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5$5$5$uFuF4j5$5$5$Fm.m.m.m.$ d$ llllll"History and Mathematics Education, History and Physics Education, History and Chemistry Education: a particular international doctorate
Filippo Spagnolo
G.R.I.M. (Research Group on the Teaching of Mathematics), Department of Mathematics, University of Palermo, Via Archirafi 34, 90123 Palermo (Italy). HYPERLINK "http://math.unipa.it/~grim" http://math.unipa.it/~grim, Email: HYPERLINK "mailto:spagnolo@math.unipa.it" spagnolo@math.unipa.it
The Research Doctorate (PhD) in "History and Didactics of Mathematics, of Physics, and of Chemistry", at the University of Palermo, is offered in collaboration. The colleggio is composed of members of the following departments, who gather online. This international doctorate is offered between the following academic centres:
CIRE (Interdepartmental Educational Research Centres, University of Palermo)
Department of Mathematics and Mathematics Applications, University of Palermo
DIFTER (Department of Physics and Technologies), University of Palermo
Department of Inorganic and Analytical Chemistry, University of Palermo
Department of Mathematics (University of Bologna)
Department of Physics (University of Bologna)
Department of Chemistry (University of Bologna)
Department of Mathematics (University of Catania)
Department of Mathematics (University of Pavia)
Department of Algebra, Geometry and Mathematics Education (University of Bratislava, Slovak)
Department of Mathematics (University of Nitra, Slovak)
Department of Physical Sciences (University of Napoli, Federico II)
Department of innovation and Didactic Training (University of Alicante, Spain)
Department of Education (University of Cyprus)
The program is offered full time. The dottorandis, for which candidates receive a 50 % scholarship, precludes full time employment. There is generally a single supervisor; there can be two supervisors depending on the nature of the thesis and the expertise of the supervisor.
The involved discipline sectors
1. MAT/04 (Complementary Mathematics). This sector includes research competence related to foundations, history and didactics of mathematics, and also concerns the development of innovative teaching methods and technologies, as well as aspects of mathematics (complementary mathematics and elementary mathematics from a higher point of view) necessary for their treatment..
2. FIS/08 (Didactics and History of Physics). It includes the expertise necessary to study the history of physics, starting from the origins of physical ideas and those necessary to study the development of didactic methodologies. The expertises of this sector also concern historical, epistemological and didactical problems related to the foundations of classical and modern physics.
3. History and Chemistry Education. It includes the expertise necessary to study the history of chemistry, starting from the origins of chemistry ideas and those necessary to study the development of didactic methodologies.
The last 40 years of research in the field of history of Mathematics, of Physics and of Chemistry have contributed to deepen the bond between historicalepistemological paths of mathematical concepts that are correlated with several experimental works on learning / teaching situations.
Courses, Program, Seminars, workshops
COURSESSEMINARSWORKSHOPSVISITS ABROADPreliminary description of the courses programs and indication of the durationThematic indications, titles and anticipated or predictable timesI YEAR1) History and Epistemology of Mathematics and History and Epistemology of Physics or History and Epistemology of Chemistry;
2) Didactics of Mathematics end Didactics of Physics or Didactics of Chemistry;
3) History of Sciences.1) International research in Didactics of Mathematics (10 Days) or The International research in Didactics of Physics or The International research in Didactics of Chemistry .
2) Monographic courses of History of Mathematics (10 Days) or Monographic courses of History of Physics (10 Days) or Monographic courses of History of the Chemistry (10 Days).
3) Monographic courses of Epistemology (10 days).At least one per year regarding one of the themes treated in the courses.1 month (at least)II YEAR1) Computer technologies for scientific communication;
2) Philosophy of Sciences.1) Cognitive Sciences also from the point of view of Neurophysiology (10 Days)
2) Tools and methods for communication: the role of technologies. (10 Days)At least one per year regarding one of the themes treated in the courses.1 month (at least)III YEARLayout of the Doctorate Thesis.Seminars defined according to the subjects of the thesis: Cognitive Psychology, Experimental Pedagogy, Neurosciences etc (10 days).At least one per year regarding one of the themes treated in the courses.1 month (at least)
The Theory of Didactic Situations, the study of didactic obstacles, of epistemological obstacles, of misconceptions, etc regarding the single scientific concepts have allowed the understanding of well focused communicative tools that also represent today exportable results outside the scholastic world; for example, scientific popularization in general and museums communicative activity, etc Disciplinary communication represents today a basic element to be able to go beyond the boundaries of Science on one the side and to deepen the epistemological contributions on the other.
All the students follow the courses of History and Didactics of the Mathematics, History and Didactics of the Physics and History of the Chemistry. Actually to today never has any student of Chemistry participated and it is for this that courses of Didactics of the Chemistry are not activated, while the history of the chemistry is an obligatory course for everybody.
These courses concern the first year. The second year is more devoted to thematic seminars concerning the subject thesis of the students. The third year is devoted to the thesis.
Expected graduate destinations
PhD graduates in "History and Didactics of Mathematics, of Physics and of Chemistry" are prepared for the following occupations:
a) preparation of futures inspectors in the educational sector that deal with teaching / learning in training agencies.
b) preparation of researchers in the History and Didactics of Mathematics, of Physics and of Chemistry.
Such sectors include disciplines that are taught in Masters Degree in Education both for Primary and Secondary School.
Quality parameters
For a PhD student, to learn to write a research article, to know how to answer to the referees and to prepare referees to scientific articles of others is very important.
