Didactics of Mathematics and Teacher Education

The purpose of this study is to find out the causes of fear in the mathematics of eleventh-grade students and to find a solution. Action research is a method that has proven to be valuable as a problem-solving tool. It can provide opportunities for reflection, improvement, transformation, and solutions to learning. The idea for this project began as a discussion among the Mathematics Phobia at Secondary school in West Bengal followed by WBCHSE Curriculum. The researchers investigate several dimensions of Mathematics Phobia. Several research questions stand out: a) Find out how much is an error in the curriculum? b) Finding students' lack of interest in learning mathematics? c) Find out how students' attitudes toward teaching methods and d) Find out Error in the learning process. The idea for this project began as a discussion among the Mathematics Phobia at Secondary school in West Bengal followed by WBCHSE Curriculum. The researchers selected 50 students from the 11th-grade class, of which 32 were male and 18 are female. Researchers formulated 12 questions and four Hypotheses. The methodology of the study is a mixed type involving interpretative, analytical study of documents, interview, survey questionnaire, observation, qualitative and quantitative data analysis, and study secondary sources, like books, university news, expert opinion, articles, journals, thesis and websites, etc. This study researcher using statistical method percentage & bar-graph & finally, meaningful suggestions are offered.

Les nombres complexes sont des objets qui se situent à la transition entre lycée et université. Mais ce sont également des objets interdisciplinaires : construits par le mathématicien, ils sont utilisés par le physicien et discutés par le philosophe. Nous examinons au cours de cet atelier des exemples de scénarios pédagogiques visant à croiser les regards sur les nombres complexes. Nous montrons également, en nous appuyant sur cet exemple, comment la réflexion épistémologique peut-être utile afin de faciliter la transition lycée-université.

The objective of this paper is to present a characterization of algebraic competence articulated in levels and development indicators. This characterization was used to analize the mathematical practice of inservice teachers of mathematics. Through a qualitative and exploratory research design, the algebraic competence in the teachers on high school (with students between 16 and 19 years old) is investigated and described. The results suggest that teachers present inconsistencies when solving tasks that demand a level three of algebraic competence, so the articulation of training programs based on this proposal will contribute to the development of algebraic competences in teachers of mathematics.

In our contemporary times-the era of the fast developments of all area, the claim that we cannot live without mathematics is justified. The culture of Math is the basic element of the culture of modern people. Thus, learning Math is not reduced to the mere assimilation of knowledge, it aims to the formation of a certain way of thinking through permanent mind training. The " taste " for Mathematics is formed in the first years of school, the lessons and complementary activities are essential for the acquisition of a mathematical thinking. The teacher, in the primary grades, has the task to put the foundations of elementary mathematical notions and has the role to make pupils to get the core mathematical concepts and, also, to insist that their thinking to be stimulated in a wonderful way. The teacher must arouse the interest and love for the study of this beautiful matter. So, what makes Math lessons more attractive? What are the factors that can increase the quality of learning mathematics? To these questions we will try to answer in this paper. We talk about some factors that influence the quality of the lessons containing Math activities, like planning of Math lessons using modern strategies of learning. So we discuss about the use of active-participative methods and also we talk about interdisciplinary approaches, illustrating the strengths and weaknesses of those strategies. Finally, we present the importance of introducing specific methods and techniques of compounding and solving problems.

En este trabajo pretendemos reflexionar sobre cómo la incorporación de las TIC modifica los escenarios de trabajo en las clases de Matemática. Se analizarán experiencias recogidas en un curso dictado a profesores de esa área, utilizando el software de geometría dinámica GeoGebra. Basaremos nuestros desarrollos en el enfoque instrumental que analiza el uso de la tecnología y de cómo un usuario (docente, alumno, etc.) se apropia de algún instrumento para integrarlo a su actividad matemática. Focalizaremos nuestras observaciones sobre dos ejes: utilización y/o incorporación de herramientas tecnológicas, la gestión de la clase para potenciar lo dinámico e interactivo que ofrece el software para el aprendizaje y la enseñanza de la matemática con la utilización de TIC.
In this work we try to think how the incorporation of the TIC modifies the scenes of work in the classes of Mathematics. There will be analysed experiences gathered in a course dictated to teachers of this area, using the software of dynamic geometry GeoGebra. We will base our developments on the instrumental approach that analyses the use of the technology and of how a user (teacher, pupil, etc.) appropriates of some instrument to integrate it to his mathematical activity. We will focus our observations on two axes: utilization and / or incorporation of technological tools, the management of the class to promote the dynamic and interactive thing that offers the software for learning and teaching mathematics with the utilization of TIC.

