In the school curriculum, mathematics is the object of education fully in its own right, but it is also a tool for the teaching of other subjects (or matter). In addition, the performance of students in mathematics plays an important role in enabling them to further their educational studies.
The distribution of class schedules between school subjects identifies certain ideological and pedagogical predetermined positions on the value or utility of each discipline. The important role played by mathematics in the curriculum, and the significant private tutoring, suggest that this discipline creates a strong social and academic consensus on its value and usefulness.
Thus, many researchers have tried to find the best place to improve the teaching of mathematics and / or other disciplines as part of a re-prioritization of the order of the spatio-temporal organization of courses in relation to their content and their epistemological value. In this sense Lenoir (1993, 1994) speaks of school interdisciplinarity. This interdisciplinarity works at teaching and curricular levels, and pedagogical interdisciplinarity is a result of prior interdisciplinary work being done at both levels. Even within academic interdisciplinarity, the risk of simplification, among other things related to the predominant empirical concern (and certainly legitimate for teachers, in order to save time and energy) as well as from ideological positions - prioritization of materials, for example , which strongly influence the conduct of primary school teachers (Lenoir, 1992) - have often led to considering the implementation of interdisciplinarity essentially in terms of pedagogical action, then forgetting that it is not independent of the teaching work and curricular structure.
However, the organization of courses in the school does not foster for students a knowledge's organisation into a coherent system for dealing with complexity. There is not enough interest in the relationship between disciplinary learning, and it is limited to the acquisition of knowledge at the technical and methodological levels, aimed at passing from one course to the next, or from one discipline to another .
In this context, the question that is often asked and repeated in various forms is "What use is mathematics?" This issue has generated a large field of research and studies in mathematics education on the relationship and impact of mathematical modeling and the development of other disciplines.
Moreover, Legendre (1993) points out that from the scientific level, where the interdisciplinary question was first developed, various ways of categorizing and prioritizing relationships between scientific disciplines have been produced from the identification of methodological links, such as languages of mathematics or cybernetics, theories such as psychogenetic study of the development of thought or systems theory, or, alternatively, from the objects themselves of the disciplines concerned.
At the Mathematics Education Research level, this issue followed from the famous question-invitation of Revuz (1980): "Is it possible to teach mathematics?” which led to the brilliance of Mathematics Education and has upgraded the importance of operational contact between mathematicians, teachers, psychologists, epistemologists and mathematics teachers at all levels, which is the core and the leitmotif of CIEAEM.
More recent researches highlight a particular way of teaching sciences through different disciplines in the prospect of promoting a cooperation of each disciplines, each of them carrying viewpoints on both the studied objects and the methodologies, while keeping the specific features of the subject. (Prieur et al., 2011, Aldon et al., 2012).
The educational institution finds itself today facing the very difficult problem of re- legitimizing its cognitive authority, its social responsibility, and pedagogic competence or teaching skills. The school must rethink its organization and content of its teaching, trying to gain the respect and attention of students and society. A formal convergence of science and technology has been promoted in many curricula since 2000 (associated with the development of skills (the 12 key skills in Europe, the American standards) and the current issue focuses on the how (Coquidé, 2008): how can the teacher grasp it and how can research help to develop or inform this?
In order to answer the previous question we must avoid the antagonism between different disciplines and realize the importance and requirement of working in a complementary way, and therefore to teach our students to work cooperatively, democratically and in an interdisciplinary way. Since 2000, the orientation of the curriculum of compulsory education has fallen within the development of scientific literacy for all (Robine, 2009), although, as pointed out byVan Haecht (1990), one of the main reasons for disciplinary curricula dominating in most schools and, thus, for integrated curricula existing only in a few schools, is as a result, at least partially, of the efforts to maximize the production of high status knowledge in the school system.
This great scientific and humanist project is joined byeducation research, taking as its object interdisciplinarity, including proposals for the space in which it is possible to construct it, taking into account the curriculum, the teaching practices that emerge, and the effects on student learning.
In this context, there is again the question of the usefulness of mathematics: how can mathematics interact with other disciplines to gain an understanding of a problem in several dimensions, seen as a complex phenomenon?
It may be a paradigm shift in science education that follows the change of the scientific landscape and its mixture with the human sciences, as well as new emerging disciplines such as bioinformatics, biophysics, ...
According to Le Moigne (2002) "... in these calls for interdisciplinarity and for research, education and human activities are expressed in two main streams, one focusing on methodological transfers from one discipline to another (known as "Pluri- ") , the other focusing on the socio-cultural legitimation of the knowledge produced and its producers (known as "Trans-" ) .
