Recent (and not so recent) Articles

by Sheldon P. Gordon

 

Feel free to download any of the following articles that have links to read final draft versions; if you want to read the final articles, you can likely get them through InterLibrary Loan or perhaps from the journals themselves (though often for a fee).

  1. Dynamic Visualizations of Taylor Approximations to Enhance Student Understanding, Int'l J. of Technology in Mathematics Education, (to appear).
  2. Approximating Exponential and Logarithmic Functions With Newton Interpolation, (with Yajun Yang), (submitted).
  3. Visualizing and Understanding the Chain Rule in Calculus, (submitted).
  4. Buffonery in the Math Classroom, (with Florence Gordon), The MathAMATYC Educator, (to appear).
  5. Exploring Log Functions with Fractional Powers, (with Florence Gordon), (to appear).
  6. Visualizing and Understanding Exponential and Logarithmic Identities Using Dynamic Software, (with Florence Gordon), The MathAMATYC Educator, 2023.
  7. Using Moving Averages to Find Trends in Data, (with Florence Gordon), The MathAMATYC Educator, 2023.
  8. Investigating Tangentoidal Functions, (with Florence Gordon), The MathAMATYC Educator, 2023.
  9. Variations on a Theme of Fibonacci, (with Michael Burns), The Mathematics Teacher: Teaching and Learning, 2022.
  10. Visualizing and Understanding P-Values in Hypothesis Testing.(with Florence Gordon), The MathAMATYC Educator, 2022.
  11. The "Calculus" of Moving Averages (with Florence Gordon), PRIMUS, 2022.
  12. Doubling A Cube and Other Mathematical Solids (with Michael Burns), The MathAMATYC Educator, The MathAMATYC Educator, 2021.
  13. Incorporating Statistics into College Algebra, (with Florence S. Gordon), Int’l J of Tech in Math Education, 2021.
  14. Developing a Mathematics Curriculum for the Biosciences, (with Sarah Gross, Yajun Yang, Jessica Seifert, Carla Martin, Matthew Bahamonde, and Jack Winn), PRIMUS, 2021.
  15. Visualizing and Understanding Optimization Problems Using Dynamic Software, Int'l J. of Technology in Mathematics Education, 2020.
  16. Visualizing and Understanding Sampling Distributions Using Dynamic Software, (with Florence Gordon), Int'l J. of Technology in Mathematics Education, 2019.
  17. Using Secant Parabolas for Root Finding, (with Yajun Yang), The Mathematics Teacher, 2018.
  18. Visualizing and Understanding Regression and Correlation using Dynamic Software, (with Florence Gordon), Int'l J. of Technology in Mathematics Education, 2018.
  19. Approximating Sinusoidal Functions Using Lagrange Interpolation, (with Yajun Yang), The MathAMATYC Educator, 2018.
  20. Visualizing and Understanding Hypothesis Testing Using Dynamic Software, (with Florence Gordon), PRIMUS, 2018.
  21. Visualizing and Understanding l'Hopital's Rule,  Int'l J of Math Education in Science and Technology, 2017.
  22. Approximating Exponential and Logarithmic Functions with Lagrange Interpolating Polynomials, (with Yajun Yang), Int'l J of Math Education in Science and Technology, 2017.
  23. Visualizing and Understanding Confidence Intervals Using Dynamic Software, (with Florence Gordon), Math and Computer Education, 2016.
