Why Mathematics is essential in Biomedical Sciences degree?

Improvement of mathematical education and motivation of students in the mathematics" area is needed. What can be done? We introduce some ideas to generate the student"s interest for mathematics, because they often present difficulties in appreciating the relevance of mathematics and its role in the health sciences. We consider that a cornerstone in the strategy to attract the students" interest is linking the mathematics with real biomedical situations. We proceed in the following manner: We first present a real biomedical situation to produce interest and to generate curiosity. Second, we ask thought-provoking questions to students as: Which is the biomedical problem presented? Which is my knowledge on this situation? What could I do to solve this biomedical situation? Do I need some new mathematical concepts and procedures? Thereupon, the teacher explains the mathematical concepts necessary to solve the case presented, providing definitions, properties and tools for graphical display and/or mathematical calculations. In this learning methodology, ICTs were cornerstones for reaching the proposed competences. Furthermore, ICTs can also be used in the evaluative task in its two possible aspects: formative and for obtaining a qualification. Comments from students about this new mathematics teaching method indicate that the use of real biomedical case studies kept the lessons in mathematics interesting.

A virtual learning environment for pregraduate mathematical students

Peer-reviewed

Interactive Calculus in a Virtual Learning Environment

The teaching of higher level mathematics for technical students in a virtual learningenvironment poses some difficulties, but also opportunities, now specific to that virtuality.On the other hand, resources and ways to do now manly available in VLEs might soon extend to all kinds of environments.In this short presentation we will discuss anexperience carried at Universitat Oberta deCatalunya (UOC) involving (an on line university), first, the translation of LaTeX written existent materials to a web based format(specifically, a combination of XHTML andMathML), and then the integration of a symbolic calculator software (WIRIS) running as a Java applet embedded in the materials, intending to achieve an evolution from memorising concepts and repetitive algorithms to understanding and experiment concepts and the use of those algorithms.

El aprendizaje reflexivo en la formación inicial del profesorado: un modelo para aprender a enseñar matemáticas = Reflective learning in the early formation of teachers: a model to learn to teach maths

In this study we analize the application of the reflective learning during initial formation mathematics teachers. This model is based on the sociocultural theories of the human learning and assumes that the interaction and the contrast make possible the coconstruction and the active reconstruction of knowledge.In order to make the study, it was left from a sample of 29 teaching students. The qualitative analysis allowed to identify factors that facilitate the incorporation of the reflective learning in university teaching, as well as the degree of effectiveness of this model to learn to teach mathematics

Cómo enseñar matemáticas en las primeras edades a partir de contextos de vida cotidiana = How to teach mathematics to young students based on everyday contexts

This paper stresses the importance of developing mathematical thought in young children based on everyday contexts, since these are meaningful learning situations with an interdisciplinary, globalised focus. The first part sets out the framework of reference that lays the theoretical foundations for these kinds of educational practices. The second part gives some teaching orientations for work based on everyday contexts. It concludes with the presentation of the activity 'We’re off to the cinema to learn mathematics!'

Matemáticas y juego = Mathematics and games

In this article we try to look at the learning of mathematics through games in the first years of schooling. The use of game resources in the class should not be carried out in a uniquely intuitive way but rather in a manner that contains some preliminary reflections such as, what do we understand by games? Why use games as a resource in the Mathematics classroom? And what does its use imply?

