Innovación en la educación matemática: más allá de la tecnología

La relación entre el desarrollo de la competencia matemática de los estudiantes y la innovación en la enseñanza hace emerger la necesidad de nuevas prácticas matemáticas en el aula. Uno de los aspectos que definen estas nuevas prácticas es la emergencia de nuevos patrones de interacción en el aula que deben caracterizar el discurso matemático. Desde esta perspectiva, la relación entre innovación y desarrollo de nuevas prácticas define ámbitos para el desarrollo profesional del profesor de matemáticas.

Development of prospective mathematics teachers’ professional noticing in a specific domain: proportional reasoning

The aim of this research is to identify aspects that support the development of prospective mathematics teachers’ professional noticing in a b-learning context. The study presented here investigates the extent to which prospective secondary mathematics teachers attend and interpret secondary school students’ proportional reasoning and decide how to respond. Results show that interactions in an on-line discussion improve prospective mathematics teachers’ ability to identify and interpret important aspects of secondary school students’ mathematical thinking.

Development of multidisciplinary workshops between different subjects as an innovative teaching methodology for the acquisition of professional skills of the future architect

The implantation of the new Architecture Degree and the important normative changes in the building sector imply the need to use new teaching methodologies that enhance skills and competences in order to response to the increasing requirements demanded by society to the future architect. The aim of this paper is to present, analyze and discuss the development of multidisciplinary workshops as a new teaching methodology used in several Construction subjects of the Architecture Degree in the University of Alicante. Workshops conceived with the aim to synthesize and complement the technical knowledge acquired by the students during the Degree and to enhance the skills and competencies necessary for the professional practice. With that purpose, we decided to experiment on current subjects of the degree during this academic year, by applying the requirements defined in the future Architecture Degree in a practical way, through workshops between different subjects, superposing the technical knowledge with the resolution of constructive problems in the development of an architectural project. Developing these workshops between subjects we can dissolve the traditional boundaries between different areas of the Degree. This multidisciplinary workshop methodology allows the use of all the global knowledge acquired by students during their studies and at the same time, it enhances students’ ability to communicate and discuss their ideas and solutions in public. It also increases their capacity of self-criticism, and it foments their ability to undertake learning strategies and research in an autonomous way. The used methodology is based on the development of a practical work common to several subjects of different knowledge areas within the "Technology Block" of the future Architecture Degree. Thus, students work approaching the problem in a global way discussing simultaneously with teachers from different areas. By using these new workshops we stimulate an interactive class versus a traditional lecture. Work is evaluated continuously, valuing the participative pupil´s attitude, working in groups in class time, reaching weekly objectives and stimulating the individual responsibility and positive interdependence of the pupil inside the working group. The exercises are designed to improve students’ ability to transmit their ideas and solutions in public, knowing how to discuss and defend their technical resolutions to peers and teachers (Peer Reviewing), their capacity for self-criticism and their capacity to undertake strategies and autonomous learning processes at the same time they develop a personal research into new technologies, systems and materials. Students have shown their majority preference for this teaching methodology by the multidisciplinary workshops offered in the last years, with very satisfactory academic results. In conclusion, it can be verified nowadays the viability of the introduction of new contents and new teaching methodologies necessary for the acquisition of the skills in the future Architecture Degree, through workshops between several subjects that have had a great acceptance in students and positive contrasted academic results.

Características del desarrollo de una mirada profesional en estudiantes para profesor de matemáticas en un contexto b-learning

Esta investigación presenta un estudio cuyo objetivo es identificar aspectos que apoyan el desarrollo de la mirada profesional en estudiantes para profesores de matemáticas en un contexto b-learning. Analizamos las producciones de un grupo de estudiantes para profesores de matemáticas de educación secundaria (documentos escritos y participaciones en un debate on-line) cuando analizaban el razonamiento proporcional de estudiantes de educación secundaria. Los resultados indican que la interacción en el debate en línea permitió a algunos estudiantes para profesor mejorar su capacidad de identificar e interpretar aspectos relevantes del pensamiento matemático de los estudiantes de educación secundaria. Estos resultados indican que el desarrollo de “una mirada profesional” del profesor es un proceso complicado pero que la posibilidad de construir un discurso progresivo en línea es un factor importante para su desarrollo.

Cómo estudiantes para profesor interpretan el pensamiento matemático de los estudiantes de Bachillerato: la derivada de una función en un punto

El objetivo de esta investigación es caracterizar grados de desarrollo de la competencia docente “mirar con sentido” el pensamiento matemático de los estudiantes en el ámbito específico de la derivada de una función en un punto. A partir de los resultados de las investigaciones previas sobre la derivada diseñamos un cuestionario formado por tres tareas a partir de las respuestas de estudiantes a 3 problemas sobre el concepto de derivada en un punto. Los resultados han permitido generar descriptores de niveles de desarrollo de la competencia docente “mirar con sentido” el pensamiento matemático de los estudiantes. Estos resultados aportan información para el diseño de intervenciones en la formación de profesores de matemáticas que tengan como uno de sus objetivos el desarrollo de la competencia docente “mirar con sentido” el pensamiento matemático de los estudiantes.

