1 mode matrix file of the general model

Here is the matrix file of the general model, unfortunately it is in one-mode because when I tried to manipulate it in R, embarassing as it is to admit, I totally forgot basic data manipulation in R.

	adaptive system	course page	resource 1	resource 2	resource 3	concept 1	concept 2	concept 3	teacher	student
adaptive system	0	1	1	1	1	1	1	1	1	1
course page	1	0	1	1	1	0	0	0	1	1
resource 1	1	1	0	1	1	1	0	0	1	1
resource 2	1	1	1	0	1	0	1	0	1	1
resource 3	1	1	1	1	0	0	0	1	1	1
concept 1	1	0	1	0	0	0	1	1	1	1
concept 2	1	0	0	1	0	1	0	1	1	1
concept 3	1	0	0	0	1	1	1	0	1	1
teacher	1	1	1	1	1	1	1	1	0	1
student	1	1	1	1	1	1	1	1	1	0

Link to the matrix file in different formats (zipped 11.83 kb): http://www.mediafire.com/file/y2gynzzd2e2/genmodel_matrix.zip

Matrices of the general connectivist model of distance learning

by
Roel Cantada

The matrices of the general connectivist model of distance learning are composed of a 3-mode matrix and three 1-mode square matrices.

The 3-mode matrix is made up of the following 2-mode matrices:

1. actor x learning environment
2. actor x concept
3. learning environment x concept

The 1-mode square matrices are:

1. actor x actor
2. learning environment x learning environment
3. concept x concept

Since this is a signed network, these ties could take on negative values as well.

The network model can also factor attribute data with vectors (i.e. n x 1 matrices) that could be vizualized as partitions or sizes of nodes. These are represented in the graph as node properties in general. For example if the actor mode is made up of groups of students engaged in collaborative learning, then the individual students can be partitioned into their groups. There would be a vector of group numbers.

With this model, we can ask a lot of testable questions like, is there a correlation between the change in actor x learning environment ties with the change in the actor x concept ties? What is the probability that y can be known given x sub 1, x sub 2, x sub 3 ... x sub n precedent?

We can compare a learning network centered on an LMS with one centered on a wiki. We can compare the density or average degree of the personal network of one student with another. We could trace paths from start of the course to the end i.e. when goals are achieved, and compare the paths taken by different students to identify the most efficient path.

We can diagnose a misunderstanding by comparing concept networks, or using bayesian network analysis to seek factors that may have contributed to mistakes. We can prescribe better paths, better nodes based on adaptive techniques. User modeling can reside in the concept mode while the mechanisms will reside in the learning environment.

And we can ask all or one of these questions in the model and see the effect of it to the entire network. It is a holistic analysis.

My proposed general connectivist model of distance learning

by

Roel P. Cantada



Figure 1: General connectivist model of distance learning


The charactersitics of the network

1. 3-mode
2. multi-relational
3. signed
4. allows for arcs and edges
5. allows for timeslice generation

The model is not static but is dynamic. It must be modified depending on the data from real world observations. It can also be modified in time.

Relations

Figure 2: Student relations

Figure 3: Teacher relations

Figure 4: Adaptive system relations

I believe the model can be used to model precedent theories. It will generate similar and new testable hypotheses that relate variables from and across those theories. In other words I think this model synthesizes what has been done in earlier distance education theories.

But this is still a work-in-progress. There is a need to develop the mathematical analysis associated with this kind of network and restate past hypotheses in terms of these computations.

pajek data file (1.56 kb) : http://www.mediafire.com/file/dx5q0jgazhy/genmodel.zip

See this blog for application: http://paaralan.blogspot.com/2009/06/interpreting-transactional-distance.html

Interpreting transactional distance theory and guided didactic conversation in connectivist terms

by
Roel Cantada

In this paper I will attempt to interpret and visualize Moore's Transactional Distance Theory (TDT) and Holmberg's guided didactic conversation (GDC) through a connectivist perspective. My contention is that connectivism can explicate these precedent distance learning theories (probably with distortion) and may be the universal theory for open and distance learning.