Teaching mathematics and programming : new approaches with empirical evaluation

Programming and mathematics are core areas of computer science (CS) and consequently also important parts of CS education. Introductory instruction in these two topics is, however, not without problems. Studies show that CS students find programming difficult to learn and that teaching mathematical topics to CS novices is challenging. One reason for the latter is the disconnection between mathematics and programming found in many CS curricula, which results in students not seeing the relevance of the subject for their studies. In addition, reports indicate that students' mathematical capability and maturity levels are dropping. The challenges faced when teaching mathematics and programming at CS departments can also be traced back to gaps in students' prior education. In Finland the high school curriculum does not include CS as a subject; instead, focus is on learning to use the computer and its applications as tools. Similarly, many of the mathematics courses emphasize application of formulas, while logic, formalisms and proofs, which are important in CS, are avoided. Consequently, high school graduates are not well prepared for studies in CS. Motivated by these challenges, the goal of the present work is to describe new approaches to teaching mathematics and programming aimed at addressing these issues: Structured derivations is a logic-based approach to teaching mathematics, where formalisms and justifications are made explicit. The aim is to help students become better at communicating their reasoning using mathematical language and logical notation at the same time as they become more confident with formalisms. The Python programming language was originally designed with education in mind, and has a simple syntax compared to many other popular languages. The aim of using it in instruction is to address algorithms and their implementation in a way that allows focus to be put on learning algorithmic thinking and programming instead of on learning a complex syntax. Invariant based programming is a diagrammatic approach to developing programs that are correct by construction. The approach is based on elementary propositional and predicate logic, and makes explicit the underlying mathematical foundations of programming. The aim is also to show how mathematics in general, and logic in particular, can be used to create better programs.

Conceptions of mathematics teacher education : thoughts among teacher educators in Tanzania

This study addresses the question of teacher educators’ conceptions of mathematics teacher education (MTE) in teacher colleges in Tanzania, and their thoughts on how to further develop it. The tension between exponents of content as opposed to pedagogy has continued to cause challenging conceptual differences, which also influences what teacher educators conceive as desirable in the development of this domain. This tension is connected to the dissatisfaction of parents and teachers with the failure of school mathematics. From this point of view, the overall aim was to identify and describe teacher educators’ various conceptions of MTE. Inspired by the debate among teacher educators about what the balance should be between subject matter and pedagogical knowledge, it was important to look at the theoretical faces of MTE. The theoretical background involved the review of what is visible in MTE, what is yet to be known and the challenges within the practice. This task revealed meanings, perspectives in MTE, professional development and assessment. To do this, two questions were asked, to which no clear solutions satisfactorily existed. The questions to guide the investigation were, firstly, what are teacher educators’ conceptions of MTE, and secondly, what are teacher educators’ thoughts on the development of MTE? The two questions led to the choice of phenomenography as the methodological approach. Against the guiding questions, 27 mathematics teacher educators were interviewed in relation to the first question, while 32 responded to an open-ended questionnaire regarding question two. The interview statements as well as the questionnaire responses were coded and analysed (classified). The process of classification generated patterns of qualitatively different ways of seeing MTE. The results indicate that MTE is conceived as a process of learning through investigation, fostering inspiration, an approach to learning with an emphasis on problem solving, and a focus on pedagogical knowledge and skills in the process of teaching and learning. In addition, the teaching and learning of mathematics is seen as subject didactics with a focus on subject matter and as an organized integration of subject matter, pedagogical knowledge and some school practice; and also as academic content knowledge in which assessment is inherent. The respondents also saw the need to build learner-educator relationships. Finally, they emphasized taking advantage of teacher educators’ neighbourhood learning groups, networking and collaboration as sustainable knowledge and skills sharing strategies in professional development. Regarding desirable development, teacher educators’ thoughts emphasised enhancing pedagogical knowledge and subject matter, and to be determined by them as opposed to conventional top-down seminars and workshops. This study has revealed various conceptions and thoughts about MTE based on teacher educators´ diverse history of professional development in mathematics. It has been reasonably substantiated that some teacher educators teach school mathematics in the name of MTE, hardly distinguishing between the role and purpose of the two in developing a mathematics teacher. What teacher educators conceive as MTE and what they do regarding the education of teachers of mathematics revealed variations in terms of seeing the phenomenon of interest. Within limits, desirable thoughts shed light on solutions to phobias, and in the same way low self-esteem and stigmatization call for the building of teacher educator-student teacher relationships.

