W. Stephen Wilson Professor Department of Mathematics and the School of Education 421 Krieger Hall Johns Hopkins University Baltimore, MD 21218 410-516-7413 wsw@math.jhu.edu

My field of interest and research is homotopy theory, generally from an algebraic viewpoint. I tend to specialize in the use and development of complex (co)bordism, Brown-Peterson (co)homology and Morava K-theory. In addition, I am a Professor in the School of Education as a result of my interest in K-12 mathematics education. This interest led to a full time position for 8 months of 2006 when I served as Senior Advisor for Mathematics in the Office of Elementary and Secondary Education, United States Department of Education. I own lots of suits and ties now. Spring 2012 website for Topology (413). For my CV, educational activities and papers. My personal Home page, where most things are. Education S.B. M.I.T. 1969 S.M. M.I.T. 1969 Ph.D. M.I.T. 1972 under the direction of Franklin P. Peterson (1930-2000). 60th birthday conference stuff. Slides for my talk and photos of the conference and banquet. Keep in mind that these were mostly taken by my son Saul, which explains why there are 300+ of them. The whole collection runs about 1.3GB.

Recent K-12 Education Activities

• January 2012, made a member of PARCC's Content Technical Working Group for Mathematics.

• Speaker at conference, November 19, 2011. The Art and Science of Math Education.

• On an expert panel to advise a task force in Frederick County, Maryland, on the choice of a new elementary school math program, March 2, 2011. My introductory comments.

• Johns Hopkins Magazine, Winter, 2010, Back to basics for the "division clueless."

• More recent education activities include being on the mathematics Feedback Group for the Common Core State Standards of the National Governors Association (NGA) and the Council of Chief State School Officers (CCSSO).

• The Learning Institute, June 15, 2010. Common Standards, Common Sense: What the Common Core State Standards Mean for Arkansas. Featured math panelist. Bryant, Arkansas.

• The Thomas B. Fordham Institute November 4, 2009, panel on National Education Standards; the video and the powerpoint. This is all associated with being the mathematics author of Stars by which to Navigate? Scanning National and International Education Standards in 2009. An Interim Report on Common Core, NAEP, TIMSS, and PISA.

• October 16, 2009, a panel discussion on Gaining Clarity on the Common Core Standards Initiative - Implications for Us All at the Maryland Council of Teachers of Mathematics 2009 Annual Conference. The video. That video is in wmv format and there seem to be some problems with it. I've converted it into two videos in avi format here and here. The wmv is higher quality, but problematic.

• January 22, 2009, a panel discussion on Math background and skills necessary for success in mathematics in college at Sidwell Friends School, Washington D.C. My presentation.

• Leading Minds K-12 Math Education Forum, April 24, 2008. My powerpoint presentation. The web page for the whole symposium, including everyone's powerpoints and videos of the whole event.

Recent Papers

• W. Stephen Wilson. Review of Draft Texas Mathematics Standards 2012. Common Core Watch, Fordham Institute, April 17, 2012.

• Nitu Kitchloo and W. Stephen Wilson. Unstable splittings for real spectra. Submitted.

• Ze'ev Wurman and W. Stephen Wilson. The Common Core Math Standards Education Next, 12(3), Summer 2012.

• W. Stephen Wilson. Arithmetic versus the Elite. A look at individual problems in my old arithmetic test. December 2011.

• Jesús González, Maurilio Velasco and W. Stephen Wilson. Biequivariant maps on spheres and topological complexity of lens spaces. Submitted.

• W. Stephen Wilson and Dung Yung Yan. Stable splitting of the complex connective K-theory of BO(n). Topology and its Applications 159 (2012) 1409-1414.

• W. Stephen Wilson. SBAC Math Specifications Don't Add Up. Flypaper, Thomas B. Fordham Institute, September 19, 2011.

• Guershon Harel and W. Stephen Wilson. The State of High School Textbooks Notices of the AMS, 58(6):823-826, June/July 2011.

• W. Stephen Wilson. In Defense of Mathematical Foundations. Educational Leadership, 68(6):70-73, March 2011.

• W. Stephen Wilson. Arithmetic, Division, Calculus III, and Beyond. A look at students who don't know arithmetic when they come to JHU, with a special look at those who never learned long division. September, 2010.

• Sheila Byrd Carmichael, Gabrielle Martino, Kathleen Porter-Magee, and W. Stephen Wilson with Daniela Fairchild, Elizabeth Haydel, Diana Senechal, and Amber M. Winkler. Foreword by Chester E. Finn, Jr., and Michael J. Petrilli. The State of State Standards-and the Common Core-in 2010. Thomas B. Fordham Institute. Washington, D.C. July 2010.

• S.B. Carmichael, W.S. Wilson, G. Martino, C.E. Finn,JR., K. Porter-Magee, A.M. Winkler. Review of the Draft K-12 Common Core Standards. Thomas B. Fordham Institute. Washington, D.C. March 23, 2010.