Moore's TDT

Michael G. Moore proposed three concepts that are interrelated in TDT. They are briefly defined below:

1. Transactional Distance (TD) - a psychological and communication space that separates the learner and the teacher. It the space of potential misunderstanding between the inputs of instructor and those of the learner. Btw. transaction 'connotes the interplay among the environment, the individuals and the patterns of behaviors in a situation' (Boyd and Apps, as cited in Moore, 1997, p.22). For Moore, distance education is a transaction.
2. Dialogue - is purposeful, constructive and valued by each party. Each party in a dialogue is a respectful and active listener; each is a contributor, and builds on the contributions of the other party or parties....The direction of a dialogue in an educational relationship is towards the improved understanding of the student (Moore, p. 24).
3. Structure - expresses the rigidity or flexibility of the programme's educational objectives, teaching strategies, and evaluation methods It describes the extent to which an educational programme can accommodate or be responsive to each learner's individual needs (Moore, p. 26).
4. Learner autonomy - is the extent to which in the teaching/learning relationship, it is the learner rather than the teacher who determines the goals, the learning experiences, and the evaluation decisions of the learning programme (Moore, p. 31).

Structure and autonomy

Let me start with learner autonomy and and structure. These two concepts have been expressed as having an inverse relationship. And that "structure and autonomy can be further represented in relationships that define learner control and instructor control. (Saba, 2003, p.13)". IMHO learner control and instructor control are two states of the concept "locus of control".

How do we visualize this in connectivism? Connectivism in my simplest understanding is the pedagogy of links/connections. (For a better explanation see George Siemens' "Connectivism: A learning theory for the digital age"). So the control is over the links. If expressed in terms of Adaptive Navigation Support (Busilovsky, 2007), it is the ability to generate, remove, hide, sequence, and annotate links. Siemens himself does not negate the possibility of control when he said "Learning is a process that occurs within nebulous environments of shifting core elements – "not entirely" under the control of the individual. (Siemens, 2004) [my emphasis]". And true enough in a networked environment, we will find varying degrees of constraints to our ability to manipulate links. This is particularly true with Learning Management Systems, dubbed as "walled gardens", as oppose to open evironments like those espoused by "loosely coupled teaching" or the principle of "small pieces, loosely joined".

Currently, software developers had implemented the rules of constraints to linking in terms of role permissions. For instance, in Moodle, the student has no permission to create links in the course page. Only users with the role editing teachers, course editors, and administrators have those permissions. Of course the permissions can be changed by those who have permissions to grant permissions (usually the administrator).

To model the change in the locus of control over time in a system, I have graphed a closed learning network with three actors namely: a student, teacher and an adaptive system or machine. To simplify what I my illustration of a shifting control over the network in a turn-based manner, I have made the links static. But you can imagine that when an actor has grabbed control over the network of links then he/she/it can manipulate the nodes and links to her/his/it needs and wants. Turn based concept usually involve locking the resource being edited at the time by an actor, such that the other actors may not edit it at the same time.

The graphs below are multi-relational, 3-mode, signed graphs. The relations are color coded. Each relation (or set of links in one color) is owned by an actor. It can be interpreted as his/her personal learning space. But in this case, it is interpreted as power relations between actors, in relation to their learning environment, and the concept level. I have expressed the control as thicker lines.


Figure 1: Equalibrium (Time 0)

Figure 2: Time 1, Teacher has control

Figure 3: Time 2, Student has control

Figure 4: Time 3, Adaptive System has control



Figure 5: Animated video of turn-based passing of locus of control

The passing of control does not have to be turn-based at all. And it does not have to be control over the entire system. In an open environment, certain parts of the network are in the control of one person at the same time as other parts of the network are controlled by others. I will try to model this in another blog later on, as it could get very complicated. But you can think of let's say a student keeping a blog outside the LMS. It is connected to the LMS only via RSS but the teacher has no control over the blog.

When viewed this way, the term structure by Moore is not equivalent to structure in connectivism. Moore's structure is only a subset of many patterns of control over the network at different time period. It is equivalent to a structure that is NOT controlled by the student.

Control is usually described as control of sequencing the learning resources or links to the resources. This is expressed below as arcs in the learning environment level.

Figure 6a: No sequencing

Figure 6b: Sequencing by student and teacher

Fig.6b above shows that there is a contradiction between how the student sequence the resources and how the teacher sequence them. The teacher starts from resource 1 and ends with resource 3; but the student start from resource 3 and work backwards.

Control can also be expressed as control over the concepts themselves, especially when there is assessment of the personal conceptual network of the student.