Learning information technology business in a changing industry landscape. Introducing Team Entrepreneurship in Renewing Bachelor Education in Renewing Bachelor Education in Information

Speed, uncertainty and complexity are increasing in the business world all the time. When knowledge and skills become quickly irrelevant, new challenges are set for information technology (IT) education. Meta-learning skills – learning how to learn rapidly - and innovation skills have become more essential than single technologies or other specific issues. The drastic changes in the information and communications technology (ICT) sector have caused a need to reconsider how IT Bachelor education in Universities of Applied Sciences should be organized and employed to cope with the change. The objective of the study was to evaluate how a new approach to IT Bachelor education, the ICT entrepreneurship study path (ICT-ESP) fits IT Bachelor education in a Finnish University of Applied Sciences. This kind of educational arrangement has not been employed elsewhere in the context of IT Bachelor education. The study presents the results of a four-year period during which IT Bachelor education was renewed in a Finnish University of Applied Sciences. The learning environment was organized into an ICT-ESP based on Nonaka’s knowledge theory and Kolb’s experiental learning. The IT students who studied in the ICT-ESP established a cooperative and learned ICT by running their cooperative at the University of Applied Sciences. The students (called team entrepreneurs) studied by reading theory in books and other sources of explicit information, doing projects for their customers, and reflecting in training sessions on what was learnt by doing and by studying the literature. Action research was used as the research strategy in this study. Empirical data was collected via theme-based interviews, direct observation, and participative observation. Grounded theory method was utilized in the data analysis and the theoretical sampling was used to guide the data collection. The context of the University of Applied Sciences provided a good basis for fostering team entrepreneurship. However, the results showed that the employment of the ICT-ESP did not fit into the IT Bachelor education well enough. The ICT-ESP was cognitively too tough for the team entrepreneurs because they had two different set of rules to follow in their studies. The conventional courses engaged lot of energy which should have been spent for professional development in the ICT-ESP. The amount of competencies needed in the ICT-ESP for professional development was greater than those needed for any other ways of studying. The team entrepreneurs needed to develop skills in ICT, leadership and self-leadership, team development and entrepreneurship skills. The entrepreneurship skills included skills on marketing and sales, brand development, productization, and business administration. Considering the three-year time the team entrepreneurs spent in the ICT-ESP, the challenges were remarkable. Changes to the organization of IT Bachelor education are also suggested in the study. At first, it should be admitted that the ICT-ESP produces IT Bachelors with a different set of competencies compared to the conventional way of educating IT Bachelors. Secondly, the number of courses on general topics in mathematics, physics, and languages for team entrepreneurs studying in the ICTESP should be reconsidered and the conventional course-based teaching of the topics should be reorganized to support the team coaching process of the team entrepreneurs with their practiceoriented projects. Third, the upcoming team entrepreneurs should be equipped with relevant information about the ICT-ESP and what it would require in practice to study as a team entrepreneur. Finally, the upcoming team entrepreneurs should be carefully selected before they start in the ICT-ESP to have a possibility to eliminate solo players and those who have a too romantic view of being a team entrepreneur. The results gained in the study provided answers to the original research questions and the objectives of the study were met. Even though the IT degree programme was terminated during the research process, the amount of qualitative data gathered made it possible to justify the interpretations done.

Utilising student profiles in mathematics course arrangements

This thesis develops a method for identifying students struggling in their mathematical studies at an early stage. It helps in directing support to students needing and benefiting from it the most. Thus, frustration felt by weaker students may decrease and therefore, hopefully, also drop outs of potential engineering students. The research concentrates on a combination of personality and intelligence aspects. Personality aspects gave information on conation and motivation for learning. This part was studied from the perspective of motivation and self-regulation. Intelligence aspects gave information on declarative and procedural knowledge: what had been taught and what was actually mastered. Students answered surveys on motivation and self-regulation in 2010 and 2011. Based on their answers, background information, results in the proficiency test, and grades in the first mathematics course, profiles describing the students were formed. In the following years, the profiles were updated with new information obtained each year. The profiles used to identify struggling students combine personality (motivation, selfregulation, and self-efficacy) and intelligence (declarative and procedural knowledge) aspects at the beginning of their studies. Identifying students in need of extra support is a good start, but methods for providing support must be found. This thesis also studies how this support could be taken into account in course arrangements. The methods used include, for example, languaging and scaffolding, and continuous feedback. The analysis revealed that allocating resources based on the predicted progress does not increase costs or lower the results of better students. Instead, it will help weaker students obtain passing grades.

