Developing multiple - choice questions in mathematics

In this paper we wish to illustrate different perspectives used to create Multiple-Choice questions and we will show how we can improve these in the construction of math tests. As it is known, web technologies have a great influence on student’s behaviour. Based on an on-line project beginning at 2007 which has been contributing to help students on their individual work, we would like to share our experience and thoughts with colleagues who have a common concern when they have the task of constructing Multiple-Choice tests. We feel that Multiple-Choice tests play an important and a very useful supporting role in selfevaluation or self-examination of our students. Nonetheless, good Multiple–Choice Test Items are generally more complex and time-consuming to create than other types of tests. It requires a certain amount of skill. However, this skill maybe increases through study, practice and experience. This paper discusses a number of issues related to the use of Multiple-Choice questions, lists the advantages and disadvantages of this question format contrasting it with open questions. Some examples are given in this context.

New challenges in mathematics for the european higher education

In this paper we will talk about a math project submitted to the Lifelong Learning Programme. European higher education needs a reform in order to play its full role in the Europe of Knowledge. Modernisation of higher education is necessary in the areas of curricula (Bologna process), funding and governance so that higher education institutions can face the challenges posed by globalisation and contribute more effectively to the training and retraining of the European workforce. On the other hand Mathematics is an essential component of all educational systems. Mathematical literacy is being scrutinized in assessment efforts such as the OCDE Programme for International Student Assessment (PISA). This showed a low level in Europe. Due to the Bologna Process, which brought several didactical implications for Higher Education (HE) institutions, there is the need of lifelong learning. This evolution is in conflict with the earlier mentioned lack of competencies on basic sciences, such as Mathematics. Forced by this duality, efforts are combined to share expertise in the Math field and the integration of pedagogical methodologies becomes a necessity. Thus, several European countries have proposed an International Project to the Lifelong Learning Programme, Action ERASMUS Modernisation of Higher Education, to make institutions more attractive and more responsive to the needs of the labour market, citizens and society at large. One of the main goals of the project is to attract students to math through high-quality instructional units in an understandable, exciting and attractive way.

Evaluation of ochratoxin A exposure degree in two Portuguese cities through wheat and maize bread consumption during the winter 2007

The occurrence of OTA in fresh and packed wheat and in maize bread and the evaluation of the exposure degree through their consumption in two Portuguese populations from Porto and Coimbra, during the winter of 2007, were studied. One hundred and sixty eight bread samples, 61 maize and 107 wheat, were analysed by liquid chromatography–fluorescence detection (LC–FD). The results showed that 84% of samples were contaminated, with a maximum level of 3.85 ng/g (above the EU maximum limit, 3 ng/g). Fresh wheat bread presented higher levels than packed wheat bread. Moreover, the traditional maize bread, in either city, was consistently more contaminated than wheat bread, 0.25 vs 0.19 ng/g, and 0.48 vs 0.34 ng/ g for Porto and Coimbra, respectively. Avintes maize bread showed the highest mean contamination and maximum levels. The higher estimated daily intake of OTA from both types of bread in the population of Coimbra compared to Porto reflects the higher average contamination of bread in the first city.

E-assessment in mathematics courses with multiple-choice questions tests

With the implementation of the Bologna Process several challenges have been posed to higher education institution, particularly in Portugal. One of the main implications is related to the change of the paradigm of a teacher centered education, to a paradigm that is student centered. This change implies the change of the way to assess courses in higher education institutions. Continuous and formative assessments emerged as the focus, catalyzed by electronic assessment, or e-assessment. This paper presents a case of the implementation of an e-assessment strategy, implemented in order to allow continuous, formative assessment in numerous mathematics classes using multiple-choice questions tests implement in Moodle open-source learning management system. The implementation can be considered a success.