• S.B. Carmichael, W.S. Wilson, C.E. Finn, Jr., A.M. Winkler, and S. Palmieri. Stars by which to Navigate? Scanning National and International Education Standards in 2009. An Interim Report on Common Core, NAEP, TIMSS, and PISA. Thomas B. Fordham Institute. Washington, D.C. October 2009.

• G. Martino with W.S. Wilson. Doing the Math: Are Maryland's High School Math Standards Adding up to College Success? The Abell Foundation, Baltimore, Maryland. April 2009.

• W.S. Wilson. Elementary School Mathematics Priorities. AASA Journal of Scholarship & Practice, 6(1):40-49, Spring 2009. This comes complete with a rebuttal to precision. My preferred, prepublication, edition.

• W.S. Wilson. Washington State High School Math Text Review. A colleague, Guershon Harel, also did a review. These both go with the report. March 2009.

• W.S. Wilson. Arithmetic, Geometry, and Calculus III. Preprint. Probably not for publication. An MSWord version is here. I gave arithmetic and geometry tests to my Calculus III students. The exams are linked in the paper, but here is the geometry test and here are the answers to the geometry test for the first 9 questions, with the answers in numerical order. Here are the answers to the entire exam. Here are the solutions to the problems. December 2008.

• J. González and W.S. Wilson. The BP-theory of two-fold products of projective spaces. Homology, Homotopy and Applications, Volume 10(3), 2008, pp. 181-192.

• N. Kitchloo and W.S. Wilson. The second real Johnson-Wilson theory and non-immersions of RPⁿ, Part II. Homology, Homotopy and Applications, Volume 10(3), 2008, pp. 269-290.

• N. Kitchloo and W.S. Wilson. The second real Johnson-Wilson theory and non-immersions of RPⁿ. Homology, Homotopy and Applications, Volume 10(3), 2008, pp. 223-268.

• W.S. Wilson. Review of Mathematial Soundness: Background Notes for WA State Curriculum Study. October 27, 2008. This goes with Independent Study of Washington State K-8 Curriculum Review by Strategic Teaching for the Washington State Board of Education. The review takes into consideration supplements prepared by TERC Investigations just for the state of Washington. We learned about the supplements late so there is a review that only uses the basic TERC Investigations program that does not include the supplements. This may be of interest to people outside the state of Washington.

• W.S. Wilson. Are our students better now? Published under the title What Do College Students Know? Education Next, 8(4):88, Fall 2008.

• Contributing author, W.S. Wilson. Primary author: Linda Plattner. Revised 9-12 mathematics standards approved by the Washington State Board of Education. July, 2008.

• Contributing author, W.S. Wilson. Primary author: Linda Plattner. Revised K-8 mathematics standards approved by the Washington State Board of Education. April 28, 2008.

• Contributing author, W.S. Wilson. Primary author: Linda Plattner. A Report to the Washington State Board of Education: Second Review of Washington K-12 Mathematics Standards. March 10, 2008.

• Contributing author, W.S. Wilson. Primary author: Linda Plattner. A Report to the Washington State Board of Education: Follow-Up to Review and Recommendations. February 5, 2008.

• Contributing author, W.S. Wilson. Primary author: Linda Plattner. Washington State Mathematics Standards: Review and Recommendations. August 30, 2007.

• J. M. Boardman and W.S. Wilson. k(n)-torsion-free H-spaces and P(n)-cohomology. Canadian Journal of Mathematics, 59(6):1154-1206, 2007

• N. Kitchloo and W.S. Wilson. On the Hopf ring for ER(n). Topology and its Applications, 154:1608-1640, 2007.

• M. Ando, N. Minami, J. Morava, and W.S. Wilson, editors, Proceedings of the Nishida Fest (Kinosaki 2003), volume 10 of Geometry & Topology Monographs, 2007.

• N. Kitchloo and W.S. Wilson. On fibrations related to real spectra. In M. Ando, N. Minami, J. Morava, and W.S. Wilson, editors, Proceedings of the Nishida Fest (Kinosaki 2003), volume 10 of Geometry & Topology Monographs, pages 237-244, 2007.

• Barbara Reys, Carolyn Baldree, Donna Taylor, and W.S. Wilson. Grade 6: Process and standards. In Johnny W. Lott and Kathleen Nishimura, editors, Standards & Curriculum: A view from the Nation, pages 29-32, Reston, Virginia, 2005. NCTM.

• One of 10 authors of Ten Myths about Math Education and why you shouldn't believe them.

• W. S. Wilson. Short response to Tunis's letter to the editor on technology in college. Educational Studies in Mathematics, 2005 (58):415-420. This is in response to a letter published in response to the paper below with Naiman.

• David Klein, with Bastiaan J. Braams, Thomas Parker, William Quirk, Wilfried Schmid, and W. Stephen Wilson. Technical assistance from Ralph A. Raimi and Lawrence Braden. Analysis by Justin Torres. Foreword by Chester E. Finn, Jr. The State of the State MATH Standards. Thomas B. Fordham Foundation. Washington, D.C. January 2005.

• E. C. Scott with a few hundred Steves including W. S. Wilson. The Morphology of Steve Annals of Improbable Research, 10(4):24-29, July/August 2004.