Introduction to engineering : a case study of an interdisciplinary course in Mathematics, Science and Technology

This thesis research was a qualitative case study of a single class of Interdisciplinary Studies: Introduction to Engineering taught in a secondary school. The study endeavoured to explore students' experiences in and perceptions of the course, and to investigate the viability of engineering as an interdisciplinary theme at the secondary school level. Data were collected in the form of student questionnaires, the researcher's observations and reflections, and artefacts representative of students' work. Data analysis was performed by coding textual data and classifying text segments into common themes. The themes that emerged from the data were aligned with facets of interdisciplinary study, including making connections, project-based learning, and student engagement and affective outcomes. The findings of the study showed that students were positive about their experiences in the course, and enjoyed its project-driven nature. Content from mathematics, physics, and technological design was easily integrated under the umbrella of engineering. Students felt that the opportunity to develop problem solving and teamwork skills were two of the most important aspects of the course and could be relevant not only for engineering, but for other disciplines or their day-to-day lives after secondary school. The study concluded that engineering education in secondary school can be a worthwhile experience for a variety of students and not just those intending postsecondary study in engineering. This has implications for the inclusion of engineering in the secondary school curriculum and can inform the practice of curriculum planners at the school, school board, and provincial levels. Suggested directions for further research include classroom-based action research in the areas of technological education, engineering education in secondary school, and interdisciplinary education.

How Learning Styles, Chemistry Attitudes and Experiences, Confidence, and Demographics Correlate with Academic Success in First and Second Year Chemistry Courses

At Brock University, the Faculty of Mathematics and Science currently has one of the highest percentages of students on academic probation, with many students reporting the most difficulty with Introductory Chemistry in first year and Organic Chemistry in second year. To identify strategies to improve students' performance and reduce the number of students on academic probation, a multi-year research project was undertaken involving several chemistry courses. Students were asked to complete three questionnaires, and provide consent to obtain their final Chemistry grade from the Registrar's Office. Research began at the end of the 2007-08 academic year with CHEM IPOO, and in the 2008-09 academic year, students in the larger CHEM IF92 Introductory Chemistry course were invited to participate in this research near the beginning of the academic year. Students who went on to take second year Organic and Analytical Chemistry were asked to complete these questionnaires in each second year course. The three questionnaires included the Kolb Learning Styles Inventory (Kolb, 1984) modified to include specific reference to Chemistry in each question, Dalgety, ColI, and Jones' (2002) Chemistry Attitudes and Experiences Questionnaire (CAEQ), and lastly, a demographic survey. Correlations were found between learning style and academic success; concrete learners were not as successful as abstract learners. Differences were noted between females and males with respect to learning styles, academic success, and confidence. Several differences were also noted between those who are the First in the Family to attend university and those who are not First in the Family to attend university.

Statistical Machine Learning Techniques for the Prediction of Learning Disabilities in School-Age Children