E-assessment in mathematics courses with multiple-choice questions tests

With the implementation of the Bologna Process several challenges have been posed to higher education institution, particularly in Portugal. One of the main implications is related to the change of the paradigm of a teacher centered education, to a paradigm that is student centered. This change implies the change of the way to assess courses in higher education institutions. Continuous and formative assessments emerged as the focus, catalyzed by electronic assessment, or e-assessment. This paper presents a case of the implementation of an e-assessment strategy, implemented in order to allow continuous, formative assessment in numerous mathematics classes using multiple-choice questions tests implement in Moodle open-source learning management system. The implementation can be considered a success.

The background impact in HEI math lectures: an experience in math in the 1st year of Accounting and Management Degree

It is a fact, and far from being a new one, that students have been entering Higher Education courses with many different backgrounds in terms of secondary school programs they attended. The impact of these basic skills is a general and worldwide challenge, fundamentally when facing some specific “constructive” subjects like foreign languages and Mathematics. Working with students with an extensive variety of Math qualifications is an outrageous challenge when they enter an advanced Math course, leading to an almost generalized expectations’ failure - from students enrolled in course and from their teachers, who feel powerless in trying to monitor knowledge construction from completely different “starting points”. If teachers’ "haste" is average, more than half of the students do not “go along” and give up, even before experiencing any kind of evaluation procedure. On the contrary, if the “speed” is too low, others are discouraged (feeling not progressing at all) and the teacher runs the risk of not meeting the minimum objectives (general and specific) of its course, which may have a negative impact on students’ future training development. Failure in Mathematics, despite being a recurrent and global issue, does not have any “magical solution”, however, in general, teachers in this area seem untiring, searching, investigating, trying and implementing new and old “recipes” to tackle and demystify this subject. In this article we describe a project developed in a Math course, with the first year students from an Accounting and Management bachelor degree, and its outcomes since it was brought to practice, revealing its impact in students’ success, from approval to dropout rates, in this course. We will shortly describe students’ differentiated Math backgrounds, their results in a pre-assessment analysis and how we try to deal with these differences and level them up, having in mind the same “finish line”. One should never forget that all these students where officially accepted in higher education institutions, so they are ones’ reality, the reality of institutions whose name one should value and strive to defend.

Teaching and learning mathematics using moodle

This paper summarizes a project that is contributing to a change in the way of teaching and learning Mathematics. Mathematics is a subject of the Accounting and Administration course. In this subject we teach: Functions and Algebra. The aim is that the student understand the basic concepts and is able to apply them in other issues, when possible, establishing a bridge between the issues that they have studied and their application in Accounting. As from this year, the Accounting course falls under in Bologna Process. The teacher and the student roles have changed. The time for theoretical and practical classes has been reduced, so it was necessary to modify the way of teaching and learning. In the theoretical classes we use systems of multimedia projection to present the concepts, and in the practical classes we solve exercises. We also use the Excel and the mathematical open source software wxMaxima. To supplement our theoretical and practical classes we have developed a project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio Online (Online Support Project). With the creation of this new project we wanted to take advantage already obtained results with the previous experiences, giving to the students opportunities to complement their study in Mathematics. One of the great objectives is to motivate students, encourage them to overcome theirs difficulties through an auto-study giving them more confidence. In the MatActiva project the students have a big collection of information about the way of the subject works, which includes the objectives, the program, recommended bibliography, evaluation method and summaries. It works as material support for the practical and theoretical classes, the slides of the theoretical classes are available, the sheets with exercises for the students to do in the classroom and complementary exercises, as well as the exams of previous years. Students can also do diagnostic tests and evaluation tests online. Our approach is a reflexive one, based on the professional experience of the teachers that explore and incorporate new tools of Moodle with their students and coordinate the project MatActiva.