This paper reports a joint research project by
researchers from three countries on an international comparative
study that examines the professional knowledge of
prospective mathematics teachers in elementary mathematics
from an advanced standpoint. For this study,
mathematical problems on various topics of elementary
mathematical content were developed. Using this instrument,
the mathematical knowledge of future teachers from
Germany, Hong Kong, China (Hangzhou) and South Korea
was measured empirically. The paper presents the design of
the study, and also results are discussed. The results show
that there are systematic differences among the participating
countries; for example, the Korean future teachers outperform
their counterparts in other countries. A more detailed analysis
of the results suggests that the future teachers often do not
seem to be able to link school and university knowledge
systematically and cannot achieve the crucial ‘‘advanced
standpoint’’ from the teacher training programme.

How can the didactic and philosophical approach in mathematics, an interdisciplinary device for the training of secondary school teachers, contribute to pedagogical innovation in higher education and develop students' reflexivity? We present in this paper our device and the results obtained, in the case of a pedagogical sequence on the didactic and the epistemology of the proof. In particular, this sequence aims to develop in students representations consistent with contemporary mathematical practice, in connection with the questions of teaching and learning. Keywords: Teacher training, didactics and epistemology of mathematical proof, discussion in philosophical research community, reflexivity on the mathematical object to be taught

Lo spunto per questo articolo proviene da uno spettacolo-conferenza dal titolo Magia Matematica tenuto dal sottoscritto in collaborazione col Mago Vago presso il Liceo Leonardo Da Vinci di Cassano delle Murge (Ba), parallelamente ad un laboratorio di magia matematica per gli studenti promosso dalla docente Luciana Loconsole, in concomitanza con i preparativi per la manifestazione CassanoScienza, in programma dal 30 Marzo al 5 Aprile 2020 a Cassano (Ba). In effetti, magia e scienza si presentano normalmente come paradigmi diametral-mente opposti. Ovviamente in molti casi lo sono. Ma in realtà il pensiero magico è strettamente correlato con l'instaurarsi della scienza moderna. Uno degli scopi della conferenza citata era proprio quello di mostrare come, in un certo senso, la scienza moderna sia in qualche modo una sorta di magia matematizzata (si veda [4] per una esposizione introduttiva). Ad ogni modo, al di là degli aspetti storici, filosofici ed epistemologici (un'accurata ed esaustiva discussione del tema si trova in [6]), sfruttare principi matematici per la realizzazione di trucchi di magia può essere un valido strumento per porre conoscenze matematiche di base sotto una luce diversa e ma-gari anche per introdurre problematiche nuove. Ovviamente questi temi hanno una lunga storia. Una ricca fonte di materiale utile a questi fini si trova ad esempio nel recente [1]. In questo articolo ci limitiamo a presentare un gioco basato sul numero 9 utile per valorizzare l'aritmetica e anche per spingersi su temi più avanzati.

En general en nuestro país, y sobre todo en carreras científicotecnológicas, los docentes universitarios son profesionales expertos en los temas de sus materias, pero con escasa formación pedagógica. La misma habitualmente se impulsa a través de programas específicos organizados desde las instituciones. Otro modo de llevar adelante esta formación es de manera autogestionada, a partir de los intereses de los propios docentes.
La Investigación-Acción es, precisamente, un proceso de indagación
iniciado por los profesores a partir de la necesidad de comprender
lo que acontece en su práctica docente cotidiana para mejorarla.
Este trabajo relata cómo, a través de la Investigación-Acción,un
grupo de docentes organiza su formación mediante la realización
de seminarios, la selección de lecturas, la reflexión y el debate,
indagando,así,sobre los sentidos de la evaluación en la Universidad
y en los cursos de Matemática en los primeros años del trayecto
universitario. De este modoredescubrimos el sentido formativo de la
evaluación, opacado por la tradición de evaluar para constatar los
logros alcanzados por los estudiantes al finalizar un curso.A través
de este proceso modificamoslas estrategias didácticas
incorporando instancias de evaluación formativaen los cursos que
impartimos.

In our country (Argentina), and especially in scientific and
technological programs, university teachers are generally
professionals who are experts in the topics of their subjects with
little pedagogical training. This lack is usually addressed through
specific programs organized by higher education institutions.
Another way to carry out this training is through self-directed
learning, based on the interests of the teachers themselves. Action-Research is precisely a process of inquiry initiated by teachers
based on the need to understand what happens in their daily
teaching practice in order to improve it. This work reports on how,
through an Action-Research approach, a group of teachers took the
initiative and the responsibility to pursue their own learning
experience through seminars, the selection of reading materials,
reflection and debate. This allowed them to investigate about the
purpose of assessment in higher education settings, especially in
Mathematics first year courses. In this way, they rediscovered the
formative aspect of assessment which has been somehow obscured
by summative evaluation. Through this process, they modified their
didactic strategies and incorporated instances of formative
assessment in the courses they teach.

