Personal learning environment and the learning of mathematics. Possibility or reality?

E-DynamicSpace with no frame
I have participated in a conference organised in Belgrade by Singidunum University. They are oriented towards business and the conference mainly approached themes about the impact of the Internet on business activities in Serbia. They  have plans to broaden their offer and include educational studies. So for this conference they invited speakers and papers that relate education and the Internet, which is my case. My interest lies in between these two areas.  I am looking at how can the affordances of digital technologies be explored and exploited by teacher-students (prospective teachers)  in the learning of mathematics. Is a personal learning environment an effective and powerful tool to stage-manage the learning/teaching experience of teacher-students and build experience in the field? If the hypothetical answer is yes, why is it so and how should this space be conceived? What are some features such a space should have?
In the time I have been working in this -for now only theoretically prototype idea-  I have changed the RME for just an E.  It is now EDynamicSpace (E stands for empty, as this space starts as an empty workbench for teacher-students which will be filled with their work, ideas, knowledge artefacts, tools and all what for them is needed to process and learn mathematics through its history and the ignitors for the work are teacher-student questions.
So it starts as an empty place and it will end as the imagination and curiosity of each user will take them.
More details of my idea in this paper which is online in the conference site:

The role of theory in educational research. I part

Notes from my readings on: The Routledge Doctoral Student’s Companion. Pat Thomson and Melanie Walker. 2010
Chapter 2: Ignorance in educational research
Theory in research problematise, critiques, challenges and complexifies. It allows you to challenge taken-for-granted orthodoxies and it opens up the space to understand the social conditions for the production of knowledge.
It helps us to find concepts that frame our study, to analyse it, interpret it and reflect.
We must be capable to locate our selves with confidence within a theoretical landscape appropriate to the study. Through concepts we come to know what we are looking for and what we are looking at. There are signposts that show us where to go in a crossroad or in the middle of the vastness of an empty landscape. They tell us how to get where we are aiming to.
The search to understand requires solid conceptual work and conceptual mediation in communicating ideas and understanding to different audiences. The researcher must construct their own frameworks in the early stages of the study. Methodology shall grow out of this theory and conceptualisation. It is important to understand the pragmatic contexts in which knowledge can be defined as new.
The different materials a researcher grabs in order to construct new knowledge varies from data of various forms and types, direct experience, concepts, theories of their own, or those developed by others, etc. All these materials help researchers to answer questions they have already considered, already familiar to them -blank spots- in emergent theories and conceptions of knowledge, or to consider questions they haven’t considered before -blind spots-. 
What could be the characteristic configuration of the blind or blank spots?
Thomas Kuhn (1970), represented this structure like a disciplinary matrix. Rows represent concepts or methods of investigation, the columns phenomena that members of the discipline tend to examine. Such a matrix defines sets of related cells, each corresponding to the intersection of a particular concept or method and and a particular object of investigation.
Matrix of sociology inquiry

Phenomena under investigation
Themes of analysis Jobs + work Sociology of education Sociology of religion Medical sociology Political
  • Social control
  • Social stratification
  • Status attainment
  • Bases of integration and
    differentiation: class,
    gender, race
  • Social relationships: groups,
    household, community
  • Social change

The other option would be changing the phenomena under investigation to a school context. That would mean being the phenomena the lesson, the classroom, the schools, the school district and communities, the state.
Blank spot ignorance corresponds to cells of the sub-matrix (the second one) that are visible, clearly marked, but have not been investigated as adequately as scholars would like. Blind spot ignorance  corresponds to matters that don’t fit anywhere on the grid. The concepts or phenomena they implicate are not so much missing from cells where we think they should belong, but obscured by the matrix itself.
It is important THE WAY TO LOOK AT A PHENOMENA ??? Don’t understand what means the way, Is it maybe regarding if I see the classroom (student population) as a whole instead of seeing at the student as an individual in individual classes. If you ask questions to different schools and not to different classrooms you may make some differences invisible. Instead if you ask about classrooms within schools then you may find some differences in outcomes.
Well defined blind spots or blank spots can provide a map that helps the researcher to stay on track. Even when all the blanks are covered the disciplinary rows can still create opportunities for generating new knowledge. The stimulus required can be as simple as renaming a row or a column, or merging a pair of cells or as complex as adding a row or a columns from the matrix of another discipline. An example is the new knowledge regarding ‘social context for learning’ within the educational profession.
Knowledge about ignorance: It is far more better to talk about reducing ignorance than to pursue new knowledge. The same research methods, criteria for evaluating evidence, and logic of argumentation or exposition can apply within either perspective. Weather people, researcher, students regard something as new knowledge depends on what the person already knows about the subject. Do the propositions help to fill in a gap blank spot or reveal a blind spot in current theories of doctoral education?
An interesting paragraph that summarises a research speech:
“So what does this mean? It is definitely a compelling argument, but is there empirical evidence to substantiate what would otherwise remain as an unwarranted claim? If evidence is wanting, then how can we best translate the proposition into testable hypotheses, (ii) apply an effective research design, (iv) develop appropriate sampling and data collection procedures, preferably random and N>200, so that we can (v) conducto rigorous statistical analysis of the data, preferably using the “definite” causal modelling techniques to achieve the highest levels of confidence and reliability and validity? ”
Important to consider as a researcher: To have a a master of well-crafted arguments supported by good data (qualitative or quatitative).
Important to have a position and a bunch of concept in order to do research, that will shape the research object.