emphasized mathematical sense-making and justification of ideas and arguments and to illustrate the learning practices that students developed in response to these expectations.