En general en nuestro país, y sobre todo en carreras científicotecnológicas, los docentes universitarios son profesionales expertos en los temas de sus materias, pero con escasa formación pedagógica. La misma habitualmente se impulsa a través de programas específicos organizados desde las instituciones. Otro modo de llevar adelante esta formación es de manera autogestionada, a partir de los intereses de los propios docentes. La Investigación-Acción es, precisamente, un proceso de indagación iniciado por los profesores a partir de la necesidad de comprender lo que acontece en su práctica docente cotidiana para mejorarla. Este trabajo relata cómo, a través de la Investigación-Acción,un grupo de docentes organiza su formación mediante la realización de seminarios, la selección de lecturas, la reflexión y el debate, indagando,así,sobre los sentidos de la evaluación en la Universidad y en los cursos de Matemática en los primeros años del trayecto universitario. De este modoredescubrimos ...

The present article is an excerpt of a developed research about Mathematics teaching and the inclusion of students with visual disabilities in regular education. It deals specifically with one possibility of methodological and didactic adaptation for the Notable Products teaching. It presents a qualitative approach, using the case study as a strategy. Its main objective is the development of methodological and didactic procedures that enable students that are visually disabled and are included in regular education to appropriate mathematical knowledge, together with other students. It was based in the plans of Vygotski´s historic-cultural theory for the development of a pedagogical intervention in an 8th grade class of basic education in a public school in Parana, when some mathematical concepts in Geometry, Algebra and Quantities and Measurements were approached, with inference to the Notable Products. The activities were carried out from the teaching stages proposed by Galperin. It was possible to verify that the proposal allowed the students to elaborate the mathematics concepts involved during the didactic sessions, and mainly, that it is possible to teach Mathematics to students that are visually disabled together with the others and that all of them, despite their limitations, are able to organize necessary concepts in order to achieve autonomy and practice their citizenship.

I would like to announce the Scriba Memorial Meeting - History of Mathematics - Scientific Colloquium and meeting of the working groups "history of mathematics" in the German association of mathmaticians (Geschichte der Mathematik in der "Deutschen Mathematiker-Vereinigung", DMV) and the "Society for Didactics of Mathmatics" ("Gesellschaft für Didaktik der Mathematik", GDM):
http://www.hs.uni-hamburg.de/DE/GNT/events/Scriba-Mathe-2015.php
organized by Gudrun Wolfschmidt and Hans Fischer, Geomatikum, Bundesstrasse 55, 20146 Hamburg, 12. - 17. Mai 2015.

In addition an exhibition will be opened: "From Abacus to Computer" (Vom Abakus zum Computer), May 13, 2015, 16:00 h, in the Lehrerbildungsinstitut Hamburg (Teacher Training Institute), Felix-Dahn-Straße 3, 20357 Hamburg,
http://li.hamburg.de/physik/4493222/physik/, see also:

Exhibitions of the Center for History of Science and Technology (Ausstellungen des Zentrums für Geschichte der Naturwissenschaft und Technik):
http://www.hs.uni-hamburg.de/DE/GNT/events/ausstell.php
Collections of the Center for History of Science and Technology, Hamburg Observatory, University of Hamburg,http://www.hs.uni-hamburg.de/DE/GNT/events/Sammlungen_IGN.htm
Lehrerbildungsinstitut, new Link
http://li.hamburg.de/physik/4493222/physik/

Planned Publication / catalogue: Nuncius Hamburgensis; Vol. 21 (2016)
http://www.hs.uni-hamburg.de/DE/GNT/research/nuncius.php 

Wolfschmidt, Gudrun (ed.): Scriba Memorial Meeting - History of Mathematics - Scientific Colloquium and meeting of the working groups "history of mathematics" in the German association of mathmaticians (Geschichte der Mathematik in der "Deutschen Mathematiker-Vereinigung", DMV) and the "Society for Didactics of Mathmatics" ("Gesellschaft für Didaktik der Mathematik", GDM). Hamburg: GNT 2015.. Available from: https://www.researchgate.net/publication/276058621_Wolfschmidt_Gudrun_(ed.)_Scriba_Memorial_Meeting_-_History_of_Mathematics_-_Scientific_Colloquium_and_meeting_of_the_working_groups_history_of_mathematics_in_the_German_association_of_mathmaticians_(Geschichte_der_Mathematik_in_der_Deutschen_Mathematiker-Vereinigung_DMV)_and_the_Society_for_Didactics_of_Mathmatics_(Gesellschaft_fr_Didaktik_der_Mathematik_GDM)._Hamburg_GNT_2015#share [accessed May 10, 2015].

