LETTERS TO THE EDITOR

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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. That is to say, students aren’t using calculators”͒. 5 R. Núñez, “Mathematical idea analysis: What might be able to memorize these state- ͑3͒ Understand the limits of research embodied cognitive science can say about the in assessing curricula. In physics, human nature of mathematics,” opening ple- ments, but they will not be able to nary address in Proceedings of the 24th Inter- make sense of them, they will not un- if two ideas are different, one of national Conference for the Psychology of derstand the development of the ideas them is wrong. Education research Mathematics Education, Hiroshima, Japan, is another matter entirely. Not only Vol. 1, pp. 3–22. nor be able to reason creatively and 6 are goals hard to determine and D. Klein, B. J. Braams, T. Parker, W. Quirk, flexibly using these ideas. Students are W. Schmid, W. S. Wilson, C. E. Finn, Jr., J. destined for failure, teachers are frus- harder still to assess, but determin- Torres, L. Braden, and R. A. Raimi, “The trated by another round of reforms, and ing those goals is a value-laden en- State of Math Standards 2005,” from http:// those who added more “rigor” to the terprise involving a setting of pri- www.edexcellence.net/foundation/publication ϭ orities. There are many dimensions /publication.cfm?id 338 Standards can only wring their hands 7 See, e.g., ARC Center, 2003. Full report of and wonder why no one is learning. to scientific thinking, and pitting the tri-state student achievement study. Re- So how can science education re- these against one another, as if trieved from www.comap.com/elementary/ search and reform avoid the wars and they were either/or, belies a naive projects/arc/tri-state%20achievement%20full %20report.htm; S. Senk and D. Thompson vitriol that mathematics education has understanding of education and ͑eds.͒ Standards-oriented School Mathematics not? To a large degree, we cannot: learning. Curricula: What Does the Research Say about there will always be uninformed dis- Historically, physics education re- Student Outcomes? ͑Erlbaum, Mahwah, NJ, ͒ sent from well-meaning scientists and search held itself to a relatively behav- 2003 . 8 A. H. Schoenfeld, “The math wars,” Educ. parents; there will even be informed iorist perspective: we looked at gains Policy 18͑1͒, 253–286 ͑2004͒. dissent, largely within the education in scores as measures of improvement, 9 Examples can be found on anti-mathematic research community but also from speculated in private about the minds education reform websites, such as http:// without, and the sides in this tug-of- that were improving, and tended to www.mathematicallycorrect.com and http:// www.nychold.com. ͑More moderate websites, war are often defined by differences in steer clear of the less-understood as- such as http://mathematicallysane.com, give a values, and values are rarely swayed pects of scientific thinking in the as- more complete picture of the debates.͒

774 Am. J. Phys., Vol. 75, No. 9, September 2007 Letters to the Editor 774 10 J. A. Bianchini and G. J. Kelly, “Challenges versity, Northridge ͑CSUN͒. SCALE’s and state standards that guide the dis- of standards-based reform: The example of overarching goal is to improve K–12 trict’s curricular and professional de- California’s science content standards and textbook adoption process,” Sci. Educ. 87͑3͒, math and science education, pre- velopment choices. 378–389 ͑2003͒. service math and science teacher Since SCALE believes it is impor- 11 The California Science Education Standards: preparation, and in-service math and tant in general to seek and then to pro- http://www.cde.ca.gov/be/st/ss/scmain.asp. science teacher professional develop- vide evidence, and even more so when For examples of test items related to these standards ͑with occasional incorrect items in ment. The most important strategy for addressing a national audience, let me the answer key͒, see http://star.cde.ca.gov doing this is the key feature of the NSF examine further Professor Klein’s 12 E. Etkina, A. Van Heuvelen, S. White- MSP program—innovative partner- claim that “SCALE promotes ͓empha- Brahmia, D. T. Brookes, M. Gentile, S. Mur- ships among K–12 and postsecondary sis mine͔ IMP, CMP, and TERC.” thy, D. Rosengrant, and A. Warren, “Scientific abilities and their assessment,” Phys. Rev. ST institutions, with substantive participa- In a footnote, Professor Klein includes Phys. Educ. Res. 2, ͑1998͒. tion by science, technology, engineer- a SCALE website. On 7 February 13 E. Redish, J. Saul, and R. Steinberg, “Student ing, and mathematics ͑STEM͒ faculty. 