abstraction/application: These are complementary processes that should be learned together. Abstraction can be the simple categorization of concepts into larger categories and application can be simply applying the rules of a general category to a specific example. Many problems however require changing the form of the information at different levels of abstraction. This may be verbal to algebraic or there may be logical structures that are used. Table 2 lists some of the representational transitions that students might be expected to make. The instructor needs to be explicit about the need for these transitions and the value of multiple representations.
In Environmental Science much of the abstraction has to do with mathematics. Students are expected to develop an appreciation for the similarity of underlying processes by seeing the similarity in the mathematical descriptions of these processes. Then when they see a problem that deals with a certain set of concepts or a particular "form" they are expected to apply the mathematical approach to this problem. Learning to interact with information in this manner requires many examples and extensive practice.
The ability to make abstractions or to apply abstract processes to a problem is assumed to be taught in mathematics. I don't think the students learn this well enough in these courses that they can apply them in a separate discipline. This seems to be a major stumbling block for many students. I think this difficulty illustrates the different views of the structure of information between the students and the faculty. The faculty understand the structure of the problems in their discipline and try to teach the students that structure, which they see as how to apply the mathematics. The students never really learned the art of abstraction in their math courses. They were too busy learning the algebra, statistics or other content in those classes. The faculty need to construct activities that help the student
Abstraction
includes search, categorization, cues
General categories of problem solving
from other disciplines - traditional
is it a mathematics problem, a chemistry problem, etc.
did they learn how to do a similar problem in those courses
more general categories of problems
mathematics skills (arithmetic, algebra, geometry, calculator use, etc.)
statistics (statistical models, terminology)
information literacy (searching, stopping rule, decision)
presentation (writing, graphics, oral)
scientific method (many steps including logic and presentation)
modeling
analysis, synthesis and evaluation
policy analysis (economics,
social analsysis (
systems approach (box models, feedback, etc)
teaching advice
explicitly link concepts and tools from other disciplines
link to specific chapters in the text for the prerequisite courses
examples from one area, such as toxicity studies
LD50 - genetics (variability) - statistics (normal distribution)
acute dose - chemistry (concentration, flux, permeability) - biology and chemistry (reaction rates)
chronic dose - biology (cell biology of toxins, developmental biology)