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One of the difficulties that Colombian students face in order to access higher education lies in their low performance in primary and secondary education levels, in areas like writing and mathematics. This is demonstrated, for example, in the results reported from their exams on international (Report PISA ), national (Saber 11, ICFES ), and local (UN admissions exam) scales. The admissions exam for UN allows incoming students to be identified who need to strengthen their performance in areas of which UN offers leveling tests. In this context, I was invited by the DNIA, the DNPPr, and the Academic Vice-Rector of the UN, in order to design of a pedagogical proposal mediated by the use of ICT to support these leveling courses. The pedagogical proposal revolved around the implementation of an open educational practice, a type of “open teaching” (Chiappe, 2012), in order to promote the “empowerment of learners as co-producers on the road towards lifelong learning,” in other words, self-regulated or autonomous (Ehlers & Conole, 2010; Ehlers, 2011). In this document I describe the theoretical underpinnings and criteria that guided the design of each one of the components of this type of educational practice, namely: (a) a virtual site for the interaction between students, professors, and content in order to achieve the construction of a “Virtual Learning Community”; (b) the norms and rules of behavior to regulate the social relations of that community; (c) the instruments utilized in the interactive activities; and (d) the rules that establish the division of tasks in the same activity (Engeström, 1996; Cole & Engeström, 2001; Diaz Barriga, 2003; Onrubia, 2005; Coll, et al., 2008). The central axis of these components refers to the construction of a virtual learning community; therefore, the main objective of the project was to promote this construction. Faced with the potential offered by virtual learning communities, I wondered what and how does people, who decide to participate in them, learn. Some constructivist conceptions of human learning suggest that in VLC people participate to learn, learn by interacting with others, learn to understand and manifest understanding by performing cognitive performances such as: explaining, arguing, generalizing, applying, representing in a novel way, build, model, etc. Based on these conceptions, I set out to identify the potential of the VLC that I designed to strengthen the mathematical learning competencies of its participants. Thus, I analyzed the messages added by the participants in the virtual forums to characterize the processes of: a) participation, following the elements proposed by Hrastinski, (2008; 2009); b) interaction, from the community of inquiry approach (Garrison et al., 2010); c) mathematical learning, based on the basic standards of mathematical competences (MEN, 2006) and the ontosemiotic approach (Godino, 2017). I developed this research project using a mixed approach: the technique of content analysis and a combination of qualitative and quantitative methods. The proposed research design constitutes a significant contribution to the analysis of the mathematical learning achieved by the VLC participants, given its approach from different perspectives. Upon application, the following was revealed: On the one hand, the majority managed to: meet the criteria that characterize a participation in high quality virtual forums; weave an optimal network structure for interaction; show, in an authentic way, the skills and difficulties they have in communicating their ideas and learning with others; demonstrate good performance to correctly deal with mathematical concepts and to apply algorithms. Within the framework of this research, the importance of having expert moderators in guiding the discussions, from the side, was stressed in order to get VLC participants to develop high-level thoughts. Computing tools are also required to monitor and evaluate the discussion process in real time. In addition, it is essential to achieve the design of situations-generating problems of discussion and the implementation of an evaluation process that incorporates various sources and perspectives, to identify in a concrete and effective way the types of learning achieved. According to the above, it can be affirmed that the VLCs offer a high potential to strengthen the mathematical learning process of their participants, since in the debate zones you can easily observe the types of thoughts that they activate and put into operation when trying to find a solution to mathematical situations. This highlights the