2007, SCALE staff searched expectations in introductory physics,” Am. J. SCALE-supported work in mathemat- the entire SCALE website ͑http:// Phys. 66͑3͒, 101–102 ͑2007͒. 14 scalemsp.wceruw.org/͒ for IMP, CMP, B. White, A. Elby, J. Frederiksen, and C. ics in the Los Angeles Unified School Schwarz, The Epistemological Beliefs Assess- District ͑LAUSD͒ includes promoting and TERC and found 13 hits. I invite ment for Physical Science, AERA Annual a new partnership comprising some the reader to do a similar search and Meeting, Montreal, 1999. CSUN mathematics faculty, CSUDH decide which description of SCALE Leslie J. Atkins mathematics and mathematics educa- activities is more accurately described LessonLab Research Institute tion faculty, and LAUSD mathematics by this evidence: Professor Klein’s Santa Monica, California 90405 master teachers. This new partnership claim that SCALE “promotes” these has provided three-week professional curricula, or mine that SCALE “sup- development institutes for middle ports” their use in districts that choose COMMENT ON “SCHOOL MATH school mathematics and high school to use them. BOOKS, NONSENSE, AND algebra teachers. These institutes Here is one example in THE NATIONAL SCIENCE have been conducted at both CSUDH detail ͑www.scalemsp.org/index.php?q FOUNDATION,” BY and CSUN. SCALE is doing parallel ϭMMSD_Mathematics_Masters͒, de- DAVID KLEIN [AM. J. PHYS. 75 work in elementary and middle scribing the Madison Metropolitan (2), 101–102 (2007)] school science teacher professional School District ͑MMSD͒ Math Masters development,1 again through partner- Program, a middle school mathematics Mathematics Professor David Klein ship of CSUN and CSUDH STEM and professional development program that ͑ California State University, North- STEM education faculty, together with has been running in Madison for the ͒ ridge presented an editorial in Am. J. their LAUSD science colleagues. last two and a half years: Phys., Vol. 75, No. 2, February 2007, Professor Klein claims that SCALE titled “School math books, nonsense, “promotes” three mathematics The first course sponsored by and the National Science Foundation.” curricula—Interactive Mathematics MMSD’s Title II Wisconsin As the Principal Investigator and Program ͑IMP͒, Connected Mathemat- Math Science Partnership Project Director for System-wide ics Program ͑CMP͒, and TERC: Inves- ͑MSP͒ Block Grant, tailored Change for All Learners and Educators tigations in Number, Data, and Space to support SCALE-aligned ͑SCALE͒, the NSF comprehensive ͑TERC͒—“even in California where middle school math content Math and Science Partnership ͑MSP͒ those books are not state approved.” As instruction, begins August project mentioned in his editorial, I I indicated above, SCALE support is 2004 at the University of feel obliged to correct at least some of primarily through content-focused Wisconsin—Madison. The Professor Klein’s misrepresentations. teacher professional development us- class focuses on statistics Professor Klein cites SCALE as an ing the expertise of STEM faculty, and probability, and claims example of a multimillion dollar grant STEM education faculty, and district UW—Madison Mathematics awarded by NSF to distribute “‘fuzzy professionals. In undertaking this Department Chair Dr. David math’ programs” to schools. Professor work, SCALE supports the partner dis- Griffeath as its instructor. Klein’s assertion is a misrepresentation tricts’ curricula choices and, if re- Forty teachers from MMSD of the intent of the NSF MSP program quested, provides national expertise plus four surrounding school and is false and misleading with re- with regard to those choices. For ex- districts are registered. The spect to the SCALE MSP work. ample, in California, SCALE supports course modules are designed First, some background. SCALE is a the state-adopted programs chosen by to enable any teacher to pro- partnership of the major urban school its district member, LAUSD. SCALE duce proficient standards- districts in Denver, Madison ͑WI͒, attempts to do this in ways that will based curriculum regardless Providence ͑RI͒, and Los Angeles, to- help teachers use the district’s curricula of chosen textbook. gether with UW—Madison, California and other resources to advance the un- State University, Dominguez Hills derstanding and performance of district Through the Math Masters ͑CSUDH͒, and California State Uni- students, in alignment with the local project, the Madison Metro-

