6.1 Elements related to Maple

Maple, by nature, is a professional working environment that has been applied in teaching mathematics; however, to make it a truly learning environment, some components are needed to be redesigned. 
From Zhao (2009, p28-32)
 
How have I chosen to work on this thesis-equivalent project?
My original choice of this thesis-equivalent project was on teaching mathematics assisted by Computer Algebra System (CAS), such as Maple. Choosing this topic originated from my intention of relating cognitive tools to mathematics education. I read two articles on cognitive tools, one is by Jonassen & Reeves (1996), and the other one is by Salomon (1988). I devoted great efforts to understanding these two articles. Salomon’s article is more difficult for me because I encountered great difficulty in understanding the concept of internalization. However, it is Salomon’s article that has eventually affected me more since I had to trace back to Vygotsky’s concept of internalization.
On the CAS topic, I read about two dozens of journal articles, and often one author stands in an opposite position from another one. Some articles focus on the potential use of CAS, others focus on the realistic problems encountered in practice. Most of these researchers hold an assumption by accepting whatever the CAS tool is.
 
However, the problem is: most CAS programs were originally designed for use in professional field, which means that the person who uses the CAS software knows mathematics. When trying to use CAS in learning mathematics, the learner needs to have some prior mathematics knowledge. I realized that it would be very difficult for CAS to play the role of cognitive tools as the one proposed by Salomon. CAS simply does not provide explicit operations, which is the necessary condition for a cognitive tool candidate; therefore a learner cannot internalize the intelligence from the cognitive tool (AI in reverse). If a CAS program can be re-designed to embed explicit operations, it might be able to achieve the goal of AI in reverse.
 
Although I did not achieve the goal of explaining CAS-assisted mathematics education by using the concept of AI in reverse, this experience brought me to somewhere. I frequently referred back to Driscoll’s textbook in order to understand various aspects of educational problems mentioned in the CAS journal articles and two cognitive tool articles. I re-interpreted my prior experience with new understanding through re-reading the book. This rewarding experience made me realize that, whatever the subject matter is, learning theories can explain learning in similar ways; there will not be great differences for explaining a mathematics learning problem, a second language learning problem, or any other learning problems.
Therefore, I had the idea of working on a project in helping me gain instructional design expertise. The concept of “AI in reverse” and “designer as learner” inspired my choice on the approach of gaining expertise through the recursive processes of designing, using, and evaluating an instructional design performance support system.
 
AI in reverse.
Salomon (1988) proposed that as computer software can simulate some human intelligence (which is artificial intelligence [AI]), under certain conditions, human beings can simulate some computer embedded intelligence too. This is called AI in reverse. Salomon justified his theory by using Vygotsky’s concept of Internalization. According to Vygotsky(1962), a child’s language development experiences two phases: interpersonal and intrapersonal, and the transition from inter to intra is called internalization. Salomon argued that while a learner works with a computer cognitive tool, at first, it is the inter-relationship between he and the intelligence embedded in the tool, then under certain conditions, the learner might internalize the intelligence, which becomes the intra-relationship between he and the intelligence. In other words, the learner has internalized the intelligence.
 
Salomon then further examined the conditions for a candidate cognitive tool: tool-like nature, relatively novel functions, compatible with the learner’s prior knowledge, and most importantly, the operations should be explicit. Only when the operations are explicit, can the learner interact with the intelligence explicitly and then eventually internalize it. In order for the internalization happens, the learner need engage in mindful-learning activities.
 
Designer as learner.
Jonassen and Reeves (1996) defined cognitive tools as "technologies, tangible or intangible, that enhance the cognitive power of human beings during thinking, problem solving, and learning"(p.693). They made a review on the use of a series of computer software as cognitive tools, such as computer programming language, database, and expert system. An expert system refers to a computer-based tool that simulates the intelligence of human experts; therefore, when one consults this system for decision making, this system acts as an expert. One might learn through designing an expert system, which is designer as learner.
 
In order to design an expert system, a learner needs to systematically identify and classify both declarative knowledge and procedural knowledge in the field; therefore, the learner access to the knowledge of a subject intensively and systematically. Since most expert systems consist of knowledge database, inference engine, and user interface, the learner needs to figure out the operating logic of the inference engine, which is certainly a very complex task. Designing expert systems is undoubtedly a great way of learning; however, a truly functional expert system is unbelievable complex, and difficult to design and develop. So, I decide to borrow some elements from expert systems, such as the systematical content and figuring out some operating logic.
 
The orientation towards systematic content could help me learn ID relevant concepts and tools as systematically as possible; I try to extend the possibility of “engaging in meaningful reception learning” into my after-formal-education daily practice.