Formal Reasoning and Academic Performance in College Mathematics and Psychology Courses

Article excerpt

This study examined the relationship between students ' levels of cognitive reasoning and their academic performance in college mathematics and psychology courses. We also analyzed students ' SAT scores, high school GPAs and college GPAs in relation to their levels of reasoning. The sample consisted of 163 college freshmen and sophomores who were classified as concrete, transitional, or formal reasoners using the Group Assessment of Logical Thinking (GALT). Using analysis of variance tests, we found that formal and transitional reasoners averaged significantly higher grades than concrete reasoners in the psychology classes, but not in the mathematics classes. Formal reasoners also averaged significantly higher SAT scores (both math and verbal) and college grade point averages than concrete reasoners.

College instructors generally assume that students are capable of engaging in higher cognitive processes such as analysis and critical thinking. These types of cognitive processes coincide with Piaget's concept of formal operational thought. In his theory of cognitive development, Piaget distinguished between two levels of logical thought called concrete operations and formal operations. Concrete reasoners can understand the logic involved in direct, observable experiences, but they are much less flexible than formal reasoners in dealing with systematic logic and abstract issues. In the more advanced level of logical thought, formal reasoners can engage in abstract thinking and hypothetical-- deductive reasoning. Piaget's theory supports the assumption that college students generally should be capable of reasoning at the level of formal operational thought, thereby demonstrating the cognitive abilities which are central to the college level learning that involves critical thinking and abstract reasoning.

However, several researchers report that many college students have not reached the level of formal operational reasoning, but are still characterized by either the concrete level of reasoning or a transitional level between concrete and formal thought (Berenson, Carter, & Norwood, 1992; Lawson, 1992; McKinnon & Renner, 1971). For example, McKinnon and Renner reported that their sample of 131 college freshmen consisted of 50% concrete, 25% transitional, and 25% formal reasoners. Berenson et al. reported that in a sample of 263 freshmen enrolled in remedial mathematics courses, 18% were concrete reasoners, 38% were transitional, and 44% were formal reasoners. Similarly, in a sample of 922 college freshmen, Lawson reported that 14% were classified as concrete, 47% as transitional, and 41 % as formal reasoners. These studies indicate that a large percentage of college freshmen and sophomores function below the formal level of reasoning. As Reyes & Capsel (1986) point out, we cannot assume that all college students are mature formal reasoners simply because of their chronological age. Although most texts describing Piaget's theory indicate that formal operational thought usually develops between the ages of 12 and 15, Piaget (1972) reported that formal operational thought may develop between the ages of 15 to 20 years, or it may possibly never develop in some individuals.

As college teachers, we are interested in the possible influence that students' levels of reasoning might have on their academic performance in college. Many researchers believe that students who cannot function at the formal level of thought experience more difficulty in successfully performing college work (Reyes & Capsel, 1986). Research studies conducted at the college level support the idea that students who do not demonstrate formal reasoning abilities experienced difficulties in mathematics and science courses (Bunce & Hutchinson, 1993; Niaz, 1989). For example, Niaz found that non-formal thinkers could not translate algebraic equations as effectively as formal thinkers. Bunce and Hutchinson found that a higher level of cognitive reasoning predicted success in college chemistry classes for non-science majors. …

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