Putting early algebra in the hands of elementary school teachers: examining fidelity of implementation and its relation to student performance / El álgebra temprana en manos del docente de primaria: un análisis de la fidelidad de ejecución y su relación con el rendimiento de los escolares

References / Referencias

• Blanton, M., Isler, I., Stroud, R., Stephens, A., Knuth, E., & Gardiner, A. (in press). Growth in children’s understanding of generalizing and representing mathematical structure and relationships. Educational Studies in Mathematics.
   Google Scholar
• Blanton, M., Stephens, A., Knuth, E., Gardiner, A., Isler, I., & Kim, J. (2015). The development of children’s algebraic thinking: The impact of a comprehensive early algebra intervention in third grade. Journal for Research in Mathematics Education, 46, 39–87.
   Web of Science ®Google Scholar
• Blanton, M., Stephens, A., Stroud, R., Knuth, E., Stylianou, D., & Gardiner, A. (in press). Does early algebra matter? The effectiveness of an early algebra intervention in grades 3–5. American Educational Research Journal.
   Google Scholar
• Brizuela, B. M., & Earnest, D. (2008). Multiple notational systems and algebraic understandings: The case of the “best deal” problem. In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 273–301). New York, NY: Lawrence Erlbaum Associates.
   Google Scholar
• Cai, J., & Knuth, E. (Eds.). (2011). Early algebraization: A global dialogue from multiple perspectives. Heidelberg: Springer.
   Google Scholar
• Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in the elementary school. Portsmouth, NH: Heinemann.
   Google Scholar
• Carraher, D. W., Schliemann, A. D., Brizuela, B. M., & Earnest, D. (2006). Arithmetic and algebra in early mathematics education. Journal for Research in Mathematics Education, 37, 87–115.
   Web of Science ®Google Scholar
• Carraher, D. W., Schliemann, A. D., & Schwartz, J. L. (2008). Early algebra is not the same as algebra early. In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 235–272). New York, NY: Lawrence Erlbaum Associates.
   Google Scholar
• Dorland, W. A. (1994). Borland‘s illustrated medical dictionary (28th ed.). Philadelphia: W. B. Saunder.
   Google Scholar
• Dusenbury, L., Brannigan, R., Hansen, W. B., & Walsh, J. (2003). Quality of implementation: developing measures to crucial to understanding the diffusion of preventive interventions. Health Education Research 20, 308–313.
   Web of Science ®Google Scholar
• Fonger, N. L., Stephens, A., Blanton, M., Isler, I., Knuth, E., & Gardiner, A. (2018). Developing a learning progression for curriculum, instruction, and student learning: An example from mathematics education. Cognition and Instruction, 36, 30–55.
   Web of Science ®Google Scholar
• Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K. C., Wearne, D., Murray, H., & Human, P. (1997). Making sense: Teaching and learning mathematics with understanding (Vol. 361, pp. 3801–3912). Portsmouth, NH: Heinemann.
   Google Scholar
• Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41, 169–202.
   Web of Science ®Google Scholar
• Kaput, J. (1999). Teaching and learning a new algebra. In E. Fennema, & T. A. Romberg (Eds.), Mathematical classrooms that promote understanding (pp. 133–155). Mahwah, NJ: Lawrence Erlbaum Associates.
   Google Scholar
• Kaput, J. (2008). What is algebra? What is algebraic reasoning? In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp. 5–17). New York, NY: Lawrence Erlbaum Associates.
   Google Scholar
• Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
   Google Scholar
• Kaput, J. J., Carraher, D. W., & Blanton, M. L. (Eds.). (2008). Algebra in the early grades. New York, NY: Lawrence Erlbaum Associates.
   Google Scholar
• Kline, M. (1972). Mathematical thought from ancient to modern times. New York, NY: Oxford University Press.