• W. S. Wilson and D. Q. Naiman. K-12 Calculator usage and college grades. Educational Studies in Mathematics, 56:119-122, 2004. The dvi version of the paper. Older, slightly longer versions of the paper: The dvi version. The pdf version. The word perfect version.

• N. Kitchloo, G. Laures, and W.S. Wilson. Splittings of bicommutative Hopf algebras. Journal of Pure and Applied Algebra. 194: 159-168, 2004.

• N. Kitchloo, G. Laures, and W.S. Wilson. The Morava K-theory of spaces related to BO. Advances in Mathematics. 189(1):192-236, 2004.

• D. Davis, J. Morava, G. Nishida, W.S. Wilson, and N. Yagita, editors. Recent Progress in Homotopy Theory: Proceedings of a conference on Recent Progress in Homotopy Theory, March 17-27, 2000, Johns Hopkins University, Baltimore, MD., volume 293 of Contemporary Mathematics. American Mathematical Society, Providence, Rhode Island, 2002.

• T. Kashiwabara and W. S. Wilson. The Morava K-theory and Brown-Peterson cohomology of spaces related to BP. Journal of Mathematics of Kyoto University, 41(1):43-95, March 2001.

• J. M. Boardman and W. S. Wilson. Unstable splittings related to Brown-Peterson cohomology. In J. Aguade, C. Broto, and C. Casacuberta, editors, Cohomological Methods in Homotopy Theory, Barcelona Conference on Algebraic Topology, Bellaterra, Spain. June 4-10, 1998, volume 196 of Progress in Mathematics, pages 35--45, Basel/Switzerland, 2001. Birkhauser Verlag.

• W. S. Wilson. Hopf rings in algebraic topology. Expositiones Mathematicae, 18:369-388, 2000.

• W. S. Wilson. The impossible made easy: Learning to calculate with generalized cohomology. In 46-th Annual Japanese Topology Symposium Proceedings. pages 20-30. Hokkaido University, July, 1999.

• J.-P. Meyer, J. Morava, and W.S. Wilson, editors. Homotopy invariant algebraic structures: a conference in honor of J. Michael Boardman, volume 239 of Contemporary Mathematics. American Mathematical Society, Providence, Rhode Island, 1999.

• J. M. Boardman, R. L. Kramer, and W. S. Wilson. The periodic Hopf ring of connective Morava K-theory. Forum Mathematicum, 11:761-767, 1999.

• W. S. Wilson. K(n+1) equivalence implies K(n) equivalence. In J.-P. Meyer, J. Morava, and W. S. Wilson, editors, Homotopy invariant algebraic structures: a conference in honor of J. Michael Boardman, Contemporary Mathematics, pages 375-376. American Mathematical Society, Providence, Rhode Island, 1999.

• W. S. Wilson. Brown-Peterson Cohomology from Morava K-Theory, II. K-Theory, 17:95-101, 1999.

• H. Sadofsky and W. S. Wilson. Commutative Morava homology Hopf algebras . In M.E. Mahowald and S. Priddy, editors, Homotopy Theory in Algebraic Topology, volume 220 of Contemporary Mathematics, pages 367-373, Providence, Rhode Island, 1998, American Mathematical Society. The original submission is included here because the referee made us take out all of the proofs. Honest.

• D. C. Ravenel, W. S. Wilson, and N. Yagita. Brown-Peterson Cohomology from Morava K-Theory. K-Theory, 15(2):149-199, 1998.

• M. J. Hopkins, D. C. Ravenel and W. S. Wilson. Morava Hopf algebras and spaces K(n)-equivalent to finite Postnikov systems . W. G. Dwyer, et. al., editors, Stable and Unstable Homotopy , volume 19 of The Fields Institute for Research in Mathematical Sciences Communications Series, pages 137-163, Providence, R.I., 1998. American Mathematical Society.

• W. S. Wilson. Hopf ring . In Encyclopaedia of Mathematics, Supplementary Volume I , pages 299-300. Kluwer Academic Publishers, 1997.

• D. C. Johnson and W. S. Wilson. On a Theorem of Ossa . Proc. Amer. Math. Soc., 125(12):3753-3755, 1997.

• P. J. Eccles, P. R. Turner, and W. S. Wilson. On the Hopf ring for the sphere. Mathematische Zeitschrift. 224:229-233, 1997.

• W. S. Wilson. Wei-Liang Chow . Notices of the American Mathematical Society. 43(10):1117-1124, October 1996. Organizer.

• D. C. Ravenel and W. S. Wilson. The Hopf ring for P(n). Canadian Journal of Mathematics, 48(5):1044-1063, 1996.

• J. M. Boardman, D. C. Johnson, and W. S. Wilson. Unstable operations in generalized cohomology. In I. M. James, editor, The Handbook of Algebraic Topology, chapter 15, pages 687-828. Elsevier, 1995. The companion paper by J. Michael Boardman precedes it in the Handbook: Stable operations in generalized cohomology.

• D. C. Johnson, W. S. Wilson, and D. Y. Yan. Brown-Peterson homology of elementary p-groups, II. Topology and its applications, 59:117-136, 1994.