mathematical competences that each participant dominates and those that are difficult to understand, which makes it possible to develop targeted support strategies by teachers and moderators. The analysis of the mathematical learning of participants in virtual communities has not been sufficiently explored; In some cases, it has been limited to quantitatively reviewing the aggregate contributions in the discussion spaces, but a qualitative investigation of the discursive processes that demonstrate the concrete learning achievements has not been proposed, the combination of these two forms of analysis is one of the greatest contributions of this thesis.:Contents I. Introduction 13 a) How did I learn to learn? 13 b) How was my doctoral research project born? 17 c) Characteristics and purposes of the project 21 Theoretical Considerations 25 1 Chapter I: Human learning in community 25 1.1 Human learning from the constructivist perspective 25 1.2 The scope of learning 27 1.3 School learning from constructivism 29 1.4 Mathematical learning 31 1.5 Educational practices based on constructivism 39 1.6 How to define the notion of community? Contexts and debates 40 1.7 A definition of virtual learning community 45 1.8 Theoretical references for the design of virtual learning environments 53 Practical design considerations 61 2 Chapter II: Design Process of the Virtual Learning Community of Basic Mathematics 61 2.1 Academic activities carried out in the pre-project execution stage 61 2.2 First pilot test of the basic math virtual learning community design 64 2.2.1 Pedagogical Knowledge (PK) 65 2.2.2 Content Knowledge (CK) 65 2.2.3 Pedagogical Content Knowledge (PCK) 65 2.2.4 Technological knowledge (TK) 68 2.2.5 Technological Pedagogical Knowledge (TPK), Technological Content Knowledge (TCK) and Typology of uses of ICT 68 2.2.6 Rules for participation and feedback 73 2.2.7 Results obtained in the first pilot test offered by the basic math virtual learning community 76 2.3 Second pilot test of basic math virtual learning community design 76 2.3.1 Content Knowledge (CK) 77 2.3.2 Pedagogical Knowledge (PK) 77 2.3.3 Pedagogical Content Knowledge (PCK) 78 2.3.4 Technological knowledge (TK) 78 2.3.5 Technological Pedagogical Knowledge (TPK), Technological Content Knowledge (TCK) and Typology of uses of ICT 79 2.3.6 Norms or rules for participation and feedback 86 2.3.7 Results obtained in the second pilot test of the basic math virtual learning community 86 Methodological considerations 88 3 Chapter III: Final version of the virtual learning community offered 88 3.1 Characteristics of the website that hosted the virtual learning community 88 3.2 Human team that participated in the design process of the VLC, in its final version. 94 3.3 Activities that characterized the implementation of the Virtual Learning Community 95 3.3.1 Who was invited to participate and in what context was this invitation made? 95 3.3.2 What evaluation agreements were generated? 96 3.3.3 What academic units were offered? 96 3.3.4 What activities were carried out to promote the effective participation of students in the virtual learning community? 96 3.4 Global map of the Virtual Learning Community offered. Final version. 98 3.4.1 Pedagogical conceptions that support open educational practices, of the 'open teaching' type 99 3.4.2 Connections between technological, pedagogical and content knowledge. 104 3.4.3 Key elements for the design of Virtual Learning Communities (VLC). 111 3.4.4 Dynamics that characterized the VLC offered, in its final version. 113 4 Chapter IV: Research Design 116 4.1 Mixed approach on educational research 116 4.2 Research questions 120 4.3 Analysis of online participation 120 4.4 Analysis of online interaction 127 4.5 Analysis of mathematical learning 132 Empirical Findings and Discussion 148 5 Chapter V: Research data and process of analysis 148 5.1 Collection and selection of data 148 5.2 Structural Analysis 149 5.2.1 First research question about the online participation 149 5.3 Content Analysis 154 5.3.1 Second research question about the online interaction 154 5.3.2 Third research question about the mathematical learning 165 5.3.3 Analysis based on the basic standards of mathematical competences 166 5.3.4 Analysis based on the ontosemiotic approach 169 6 Chapter VI: Results of data analysis and discussion of results 176 6.1 Structural analysis results 176 6.1.1 Online participation 176 6.2 Results of content analysis 194 6.2.1 Online interaction 194 6.2.2 Mathematical Learning 221 6.3 Review of results and conclusions 285 6.3.1 Results and discussion 285 6.3.2 Conclusions 301 7 References 307 8 Annexes 325 |