The active mathematics project at ISCAP

This paper summarizes a project that is contributing to a change in the way of teaching and learning Mathematics. Mathematics is a subject of the Accounting and Administration course. In this subject we teach: Functions and Algebra. The aim is that the students understand the basic concepts and is able to apply them in other issues, when possible, establishing a bridge between the issues that they have studied and their application in Accounting. As from this year, the Accounting course falls under in Bologna Process. The teacher and the student roles have changed. The time for theoretical and practical classes has been reduced, so it was necessary to modify the way of teaching and learning. In the theoretical classes we use systems of multimedia projection to present the concepts, and in the practical classes we solve exercises. To supplement our theoretical and practical classes we have developed an active mathematics project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio Online (Online Support Project). In the last versions of Moodle, it is possible use the TeX language to create math questions. Using this tool we created a set of interactive materials. With the creation of this new project we wanted to take advantage already obtained results with the previous experiences, giving to the students opportunities to complement their study in Mathematics. One of the great objectives is to motivate students, encourage them to overcome theirs difficulties through an auto-study, giving them more confidence and the opportunity to seeing others perspectives of the mathematics subjects. In the MatActiva project the students have a big collection of information about the way of the subject works, which includes the objectives, the program, recommended bibliography, evaluation method and summaries. It works as material support for the practical and theoretical classes, the slides of the theoretical classes are available, the sheets with exercises for the students to do in the classroom and complementary exercises, as well as the exams of previous years. Students can also do diagnostic tests and evaluation tests online. Our approach is a reflexive one, based on the professional experience of the teachers that explore and incorporate new tools of Moodle with their students and coordinate the project MatActiva.

Master's in autonomous systems: an overview of the robotics curriculum and outcomes at ISEP, Portugal

Robotics research in Portugal is increasing every year, but few students embrace it as one of their first choices for study. Until recently, job offers for engineers were plentiful, and those looking for a degree in science and technology would avoid areas considered to be demanding, like robotics. At the undergraduate level, robotics programs are still competing for a place in the classical engineering graduate curricula. Innovative and dynamic Master’s programs may offer the solution to this gap. The Master’s degree in autonomous systems at the Instituto Superior de Engenharia do Porto (ISEP), Porto, Portugal, was designed to provide a solid training in robotics and has been showing interesting results, mainly due to differences in course structure and the context in which students are welcomed to study and work

Application of fractional order concepts in the study of electrical potential

The Maxwell equations, expressing the fundamental laws of electricity and magnetism, only involve the integer-order calculus. However, several effects present in electromagnetism, motivated recently an analysis under the fractional calculus (FC) perspective. In fact, this mathematical concept allows a deeper insight into many phenomena that classical models overlook. On the other hand, genetic algorithms (GA) are an important tool to solve optimization problems that occur in engineering. In this work we use FC and GA to implement the electrical potential of fractional order. The performance of the GA scheme and the convergence of the resulting approximations are analyzed.

Application of fractional calculus in engineering

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades. It has been recognized the advantageous use of this mathematical tool in the modelling and control of many dynamical systems. Having these ideas in mind, this paper discusses a FC perspective in the study of the dynamics and control of several systems. The paper investigates the use of FC in the fields of controller tuning, legged robots, electrical systems and digital circuit synthesis.

Innovations in technology: a friendly math project and the learning analytics “challenge”

Currently the world around us "reboots" every minute and “staying at the forefront” seems to be a very arduous task. The continuous and “speeded” progress of society requires, from all the actors, a dynamic and efficient attitude both in terms progress monitoring and moving adaptation. With regard to education, no matter how updated we are in relation to the contents, the didactic strategies and technological resources, we are inevitably compelled to adapt to new paradigms and rethink the traditional teaching methods. It is in this context that the contribution of e-learning platforms arises. Here teachers and students have at their disposal new ways to enhance the teaching and learning process, and these platforms are seen, at the present time, as significant virtual teaching and learning supporting environments. This paper presents a Project and attempts to illustrate the potential that new technologies present as a “backing” tool in different stages of teaching and learning at different levels and areas of knowledge, particularly in Mathematics. We intend to promote a constructive discussion moment, exposing our actual perception - that the use of the Learning Management System Moodle, by Higher Education teachers, as supplementary teaching-learning environment for virtual classroom sessions can contribute for greater efficiency and effectiveness of teaching practice and to improve student achievement. Regarding the Learning analytics experience we will present a few results obtained with some assessment Learning Analytics tools, where we profoundly felt that the assessment of students’ performance in online learning environments is a challenging and demanding task.