775 Am. J. Phys., Vol. 75, No. 9, September 2007 Letters to the Editor 775 politan School District, tent area courses for the Math Masters proaches to those challenges, that unite School District of Beloit Program. Professor Griffeath, former rather than divide. ͑SDB͒, School District chair of the UW—Madison Mathemat- It is my opinion that Dr. Klein’s re- of Juda ͑SDJ͒, Sauk Prairie ics Department, is one of six professors sponse to this letter does not advance School District ͑SPSD͒, ͑five from mathematics, one from me- the claim he made in his original edi- and the University of chanical engineering͒ who have par- torial that SCALE distributes or pro- Wisconsin—Madison De- ticipated in the program. CMP is the motes particular mathematical cur- partment of Mathematics district-adopted middle school math ricula. We also disagree with his newly ͑UW͒ will join forces to raise curriculum. Note that the goals of the introduced opinions of SCALE work at mathematics achievement Math Masters Program include helping CSU Northridge. These opinions ͑that via an ongoing, intensive, teachers “effectively utilize the ‘Con- do not address the issues of “promote program of content-based nected Mathematics Project’ ͑CMP͒ and distribute”͒ are just that, they are teacher professional develop- curriculum” and “enhance implementa- not based on a systematic evaluation of ment that will bring the part- tion of the CMP curriculum within par- the SCALE teacher professional devel- ners’ middle school math- ticipating teachers’ classrooms.” These opment program ͑and we note that the ematics teachers together in are the references to CMP at this URL. chair of his department and his provost ͒ courses taught by UW— This SCALE-related work is intended support this SCALE work . Madison mathematicians and to support the districts’ curricula applied mathematicians. In choice in middle school mathematics, 1 addition to content knowl- For an example of SCALE science immer- not to promote a particular mathemat- sion, see J. Folsom, Catherine Hunt, Maria edge, teachers will receive ics curriculum. This SCALE support is Cavicchio, Anne Schoenemann, and Matthew content-specific pedagogical D’Amato, “How Do You Know That? Guid- intended to increase the content mas- instruction and other forms ing early elementary students to develop tery of the teachers so that they can evidence-based explanations about animals,” of pedagogical support and better serve their students’ learning Sci. Child. 44͑5͒, 20–25 ͑2007͒. modeling that will help them create standards-based math- needs. Terry Millar ematics classrooms and ef- NSF is providing MSP funding to al- Professor of Mathematics, UW—Madison, Associate Dean for the Physical Sciences, fectively utilize the “Con- low cross-institutional and cross- disciplinary teams to explore and de- Graduate School nected Mathematics Project” SCALE PI and Project Director ͑CMP͒ curriculum. sign new forms of partnership that might help solve the difficult and com- plex problems of improving math and REPLY TO COMMENTS ON The goal of the project is to science education in this country. This “SCHOOL MATH BOOKS, increase middle school stu- is a discovery process—something that NONSENSE, AND THE dents’ achievement in math- is at the heart of the NSF mission. NATIONAL SCIENCE ematics by strengthening the Based on early evidence, I believe FOUNDATION,” BY DAVID quality of mathematics in- SCALE has made measurable gains. I KLEIN [AM. J. PHYS. 75 (2), struction through the provi- venture that the CSUDH and CSUN 101–102 (2007)] sion of content-based profes- administrations believe this too, as the sional development linked to provosts at those two institutions are Wisconsin’s