Abstract knowledge

Finally, this was a school that defined theoretical chemistry as a kind of chemistry (and a kind of science) that aimed at abstract knowledge in the purest sense. This science could not yet achieve the level of abstraction, or the level of prestige, of mathematics, but it was more free than other kinds of chemistry from practical ends and applications. 

As instructors of physical chemistry, we all too often hear comments like the one in the title of this chapter. The prevailing attitude with which many students approach physical chemistry is one of fear for their academic survival. The concerns they have are not so much with the chemistry but with the math. For some students, the physical chemistry course is the first time they must authentically apply advanced mathematical concepts to solve real problems. Instructors can facilitate this transformation with exercises that demand critical thinking skills, but developing such materials requires extensive time and talent. The Virtual Substance molecular dynamics program is a powerful tool in our efforts as educators to help students successfully transition from abstract knowledge of mathematics to its application to scientific concepts. 

Abstract Knowledge of the complex life cycle of Phaeocystis is a key to understanding its role in marine ecosystems and global biogeochemistry. An existing life cycle model was modified and used to integrate understanding of the Phaeocystis... 

The Task Level is where the formulation problemsolving activity takes place. The formulation process is driven via the generation of a hierarchy of tasks. A task represents some well-defined activity. The hierarchy has an indefinite number of task levels. Domain knowledge about the formulation application is distributed throughout the hierarchy, with more abstract knowledge represented towards the top of the hierarchy and more specific knowledge toward the bottom. 

A general pattern of encoding was apparent from the students responses. If students had abstract knowledge, they always seemed to use it in preference to giving example details. That is, their initial responses were generalizations, but when prompted for more information, they were usually able to provide example details to support their abstract descriptions. In contrast, several students described the situations only in terms of the examples. When prompted, they were unable to embellish their descriptions by using abstract characterizations. We recorded a number of instances in which the abstract information was followed by an example but never observed the opposite case of an example followed by abstract information. 

The statistical analyses suggest that the degree to which a student is able to use his or her abstract information is positively related to the student s success on the identification task. Those able to express mainly abstract knowledge apparently had the best understanding of the five concepts and were most easily able to identify them. Those for whom the abstract characterizations were somewhat incomplete (e.g., those who were able to give abstract description for some concepts but needed example details to describe others) performed less well but still were more successful than those who predominantly relied on example details. 

The primary instructional implication of these findings is that instruction should be developed to facilitate the linkage of abstract knowledge to easily understood example knowledge. The examples used in SPS were salient and easily encoded by almost all students. For some students, the abstract characterizations were equally easy to encode, but this was not true for everyone. 

An alternative argument takes the reverse position, namely, that the abstract information is encoded first and then is used subsequently to encode the example information. The possibility that this argument holds cannot be ruled out without additional experimentation. For this case, we would have to explain why students could readily provide details about the examples but were unable to articulate abstract knowledge, which they must have already encoded under this argument. Experiment II sheds additional light on this issue. 

Mediation of (abstract) knowledge based on the user s experiences (e.g., exploring a molecular structure)... 

AIMB is a type of expert system and so it has a knowledge base. This is a file of known 3-D structures (a library of X-ray crystal data and abstracted knowledge of X-ray data). There are also a 3-D graphical interface a problem analyser and decomposer an analogy finder an analogy (similarity) evaluator a model constructor and an explanation and next best model module. 

Library of X-Ray Crystal Compounds Abstracted Knowledge of X-Ray Data 3-D Graphical Interface Problem Analyser and Decomposer Analogy Finder Analogy (Similarity) Evaluator Model Assembler Explanation Facility Conformational Analysis Module... 

Conceptual inspiration in inventive conceptual designing is a process of acquiring knowledge from nature and transforming it into abstract knowledge useful for a large class of inventive problem. 

It is important to acknowledge that bodies of abstract knowledge originating in the social sciences, humanities, or business management typically do not exist in a form ready for easy and uncontroversial incorporation into the heart of formal engineering education. Faculty from liberal arts disciplines can be inflexible themselves, especially when they seek to reproduce themselves in students rather than to adapt modes of knowledge and practical reasoning to student trajectories. 

The paper has two main sections. The first section develops the distinction between abstract knowledge and cognitive skill in more detail, and provides evidence that the power of abstract knowledge cannot be captured in procedures. Developing a theory of abstract knowledge requires answers to the following five research questions ... 

What is the nature o/abstract knowledge What is a unit of abstract knowledge What different kinds of attract knowledge are there ... 

What is the function o/abstract knowledge If abstract knowledge does not consist of procedures, why is it useful How does stract knowledge interact with the performance system so as to facilitate and improve problem solving and learning ... 

How is abstract knowledge acquired When, under what mental circumstances, do people construct new concepts and principles ... 

What methods of task analysis are required to identify the abstract knowledge that underlies a particular cognitive skill What are the concepts and principles of any given subject matter topic ... 

What methods of cognitive diagnosis are required to track the acquisition of abstract knowledge How do we assess whether a student knows a particular concept or principle ... 

The issues involved in refuting these objections are deep and difficult, and a conclusive rebuttal cannot be attempted in this paper. The purpose of this subsection is to make the objections implausible by discussing examples that illustrate the power of abstract knowledge. 

---