  24. Taking Your Chances on Excel, (submitted).
  25. Taking Control of Excel, Math and Computer Education, 2016. 
  26. Visualizing the Components of Lagrange and Newton Interpolation (with Yajun Yang), PRIMUS, 2015.
  27. Curve Fitting and Lagrange Interpolation, (with Yajun Yang).
  28. Deriving Simpson's Rule Using Newton Interpolation, (with Yajun Yang), Math and Computer Education, 2016.
  29. Functioning in Excel, Math and Computer Education, 2016.
  30. The Flavor of a Modeling Based College Algebra or Precalculus Course, UMAP Journal, 2016.
  31. Finding the Complex Roots of Polynomials, The MathAMATYC Educator, 2016.
  32. Visualizing Techniques of Integration, Math and Computer Education, 2015.
  33. Numerical Integration - One Step at a Time, (with Yajun Yang), PRIMUS, 2016.
  34. How Rational is the Tangent Function, The MathAMATYC Educator, 2015.
  35. Using Quartile-Quartile Lines as Linear Models, PRIMUS, 2015.
  36. Approximating Sinusoidal Functions with Interpolating Polynomials, (with Yajun Yang).
  37. Finding Polynomial Patterns and Newton Interpolation, (with Yajun Yang), Math and Computer Education, 2014.
  38. How Rational is a Logarithmic Function, Math and Computer Education, 2014.
  39. Subdivisions for Definite Integrals with Uniform Spacing, Math and Computer Education, 2014.
  40. Interpolation and Polynomial Curve Fitting (with Yajun Yang), The Mathematics Teacher, 2014. 
  41. The Geology of Mathematics, Guest Editorial, UMAP Journal, 2014.
  42. Integrating Statistics into College Algebra to Meet the Needs of Biology Students, (with Florence Gordon), in Undergraduate Mathematics for the Life Sciences: Processes, Models, Assessment, and Directions, MAA Notes, 2013.
  43. Investigating Convergence Patterns for Numerical Methods Using Data Analysis, PRIMUS, 2013.
  44. Adding A New Dimension to Mathematics, The Mathematics Teacher, 2013.
  45. Mathematics Education Must Evolve, Math and Computer Education, 2013.
  46. Fitting Tangent Functions to Data, Math and Computer Education, 2013.
  47. Time, Tides, and Temps Wait for All Students The MathAMATYC Educator, 2013.
  48. Some Surprising Errors in Numerical Differentiation, PRIMUS, 2012.
  49. Algebra Must Evolve,  Math & Computer Education, 2012. 
  50. Building on Errors in Numerical Integration, Math & Computer Education, 2011.
  51. Introducing Functions of Several Variables in Lower Division Courses, MathAMATYC Educator, 2011.
  52. Placement Testing: The Great Abyss, Vision -- Potential, 2011.
  53. Errors in Mathematics are Not Always Bad, The Mathematics Teacher, 2011.
  54. Finding the Best Quadratic Fit to a Function (with Yajun Yang), Int'l J. of Mathematics Education in Science and Technology, 2011.
  55. Exposing the Mathematical Wizard: Approximating Trigonometric and Other Transcendental Functions, The Mathematics Teacher, 2011.
  56. Intermediate Algebra in High School vs. College, Vision - Potential: College Algebra Newsletter, 2011.
  57. The Average Distance in an Ellipse, Math and Computer Education, 2010.
  58. The State of Mathematics Education Today:  What Happens in the Classroom, J of Economics and Finance, 2010.
  59. What the Partner Disciplines Want from College Algebra, Vision - Potential: College Algebra Newsletter, 2010.
  60. The Status and Purpose of College Algebra, Vision - Potential: College Algebra Newsletter, 2010.
  61. The Statistics of a Function (with Florence Gordon), International J. of Mathematics Education in Science and Technology, 2010.
  62. Mathematics for the Laboratory Sciences, MathAMATYC Educator (premier issue), 2009.
  63. Visualizing and Understanding Probability and Statistics: Graphical Simulations Using Excel, (with Florence Gordon), PRIMUS, 2009.
  64. Doubling Time for Non-Exponential Families of Functions The Mathematics Teacher, 2009.
  65. Modeling Population Growth and Extinction PRIMUS, 2009.
  66. The Curriculum Foundations Project in Mathematics and Economics, (with Richard Vogel), MAA Focus, 2009.
  67. What's Wrong with College Algebra?, PRIMUS, 2008.
  68. A Tale of Two Students, PRIMUS, 2008.
  69. Taylor Approximations and Definite Integrals, PRIMUS, 2007.
  70. Using the Sum of the Squares, (with Florence Gordon), Mathematics and Computer Education, 2008.
  71. Finding the Best Linear Approximation to a Function (with Yajun Yang), Mathematics and Computer Education, 2008.
  72. Comparing the Continuous and Discrete Logistic Models, PRIMUS, 2008.
  73. College Algebra:  Today's Students, Tomorrow's Courses,  MAA Focus, 2008.
  74. Discovering the Fundamental Theorem of Calculus using Data Analysis, (with Florence Gordon), The Mathematics Teacher, 2007.