The Italian Ministry of the University asks, for every year of the PhD course, the scientific production of the single dottorandis.
Quality parameters are so defined by:
1) PhD students publications of articles in national and international journals;
2) Reports of experts involved in the project activities;
3) PhD students lectures in National Conferences;
4) PhD students lectures in International Conferences;
At the end of every year, PhD students and teachers who took part in the activities have to prepare an evaluation report.
The evaluation parameters regard the effectiveness of the seminars, the transferability of the experience to products of research, and the involvement of teachers and students.
The teaching staff establishes from year to year didactic activities according to the financial situation. We provide: online didactic activity, construction of a common web site, video conference meetings, online forums between students and teachers, publication of an online journal managed by the PhD students with scientific supervision by at least 2 members of the doctoral board.
The consortiums web site is established on the server of the Department of Mathematics, University of Palermo, managed by the GRIM (Research group in the teaching of Mathematics).
HYPERLINK "http://math.unipa.it/~grim/dott_HD_MphCh/dott_HD_index.htm" http://math.unipa.it/~grim/dott_HD_MphCh/dott_HD_index.htm
The meetings can be held in one of the University centres of the Consortium and also in video conference. We also provide online meetings with the college staff. Every meeting is then certified through signatures. For online meetings we draft minutes that are sent to all the other members of the consortium.
Doctoral thesis
Every PhD candidate presents a thesis that must be equipped with a report of the thesis advisor (assumption of thesis responsibility) and then certified at majority by the teaching staff.
The candidates, by mutual consent with his thesis advisor, present their theses to the teaching staff. The staff appoints a board of referees (at least 5) selected among members of the teaching staff but also outside according to the subject. The referees draft a maximum 3 page report with deadline fixed by the teaching staff. If three referees out of 5 express a completely negative judgement, the thesis cannot be discussed for the final examination. If the judgment is positive with only some remarks, the candidate will have to modify parts to address the referees observations. After these possible further corrections the thesis can be approved for discussion. There is no established limit regarding the number of pages of the thesis. The size of the thesis depends on the introduced hypotheses, on the methodology and on the way according to which the conclusions are deduced.
The staff appoints a board of at least 6 members (at most 2 not belonging to the staff) that will examine the final editing and judge the discussion of the thesis.
The students' origin
Each student can choose one specialization of the PhD course. After the courses of epistemology, methodology of research in didactics and history of the sciences (1 year) he/she directs his/her study toward the didactics of the discipline or the history of this (2 and 3 year). Naturally the students, since the first year of the study course, already have an oriented research project that they could also change in timetable.
The students can be graduated in Mathematics, Physics or other scientific disciplines.
We already are at the third year and, at the end of this year, we will have the first PhDs. The following chart synthesizes the actual situation.
Students XX Cycle
20052008 Students XXI Cycle
20062009Students XXII Cycle
200720101 History of Mathematics
2 Didactics of Mathematics
3 Didactics of Physics3 Didactics of Mathematics3 Didactics of Mathematics
2 Didactics of Physics3 Graduated in Mathematics
2 with Master Degree in Education for secondary school (age 1118) in Mathematics and Physics (2 years post graduate school) 1 Graduated in Mathematics
1 Graduated in Physics
1 Graduated in Economy
3 with Master Degree in Education for secondary school (age 1118) in Mathematics and Physics (2 years post graduate school)1 Graduated in Mathematics
3 Graduated in Physics
1 Graduated in Engineering
2 with Master Degree in Education for secondary school (age 1118) in Mathematics and Physics (2 years post graduate school)
Stable connections with other doctorates of the consortium
For the preparation of the PhD students the exchange with other experiences is very important. Besides the stages in other university structures, some stable connections can be servants. This happened with the doctorate in Mathematics Education of Slovakia.
Since 1999 there are connections with the University "Comenius" of Bratislava (Slovak Republic). Exchanges of students, in average a month long, have taken place. Theses have been presented and discussed in English until 2005 in Bratislava and those of Italian students are at the following web addresses:
HYPERLINK "http://math.unipa.it/~grim/tesi_it.htm" http://math.unipa.it/~grim/tesi_it.htm
PhD students research activities have also been documented by mathematics education research journals managed by the respective research groups:
Quaderni di Ricerca in Didattica (Mathematics Section):
HYPERLINK "http://math.unipa.it/~grim/menuquad.htm" http://math.unipa.it/~grim/menuquad.htm
Acta Didactica Universitatis Comeniae Mathematics :
HYPERLINK "http://www.ddm.fmph.uniba.sk/ADUC/index.html" http://www.ddm.fmph.uniba.sk/ADUC/index.html
Filippo Spagnolo is the Coordinator of the History and Mathematics Education, History and Physics Education, History and Chemistry Education Doctorate
The disciplinary sectors are those also recognized by the Italian university system.
For example: Matematiche Complementari (Code MAT04) is a disciplinary sector for Mathematics Education, History of Mathematics, Fundamenta of Mathematics, Mathematics Elementary; Code FIS08, Physics Education, History of Physics is another sector: etc
The Italian and German tradition of the "Elementary Mathematics from a higher point of view" go up again at the end of the 800. They also exist of the "Encyclopedias of the Elementary Mathematics from a higher superior point of view" of the beginnings of the '900.
In Italy there are inspectors of disciplines: inspector of mathematics and physics, etc... Currently the preparation of the inspectors is based on the epistemology and didactics of the dicipline.
For example, regional Institutes of educational research. In Italy there are institutes that have national and international contacts and they deal with the formation of the teachers in service.
PAGE
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