• Cynthia S. Paul
  • Sheila R. VaidyaEmail author


What does it take to change a school’s mathematics achievement profile from low to one that is proficient and advanced? Is this transformed achievement profile sustainable? Such is the story presented here, in this three-phase case study of a K-8 urban charter school’s mathematics program. The first phase discusses the school’s mathematics program as it existed in 2006. The second phase discusses the contents and interventions implemented which transformed the student achievement scores over a period of 3 years (2006–2009) from low achieving to proficient and advanced. The third phase is a follow-up mixed-methods investigation that was conducted to determine whether the achievement was sustainable and how the program changed. The interventions designed and implemented over the initial 3-year period are discussed, as are the findings of the follow-up study. This is discussed with reference to impacting change in student achievement and its relative significance for future work.

Key words

mathematics achievement mathematics achievement gap middle school urban school 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Auguste, Hancock & Miller (2009). The economic impact of the achievement gap in America’s schools. Boston, MA: McKinsey & Company.Google Scholar
  2. Bailey, M. J. & Dynarski, S. M. (2011). Inequality in postsecondary education. In G. J. Duncan & R. J. Murnane (Eds.), Whither opportunity?: Rising inequality, schools, and children’s life chances. New York, NY: Russell Sage.Google Scholar
  3. Baker, S., Gersten, R. & Lee, D. (2002). A synthesis of empirical research on teaching mathematics to low-achieving students. The Elementary School Journal, 103(1), 52–73.CrossRefGoogle Scholar
  4. Ball, D. L., Ferrini-Mundy, J., Kilpatrick, J., Milgram, R. J., Schmid, W. & Schaar, R. (2005). Reaching for common ground in K-12 mathematics education. Notices of the AMS, 52(9), 1055–1058.Google Scholar
  5. Banathy, B. H. (1992). A systems view of education: Concepts and principles for effective practice. Englewood Cliffs, NJ: Educational Technology.Google Scholar
  6. Barber, M. & Mourshed, M. (2007). How the world’s best-performing school systems come out on top. Boston, MA: McKinsey & Company.Google Scholar
  7. Baxter, J. A., Woodward, J. & Olson, D. (2001). Effects of reform-based mathematics instruction on low achievers in five third-grade classrooms. The Elementary School Journal, 101(5), 529–547.CrossRefGoogle Scholar
  8. Collins, M. A. & Amabile, T. M. (2009). Motivation and creativity. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 297–312). Cambridge, UK: Cambridge University Press.Google Scholar
  9. Common Core State Standards Initiative (CCSSI) (2010). Accessed 5 Dec 2010.
  10. Creswell, J. W. (2008). Educational research: Planning, conducting, and evaluating quantitative and qualitative research. Upper Saddle River, NJ: Pearson.Google Scholar
  11. Data Recognition Corporation (2010). https:// Accessed 15 Dec 2010.
  12. Dillon, S. (2010, December 7). Top test scores from shanghai stun educators, The New York Times. Accessed 8 Dec 2010.
  13. Every Child a Chance Trust (2009). The long-term costs of numeracy difficulties. Accessed 17 Sep 2011
  14. Friedman, T.L. (2010, November 21). Teaching for America, The New York Times, p. WK 8.
  15. Fullan, M. & Pomfret, A. (1977). Research on curriculum and instruction implementation. Review of Educational Research, 47(1), 335–397.CrossRefGoogle Scholar
  16. Hanushek, E. A. (2010). The high cost of low educational performance: The long-run economic impact of improving PISA outcomes. Paris: Organisation for Economic Co-Operation and Development (OECD).Google Scholar
  17. Heifetz, R. A. & Linsky, M. (2002). Leadership on the Line. Boston, MA: Harvard Business School Press.Google Scholar
  18. Hembree, R. & Dessart, D. J. (1986). Effects of hand-held calculators in precollege mathematics education: A meta-analysis. Journal for Research in Mathematics Education, 17(2), 83–99.CrossRefGoogle Scholar
  19. Izumi, L. T. (2002). They have overcome: High-poverty, high-performing schools in California. San Francisco, CA: Pacific Research Institute.Google Scholar