En general en nuestro pais, y sobre todo en carreras cientifico-tecnologicas, los docentes universitarios son profesionales expertos en los temas de sus materias, pero con escasa formacion pedagogica. La misma habitualmente se impulsa a traves de programas especificos organizados desde las instituciones. Otro modo de llevar adelante esta formacion es de manera autogestionada, a partir de los intereses de los propios docentes. La Investigacion-Accion es,precisamente, un proceso de indagacion iniciado por los profesores a partir de la necesidad de comprender lo que acontece en su practica docente cotidiana para mejorarla. Este trabajo relata como, a traves de la Investigacion-Accion,un grupo de docentes organiza su formacion mediante la realizacion de seminarios, la seleccion de lecturas, la reflexion y el debate, indagando,asi,sobre los sentidos de la evaluacion en la Universidad y en los cursos deMatematica en los primeros anos del trayecto universitario. De este modoredescubrimos e...

Dans le contexte institutionnel de la formation des enseignants du secondaire en France, nous avons élaboré un problème qui vise à créer des liens entre l'intégrale du Lycée (upper secondary) et les théories de Riemann et de Lebesgue enseignées à l'Université. En d'autres termes, il s'agit d'une réponse à la question de l'implémentation du plan B de Klein, dans le cas de l'intégrale, comme stratégie pour pallier à la seconde discontinuité de Klein. La méthodologie se fonde sur l'exploitation d'un modèle praxéologique de référence pour les différents objets de savoir. Les premiers résultats suggèrent que la modalité sous forme de problème écrit est insuffisante pour produire le transfert des connaissances mathématiques académiques en des connaissances utiles pour un enseignant du secondaire.

The project MaT²SMc is implemented in the frame of EU Lifelong Learning Pro-gramme. The main idea of the project is to find a way to increase students' motivation to learn in the key subjects mathematics and science. From one side, mathematics teachers should understand that there is a meaningful and realistic context to use mathematics. From the other side, science teachers should understand that the mathematics compe-tences required for more effective science teaching and learning. In such a context the collaboration of science and mathematics teachers is very relevant. Currently it is obvious that mathematics and natural science teachers‘ collaboration on integration purposes at school is limited by some factors. Collaboration of mathematics and natural science te-achers should be expanded, for this purpose, it is necessary to create all necessary condi-tions and didactic providing (support).
Partners of the project are: Palacky university, Faculty of Science (Czechia); Univer-sity of Nicosia (Cyprus), University of Vienna, Faculty of Mathematics (Austria), University of Šiauliai, Natural Science Education Research Centre (Lithuania), University of Sunderland, Faculty of Education & Society (UK), Constantine the Philosopher University in Nitra, Faculty of Natural Science (Slovakia), University of Palermo, Faculty of Educational Studies (Italy).
During the project implementation it is expected to develop didactic materials in a real European context. There is a dire need to strengthen the learning of basic skills in mathematics and science by fostering and promoting collaboration among the teachers. There are at least three main activities: common lesson planning, collaborative projects and team-teaching.
Dissemination of project results will be very important for the partners. In all parti-cipating countries the knowledge and skills learned under the project will be distributed to all the target groups, for example, universities, students and teachers, schools.
All partners believe that the outputs of the project will be useful in all science te-acher training institutions in EU countries.

En general en nuestro país, y sobre todo en carreras científicotecnológicas, los docentes universitarios son profesionales expertos en los temas de sus materias, pero con escasa formación pedagógica. La misma habitualmente se impulsa a través de programas específicos organizados desde las instituciones. Otro modo de llevar adelante esta formación es de manera autogestionada, a partir de los intereses de los propios docentes. La Investigación-Acción es, precisamente, un proceso de indagación iniciado por los profesores a partir de la necesidad de comprender lo que acontece en su práctica docente cotidiana para mejorarla. Este trabajo relata cómo, a través de la Investigación-Acción,un grupo de docentes organiza su formación mediante la realización de seminarios, la selección de lecturas, la reflexión y el debate, indagando,así,sobre los sentidos de la evaluación en la Universidad y en los cursos de Matemática en los primeros años del trayecto universitario. De este modoredescubrimos ...