Quantitative problem-solving is a challenging aspect of any physical science course. Traditionally, students have been encouraged to pursue various techniques in an effort to provide structure to this task. While such methods may help students to generate numerical answers, they can become exercises in symbol manipulation that leave the student without a clear picture of the physical situation associated with the problem. This paper describes the efforts of a group of teachers to help college freshman chemistry students and high school science students to improve their problem-solving skills. The presentation includes several sets of questions intended to elucidate ideas and to involve the reader in the process of reflecting upon his or her own problem-solving strategies.

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This paper summarizes difficulties that chemistry students at all levels commonly exhibit when translating, manipulating, and interpreting mathematical expressions that contain logarithms, and offers approaches that the authors have found useful to help students overcome such difficulties. The online supplement provides problem sets created by the authors, based on student–instructor interactions that have taken place during many classes, help sessions, and laboratories. They range in level of difficulty from those appropriate for high school and first-year college students, to those appropriate for more advanced students.

The concept of gravitational mass is usually introduced to chemistry students as a measure of the amount of matter in a given object. Although this definition can be useful as a starting point for quantitative investigations in chemistry, it does not refer explicitly to the direct experimental observations upon which the concept is actually based. This traditional approach also misses an opportunity to help students connect observations in the see-touch world with inferences about the atomic realm, and may contribute to the incomplete understanding exhibited by many high school and first-year college students of mass and other fundamental concepts, like weight and density. This paper presents a Socratic dialog between a hypothetical instructor and student, which uses experimental evidence and operational definitions to introduce these concepts. The student's responses are based on those of many individuals in a college freshman chemistry course, and point out the difficulties associated with learning the concepts. The question sequence has evolved to its current form based on student feedback obtained over the course of several years. A theoretical basis for this type of instruction is discussed, as well as the benefits and challenges associated with its application to this particular material.

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