  20. Kitchen, R. S., DePree, J., Celedon-Pattichis, S. & Brinkerhoff, J. (2007). Mathematics education at highly effective schools that serve the poor. Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  21. Klein, D. (2003). A brief history of American K-12 mathematics education in the 20th century. In J. M. Royer (Ed.), Mathematical cognition. Greenwich, UK: Information Age.Google Scholar
  22. Kroesbergen, E. H., Van Luit, J. E. H. & Maas, C. J. M. (2004). Effectiveness of explicit and constructivist mathematics instruction for low-achieving students in the Netherlands. The Elementary School Journal, 104(3), 233–251.CrossRefGoogle Scholar
  23. Loveless, T. & Coughlan, J. (2004). The arithmetic gap. Educational Leadership, 61(5), 55–59.Google Scholar
  24. Mourshed, M., Chijioke, C. & Barber, M. (2010). How the world’s most improved school systems keep getting better. Boston, MA: McKinsey & Company.Google Scholar
  25. Murnane, R. J., Willett, J. B. & Levy, F. (1995). The growing importance of cognitive skills in wage determination. The Review of Economics and Statistics, 77(2), 251–266.CrossRefGoogle Scholar
  26. National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. Reston, VA: NCTM.Google Scholar
  27. National Council of Teachers of Mathematics (NCTM) (2006). Curriculum focal points: For pre-kindergarten through grade 8 mathematics. Reston, VA: NCTM.Google Scholar
  28. OEDC Programme for International Student Assessment (PISA) (2009). PISA 2009 results.,3746,en_32252351_32235731_46567613_1_1_1_1,00.html. Accessed 11 Mar 2012.
  29. Pennsylvania Department of Education (PDE) (2010). Assessment anchors and eligible content. , Accessed 23 May 2010.
  30. Phillipp, R. A. & Schappelle, B. P. (1999). Algebra as generalized arithmetic: Starting with the known for a change. The Mathematics Teacher, 92(4), 310–316.Google Scholar
  31. Rittle-Johnson, B. & Kmicikewycz, A. O. (2008). When generating answers benefits arithmetic skill: The importance of prior knowledge. Journal of Experimental Child Psychology, 101, 75–81.CrossRefGoogle Scholar
  32. Rittle-Johnson, B. & Koedinger, K. (2009). Iterating between lessons on concepts and procedures can improve mathematics knowledge. British Journal of Educational Psychology, 79, 18.CrossRefGoogle Scholar
  33. Schneider, M. & Stern, E. (2010). The developmental relations between conceptual and procedural knowledge: A multimethod approach. Developmental Psychology, 46(1), 178–192.CrossRefGoogle Scholar
  34. Senge, P. M. (1990). The leader’s new work: Building learning organizations. Sloan Management Review, 32(1), 7–23.Google Scholar
  35. Siegler, R.S., Duncan, G.J., Davis-Kean, P.E., Duckworth, K., Claessens, A., Engel, M., Susperreguy, M.I., et al. (2012). Early predictors of high school mathematics achievement. Psychological Science, 23, 691–697. doi: 10.1177/0956797612440101 Google Scholar
  36. Stein, M. K., Remillard, J. & Smith, M. S. (2007). How curriculum influences student learning. In J. Frank & K. Lester (Eds.), Second handbook of research on mathematics teaching and learning. Charlotte, NC: Information Age.Google Scholar
  37. Suydam, M. N. (1979). The use of calculators in pre-college education: A state-of-the-art review. Washington, DC: National Institute of Education.Google Scholar
  38. Top PSSA Performers (2008, August 16). Philadelphia Inquirer.Google Scholar
  39. U.S. Department of Education (2008). Foundations for success: The final report of the national mathematics advisory panel. Washington, DC: U.S. Department of Education.Google Scholar
  40. Wilson, W. S. & Naiman, D. Q. (2004). K-12 calculator usage and college grades. Educational Studies in Mathematics, 56(1), 119–122.CrossRefGoogle Scholar
  41. Woodward, J. (2004). Mathematics education in the U.S.: Past to present. Journal of Learning Difficulties, 37(1), 16–31.Google Scholar
  42. Wu, H. (2001). How to prepare students for algebra. American Educator, 25(Summer), 1–7.Google Scholar
  43. Yin, R. K. (2009). Case study research: Design and methods. Los Angeles: Sage Publications, Inc.Google Scholar

Copyright information

© National Science Council, Taiwan 2013

Authors and Affiliations

  1. 1.School of EducationDrexel UniversityPhiladelphiaUSA

Personalised recommendations