Dialogue

Dialogue can be modelled as links between actors, or mediated by the learning environment. Take note that Moore's dialogue is always positive, which may not be the case when modelled here.

Figure 7: Dialogue between student and teacher

Distance

In my model of distance, I hooked on the concept of misunderstanding. IMHO misunderstanding occurs at the concept level. It is expressed here as the difference between the personal conceptual subnetwork of the learner and that of the teacher. Here are three possible interpretations of distance:

Figure 8: Distance 1

In Fig.8 the student has not linked the concepts, while the teacher has linked them. We may say that the student does not see any connection, may be confused, or is a beginner. But these are value statements. The graph does not state that the teacher's version is correct, and the student is wrong. It simply states that there is a difference between the coneptual network of student and teacher.

Figure 9. Distance 2

In Fig. 9 the student has linked concept 1 and concept 2 but not concept 3. Can we say then that this student has less distance with the teacher than that in Fig.8?

Figure 10. Distance 3

In Fig.10, the student has linked the concepts like the teacher, but negatively. We can interpret it as that the student thinks the concepts are contradictory, or conflicting. Definitely, the teacher and student are in disagreement.

In addition, if we go back to Fig. 6b you'll notice that there is no difference between the conceptual network of the student and the teacher, despite the fact that they sequenced the resources contradictorilly. Is this possible in real life? Only empirical data will show.

So in summary there are many patterns of interpreting transactional distance in connectivism. What excites me about this is that, it is a formal presentation wherein we can apply mathematical techniques. Although I still don't know what computational analysis is appropriate.

Using Pajek I was able to extract the individual relations from the network above. And here they are for clarity.

Figure 11: Student Control

Figure 12: Teacher Control

Figure 13: Adaptive System Control

Holmberg's Guided Didactic Conversation

Let me now turn to Borje Holmberg's theory. Unfortunately I've lost my reference while I'm typing this, so I will try to reconstruct what I remember about it. I belive it's a conversation of the student with himself as a reflection of content. It is therefore a relation between the student and the resources of the learning environment. But if we push back the time slice far enough, each resource will have an actor developer, author, etc. node associated with it. That is why I usually call these ghost nodes. But since the teacher in distance learning is also not physically present before the learner, is the teacher a ghost in the machine as well?

Anyway, I've modelled it below.

Figure 14: Guided Didactic Conversation in a Network

I interpret it as a process of increasing or decreasing the link property e.g. significance, usefulness, relevance, etc. between actor and the learning environment's resources. This is visualized as varying line weights and varying distances of nodes relative to the student node.


References

Brusilovsky, P. (2007). Adaptive navigation support. In P. Brusilovsky, A. Kobsa, & W. Nejdl (Eds.), The adaptive web, methods and strategies of web personalization. Springer, pp.263-290.

Moore, M. "Theory of transactional distance." In Keegan, D., ed. "Theoretical Principles of Distance Education (1997), Routledge, pp. 22-38.

Saba, F. (2003). Distance education theory, methodology, and epistemology: A pragmatic paradigm. In Moore, M.G., & Anderson, W.G. (eds.) Handbook of distance education. New Jersey: Lawrence Erlbaum.

Siemens, G. (2004). Connectivism: A learning theory for the digital age. Retrieved June 17, 2009 from http://www.elearnspace.org/Articles/connectivism.htm .

3 mode network modelling connectivist learning

Fig. 1: network from top

Seen from 2d on top doesn't show the different sets of nodes fully, but it does show it as partitions. But if spinned at 90 degrees we can see that there are at least three sets. The human actors e.g. teachers and students; the physical learning environment e.g. a course page and linked documents; and the concepts which could be ideas, processes, tasks, goals, beliefs etc.



Fig. 2: network at 90 degrees spin

Note also above that I consider the concept level as the level of abstraction that is used for student modelling, at least with an knowledge overlay method.

My problem with the method of analysis of this network is that a 2-mode network graphing already demands that "In a two-mode network, vertices are divided into two sets and vertices can only be related to vertices in the other set. (De Nooy, Mrvar, & Batagelj, 2005, p. 103)" and I have not yet found the methodology for k-node, or 3-node networks.

Ref:

De Nooy, W., Mrvar, A., & Batagelj, V. (2005). Exploratory network analysis with Pajek. Cambridge: Cambridge University.

My interpretation of ties in connectivist learning

by

Roel Cantada

My 3 week connectivist learning in a University of the Philippines Open University course on Research in Distance Education.






