Chemical educators have often assumed that success in solving mathematical problems should indicate mastery of a chemical concept. To this end, we have developed algorithms. However, Nurrenbern and Piekering (1) and Pick-ering (2) found little connection between solving an algo-rithmically-based problem and understanding the chemical concept behind that problem. Sawrey (3) further supported Nurrenbern and Pickering's findings. These studies quantitatively evaluated success in solving a conceptual problem versus a similar algorithmic problem. These studies found that many students could not use chemical concepts to solve conceptual problems. These findings were further supported by Nakhleh (4). Nakhleh found that across all levels of first-year chemistry students (from remedial to honors) conceptual problem solving ability lagged far behind algorithmic problem-solving ability. She determined through the use of paired exam questions, that a sizable percentage (31% in that sample) of our firsbyear students are low conceptualhigh algorithmic students; students adept a t solving problems with algebraic equations, hut having only limited understanding of the chemistry behind their algorithmic manipulations. In the present study our objective was to ascertain what students do think about when they solve conceptual and algorithmic problems and to determine further if there are differences andlor preferences in their approach to each. We. therefore. used aired exam auestions on rras laws to select studentsfor interviews. In tke interviewwe probed their conce~tual understandinrr and their ~roblem solvine in detail. w e tried to determhe how the' students weni about solving a conceptual problem versus an algorithmic problem. We also endeavored to probe their preferences for solving either type of problem. Method Our sample consisted of 60 freshmen chemistry students who were all enrolled in the same introductory course for declared chemistry majors. No other majors were represented in this sample. The professor for the course used a traditional problem-oriented lecture approach. This study was completed in two parts. The first part of the study used the paired questions technique to identify students as being either conceptual or algorithmic problem solvers. Two problems-one conceptual gas law problem and one algorithmic gas law problem-were placed on the third exam in the course where gas laws were being examined. Success or failure on these were recorded and students were grouped in one of four categories: High AleorithmiJHirrh Conce~tual (answerine both ~ m b l e m s coFrectly,; ~ i ~ t ~ l ~ o r i t h m i r / ~ o w ~once&al (&swering the conceptual prohlem incorrectly J; Low AlgorithmiJHigh Conceptual (answering the algorithmic problem incor-rwtlv); Low AleorithmidLow Conce~tual (answering nei-Problem I. The following diagram represents a cross-sectional area of a rigid sealed steel tank filled with hydrogen gas at 20 ' C and 3 atm pressure. The dots represent the distribution of all the hydrogen molecules in the tank....

Are there two kinds of students, some who possess an ability to do conceptual problems and some who can do mathematical problems without molecular understanding?

No abstract

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Several studies have identified the score on the math SAT as the best predictor of subsequent performance in freshman chemistry courses2-4, but what predicts success in organic chemistry, and how well does freshman chemistry predict grades in other science courses and success in entering medical school? We have tried to answer these questions by following a group of students through their four years at Columbia University and correlating various measures of their performance. MethodGrades and SAT data were obtained for all 254 freshmen enrolling in freshman chemistry at Columbia College, the all-male undergraduate division of Columbia University, in the fall of 1978, The overwhelming majority of these students are premed since engineers enroll in the School of Engineering from the beginning and only a tiny minority goes on in pure science. Few freshmen take biology or physics concurrently with freshman chemistry because of Columbia's other requirements.The raw grade data were converted to a numerical scale (A+ = 13, A = 12,... F = 0) and in all cases were "corrected" by subtracting the course mean. Thus a student who obtained a grade of B in a course with a mean of 8.19 would have a corrected grade of 9 -8.19 = +0.81. This corrects for differences in course means between years and between departments.