Using the concept of stoichiometry we examined the ability of beginning college chemistry students to make connections among the molecular, symbolic, and graphical representations of chemical phenomena, as well as to conceptualize, visualize, and solve numerical problems. Students took a test designed to follow conceptual development; we then analyzed student responses and the connectivities of their responses, or the cognitive organization of the material or thinking patterns, applying knowledge space theory (KST). The results reveal that the students' logical frameworks of conceptual understanding were very weak and lacked an integrated understanding of some of the fundamental aspects of chemical reactivity. Analysis of response states indicates that the overall thinking patterns began with symbolic representations, moved to numerical problem solving, and then lastly to visualization: the acquisition of visualization skills comes later in the knowledge structure. The results strongly suggest the need for teaching approaches that help students integrate their knowledge by emphasizing the relationships between the different representations and presenting them concurrently during instruction. Also, the results indicate that KST is a useful tool for revealing various aspects of students' cognitive structure in chemistry and can be used as an assessment tool or as a pedagogical tool to address a number of student-learning issues.
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