   Google Scholar
• Mihalic, S. (2002). The importance of implementation fidelity. Boulder, CO: Center for the Study and Prevention of Violence. Retrieved from: http://www.incredibleyears.com/wp-content/uploads/fidelity-importance.pdf
   Google Scholar
• Moses, R. P., & Cobb, C. E. (2001). Radical equations: Math literacy and civil rights. Boston, MA: Beacon Press.
   Google Scholar
• Mowbray, C., Holter, M. C., Teague, G. B., & Bybee, D. (2003). Fidelity criteria: Development, measurement, and validation. American Journal of Evaluation, 24, 315–340.
   Web of Science ®Google Scholar
• National Center for Teacher Effectiveness. (2014). Mathematical Quality of Instruction. Retrieved from http://isites.harvard.edu/icb/icb.do?keyword=mqi_training.
   Google Scholar
• National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: Author.
   Google Scholar
• National Governors Association Center for Best Practices [NGA] & Council of Chief State School Officers [CCSO]. 2010. Common core state standards for mathematics. Washington, DC: Author. Retrieved from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf
   Google Scholar
• National Research Council [NRC]. (2004). On curricular effectiveness: Judging the quality of K-12 mathematics evaluations. Washington, DC: National Academy Press.
   Google Scholar
• North Dakota Department of Public Instruction. (n.d.). Fidelity of implementation. Retrieved from www.dpi.state.nd.us/speced/personnel/fidelity.shtm
   Google Scholar
• O’Donnell, C. (2008). Defining, conceptualizing, and measuring fidelity of implementation and its relationship to outcomes in K-12 curriculum intervention research. Review of Educational Research, 78, 33–84.
   Web of Science ®Google Scholar
• RAND Mathematics Study Panel Report. (2003). Mathematical proficiency for all students: A strategic research and development program in mathematics education. Washington, DC: U.S. Department of Education.
   Google Scholar
• Raudenbush, S. W. (2007). Designing field trials of educational innovations. In B. Schneider, & S.-K. McDonald (Eds.), Scale-up in education: Vol. II. Ideas in practice (pp. 23–40). Lanham, MD: Rowman & Littlefiel.
   Google Scholar
• Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods (2nd ed.). Thousand Oaks: Sage Publications.
   Google Scholar
• Schoenfeld, A. (1995). Report of working group 1. In C. Lacampagne, W. Blair, & J. Kaput (Eds.), The algebra initiative colloquium (Vol. 2, pp. 11–12). Washington, DC: US Department of Education, Office of Educational Research and Improvement. Working Group papers.
   Google Scholar
• Stigler, J. W., Gonzales, P., Kawanaka, T., Knoll, S., & Serrano, A. (1999). The TIMSS videotape classroom study: Methods and findings from an exploratory research project on eighth-grade mathematics instruction in Germany, Japan, and the United States. (U.S. Department of Education National Center for Educational Statistics: NCES 99–074). Washington, DC: Government Printing Office.
   Google Scholar
• Summerfelt, W. T., & Meltzer, H. Y. (1998). Efficacy vs. effectiveness in psychiatric research. Psychiatric Services, 49, 834–835.
   PubMed Web of Science ®Google Scholar
• Superfine, A. S. (2008). Planning for mathematics instruction: A model of experienced teachers’ planning processes in the context of a reform mathematics curriculum. The Mathematics Educator, 18(2), 11–22.
   Google Scholar
• U.S. Department of Education, Office of Educational Research and Improvement, National Center for Education Statistics. (1998). Pursuing excellence: A study of U.S. twelfth-grade mathematics and science achievement in international context: Initial findings from the Third International Mathematics and Science Study (Revised, NCES 98–049). Washington, DC: Author. Retrieved from http://nces.ed.gov/pubs98/98049.pdf
   Google Scholar
• Yap, K., Aldersebaes, I., Railsback, J., Shaughnessy, J., & Speth, T. (2000). Evaluating whole-school reform efforts: A guide for district and school staff (2nd ed.). Portland, OR: Northwest Regional Educational Laboratory.
   Google Scholar