Model Aca- Professor Millar objects to my use SCALE co-PIs. demic Standards for Math- of the word “promotes” in this state- The role and nature of curricula in ematics and professional de- ment from my editorial: math and science education are impor- velopment on high leverage tant issues and worthy of close scrutiny research-based strategies to In addition to other activi- by stakeholders representing different develop student understand- ties, SCALE promotes IMP, perspectives and expertise. In the spirit ing. Project objectives are: 1͒ CMP, and TERC even in of partnership, it would be advanta- to increase the content California where those books geous if contributors to these important knowledge of 150 middle are not state approved. These national discussions were accurate in school mathematics teachers; textbooks lack the math- 2͒ to improve these teachers’ their details and representations. I per- ematical content necessary to understanding of how stu- sonally believe that new kinds of part- meet the state’s K–12 math dents learn mathematics; nerships across traditional disciplinary standards. and, 3͒ to enhance imple- and institutional boundaries—the key mentation of the CMP cur- concept in the NSF Math and Science According to Dr. Millar, “SCALE- riculum within participating Partnership initiative—hold great related work is intended to support the teachers’ classrooms. promise for improving math and sci- district’s curricula choice in middle ence education at all levels. And I also school mathematics, not to promote a This statistics and probability course believe that these new partnerships particular mathematics curriculum.” was the first of what became six con- should focus on challenges, and ap- Yet, the 2005 conference co-sponsored

776 Am. J. Phys., Vol. 75, No. 9, September 2007 Letters to the Editor 776 by SCALE held in Los Angeles fea- promotion, and distribution of inferior ics curriculum materials.” The commit- tured as one of the keynote speakers, math textbooks, and training teachers tee “concluded that the corpus of Diane Resek, co-author of Interactive to use them. evaluation studies as a whole across Mathematics Program ͑IMP͒. Her ad- Dr. Atkins asks, “how can science the 19 programs studied does not per- dress, “Challenging Courses and Cur- education research and reform avoid mit one to determine the effectiveness riculum,” included a downloadable the wars and vitriol that mathematics of individual programs with a high de- powerpoint show that presented data in education has not?” She charges critics gree of certainty, due to the restricted support of the effectiveness of IMP. of controversial math textbooks with a number of studies for any particular Another presentation at that confer- “misunderstanding of high-quality cur- curriculum, limitations in the array of ence, “Physics and Algebra for all 9th ricular reform, ͓and͔ the failure to treat methods used, and the uneven quality Graders” praised TERC and CMP as this reform as a product of research on of the studies.” “challenging curricula.” None of the learning.” Pressing her case, she Dr. Atkin’s use of the word “reform” conference materials made reference to writes, “shifting the emphasis towards should be considered in historical con- any California state adopted textbooks reasoning becomes a battle cry that ral- text. For the past century, mathematics or programs, aligned to the state’s math lies opponents to rewrite well- education has been in a perpetual state 1 standards. researched curriculum and stan- of “reform” by educational experts.6 Professor Millar also refers to the dards…” To avoid these problems in The controversies surrounding the sub- SCALE-supported three-week profes- science education, Dr. Atkins advises, ject, now and in the past, are more sional development institutes held at “take education research, methods, and similar than different, but each new my institution, CSUN. I reviewed findings seriously.” generation of educationists presents documents used for the algebra insti- Dr. Atkins’ charge that opponents of well-worn ideologies as if they were tute. Among them was an article pre- questionable math books don’t like new and revolutionary.7 Dr. Atkins’ ad- 2 senting data favorable to IMP. One them because those books emphasize monition to “take education research, and a half weeks of the institute were reasoning is improbable. Leading methods, and findings seriously” devoted to mathematical topics, and mathematicians criticize the so-called should therefore be taken with a grain the balance to preparing lesson plans. “well-researched curricul͓a͔ and stan- of salt.8 Material from IMP was used for the dards” for a dearth of reasoning and mathematical topics part of the three- lack of content. 