Abstract
concepts that required hypothetical-deductive reasoning to understand. Written explanations giving the reasons for the responses to the ten formalconcept items were classified into five categories according to what information in the test questions was used and how it was applied to reach an explanation. Categorization Scheme The test item presented in the figure demonstrates the categorization scheme and operational level of the test items. To answer this question requires propositional logic, that is, the student must construct a system (hypothetical-deductive scheme) in which the relationship between concentration and diffusion provides logical clues for arriving at an implication that can be used to select the cell that will shrink in size. A concrete model of concentration can be constructed, provided the meaning of concentration is understood, by counting the relative number of dots found in each cell. By using this model to identify which cell has the least concentration of sugar inside and the relationship between concentration and diffusion, a correct prediction is possible. Formal thinkers concentrate their attention on relationships rather than what is being related. This type of mental functioning is possible because formal thinkers possess mental structure Piaget calls lattices. In addition, a valid explanation based on the relationship established is possible. The ability to follow the line of reasoning expressed here is expected of formal operational thinkers; therefore, this kind of test item was considered formal-operational. The explanations given by the biology students in our sample to the multiple-choice test items fell into the following categories. Category N: No explanation or statement-I guessed. Category I: Reasons in which the students used concrete data that did not apply to the question-for example, Because it is in the middle and Because sugar has a smaller structure than water. Category II: Reasons in which students used concrete data as proof of explanations rather than to draw an implication. The data given were related to the question asked-for example, Because the cell has the right numbers and Cell 1 has less sugar molecules. Category III: Reasons in which the students drew implications not tied to concrete data but did not specifically express the relationship between the concepts in which the implications were inferred. In placing student responses in this category, the question of whether or not the implications the examinee believed existed were correct was not considered. The only consideration given was whether or not the reasons inferred an implication not based on concrete information-for example, As the water moves out of the cell, its volume and size will shrink. Since there is not concrete (or visual) evidence from the diagrams that water moves out of the cell, the student had to infer this action. Category IV: Reasons in which the students verbalized a relationship between the concepts and drew an implication. The implication may have been incorrect because of faulty relationship between the data given, but the reasons were evidence that the students used a hypothetical-deductive scheme-for example, Only cell one has a smaller concentration inside. Water moves to a higher concentration, therefore cell one will shrink. Following the multiple-choice examination, the students were administered one Piagetian-type task, the separation of variables (Inhelder and Piaget 1958: 46-66). This task was used because it was considered to be less content oriented than some others (for example, the exclusion task which utilizes the simple pendulum), and not as likely to be influenced by prior knowledge of material contained in the task. In the separation-of-variables task, the student is asked to In the diagram below the dots represent sugar molecules in a water solution, and the sugar molecules cannot pass through the cell membranes. Which cell(s) will shrink
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