Construcción de conocimiento y desarrollo de una mirada profesional para la práctica de enseñar matemáticas en entornos en entornos en línea

Este trabajo sintetiza en tres ámbitos algunos de los resultados de las investigaciones sobre la construcción del conocimiento de la enseñanza de las matemáticas en entornos de aprendizaje multimedia que integran espacios de interacción social en contextos b-learning. Estos ámbitos son (i) el papel de la interacción y la negociación de significados en la construcción del conocimiento; (ii) el proceso de instrumentalización del conocimiento de Didáctica de la Matemática en procesos de formación; y (iii) las características de las estructuras argumentativas en los procesos de aprender a conceptualizar la enseñanza de las matemáticas. Finalmente, se identifican nuevas cuestiones de investigación que emergen desde estas investigaciones.

Do first-year university students understand the language of mathematics?

The aim of the project is to determine if the understanding of the language of Mathematics of students starting university is propitious to the development of an appropriate cognitive structure. The objective of this current work was to analyse the ability of first-year university students to translate the registers of verbal or written expressions and their representations to the registers of algebraic language. Results indicate that students do not understand the basic elements of the language of Mathematics and this causes them to make numerous errors of construction and interpretation. The students were not able to associate concepts with definitions and were unable to offer examples.

Construction of Structures I in Moodle: a new teaching methodology in the Degree of Building Engineer

The subject of Construction of Structures I studies, from a constructive point of view and taking into account current legislation, reinforced concrete structures used in buildings, through the acquisition of knowledge and construction criteria required in the profession of a Technical Architect. The contents acquired in this course are essential for further professional development of technicians and are closely related to many of the subjects taught in the same or other courses of the Degree in Technical Architecture at the University of Alicante. The aim of this paper is to present, analyze and discuss the development of a new methodology proposed in the mentioned subject, as it supposed an important change in the traditional way of teaching Construction and Structures I. In order to incorporate new teaching tools in 2013-2014, the course has been implemented by using a Moodle software tool to promote blended learning with online exercises. Our Moodle community allows collaborative work within an open-source platform where teachers and students share a new and personalized learning environment. Students are easily used to the interface and the platform, value the constant connection with teachers or other fellows and completely agree with the possibility of making questions or share documents 24 hours a day. The proposed methodology consists of lectures and practical classes. In the lectures, the basics of each topic are discussed; class attendance, daily study and conducting scheduled exercises are indispensable. Practical classes allow to consolidate the knowledge gained in theory classes by solving professional exercises and actual construction problems related to structures, that shall be compulsorily delivered online. So, after the correction of the teacher and the subsequent feedback of students, practical exercises ensure lifelong learning of the student, who can download any kind of material at any time (constructive details, practical exercises and even corrected exams). Regarding the general evaluation system, goals achievement is assessed on an ongoing basis (65% of the final mark) along the course through written and graphic evidences in person and online, as well as a individual development of a workbook. In all cases, the acquisition of skills, the ability to synthesize, the capacity of logical and critical thinking are assessed. The other 35 % of the mark is evaluated by a complementary graphic exam. Participation in the computing platform is essential and the student is required to do and present, at least 90% of the practices proposed. Those who do not comply with the practices in each specific date could not be assessed continuously and may only choose the final exam. In conclusion, the subject of Construction of Structures I is essential in the development of the regulated profession of Technical Architect as they are considered, among other professional profiles, as specialists in construction of building structures. The use of a new communication platform and online teaching allows the acquisition of knowledge and constructive approaches in a continuous way, with a more direct and personal monitoring by the teacher that has been highly appreciated by almost 100% of the students. Ultimately, it is important to say that the use of Moodle in this subject is a very interesting tool, which was really well welcome by students in one of the densest and important subjects of the Degree of Technical Architecture.

Seeding a Profession: The Intersection of the State, International Interests, and the Early Development of Brazilian Nursing

State and international entities can have profound effects on the development of a country’s nursing profession. Through a global health governance lens, this paper explores the development of nursing in Brazil during the early twentieth century, and its intersections with national and international interests. Accordingly, we will show how state policies established an environment that fostered the institutionalization of nursing as a profession in Brazil and supported it as a means to increase the presence of females in nation building processes. The State focused on recruiting elite women for nursing, in part due to the Rockefeller Foundation’s involvement in the country. Nurses who worked for Rockefeller came from well-educated classes within US society with specific ideas about who should be a nurse and the roles of nurses in a healthcare system. These women served as the primary vehicles for interacting with Brazilian health authorities responsible for health system development. Their early efforts did not, however, ensure a system capable of producing nursing human resources at a rate that, in present day Brazil, could meet the health needs of the country. Findings from this paper offer new avenues for historians to explore the early roots of professional nursing through a global health governance lens, improve the understanding of the intersection between international politics and professionalization, and highlight how these factors may impact nursing human resources production in the long term.