1 ͗ week course, but there was no material Mathematicians are not alone. Well- See: scalemsp.wceruw.org/IHEConference 2005/main.htm͘ for that purpose from California ap- informed parents have not been per- 2 J. Boaler and M. Staples, Transforming proved textbooks. The mathematical suaded by educational researchers to Student’s lives Through an Equitable content was pitched at the low end of subject their children to these low- Mathematics Approach: The Case of ͗ high school math. The focus was on content programs. Physicians, lawyers, Railside School, preprint www.sussex.ac.uk/ education/documents/boaler_2_-_creating_ patterns and ad hoc methods, with engineers, scientists, and other parents mathematical_futures.pdf͘. little actual algebra involved. Missing across the country strenuously oppose 3 See, for example, M. McKeown et al.,“Na- were mathematical proofs or even the NSF-funded textbooks for their own tional science foundation systemic initiatives: development of technical fluency. Nev- children. If there was substance to the how a small amount of federal money pro- motes ill-designed mathematics and science ertheless, teacher participants who advocacy research supporting these programs in K–12 and undermines local con- completed the three-week workshop deeply flawed programs, parents would trol of education,” Chap. 13 in Sandra Stotsky were awarded three units of graduate be flocking to expose their children to ͑ed.͒, What’s at Stake in the K–12 Standards ͑ Wars: A Primer for Educational Policy Mak- credit in mathematics not mathematics them. Instead, parents are fleeing en ͑ ͒ ͒ ers Peter Lang, New York, 2000 , pp. 313– education at CSUDH. The net result is masse. Atkins listed two websites for 369. ͗www.csun.edu/~vcmth00m/chap13.pdf͘ that the $35 million NSF-funded parents groups opposed to “fuzzy 4 Web pages for parents’ groups such as the fol- SCALE project not only promotes de- math,” but there are many others and lowing ͑and many others͒ are easily found fective mathematics programs, not their numbers are increasing.4 through an Internet search: “Mathematically Correct,” “New York City Honest and Open aligned to California’s demanding Dr. Atkin’s faith in educational re- Logical Debate,” “Where’s the Math?,” “Illi- math standards, it drags down stan- search is not uniformly held by other nois Loop,” “Parents Concerned With Pen- dards for graduate work in mathemat- experts. A committee of the National fields Math Programs,” “Teach Utah Kids,” ics in the California State University Research Council issued a report in “Connected Mathematics, Disconnected Par- ents,” “Kitchen Table Math,” “Save Our Chil- system. 2004 that evaluated the reliability of dren from Mediocre Math.” Unfortunately, SCALE is not education research studies of curricular 5 Mathematical Sciences Education Board, On unique. Similar criticisms could be di- programs in mathematics.5 From the Evaluating Curricular Effectiveness: Judging rected toward many other programs executive summary: “this committee’s the Quality of K–12 Mathematics Evaluations, Committee for a Review of the Evaluation funded by the Education and Human charge was to evaluate the quality of Data on the Effectiveness of NSF-Supported Resources ͑EHR͒ Division of the the evaluations of the 13 mathematics and Commercially Generated Mathematics NSF.3 For more than a decade, EHR curriculum materials supported by the Curriculum Materials, National Research ͑ ͒ Council of The National Academies ͑The Na- has contributed to the dumbing-down National Science Foundation NSF ͒ ͑ ͒ tional Academies, Washington, DC, 2004 . of K–12 mathematics education in the an estimated $93 million and six of ͗books.nap.edu/openbook.php?record_id United States by funding the creation, the commercially generated mathemat- ϭ11025&pageϭR1͘.