Learning Disability (LD) is a general term that describes specific kinds of learning problems. It is a neurological condition that affects a child's brain and impairs his ability to carry out one or many specific tasks. The learning disabled children are neither slow nor mentally retarded. This disorder can make it problematic for a child to learn as quickly or in the same way as some child who isn't affected by a learning disability. An affected child can have normal or above average intelligence. They may have difficulty paying attention, with reading or letter recognition, or with mathematics. It does not mean that children who have learning disabilities are less intelligent. In fact, many children who have learning disabilities are more intelligent than an average child. Learning disabilities vary from child to child. One child with LD may not have the same kind of learning problems as another child with LD. There is no cure for learning disabilities and they are life-long. However, children with LD can be high achievers and can be taught ways to get around the learning disability. In this research work, data mining using machine learning techniques are used to analyze the symptoms of LD, establish interrelationships between them and evaluate the relative importance of these symptoms. To increase the diagnostic accuracy of learning disability prediction, a knowledge based tool based on statistical machine learning or data mining techniques, with high accuracy,according to the knowledge obtained from the clinical information, is proposed. The basic idea of the developed knowledge based tool is to increase the accuracy of the learning disability assessment and reduce the time used for the same. Different statistical machine learning techniques in data mining are used in the study. Identifying the important parameters of LD prediction using the data mining techniques, identifying the hidden relationship between the symptoms of LD and estimating the relative significance of each symptoms of LD are also the parts of the objectives of this research work. The developed tool has many advantages compared to the traditional methods of using check lists in determination of learning disabilities. For improving the performance of various classifiers, we developed some preprocessing methods for the LD prediction system. A new system based on fuzzy and rough set models are also developed for LD prediction. Here also the importance of pre-processing is studied. A Graphical User Interface (GUI) is designed for developing an integrated knowledge based tool for prediction of LD as well as its degree. The designed tool stores the details of the children in the student database and retrieves their LD report as and when required. The present study undoubtedly proves the effectiveness of the tool developed based on various machine learning techniques. It also identifies the important parameters of LD and accurately predicts the learning disability in school age children. This thesis makes several major contributions in technical, general and social areas. The results are found very beneficial to the parents, teachers and the institutions. They are able to diagnose the child’s problem at an early stage and can go for the proper treatments/counseling at the correct time so as to avoid the academic and social losses.

Mathematical modelling in mathematics education and instruction

This paper aims at giving a concise survey of the present state-of-the-art of mathematical modelling in mathematics education and instruction. It will consist of four parts. In part 1, some basic concepts relevant to the topic will be clarified and, in particular, mathematical modelling will be defined in a broad, comprehensive sense. Part 2 will review arguments for the inclusion of modelling in mathematics teaching at schools and universities, and identify certain schools of thought within mathematics education. Part 3 will describe the role of modelling in present mathematics curricula and in everyday teaching practice. Some obstacles for mathematical modelling in the classroom will be analysed, as well as the opportunities and risks of computer usage. In part 4, selected materials and resources for teaching mathematical modelling, developed in the last few years in America, Australia and Europe, will be presented. The examples will demonstrate many promising directions of development.

Blended learning in der Hochschullehre?

Im Zuge der Verbesserung der Lehre an deutschen Hochschulen und Universitäten sind in den letzten Jahren bereits vielfältige Innovationen hinsichtlich der Gestaltung von Vorlesungen und Seminaren in den unterschiedlichen Fachdisziplinen deutlich geworden. Bei größeren Vorlesungen besteht das Problem eine kognitive Mitarbeit von allen Studierenden zu fördern, vor allem in Mathematikvorlesungen. In den letzten Jahren konnten bereits vielversprechende Gestaltungsmöglichkeiten im Bereich der Fachmathematikvorlesungen eingesetzt werden, die ganz im Trend der digitalen Medien liegen. Diese sind aus dem Alltag vieler Berufsgruppen, wie auch der Lehre und in der Freizeit nicht mehr wegzudenken. Im Folgenden wird eine Pilotstudie mit ersten Ergebnissen beschrieben. Das Projekt M@thWithApps startete im WS 2012/2013 in der Fachvorlesung „Mathematische Anwendungen“ mit 120 Studierenden des Grundschullehramts an der Universität Kassel. Die Studierenden wurden mit Tablet-PCs ausgestattet, die über den gesamten Vorlesungs- und Übungszeitraum eingesetzt wurden. Somit stellt sich die Frage nach den Chancen und Risiken dieser besonderen Form des Lernens, verbunden mit einem Tablet-PC.