  75. Placement: The Shaky Bridge between School and College Mathematics, (college version), Placement and Assessment Newsletter, AMATYC, 2006
  76. Fitting Surge Functions to Data, PRIMUS, 2007.
  77. When Does a Curve Bend Most Rapidly: The Curvature Function of a Function (with Loucas Chrysafi), Mathematics and Computer Education, 2006.
  78. Placement: The Shaky Bridge between School and College Mathematics, The Mathematics Teacher, 2006.
  79. What Does Conceptual Understanding Mean?  The AMATYC Review, 2006.
  80. Interconnected Quantitative Learning at Farmingdale State University, (with Jack Winn), in Models of Quantitative Literacy, Rick Gillman, ed, MAA Notes, 2006.
  81. Approximating Functions with Exponential Functions, PRIMUS, 2006.
  82. Rethinking Placement in Mathematics, AMATYC Committee on Articulation and Placement Newsletter, 2006.
  83. Preparing Students for Calculus in the Twenty First Century, in A Fresh Start for Collegiate Mathematics: Rethinking the Road Toward Calculus, Nancy Baxter Hastings, Ed., MAA Notes, 2006.
  84. The Need to Rethink Placement in Mathematics, in A Fresh Start for Collegiate Mathematics: Rethinking the Road Toward Calculus, Nancy Baxter Hastings, Ed., MAA Notes, 2006.
  85. Where Do We Go From Here: Forging a National Initiative to Refocus the Courses Below Calculus, in A Fresh Start for Collegiate Mathematics: Rethinking the Road Toward Calculus, Nancy Baxter Hastings, Ed., MAA Notes, 2006.
  86. The Functioning in the Real World Project, in A Fresh Start for Collegiate Mathematics: Rethinking the Preparation for Calculus, Nancy Baxter Hastings, Ed., MAA Notes, 2006.
  87. Discovering the Chain Rule Graphically,  Mathematics and Computer Education, 2005.
  88. Developing a 2020 Vision for Mathematics Education, in Generating a Vision for Undergraduate Mathematics, Gary Krahn, Ed., West Point, 2005.
  89. What’s Wrong with College Algebra?  SUNY/UUP Working Papers Discussion series.
  90. Deriving the Linear Regression Equations Using Algebra, Mathematics and Computer Education, 2004.
  91. Deriving the Quadratic Regression Equations Using Algebra, Mathematics and Computer Education, 2004.
  92. Taylor's Theorem and the Derivative Tests for Optima and Inflection Points, PRIMUS, 2004.
  93. Algebra for the New Millennium, Int'l J. of Computer Algebra in Math Education, 2004.
  94. An Individualized Term Project for Multivariate Calculus, PRIMUS, 2004.
  95. Mathematics for the New Millennium, in Proc, International Conference on Math Education, Copenhagen, 2004. 
  96. Grant Writing to Enhance Teaching and Learning, Teaching-Talk, 2002.
  97. Using Data Analysis to Motivate Derivative Formulas, Mathematics and Computer Education, 2002.
  98. Using Data Analysis to Discover the Fundamental Theorem of Calculus, PRIMUS, 2003.
  99. Refocusing the Courses Below Calculus, in Proc 13th Intl Conf on Tech in Collegiate Math, Addison-Wesley, 2003.
  100. Discovering New Trig Identities, The Mathematics Teacher, 2003.
  101. Rethinking the Preparation for Calculus (co-author), MAA FOCUS, 2002.
  102. The Implications of Hand-Held Computer Algebra System Calculators Throughout the Mathematics Curriculum (with Arlene Kleinstein), AMATYC Review, 2002.
  103. A Spoonful of Medicine Makes the Mathematics Go Down, The AMATYC Review, 2001.
  104. Renewing the Precursor Courses: New Challenges, Opportunities, and Connections, in Calculus Renewal:  Issues for Undergraduate Mathematics Education in the Next Decade, Susan Ganter, Ed., Plenum Publishing, 2000.
  105. Mathematical Articulation in New York State: Smoothing the Mathematical Transitions of Students,  MetroMath, 2000.
  106. Preparing Students Mathematically for the Twenty First Century, in Proc, Int' Conf. on Mathematics Education, Tokyo, 2000.
  107. Mathematics Education at Farmingdale State College (with Arlene Kleinstein, Jack Winn).  in Proc, Int'l Conf on Mathematics Education, 2000.. 
