Abstract Reasoning | Quantitative Reasoning
An effective education should further students' ability to use analytical reasoning. Earlham's General Education Requirement in this area recognizes two distinct, though related, types of analytical reasoning: Abstract and Quantitative. While it is certainly desirable for students to improve their abilities in both types of reasoning, Earlham students take one course carrying a minimum of three credit hours, choosing from a list of designated classes in either Abstract or Quantitative Reasoning.
Abstract Reasoning — Students may fulfill the Analytical Reasoning Requirement through study in Abstract Reasoning by completing one course carrying a minimum of three semester hours of credit from a list of designated courses. Courses in Abstract Reasoning may fulfill other General Education requirements as well as major and minor requirements.
The ability to recognize patterns is a hallmark of nearly every aspect of human cognition. In the realm of human knowledge this characteristic is manifested as a process of generalization in which we form idealized models of the objects of our study. These abstract models, which suppress the detail that distinguishes individual instances of a class in favor of the properties that form its common structure, are what allow us to reason in the face of complexity.
Not surprisingly, then, the use of abstract models is a foundation of the analytic aspects of almost all areas of human knowledge. To a large degree, systematic knowledge in nearly every discipline is based on a body of abstract models; advances in these disciplines consist largely of extending existing models or constructing new ones. Experience both in working with abstract models and in understanding the process of abstraction is helpful in mastery of the theoretical aspects of every discipline and is critical for those who would work at the boundaries of our knowledge
While courses in Abstract Reasoning are intended, in part, to assure that students develop skill in applying abstract models, they go beyond that. These courses turn the process of abstraction on itself. They explore the common properties of abstract models and of the processes used in building and applying them. They provide experience in building abstract models from a collection of instances. In study within their individual disciplines students learn specific sets of abstract models and learn to apply them to the objects under study. In Abstract Reasoning courses, they learn to abstract models from those objects.
Courses qualifying for credit in Abstract Reasoning typically share these characteristics:
- They focus substantially on properties of classes of abstract models and operations that apply to them.
- They provide experience in generalizing from specific instances to appropriate classes of abstract models.
- They provide experience in solving concrete problems by a process of abstraction and manipulation at the abstract level. Typically this experience is provided by word problems which require students to formalize real-world problems in abstract terms, to solve them with techniques that apply at that abstract level, and to convert the solutions back into concrete results.
Quantitative Reasoning — One of the key forms of knowing in modern, technological society is that which comes through the use and critical evaluation of quantitative information. The ability to interpret such information is fundamental to effective and responsible decision making. Students may fulfill the Analytical Reasoning Requirement through study in Quantitative Reasoning by completing one course carrying a minimum of three semester hours of credit from a list of designated courses. Courses in Quantitative Reasoning may fulfill other General Education Requirements (e.g., Scientific Inquiry) as well as major and minor requirements.
General Education courses in Quantitative Reasoning foster students' abilities to generate, interpret and evaluate quantitative information. In particular, Quantitative Reasoning courses help students develop abilities in such areas as:
- Using and interpreting formulas, graphs and tables.
- Representing mathematical ideas symbolically, graphically, numerically and verbally.
- Using mathematical and statistical ideas to solve problems in a variety of contexts.
- Using simple models such as linear dependence, exponential growth or decay, or normal distribution.
- Understanding basic statistical ideas such as averages, variability and probability.
- Making estimates and checking the reasonableness of answers.
- Recognizing the limitations of mathematical and statistical methods.