777 Am. J. Phys., Vol. 75, No. 9, September 2007 Letters to the Editor 777 6 David Klein, “A Brief History of American pattern. They mention that it might be AUTHOR’S REPLY K–12 Mathematics Education in the 20th possible to use their method to mea- Century,” Chap. 7 in Mathematical Cogni- sure the Earth’s rotation. The Sagnac tion: A Volume in Current Perspectives on Stedman cites many successfully ex- effect ͑the beats obtained when mixing Cognition, Learning, and Instruction, edited periments regarding the measurement ͑ CW and CCW beams in a rotating po- by James Royer Information Age, Green- of the Earth’s rotation via the Sagnac wich, 2003͒, pp. 175–225. ͗www.csun.edu/ lygonal interferometer͒ has been inter- ~vcmth00m/AHistory.html͘ preted as the anisotropy effect of cu- effect. He addresses the important fact 7 David Klein, “A quarter century of US ‘math mulative Doppler shifts due to that Sagnac measurements can be in- wars’ and political partisanship,” BSHM Bul- reflection from moving mirrors.2 The terpreted as a Doppler effect. In a ro- letin: Journal of the British Society for the ͑ ͒ ͑ ͒ measurement of the Earth’s rotation via tating interferometer all optical compo- History of Mathematics, 22 1 , 22–33 2007 . the Sagnac effect dates from 1925,3 ͗www.csun.edu/~vcmth00m/bshm.html͘ 4,5 nents are moving, and therefore each 8 and with lasers it is now routine. Our For an example of shortcomings in a particu- one produces a Doppler shift. Account- lar study, see “A Case Study: An email debate most recent machine has an area of on the quality of education research in main- 833.7 m2 and a perimeter of 121.4 m ing for the total contribution of all the stream education journals between Dr. Pen- ͑filling our cavern laboratory͒. Due to mirrors, the standard Sagnac formula is dred Noyce, head of the Noyce Foundation, the Earth’s rotation, the mixing of the recovered. and David Klein focusing on the article, ‘The CW and CCW beams induces a signal impact of two standards-based mathematics We want to clarify the fact that we curricula on student achievement in Massa- at 2.177 kHz. referred to the value of the Earth’s ro- chusetts,’ J. E. Riordan and P. E. Noyce, J. tational rate as an example of what we Res. Math. Educ. 3͑4͒, 368–398 ͑2001͒. 1 Luis Bernal and Luis Bilbao, “Optical doppler ͗www.csun.edu/~vcmth00m/noyce.htm͘ call low rotational speed rather than a shift measurement using a rotating mirror,” proposal to measure the Earth’s rota- David Klein Am. J. Phys. 75, 216–219 ͑2007͒. 2 tion by means of our apparatus. As Department of Mathematics M. Dresden and C. N. Yang, “Phase shift in a rotating neutron or optical interferometer,” suggested by a reviewer, one could California State University, Northridge ͑ ͒ Northridge, California 91330-8313 Phys. Rev. D 20, 1846–1848 1979 . mount the mirror on a motorized rota- 3 A. A. Michelson, H. G. Gale, and F. Pearson, [email protected] “The effect of earth’s rotation on the velocity tion stage and move it very slowly. Our of light,” Astrophys. J. 61, 137–145 ͑1925͒. apparatus may be used to show stu- 4 R. Anderson, H. R. Bilger, and G. E. Sted- dents how to detect very low rotational man, “Sagnac effect: a century of earth- EARTH ROTATION VIA speeds. DOPPLER SHIFTS? rotated interferometers,” Am. J. Phys. 62, 975–985 ͑1994͒. 5 G. E. Stedman, “Ring laser tests of fundamen- Luis Bernal 1 Bernal and Bilbao measure rotation tal physics and geophysics,” Rep. Prog. Phys. Physics Department, Faculty of Sciences, of a mirror up to 300 rpm by reflecting 60, 615–688 ͑1997͒. University of Mar del Plata, Argentina a green He-Ne laser beam, mixing it Geoffrey E. Stedman Luis Bilbao with a part of the source beam and de- Department of Physics, INFIP, Conicet and Physics Department, termining the Doppler shift from the University of Canterbury, Faculty of Sciences, Fourier transform of the interference Christchurch 8020, New Zealand University of Buenos Aires, Argentina

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