  108. What Does Being a Good Math Student Mean?, in Technology in Mathematics Education, AMATYC, 2000.
  109. Revisiting Lanchester's Square Law for Military Stalemates, Math & Computer Education, 2000.
  110. Using Real-World Data in the Teaching and Learning of Mathematics, in Proc., 11th Int'l Conf on Tech in Collegiate Math, 2000.
  111.  Functioning in the Real World: A PreCalculus Experience. The Math Modeling/PreCalculus Reform Project, in Exemplary Programs in Introductory College Mathematics, Susan Lenker, Ed, Annenberg FDN/Corp for Public Broadcasting INPUT Competition, MAA, 1999
  112. Modeling the U.S. Population, AMATYC Review, 1999.
  113. Linking Mathematics and Physics via a Classroom Demonstration, PRIMUS, 1999.
  114. Functioning in the Real World: College Algebra and Precalculus Reform, in Crossroads in Mathematics: Programs Reflecting the Standards, Marilyn Mays, Ed., AMATYC, 1999.
  115. Comprehensive Reform of Undergraduate Mathematics Education, in Crossroads in Mathematics: Programs Reflecting the Standards, Marilyn Mays, Ed., AMATYC, 1999.
  116. On Symmetries of Polynomials, PRIMUS, 1999.
  117. A Geometric Interpretation of the Lagrange Remainder Formula, Int'l J of Math Ed, 1998.
  118. Is It Really Such A Tight Squeeze? in Confronting the Core Curriculum, John Dossey, Ed., MAA Notes, 1998.
  119. Visualizing the Chain Rule, The AMATYC Review, 1998.
  120. Out of the Mouths of Babes (expanded version), in Proc. 10th Int'l Conf on Tech in Coll Math, 1998.
  121.   Functioning in the Real World: A Reform Precalculus Experience, Proc. Int'l Conf on Teaching of Math, 1998.
  122. "New" and "Old" Calculus: Student Reactions and Comments, Focus on Calculus, 1997.
  123. Out of the Mouths of Babes: Student Questions and Comments in Reform Courses, PRIMUS, 1997.
  124. Visualizing, Understanding and Exploring Functions of Several Variables, in Proc. 9th Int'l Conf on Tech in Coll Math, 1997.
  125.   Linking the Sine and Cosine Functions to Polynomials at the Precalculus Level, in Proc. 9th Int'l Conf on Tech in Coll Math, 1997.
  126.   Using Real-World Data in the Teaching and Learning of Mathematics. MetroMath, 1998.
  127. Modeling with Difference Equation Models in Precalculus, C-ODE-E Newsletter, 1997.
  128.  A Round-Table Discussion with the Client Disciplines, in Calculus: The Dynamics of Change, Wayne Roberts, et al., Eds., MAA Notes, 1996.
  129. Connecting Calculus Reform to Related Courses and Disciplines, Focus on Calculus, 1996.
  130. Functioning in the Real World: Classroom versus Real Mathematics, in Proc.,8th Int'l Conf on Tech in Coll Math, Addison-Wesley, 1996.
  131. Computer Graphics Simulations in Contemporary Statistics, Proc., 8th Int'l Conf on Tech in Coll Math, 1996.
  132. When do Polynomials look like Circles?: Taylor Approximations in Parametric Coordinates, Math & Computer Ed, 1995.
  133. Functioning in the Real World: A Reform PreCalculus Experience, in Proc of 7th Int'l Conf on Tech in Coll Math, 1995.
  134. Precalculus and Calculus Reform at Community Colleges, (with Steve Rodi), in Preparing for the New Calculus, Anita Solow, Ed., MAA Notes #36, 1994.
  135. Functioning in the Real World: Models for PreCalculus Reform, in Preparing for the New Calculus, Anita Solow, Ed,, MAA Notes #36, 1994.
  136. Lessons from the Calculus Reform Effort for Precalculus Reform. (with Deb Hughes Hallett) in Preparing for the New Calculus, Anita Solow, Ed,, MAA Notes #36, 1994.
  137. Report of the Content Committee at the NSF-sponsored conference: Preparing for the New Calculus. in Preparing for the New Calculus, Anita Solow, Ed,, MAA Notes #36, 1994.