This is a research project I am trying to explore in this course. I conceive the ties between nodes in terms of the following. It's a scale from 1 to 5. The nodes can be actors, beliefs, digital resources and real world resources.

Here are example of my interpretation of ties between actors and resources.

• reads
• watches
• listens
• clicks on
• influenced by
• borrows ideas from
• learns from
• ignores
• denies ideas of
• reacts to (negatively/positively)
• affirms ideas
• changes perspective
• moves to action
• assimilates
• synthesize
• posts
• tags
• writes

Perhaps we could map this in Revised Bloom's Taxonomy of Educational Objectives which has the following items:

1. Remember - actor becomes aware of resource
2. Understand - actor reads resource and understands (there is no need to demonstrate the understanding since this is self-reported. This is the point when if asked "What is the resource about?" you can explain it."
3. Apply - actor uses the information in explaining existing phenomena or data without changing it. If the resource involves processes then he/she can follow instructions.
4. Analyze - breaks down the elements of the resource, including unwritten assumptions.
5. Evaluate - judges the resource as being relevant or irrelevant. Find errors in argument. Defends the resource position in a debate or argumentation.
6. Create - the actor is moved to do something after reading the resource. Either against or for the ideas of the resource. e.g. blog in favor or against the resource. Do research.

Ties between actors and goals

• states
• changes
• rejects

Ties between goals and resources

• supports
• denies
• related
• unrelated
• complements

My conceptual interpretation of connectivist learning using hypothetical data

by

Roel Cantada

The following is a descriptive-qualitative interpretation. Quantitative network analysis can be performed later on. I have not gotten the hang of that yet.

Fig. 1: Graph of Time 1 of hypothetical learning data

Fig. 1: Matrix of Time 1 data

Matrix one shows a student becoming aware of 4 resources (could be pdf readings, videos, etc.). But the student is only collecting the links and has not developed any connections among them, or to his own concepts/tasks.


Fig. 3: Graph of Time 2 data

Fig.4: Matrix of Time 2 data

The student has clustered the resources into two concepts. This clustering is similar to when we tag videos, or blogs. The tags serves as the conceptual category and becomes a hub for resources. Student 1 also found links among his/her resources. Notice here that the student is an independent learner.


Fig. 5: Graph of Time 3 data

Fig. 6: Matrix of Time 3 data

This is more complex. Student 1, with his concepts and resources, links to a course via forums and email. He/she has a teacher (Faculty-in-Charge or FIC) and another classmate (Student 2). Here student 1 becomes aware of the FIC's concept/task being taught. Student on the other hand is attracted to Student 1's concept 2 as well as the FIC. But the links here are still shallow at line weight of one.


Fig. 7: Graph of Time 4 data

Fig. 8: Matrix of Time 4 data

There is no difference between this matrix/graph and the preceding except line weights. The thicker line weights may be interpreted as more relevant resources, concepts etc. for particular students. Here Student 1 prefers his first concept and the associated resources (1 & 2), while Student 2 prefers the FIC's concept and therefore resources (5 & 6). We might interpret Student 1 as a more autonomous learner than student 2 at this point,but there could be other interpretations.

What is the significance of all this data to Adaptive Learning

The point here is that if we can quantify the lessons from all these data and find a pattern by comparing the partition of Student's or growth of their learning over time we will be able to identify resources that will optimize the learning in this domain. We can compare student's connectivist' learning and create user models or on task models from that. We can then feed this finding to an Adaptive Educational System (AES), such that when another student in the next semester goes through this course, the system can recommend the resources based on the type of student he/she is (e.g. student type 1 or student type 2). Or if the course is constructivist, then the concept nodes will be replaced by tasks or activities.

It's as if the AES recommendation system would be able to say to the student "Other students found this resource (provides link) useful to the concept/problem/tasks you are exploring. You may also want to check these other resources out." The student can then preview the recommendation and either reject or affirm it's relevance. This new data would then be fed into the system, and so on. This system therefore does not preclude the student or the teacher from recommending other tasks/problems/resources to their peers or students.

Here is the entire series animated:





Links:

Pajek - a program, for Windows, for analysis and visualization of large networks. It is is free for noncommercial use.

How to run Pajek on Linux - I ran this data on Pajek in Ubuntu Linux 64 without a hitch.

hypothetical data set (1.91 kb)