Chemical Education Today

JChemEd.chem.wisc.edu • Vol. 75 No. 7 July 1998 • Journal of Chemical Education 809

Introductory Students, Conceptual Understanding,and Algorithmic Success

by David B. Pushkin

Commentary

An article last year by Lin et al. (1) referred to researchon conceptual learners in general chemistry. In retrospect, twopoints need to be addressed: (1) the distinction between con-ceptual and algorithmic learning, and (2) the clarification ofthe “second tier student”. Until we can better rationalize thesepoints, we cannot truly understand the education process inchemistry and other physical sciences.

Conceptual versus Algorithmic Learning

Science education researchers indicate that many nov-ice learners in chemistry (2,3) and physics (4,5) are able toapply algorithms without significant conceptual understand-ing, a phenomenon independent of major. There are a num-ber of possible reasons for this:

1. Novice learners tend to be more declarative and pro-cedural in their knowledge orientation. By this, I meanthat novice learners tend to be very adept with arbi-trary facts and generalized algorithms. Rarely do nov-ices think in terms of integrated or applied knowledge.

2. Novice learners tend to be very dualistic in their think-ing regarding their role in the education process (6).To illustrate, I refer to the first two stages of WilliamPerry’s theory of adult cognitive development (7).Dualistic learners are very submissive in accepting whatthey are told by their instructors as unquestionedknowledge. Multiplistic learners will still accept thewords of their instructors but only under testing con-ditions. When a grade is not at stake, such thinkingreverts to whatever learners believe regardless of theof the instructor’s viewpoint.

3. Novice learners are subjected to science curricula andpedagogy that discourage critical and conceptual think-ing (8-10).

4. Those who teach introductory chemistry and physicsplace more value on algorithmic learning than on con-ceptual learning, giving learners the impression thatscience is “math in disguise”.

What essentially distinguishes conceptual learners fromalgorithmic ones is that the former are more advanced andless dualistic in their thinking, more experienced in problemsolving, more situational in their knowledge orientation, andmore verbal in their reasoning (6, 8, 11). By no means arethese dichotomous modes of thinking; conceptual learnersare clearly at the more evolved end of the spectrum of cogni-tive development. Conceptual learners are rarely unable tobe algorithmic. Perhaps this is because “conceptual problem–solving ability” (3) is a misnomer; science education research-ers often refer to “problems” in a quantitative context (4). Itis important to clarify items of conceptual thinking assess-ment as items of qualitative understanding. Does this meanthat such assessment items fail to encourage critical think-ing? Hardly; these items have much more potential to pro-

mote critical thinking than multi–step “plug–and–chug”problems. Algorithmic learners can master assessment itemsrequiring mimicking, regurgitation, and short–term memo-rization. They cannot, however, master assessment items re-quiring evaluation, comparison, and attribution skills. Suchassessment items would require long–term cognitive devel-opment where knowledge is genuinely stored, structured, andnetworked. Conceptual learners can master these types ofitems. They are capable of probing information and explain-ing the underlying reasons for their observations and con-clusions regarding scientific phenomena. They are capable ofrecognizing characteristics in novel situations and applyingrelevant prior knowledge. This happens primarily becauseconceptual learners evolve over a period of time from theirlearning experiences; their understanding is a manifestationof collected knowledge, not immediate knowledge. Concep-tual learning is an evolution beyond fundamental compe-tence. We can foster conceptual learning by providing stu-dents a variety of learning experiences and assessment items.A broad scope of exposure does not necessarily take away fromthe development of algorithmic skills; it can actually enhanceand strengthen those skills.

If we wish to encourage students to develop strong quali-tative and quantitative thinking skills (i.e., conceptual andalgorithmic), we should provide opportunities to demonstrateboth. For example, why not ask students to explain their rea-soning for solving a stoichiometry problem? Granted, therewill be students who can qualitatively explain but not calcu-late well. However, there will also be students who can cal-culate without the slightest clue as to why they are doing so,as well as students who can calculate and reasonably explain.As chemistry and physics educators, we would be surprisedby how many students through the years hated tests thatforced them to not use numbers and algorithms exclusively.However, when so many science departments place studentsaccording to their math placement tests—not to mentionSAT math or ACS test scores—it is no surprise that intro-ductory students walk away from courses with little if anyconceptual understanding (8). Traditional assessment is fo-cused too much on “nuts–and–bolts” content and too littleon “big picture” comprehension.