Moreover, according Resweber (2011), interdisciplinarity is part of a journey that involves upstream, the moment of the multidisciplinary and, downstream , the transdisciplinarity. Multi -, inter - and transdisciplinarity are not separate processes, but stages of the same process so that interdisciplinarity is the "middle" in the triple sense of the term: the spread or margin, the spacing or interval, and the happy medium aimed at in the interpretation
The problem thus of improving the teaching and learning of mathematics in this way does not arise in terms of utility or use of mathematics to other fields of human activity, but by the terms of complementarity and originality of mathematics in the context of a meaningful activity, or an interdisciplinary project in a scolarlydemocratic context of cooperation.
- What are the advantages and disadvantages entailed for mathematics in interdisciplinary approaches?
- What challenges does this raise for students and teachers?
- How can mathematics interact with other disciplines to support the understanding of a multi-dimensional problem, to see a complex phenomenon?
- Joint approaches of sciences and mathematics learning by experimental approaches
Gilles Aldon, Réjane Monod-Ansaldi & Michèle Prieur
Abstract : In inquiry based approaches in sciences, mathematics is usually present but often ignored or underestimated. Mathematical knowledge can be identified at different levels to allow teachers and students to become aware of the implementation of this knowledge in scientific work. Building on observations made under the project "Development of scientific culture, equal opportunities" in schools of the city of Dijon, we derive a typology characterizing the role of mathematics in science courses at different levels . We show through examples that it is possible to mobilize mathematical knowledge at various levels to conduct scientific approaches and give meaning to the mathematical knowledge mobilized.
- Deux savoirs en miroir : les procedés mathématiques et la langue latine en tant qu'exercice de la pensée
S. Attisano, L. Bisello, A. Boggio, A. Loiero, S. Rossi
Abstract: Our multidisciplinary experimentation, putting a scientific subject and a humanities one in front of each other, was born from the need of overcoming the "two cultures" prejudice, seeing them as separated, if not even antagonizing. Match the teaching of these two subjects was an attempt to develop logical processes, requisite both in the translation from latin to roman languages (specifically, italian language), and in the resolution of complex mathematical problems. The proving ground of this assumption was an atelier organized in the classroom, where students translated from medieval latin and solved some of the Propositiones ad acuendos juvenes, by Alcuino (IX century AC). What emerges is an "integrated" educational activity in which, as in classical paideia, all skills and arts concur to an individual's harmonic development.
- Analysing and construing mathematics containing designing activities in adults’ workplace competences
Lisa Björklund Boistrup1Lars Gustafsson
Abstract: In this proposal we describe a study within the theme of “Mathematics and its teaching in relation to other disciplines.” We present findings on mathematics containing activities in adults’ workplace competences. Our interest lies in a broad spectrum of aspects where mathematics is not viewed as possible to “obtain” in a pure sense but is interwoven and contextualised within workplace activities. We adopt a model where the institutional framing is emphasised: a learning design sequence (Selander, 2008). Coordinating with multimodal social semiotics, we have examined the video data and interviews with an interest in mathematical notions, interpersonal aspects, and the role of communicative resources including artefacts. In a previous study, adopting the same analytical framework, we introduced a theme on measuring which is here followed up when we present a construed theme within what Bishop (1988) labels designing: Forming as functionality and aesthetics (a tentative name). In this paper, we mainly present findings from analysis of data from a coachworks garage where a worker is fixing a bump on a car. We claim that the outcomes from our analyses hold affordances for school mathematics in general and for pre-vocational studies specifically.
- Boucles de rétroaction … à la recherche de traces efficaces et sensées.
Petronilla Bonissoni, Paolo Longoni, Gianstefano Riva, Ernesto Rottoli
Abstract: The relationship between mathematics and reality has always been a rich discussion of conflict and suggestions. In our presentation, after a brief reflection on some general aspects of this report, we focus on teaching. Leaving aside in education, the view, often dominant, only rigid mathematical, logical, abstract, lets see almost like an exciting dynamic body, which evolves continuously: a body which evolves its function of felt, which changes over time. This is especially true in the current period, where mathematics is crossed by a feeling of anxiety caused by the new challenges.
- Connecting mathematics to other disciplines as a meeting point for pre-service teachers
Javier Diez-Palomar, Joaquin Gimenez, Yuly Marsela Vanegas, Vicenç Font
Abstract: In this paper we introduce the case of a group of children being confronted to their previous conceptions about floatability. Mathematics emerges from their discussion with the teacher and the facilitators. Analysing this episode leads us to discuss with prospective teachers the challenges when connecting mathematics with other disciplines, as a modelling perspective (Garcia, Gascón, Ruiz & Bosch, 2006). We are also interested to see the possible changes on math teacher positions from Primary to Secondary School.
- Mathematics as Vocational Knowing: The Importance of Recontextualisation
Gail E. FitzSimons
Abstract: The teaching, learning, and doing of vocational mathematics at work offers a paradigmatic example relevant to the theme of “Mathematics and its teaching in relation to other disciplines.” I will draw on the work of Bernstein (2000) to theorise recontextualisation in vocational education in general, and vocational mathematics education in particular, and finally draw some implications for school mathematics.
