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Letters to the Editor LETTERS TO THE EDITOR Letters are selected for their expected interest for our readers. Some letters are sent to reviewers for advice; some are accepted or declined by the editor without review. Letters must be brief and may be edited, subject to the author’s approval of significant changes. Although some comments on published articles and notes may be appropriate as letters, most such comments are reviewed according to a special procedure and appear, if accepted, in the Notes and Discussions section. ͑See the “Statement of Editorial Policy” at http://www.kzoo.edu/ajp/docs/edpolicy.html.͒ Running controversies among letter writers will not be published. COMMENT ON “SCHOOL MATH often derided by educators”͒. Reading turns out, is not dictated by research on BOOKS, NONSENSE, AND his letter, anyone with a stake in math- learning, but by the author’s expecta- THE NATIONAL SCIENCE ematics education would have to won- tions of how calculators should be FOUNDATION,” BY der what’s going on: how could 20+ used, how number facts should be DAVID KLEIN [AM. J. PHYS. 75 years of some of the best minds in memorized, and how standard algo- (2), 101–102 (2007)] mathematics and mathematics educa- rithms should be introduced.6 His criti- tion create products that are seemingly cism of an incorrect problem and solu- so disastrous? Why would the NSF, tion in a reform textbook is not How we understand the mind filled with scientifically literate and matched by a criticism of traditional matters… it matters for what mathematically fluent Ph.D.s, sponsor coursework and assessment. When we value in ourselves and what Klein terms the “gravy train of considering independent research, the others—for education, for re- education grants and awards that stifle evidence is unambiguously in favor of 7 search, for the way we set up competent mathematics education?” NSF-sponsored reform. human institutions, and most And how can we keep this from hap- So, instead, I want to address the important for what counts as pening in science education? question: “How can we keep this from a humane way to live and It does not make sense for me to happening in science education?” By act… Our ideas about what write a rebuttal to Klein’s editorial ad- “this” I do not mean misguided cur- ͑ people can learn and should dressing the first two questions; I am ricular reform for I trust that the grant- be learning, as well as what not in mathematics education, for one, and the peer-review process, together ͒ they should be doing with and it has been done—repeatedly—for with careful assessment, limits that , what they learn, depend on another. These rebuttals have come but the misunderstanding of high- our concept of learning it- from the mathematics education re- quality curricular reform, the failure to 3 self. It is important that we search community, from mathemati- treat this reform as a product of re- have discovered that learning cians with background and research in search on learning, and the ensuing po- 4 for the most part is neither education, and from cognitive scien- litical wars that limit the adoption of rote learning nor the learning tists who study how the brain learns effective curriculum and methods. 8 of mechanical procedures. It and understands mathematical Schoenfeld details how mathemat- 5 is important that we have concepts. These rebuttals cite inde- ics education got to this point and why discovered that rational pendent evidence, research from large the rhetoric surrounding mathematics thought goes well beyond the scale studies, use measures aligned education, such as that in Klein’s edi- literal and the mechanical. with the intent of the curricula, are torial, has moved so far from tradi- -Lakoff1 consistent with findings from cognitive tional academic discourse. This rheto- science, and describe the findings and ric is usually confined to letters to local In a recent editorial in the American goals that have shaped the NSF’s ap- school boards, newspapers, and the po- Journal of Physics,2 David Klein, a proach to mathematics education. litical arena9—places where we might mathematician, derides mathematics Klein’s editorial fails to do this: it wish for scientific rigor but, in the curricula sponsored by the NSF and focuses on superficial aspects of the name of free speech and the absence of the majority of mathematics education curriculum ͑noting that students are peer-review, we have become accus- research along with it. He cites ex- not told how to do “long division, sub- tomed to statements that generate more amples of theorems that are not explic- traction with borrowing, and the usual heat than light. However, when an edi- itly taught, formulas that are not pencil-and-paper methods of multipli- torial in AJP draws analogies between memorized, a