The “Second Tier Student”

It is my understanding from Sheila Tobias’s writings(9,10,12) that “second tier” students are capable of under-standing and succeeding in science, but their experiences inscience and math courses have been unsatisfactory. As a re-sult, these students either take the minimal science and mathrequirements of their degree programs, or they avoid scienceand math altogether. It is not a matter of whether they areconceptual or algorithmic learners; they are turned off by sci-

Chemical Education Today

810 Journal of Chemical Education • Vol. 75 No. 7 July 1998 • JChemEd.chem.wisc.edu

ence and math for two of the same reasons stated earlier: (1)Novice learners are subjected to science curricula and pedagogythat discourage critical and conceptual thinking; and (2) thosewho teach introductory chemistry and physics place more valueon algorithmic learning than on conceptual learning, thus giv-ing learners the impression that science is “math in disguise”.

The sad truth is that many science instructors fail tostimulate students in introductory courses. Perhaps it is dueto these instructors’ attitudes towards introductory coursesor nonmajors versus majors (13,14). Perhaps it is due to theirunresolved epistemologies regarding teaching and learning(8,15). If instructors fail to share the joy of science with stu-dents and project instead the themes of obedience and drudg-ery, students will be turned off, regardless of major and abil-ity level.

In my mind, “second tier” students need to have boththe qualitative and quantitative aspects of science in order toappreciate science and possibly develop a career interest init. The “first tier” students are those who master an appren-ticeship. Granted, they are the best students grade–wise, butthey may not be the best future scientists. Why do I say this?Students who master an apprenticeship neither learn to thinkindependently nor contingently; they are future profession-als needing to be led, as opposed to leading themselves (6,8).It is misleading to assume “second tier” students are inca-pable of being algorithmically successful; these students arecognitively intolerant of being exclusively algorithmic. In asense, “first tier” and “second tier” students are more a con-sequence of our curricula and pedagogy than their abilitiesor career interests.

Final Thoughts

Although specific data are still being collected (and I doteach a significant number of minority students), I wouldfind it difficult to believe that minority students are moreconceptual than algorithmic, since being a novice learnershould transcend race, ethnicity, or gender. There is consid-erable literature regarding novice learners in the physical sci-ences, research that should be redirected to address learnersin terms of experience and familiarity with science conceptsand problem–solving. The foundation for research should notbe how “good” students compare to “poor” ones; consider-ing common modes of assessment this is quite subjective and

suspect.Studies focusing on the cognitive development of mi-

nority students are to be admired, respected, and encouraged;they are long overdue. However, we need to have strong theo-retical frameworks to guide our studies. Minorities are notnecessarily a unique variable. They happen to be within alarger context as learners of science. Learner–focused studiescan be quite influential in the science and education com-munities, assuming the research scope is sufficiently broadand contextual.

Literature Cited

1. Lin, Q.; Kirsch, P.; Turner, R. J. Chem. Educ. 1996, 73, 1003.2. Nakhleh, M. B. J. Chem. Educ. 1993, 70, 52.3. Nakhleh, M. B.; Mitchell, R. C. J. Chem. Educ. 1993, 70, 190.4. Maloney, D. P. Handbook of Research on Science Teaching and

Learning; Gabel, D. L., Ed.; MacMillan: New York, 1994; pp327–354.

5. McMillan, C.; Swadener, M. J. Res. Sci. Teach. 1991, 28, 661.6. Pushkin, D. B. Teachers Says; Simon Says—Dualism in Science

Learning. On Our Own Recognizance: Students and Teachers Cre-ating Knowledge; Steinberg, S., Kincheloe, J., Eds.; Routledge Pub-lishers: New York, 1998; in press.

7. Perry, W. G. Forms of Intellectual and Ethical Development in theCollege Years, A Scheme; Holt, Rinehart, and Winston: New York,1970.

8. Pushkin, D. B. Post-Formal Thinking and Science Education:How and Why Do We Understand Concepts and Solve Prob-lems? Post-Formal Thinking: Questioning Educational Psychologyand the Education it Supports; Kincheloe, J., Ed.; Garland Pub-lishers: New York, 1998; in press.

9. Tobias, S. Revitalizing Undergraduate Science: Why Some ThingsWork and Most Don’t; Research Corporation: Tucson, AZ, 1992.

10. Tobias, S.; Tomizuka, C. T. Breaking the Science Barrier: How toExplore and Understand the Sciences; The College Board: New York,1992.

11. Pushkin, D. B. J. Coll. Sci. Teach. 1997, 26, 238.12. Tobias, S. They’re Not Dumb, They’re Different: Stalking the Sec-

ond Tier; Research Corporation: Tucson, AZ, 1990.13. Hoogstraten, C. Chem. Eng. News 1996, 74 (33), 66.14. Babcock, G. T. Chem. Eng. News 1996, 74 (40), 7.15. Pushkin, D. B. Chem. Eng. News 1996, 74 (40), 7.

Dave Pushkin teaches in the Department of Chemistry andBiochemistry, Montclair State University, Upper Montclair, NJ07043; phone: 973/655-7118; email: pushkin@pegasus.montclair.edu