Open Courses in PKP

PKP is an interesting webpage where to find open courses for researcher in early years. How to write?  How to publish? How to be an editor or a reviewer?


…In contrast complex systems are based on relationships, and their properties of self-organisation, interconnectedness, and evolution. They cannot be understood solely by simple or complex approaches to evidence, policy, planning and management. The metaphor that Glauberman and Zimmerman uses for complex system is like raising a child. Formulae have little application. Raising a child provides experience but do not assure success with the next. Every child is unique and must be understood as such.  Outcomes are uncertain. You can not separate the parts from the whole. The solution to problems most of the times emerge from within the family and involve values.  In complicated systems we can build their parts and then put them together in order to create the system. They are often engineered. Instead we cannot create a complex adaptive system (CAS) from scratch and expect to turn out just how we expected.

Research methodology

Thinking about trying to find answer to my RQ with a new methodology. In some way being original could be sorting out a new methodology.  As I am looking into a complex ecosystem of many particular cases, using lots of resources, acting and interacting influenced by their particular character and also with different teachers, it would be very much in favour of the research to look at the data with a complexity framework. Working in a social domain, not a scientific one.
Looking into the paperLeslye Kuhn (2008). Complexity and educational research. A critical reflexion. Educational Philosophy and Theory, Vol. 40, No. 1. doi: 10.1111/j.1469-5812.2007.00398.x. University of Western Sidney.

Complexity offers a way to envisaging and working with complex phenomena.
‘Nothing is without being in relation, and that every thing is the way that it is -in terms and virtue of rationality. The author is bringing to life a complexity approach to social inquiry.
Her usage, complexity constitutes an umbrella description under which researchers have grouped a set of new scientific theories sharing the idea that while certain phenomena appear to be chaotic or random, they are actually part of a larger coherent process (see also Wolfram, 2002; Kauffman, 1995).  So the particular case may seem chaotic but the general process which serves as an umbrella could be a coherent process.
Complexity has been brought to many fields, among them, education (Morin, 2001)
The nature of research:
A researcher seeks to be: Clearly focussed, rigorous, ethically defensible, and valid; research is never neutral and totally objective.
Underpinning our research are basic assumptions: What is the nature of reality? What can we know ? (ontology), How can we know it? (epistemology) . Beliefs, values and aspirations are also in this list.
If one believes that knowledge about the world can be objective, then research is taken as generating foundational knowledge.  Instead, if we take research as an activity done by socially interacting individuals employing various frames of reference that orient meaningful activity, research is constituted by discourse and embedded within it creating identifiable cultures of inquiry–> What is that?? 
She speaks of the quiet revolution of qualitative research.
She says: In contrast, in more recent years, (‘now’) it seems researchers: d) Identify the discourse with which they wish to place their research approach; e) Demonstrate coherence between their ontological, epistemological and axiological (values) assumptions; and, f) Take for granted the ‘primacy of practice’ (Ulrich, 1994), where the situation under investigation is taken as guiding the choice of research methodology/methods/ techniques, rather than a desire to attain and maintain methodological purity.
Doing so involves depth of thinking, whereby a number of significant questions may be asked: Why do I prefer these research conversations above others? What ethos or disposition do I champion? What form of life do I exemplify or contribute to?
Complexity offers metaphor that can explain or allow the researcher to make sense without being bound with linearity or certainty (Kuhn, 2005). The habit of thought desired in complexity includes a recognition of complex causality or more specifically an eco-auto-causality where autocausality means recursive causality in which the organising process elaborates the products, actions, and effects necessary for its creation or regeneration  (Morin, 1992, pp. 130–131).
In other words, complexity recognises a tightly bound, mutually inducing, pairing of cause and effect.
Cause and effect are mutually induced. ???  The nature of the world and sense-making are dynamic and emergent. Complexity depicts the world as self-organising , non linear, sensitive to initial conditions and influenced by many sets of rules.  Human evolution is radically unpredictable. Humans beings are depicted as self-referential and reflexive, and human enterprise as responsive and participatory.
Complexity and education can be brought together because educational endeavour are complex and dynamic. Individual human beings (students, teacher, administrators) various associations of individuals (School, universities, ed association) and human endeavour (ed. research) are multidimensional, non-linear, interconnected, far from equilibrium and unpredictable. A research methodology in an educational endeavour must acknowledge such complexity.
In 1871, E.B.Taylor defined culture or civilisation as the complex whole that includes knowledge, beliefs, art, moral, law custom and any other capabilities acquired by man as a member of a society.
A complexity view is that ‘in human beings, as in other living creatures, the whole is present within the parts; every cell of a multicellular organism contains the totality of its genetic patrimony, and society inasmuch as a whole is present within every individual in his language, knowledge, obligations and standards’ (Morin, 2001, p. 31).
In human beings the whole is present within the parts. Every cell contains the totality of its genetic patrimony. Society as a whole is present within every individual in his language, knowledge, obligations and standards.  GOOD IDEA!!!
Semetsky (2005): Not by breadth alone: imagining a self organising classroom.
She argues that no matter how the classroom functions, self-organising is the normal state of the affairs.
[…]To not confuse ‘is and ought’ would be to ask something like, ‘
If we conceive of a classroom as self-organising, how might we participate to promote better coherence between the self-organisation of the students and the aims of the educative institution?’.
Still to understand better and I think to look for more references.
Here is one to start with:  About the outdated Newtonian paradigm in education and complexity and a complexity science of learning: How far are we from a paradigm shift?

On the role of the history of mathematics in math education

In recent years, important works on the relationship between history and mathematics
education have appeared:
(a) The Proceedings of the “European Summer University on History and Epistemology in
Mathematics Education” (Montpellier, France, 1993, Braga, Portugal, 1996, and
Leuven/Louvain-la-Neuve, Belgium, 1999),
(b) Two books based on the elaboration of papers which were presented during the satellite  meetings of HPM (History and Pedagogy of Mathematics, one of the ICMI affiliated
international groups), the first edited by R. Calinger (MAA 1996), and the second edited
by V. Katz (MAA 2000),
(c) The ICMI Study book on “History in Mathematics Education”, edited by J. Fauvel and J.
van Maanen.
(d) Journals for Mathematics Teachers and/or Mathematics Education Researchers have
published special issues on the History of Mathematics in Mathematics Teaching (e.g. For
the Learning of Mathematics in 1991, Mathematics in school in 1998 and Mathematics
teacher in 2000). The re-born newsletter of HPM (International Study Group on the
Relations between History and Pedagogy of Mathematics) is becoming (we hope) a forum
where piece of information and ideas are shared.
These material and the experiments carried out all over the world make further discussion on the role of the History of Mathematics in Mathematics Teaching both possible and necessary. In recent discussions the expression “integration of History in Mathematics Teaching” appears frequently. Which ideas are behind this expression? The main idea is that of using History as a mediator to pursue the objectives of Mathematics Education. This means that, these objectives, together with the study of the historical evolution of concepts should be analysed. This work has to be carried out by educators and historians in a collaborative way. Among the benefits, which are expected to result from this work, is the new perspective offered by History to consider students’ difficulties in learning Mathematics. To make teacher active actors in this process we need to give a convenient place to the History of Mathematics in pre-service and in-service teacher education.
Read the article

Notes from Lawrence , SMaking Sense of Newtons’ Math

It was considered that some historical insight into the study of curves by Newton, his persistent attempts to ‘resolve problems by motion‘ and his study of the curves via the readings of Descartes and van (1615-1660), and their description of dynamic generation of curves was crucial to his later work on fluxions and subsequently his formulation of calculusImage