- Modélisation et pratique scientifique en classe : défis, enjeux, exemples
Michèle Gandit, Christine Kazantsev, Hubert Proal, Dominique Spehner
Abstract: We propose a teacher education engineering about astronomy : the four largest satellites of Jupiter and the downgrading of Mars. The targeted audience are students in french « lycée » (15-16 years old) or students in preservice mathematical education of teachers. The main targeted competency is modeling real world situations. An important goal is to engage the students in making sense of mathematics (and physics) in a different framework.
- Ordinary differential equations and individual-based simulations to deal with the modelling of bacterial growth for use in diverse contexts
Marta Ginovart
Abstract: Investigation of bacterial growth provides excellent possibilities to combine laboratory exercises, mathematical modelling and model-based data analysis. The aim of the tasks designed focused on the representation, identification and analyses of the different phases (variations of the growth rate) in a bacterial growth (lag, acceleration, exponential, retardation, stationary and decline) by means of two modelling methodologies, ordinary differential equations and individual-based simulations. The students had the opportunity to investigate the growth of a bacterial population from two different perspectives, a continuous and deterministic model versus a discrete and stochastic model, which enriched the process of connecting mathematics with the study of life systems.
- Students’ expressed capabilities related to risk
Kjellrun Hiis Hauge
Abstract: Risks are intrinsic in modern society and are frequently debated. Decisions on risks are often based on risk assessments, where impacts of unfortunate events are quantified together with their probabilities. Such assessments give the impression of controlling the uncertainty of unpredictable futures, while simplifications and assumptions may turn assessments irrelevant for complex risk issues. Critical citizenship thus benefits from understanding characteristics of societal risks and of the associated mathematized assessments. In this paper I investigate students’ capabilities related to risk when 50 students in lower secondary school (14 year olds) discuss whether their local offshore area should be opened to petroleum exploitation. The students express insight in the conflicting values, in the complexity of the problem and that certain features of the future cannot be known or are associated with stochasticity and other uncertainty aspects. Although the students did not work with charts or quantified material, they demonstrated insights that are crucial for critical citizenship when facing quantified information on risk.
- Polysémie des concepts mathématiques utilisés dans les manuels de sciences
Corneille Kazadi
Abstract: This research presents an analysis of one of the seven books of sciences and technology approved by the Office of Didactic Materials Approval (BAMD) secondary. The objective of this study is to see in terms of interdisciplinarity if the concepts used simultaneously in sciences and technology in secondary have the same code meaning. From a methodological point of view, the analysis was made from a grid of conceptual analysis in terms of interdisciplinarity and concepts common to both disciplines. Partial results on the use of mathematical concepts in sciences and technology show that there are both convergence and divergence between the two basic disciplines through the polysemy of mathematical concepts. Some concrete examples of convergence and divergence taken from a sciences textbook and technology are presented.
- Teaching Hyperbolic Geometry through Drama and ICT.
Panagiota Kotarinou, Charoula Stathopoulou
Abstract: The present paper describes the experiences of 11th grade students gained through a teaching experiment regarding axiomatic definition of Hyperbolic Geometry through Poincaré model. We designed activities through ‘Drama in Education’ (DiE)1 techniques to stimulate the students, while we made use of ICT and ‘mathematical literature’ in order for them to understand the Poincaré model.
- Classe de mathématiques, réalité et communication
Luís Menezes, Véronique Delplancq, Graça Castanheira
Abstract: This study focuses on an inquiry-based teaching experience in mathematics, with 5th grade students in which we have established a strong connection with reality and intensified student’s ability to communicate, while promoting problem solving and mathematical reasoning. Mathematics lessons are organized into four phases: (i) Launching the task for students; (ii) Development of the task; (iii) Discussion of the task; and (iv) Systematization of mathematical learning. To prepare task discussion, the teacher implements a “gallery of tasks” through which students have their first contact with their colleague’s resolutions: they can ask questions and make comments in the presented sheets. This article presents the results of a lesson on percentages, in which students worked on the task entitled “Discount at Bit- @ - Byte”. The analysis of this task and the results of similar tasks of reality made throughout the school year shows that the inquiry-based teaching allows improvements in mathematics, namely learning concepts and capabilities such as reasoning, communication and problem solving.
- Critical learning in and between practices
Toril Eskeland Rangnes
Abstract: This paper explores learning taking place when 8th grade students (ca. 14 years old) are cooperating with a construction company with a purpose of learning mathematics. The study is performed in Norway. Working with mathematics in different school subjects or practices, such as school and enterprise, can make students conscious of similarities and differences between doing mathematics in different contexts. Students´ conversations are analysed and discussed in relation to Bakhtin’s dialogism. A finding indicates that learning in and between practices provides potential for pupils´ critical reflections in relation to how mathematics is performed in and outside school.