Master's in Autonomous Systems: An Overview of the Robotics Curriculum and Outcomes at ISEP, Portugal

Robotics research in Portugal is increasing every year, but few students embrace it as one of their first choices for study. Until recently, job offers for engineers were plentiful, and those looking for a degree in science and technology would avoid areas considered to be demanding, like robotics. At the undergraduate level, robotics programs are still competing for a place in the classical engineering graduate curricula. Innovative and dynamic Master's programs may offer the solution to this gap. The Master's degree in autonomous systems at the Instituto Superior de Engenharia do Porto (ISEP), Porto, Portugal, was designed to provide a solid training in robotics and has been showing interesting results, mainly due to differences in course structure and the context in which students are welcomed to study and work.

Profissionalidade docente: fonte de possibilidades e de (in)certezas

O longo percurso de formação, iniciado com a Licenciatura em Educação Básica, termina agora com a conclusão do Mestrado em Ensino do 1º e 2º Ciclos do Ensino Básico surgindo, por isso, o presente relatório de estágio no âmbito da unidade curricular de Integração Curricular: Prática Educativa Supervisionada e Relatório de Estágio. Este caminho foi trilhado tomando opções fundamentadas e intencionais, conciliando saberes teóricos e práticos, construídos e desenvolvidos nos contextos educativos onde decorreu a Prática Educativa Supervisionada (PES). Ancorada numa perspetiva de investigação, onde se reconhecem características da metodologia de investigação-ação, a supervisão pedagógica desenrolou-se por etapas que promoveram o crescimento pessoal e profissional da futura professora. Todo o percurso espelhado no decorrer das próximas páginas foi solidamente cimentado graças à experiência partilhada dos orientadores cooperantes, dos supervisores institucionais e do par pedagógico, permitindo desenvolver e consolidar competências heurísticas, bem como a transformação e o melhoramento das práticas. Atribuiu-se, neste processo, um especial significado à relação com o par pedagógico por ter constituído um apoio fundamental, valorizando-se a colaboração, enquanto agente potenciador da tomada de decisão em contextos de incerteza e de complexidade da prática docente. Este relatório de estágio configura-se como mais uma oportunidade de autoconsciência e de reflexão relativamente ao processo de construção da identidade profissional. O constante progresso do mundo atual, as dificuldades sentidas e os obstáculos ultrapassados reforçam a ideia de que o processo de formação será sempre ávido de uma permanente atualização.

Improving management skills through business simulation

A survey was conducted among students of the Accounting and Administration undergraduate degree at ISCAP – IPP (School of Accounting and Administration of Polytechnic Institute of Porto) in order to understand their perception value of their course Business Simulation (BS). This course is provided in a business environment where students can learn by doing through the management of a company as they were in the real life, but risk-free. The learning tasks are provided in an action-oriented format to maximize the learning process. Students learn by doing a set of tasks every session and have also to produce reports and presentations during the course. BS is part of the undergraduate degree of Accounting and Administration at ISCAP – IPP since the beginning of 2003. The questionnaire we used captured the students’ perception about general and specific skills and competencies considered important for managers and accountants in the real life, about the methodology used in the course, which is totally different from the traditional form, and also about the adequacy of the course included as part of the undergraduate degree. The results showed that students’ perception is highly positive and almost all of them think they improve the skills needed for a job during the course. These results are consistent with [1] Adler and Milne’s research in which the authors found that students agree with the use of action-oriented learning tasks in order to provide them the needed attitudes, skills, and knowledge. The improvement of group skills is the most important issue for students, which can be understandable as BS is the only course from the degree in Accounting and Administration they really have to work in groups.