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5.4 Mathematics and computer science
Submitted by Kathy on Fri, 2009-07-31 22:04
Operational research: such as getting the optimal result through a way of organizing various resources. In a given learning situation, we might often face the task to get optimal result with considering the balance between local and global, or short-term and long-term situations.
Chaos theory (system theory): about the depth of relationship, the patterns of relationship if TIME is an important dimension (What contextual factors, emergent factors are related to success and failure? Can we find patterns through analyzing thick data as in data-warehousing and data-mining? ).
Data-base: about data-warehousing and data-mining, not only in collective research community, but also apply to each designer/teacher/learner
Data-structure: what are the diversities of data-structure in a learner’s mind and knowledge?
AI: Internalization, AI in reverse. Learners as tool-designers and tool-collaborators
See the following on my discussion of mathematics-thinking in my thesis:
From Zhao (2009, p.40-44)
Mathematics mode
If iconic thinking and story-telling work so well for me, what is the need for mathematical thinking? An example might explain the reason. The double roles as both designer and learner often confused me, and the confusion became worse when what I am learning happens to be ID knowledge and skills. In order to get out of this confusion, I thought of a folk song: once upon a time, there was a mountain; inside the mountain, there was a temple; inside the temple, there was an old monk; and the old monk said: once upon a time, there was a mountain……” To translate my situation into this folk song, it would be in this way: there is an instructional designer; this instructional designer is designing an instruction for herself; the goal of the instruction is to help her gain the expertise of instructional design; her approach is to design a performance system for the task of instructional design…..
Through this story-reasoning, my confusion was clarified somehow, but not completely. I then told my husband about this “old monk” thinking, my husband responded: “it is called recursive function in computer science, and it is frequently used”. I answered “Vow, you are so right, why didn’t I realize it”? Then my confusion could be totally clarified through this recursive function way.
Here is how I did it:
1. I define the function of instructional design as
ID (for whom, by whom, what, why, how, when, other variables)
2. Then, to assign value to the variables in this ID function for my project
For whom=myself as the learner=the ID practitioner who needs to update ID expertise
by whom=myself as the instructional designer=the ID practitioner who designs an ID solution
what=ID expertise
why=to gain ID expertise
how= through the recursive processes of designing and using an ID performance support system
3. Everything called ID in step 2, can potentially become another ID function. Before I go to deeper levels, my attention is focused on the current level, and once I am comfortable with the current level, then I consider deeper levels. In this way, my cognitive load is decreased, my role confusion is clarified, and I can distinguish the components that otherwise tend to entangle together.
My intention was not to define a precise function for representing the current project; instead, I used this function-defining as a way of thinking to clarify my own confusion.
Statistics is used in quantitative researches for understanding the relationship between variables. My knowledge of mathematics can help me understand and solve educational problems, in ways of meaningful to me. Thinking mathematically is similar to define a model with regularities, and to use the model benchmark my thinking and solving problems. Then I might examine, refine, and reconstruct the model according to the feedbacks.
This sounds similar to the process of attaching ideas to the cognitive structure, or the processes of accreting, tuning, and restructuring of schemata. Indeed, when trying to define a mathematical model, I am trying to identify variables and relationships. And the representations of these variables and the relationships constitute my comparatively stable cognitive structure or schemata. Without using the mathematical model, I might have the same cognitive structure or schemata; however, the difference is that I might lack the more explicit and systematic way of thinking about it.
One might argue that mathematics best represents well-structured problems, not ill-structured problems. I admit this point and define my mathematical models as semi-structured models. For the well-structured part, I believe there are regularities that are provisionally, commonly agreed by the members of a community. For example, most educational practitioners might agree that both cognitive and social factors are important for understanding learning. The function of learning then should at least include two variables: cognitive and social. This is the well-structured part.
For the ill-structured part, there might be unknown variables and relationships, or the understanding of these variables and relationship are far from reaching consensus by the members of a community, for example, the tension between meaningful reception learning and discovery learning might be an ill-structured component for explaining learning. Moreover, the diverse and dynamical nature of the world determines the ill-structured part too.
From my understanding, the general goal of conducting a research is to identify regularities. And this identification might experience qualitative and quantitative phases. If I take my personal learning as a research process, I should be able to borrow some elements from research methods, and to integrate these elements into my daily learning process. Posing and testing hypothesis is an important component of discovery learning and inquiry teaching; even novice researchers are expected to know something about testing hypothesis. As I extend my thoughts along this thread of thinking, I am amazed at the hints that I can get from research skills, and at the possibilities of relating these hints to learning strategies. For example, data collection, data analysis, and graphic representation through software such as SPSS all can give me some hints. I would stop this discussion here, and I am going to explore more beyond this project.
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