NCSM Position Paper

NCSM: Leadership in Mathematics Education mathedleadership.org Permission is granted by NCSM to reprint this paper. Bruner, J. (1966). Toward a theory of instruction . Cambridge, MA: Belknap Press of Harvard University Press. Burns, M. (2007). About teaching mathematics: A K–8 resource (3rd Edition). Sausalito, CA: Math Solutions. Conference Board of the Mathematical Sciences (2012). The Mathematical Education of Teachers II. Providence, RI and Washington, DC: American Mathematical Society and Mathematical Association of America. Cramer, K., Post, T., & delMas, R., (2002). Initial fraction learning by fourth and fifth grade students: A comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum . Journal for Research in Mathematics Education, 33 (2): 111–144. Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J. R., & Witzel, B. (2009). Assisting students struggling with mathematics: Response to intervention (RtI) for elementary and middle schools (NCEE 2009- 4060). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from http://ies.ed.gov/ncee/wwc/publications/practiceguides/. Goldsby, D. (2009). Research summary: Manipulatives in middle grades mathematics. Retrieved from http://www.amle.org/Research/ResearchSummaries/ Mathematics/tabid/1832/Default.aspx. Hattie, J. A. C. (2009). Visible learning: A synthesis of 800+ meta-analyses on achievement . London: Routledge. Hattie, J. A. C. (2012). Visible learning for teachers: Maximizing impact on learning . New York: Routledge. Moyer, P., Bolyard, J., & Spikell, M. What are virtual manipulatives? Teaching Children Mathematics 8 (6). National Research Council (2001). Adding it up: Helping children learn mathematics . J. Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education, Washington, DC: National Academy Press. Stein, M. K. & Bovalino, J. W. (2001). Manipulatives: One piece of the puzzle. Mathematics Teaching in the Middle School 6 (6): 356–359. Sowell, E. (1989). Effects of maniulative materials in mathematics instruction. Journal for Research in Mathematics Education, 20 : 498–505. Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2012). Elementary and middle school mathematics: Teaching developmentally . Boston: Pearson. Wenglinsky, H. (2000). How teaching matters: Bringing the classroom back into discussions of teacher quality . Princeton, NJ: Educational Testing Service. Witzel, S. B., Mercer, C., & Miller, M. D. (2003). Teaching algebra to students with learning difficulties: An investigation of an explicit instruction model. Learning Disabilities Research and Practices, 18 : 121–131. References