  138. Combining Data Analysis and Probability in PreCalculus. (with Florence Gordon), PRIMUS, 1994.
  139.  Riemann Sums and the Exponential Function. College Math J, 1994.
  140. Implementing Change in the Undergraduate Mathematics Curriculum. AMATYC Review, 1994.
  141.  Stacking Oranges and Apples. The Math Teacher, 1994.
  142. Taylor Polynomial Approximations in Polar Coordinates, College Math Journal, 1993.
  143. Calculus Must Evolve, PRIMUS, 1993.
  144. Random Simulations of Radioactive Decay. PRIMUS, 1993.
  145. An Individualized Computer Investigation, Focus on Calculus, 1992.
  146. Perspectives on the Harvard Calculus Reform Project, UME Trends, 1992.
  147.  Sampling + Simulation = Statistical Understanding: Computer Graphics Simulations in Inferential Statistics, in Statistics for the Twenty First Century, MAA Notes #26, 1992.
  148.   Filling the Tank: Models for PreCalculus Reform, (with B. A. Fusaro), UME Trends, 1992.
  149. Two Year College Math Library Recommendations (co-editor), Lynn Steen, Ed., MAA, 1992.
  150.   MAA Library Recommendations, (co-editor), Lynn Steen, Ed., MAA, 1992.
  151. Change (with Frank Giordano), in A New Start for College Mathematics, Walter Meyer, Ed., COMAP, 1992.
  152. Some Lights in the Middle of the Mathematical Tunnel, in A New Start for College Mathematics, Walter Meyer, Ed, COMAP, 1992.
  153. Individualized Computer Investigations for Calculus. College Math Journal, 1992.
  154. On Finding the General Term of a Sequence, (with Robert Decker), AMATYC Review, 1992.
  155.   l'Hopital's Rule and Taylor Polynomials, Int'l J of Math in Sci & Eng’g Ed, 1992.
  156. Finding Patterns in Integration Formulas. Math & Computer Education, 1992.
  157. Computer Graphics Investigations of the "Social Security" Polynomial, The Mathematics Teacher, 1992.
  158. Computers are Dangerous to your Mathematical Health, Mathematics in College, 1992.
  159. The Implications of Calculus Reform on the Two Year Colleges (with Deb Hughes Hallett), AMATYC Review, 1991.
  160. Understanding Inferential Statistics via Computer Graphics Simulations, (with F. S. Gordon), PRIMUS, 1991.
  161. Discovering the Fundamental Theorem of Calculus using Computer Algebra Systems, Math & Computer Ed, 1991.
  162. On p-secting an Angle, AMATYC Review, 1991.
  163. Rethinking Calculus Across SUNY, SUNY RESEARCH, 1991.
  164.  On a Quotient Operator for Sequences, Int'l J of Math Ed in Science & Technology, 1991.
  165. Introducing Taylor Polynomial Approximations in Introductory Calculus. PRIMUS, 1991.
  166. Integrating Symbolic Manipulation Software into Calculus, Math & Computer Education, 1990.
  167. On a Parabolic Extension of Newton's Method, (with E. Von Eschen), Int'l J of Math Ed in Science and Tech, 1990.
  168.  Investigating Statistical Approximations using Computer Graphics, Int'l J of Math Ed in Sci & Tech, 1990.
  169. Applications of Monte Carlo Methods in Calculus, AMATYC Review, 1990.
  170. They Also Serve Who Only Stand and .... The Mathematics of Waiting Time Simulations, (with F. S. Gordon), The Mathematics Teacher,1990.
  171.  Mathematics for the Computing Sciences, in A Curriculum in Flux, Ron. Davis, Ed,, MAA/AMATYC Report, 1989.
  172. Computing in the Mathematics Curriculum, in A Curriculum in Flux, Ron. Davis, Ed., MAA/AMATYC Report, 1989.
  173. Discrete Mathematical Modeling for Liberal Arts Students, in Mathematics for the Nineties, AMATYC special issue, 1989.
  174. Computer Graphics Simulations of Sampling Distributions, (with F. S. Gordon), Collegiate Microcomputer 1989.
  175. Hyperbolic Probability, Math and Computer Education, 1989.
  176. The Role of Computers in the Two Year College Mathematics Curriculum (with B. A. Fusaro & R. W. Meyer), AMATYC Review, 1989.
  177. Computers in the Remedial Mathematics Curriculum (with G. Gilmer), Computers in Undergraduate Mathematics, MAA Notes, 1988.
  178. Microcomputer Graphics for Statistical Education, (with F. S. Gordon), (invited article), J of Computers and Mathematics with Applications, 1987.