If the classroom question asks for the number of rooms required to accommodate 30 students, then only by multiplying the equivalency (1 room/30 students) by the number of students can we get an answer in units of rooms. The answer to the question why one does not divide the 30 by 3000 is not because 0.010 doesn't make sense but because the question asked for the number of rooms and not rooms-'. The bie nroblem students face is not doing the math Gust as card& found with the classroom situation) but in conceptualizing what is being asked. The "simple" neon example is worded so poorly that many students could not conceptualize the situation let alone come u p with a value. ~ n i x ~ e r i e n c estudents d cannot read between those proverbial "lines" of a problem; nor should they have to. Students internret the verbaee of a nroblem literallv and, in the case of ~&dulla'sneon ekample, they are beinghctimized by the inabilitv of an author to write clearlv. How could a student a sliters? Aren't ever expect t o change 4.25 g of ~ L ~ into grams units of mass while liters are units of volume? We all "know" what the problem means, but why not propose it in a way so that students will know too? Why not write "what volume will he occupied by 4.25 g of Ne at STP"? The problem is not of comparable difficulty t o the classroom illustration because a larger numher of equivalencies needs to be recognized before it ran be solved: regardless, students familiar with the loeic of eouivalencien will have a basis of -attack. The final so1;tion is not, as Cardulla says i t is, first to divide 4.25 e of Ne bv 20.2 elm01 and then multiplv . . bv . 22.4 Llmol. hes solution Lnvolv& reexpressing 4.25 g of Ne as its eouivalent volume under the stated conditions. We do this by recognizing a sequence of equivalencies, one of which involves expressing 4.25 g Ne as an equivalent number of mol of Ne: 4.25 g Ne is equivalent t o (4.25 g Ne) (1 mol Nel20.2 g Ne). Note that 20.2 is the number of grams of Ne in one mol of Ne, not the number of grams per kol. Students learn that a t S T P 1mol of any ideal gas occupies a volume of 22.4 L. This fact can be used as an equivalency, assuming that Ne is ideal. Thus, (4.25 g Ne) (1 mol Nel20.2 g Ne) (22.4 L11 mol Ne) = 4.71 L. I t would he wonderful if we, as teachers, could take the time and had the resources t o instill in our students a feeling of familiarity with terms and units. Perhaps if "chemistry", with all its attendant trappings, were offered as a language starting in the early grades of elementary school this would be possible. Since we are, instead, obligated to present not only the language, hut the concepts as well, in an all-toobrief time, aren't we better off teaching students "coping skills" which have universal applicability rather than endeavoring to develop a familiarity with a very limited number of things which may or may not be useful in the long run? Let's concentrate on helping students develop confidence: the "gut feelings" will come in time. The significance of the material can be taught if the problems being worked are creatively written to illustrate situations that are meaningful to students. Through our own enthusiasm and constant reference t o well-written ~roblems,students will recognize the applicability of the chemical principles being taight. This will. in turn, make a temporary unfamiliarity with units for students, but not a stumbling point. a grumbling
1066
To the Editor: With all due respect, I believe Gillette has failed to understand the point I was trying to make in my article. Indeed, her own words can be ihteipreted as an argument against utilization of the factor-label approach. Gillette's comments in regard to the wording of the Ne problem are more or less correct, hut basically irrelevant. When nosine this nrohlem to students. wordines similar to ~ z e t t e ' sarz invkiahly used. We would never,-I hope, just ask students to "convert" erams of Ne into liters at STP. Yet, when one thinks ahouiit, that is exactly the approach we ask students to utilize when we teach them to solve this type of problem by the factor-label method. We may ask, "What volume is occupied by 4.25 g of Ne gas a t STP?,"but we present the "solu$on" as being simply a conversion of one unit into another. Never are they required to contemplate what is meant by terms such as 22.4 Llmol or 20.2 g/ mol. That's terribly unfortunate. All they have to do is set up "conversion factors" t o~ obtain the correct units for the an~ ~ ~ swer. Indeed, students may perhaps have t o take our physicallv meanineful wordine and change i t to "Convert 4.25 n of ~e "into 1ite;s" before tKey can hegin to apply the fact& label method with success. I think Gillette's comments in regard to the "students and rooms" nroblem are verv revealing and illustrative of an attitudeihat is not uncommon. s h e pedantically avers that rhe reason one divides 30 into 3000 is that the answer must be in rooms, not rooms-', as if no other thought could he valid. I can state, unequivocally, that no students in my 24 years of teaching have ever considered this analysis of dimensions as the "reason" they divided as they did. No, they divide the correct way because to do otherwise results in an answer that is nonsensical in the extreme, and that can see that. They do not require a lecture on "sequences of equivalencies" for this realization. Later Gilette says that the solution of the Ne problem is not first to divide 4.25 g of Ne by 20.2 glmol and then to multiply by 22.4 Llmol. Can she really believe that? There clearly are several ways one can solve that problem, and they are all valid. Her method is only one of them, and to assert otherwise borders on arrogance of the highest order. Yet I have found this to be a somewhat common posture among some factor-label enthusiasts. They have ohtained nossession of the Holv Grail. and thev are not about to hear that it may he only a paper cup. We all share the same Durnose as teachers. We want our students t o understand &d-love chemistry as we do. We differ in what we deem to be the best way of achieving this goal. I happen t o believe that the factor-label approach works against student understanding and that it is a pedantic, dry, boring, and unnecessary way to teach problem solving. Research done by Gahef and others suggests that my intuitive thoughts and feelings may he correct, although I hesitate to embrace findings such as these even when they may support my position. The situation is just too complex. Certainly one truth can be stated. There are other ways to teach prohlem solving, and they can produce competent, successful, and enthusiastic students. I happen to believe that these alternatives are not only possible, but superior. ~~
Marcia L. Glllette
Frank Cardulla
lndlsna Unlversiry at Kokamo 2300 S. Washmgon Street Kokomo. IN 46904
Nlles NwUl High Schwl Skakle. IL 60077
Journal of Chemical Education