lack of textbooks, on the cation,” but failing to address whether the skull-and-crossbones emblem on one hand, and an incorrect problem or not students learn to divide, sub- poison and the NSF logo on curricu- from one textbook that is provided. He tract, and multiply͒; when noting that lum, calling the textbooks “some of the states seemingly unreasonable stances TERC students are “two years behind worst...in the industrialized world,” it that guided the new materials ͑claim- where they should be” he cites a report seems that the physics education re- ing “the goal for students to achieve by the Fordham Foundation that he co- search community should begin to fluency in algebra and arithmetic was authored. “Where they should be,” it look more closely at how the physics 773 Am. J. Phys. 75 ͑9͒, September 2007 http://aapt.org/ajp © 2007 American Association of Physics Teachers 773 community at large understands and by data. But to the degree that we can sessment of our curriculum.12 But as supports work in education, and how engage in scientific debate, basing our physics education research broadens its we present our research and curricula curriculum on research and under- scope, builds on findings from cogni- in physics education, that this rhetoric standing the underlying values and tive science and psychology, and might not enter the physics education suppositions on which that curriculum comes to understand key elements of discourse. is based, we should. I would like to scientific thinking ͑e.g., attention to This concern is not unfounded: the encourage papers in physics education student expectations,13 epistemology,14 recent history of science education re- research to: and abilities12͒, I expect that the cur- form has had similar cries from scien- riculum we create, topics we teach, and ͑1͒ Take education research, methods, tists who, though well-intentioned, so research we conduct will begin to and findings seriously. Understand criticized the proposed science stan- move further away from traditional that, when done well, education re- dards for California and so clamored physics courses. Given the climate that 10 search is founded on a solid base for “higher” standards that now Cali- exists in mathematics education, where fornia fourth-grade students are to of cognitive science, psychology, shifting the emphasis towards reason- learn the very basics of magnetism and previous education research. ing becomes a battle cry that rallies op- ͑that magnets have a north and south We should neither write nor posi- ponents to rewrite well-researched cur- pole͒, of electromagnetism ͑that cur- tively review research articles that riculum and standards, we would do rents produce magnetic fields͒, all the do not commit to a broad under- well to enter this territory cautiously way through to the role of electromag- standing of previous research on and well-informed, and as openly and nets in motors and generators, and how learning and explicitly situate judiciously as we can. to construct them.11 Second graders themselves in this literature. ͑2͒ Careful research and strong evi- should “know the way to change how 1 dence should be made for educa- G. Lakoff, Women, Fire and Dangerous something is moving is by giving it a Things: What categories reveal about the push or a pull. The size of the change tional goals that differ from the mind ͑Univ. of Chicago, Chicago, IL, 1987͒. 2 is related to the strength, or the amount more easily assessed and more ob- D. Klein, “School math books, nonsense, and jectively defined “content” goals. the National Science Foundation,” Am. J. of force, of the push or pull.” Second ͑ ͒ ͑ ͒ Whenever possible, these goals Phys. 75 2 , 101–102 2007 . grade? Would that college students un- 3 E.g., J. Kilpatrick, W. G. Martin, and D. derstood that the change—not the and the rationale for and research Schifter, A Research Companion to Principles speed—is related to the strength of the behind them should be explicit. and Standards for School Mathematics ͑Na- Criticisms of reform curricula, tional Council of Teachers of Mathematics, force! What’s more, research in educa- ͒ ͑ therefore, should find fault in the Reston, VA, 2003 . In particular, the chapter tion and cognitive science suggests that by J. Hiebert, “What research says about the these standards are not achievable in a research that underlies the goals of NCTM Standards,” pp. 5–23.͒ 4 meaningful way by these students, at that curricula instead of critiquing E.g., A. H. Schoenfeld, “The math wars,” more superficial aspects ͑e.g., Educ. Policy 18͑1͒, 253–286 ͑2004͒ and ar- this age, in the amount of time avail- ticles by Rosenstein at http:// able and with the background knowl- “they have no textbooks” or “they dimacs.rutgers.edu/%7Ejoer/articlesm.html edge they bring.
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