Early Algebraization pp 125-130 | Cite as

# Commentary on Part I

## Abstract

During the nineteenth century, the study of algebra moved into the secondary school curriculum as colleges and universities began to require it for admission (Kilpatrick and Iszák 2008). Coming after an extensive treatment of arithmetic in the elementary grades, school algebra was commonly introduced formally as a generalization of that arithmetic, with an emphasis on symbol manipulation and equation solving. Given the well-established status of algebra in the secondary curriculum, mathematics educators today confront the question of, in the words of Subramaniam and Banerjee, how “to manage the transition from arithmetic to symbolic algebra.”

## Keywords

Mathematics Curriculum Common Core State Standard Algebraic Thinking Symbolic Algebra Early Algebra## Preview

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## References

- Daro, P., Stancavage, F., Ortega, M., DeStefano, L., & Linn, R. (2007, September). In
*Validity Study of the NAEP Mathematics Assessment: Grades 4 and 8*. Palo Alto, CA: NAEP Validity Studies, American Institutes for Research. Available from http://www.eric.ed.gov/. - Kilpatrick, J. (1990). Introduction to the English language edition. In V. V. Davydov (Ed.),
*Types of Generalization in Instruction: Logical and Psychological Problems in the Structuring of School Curricula*,*Soviet Studies in Mathematics Education*(Vol. 2, pp. xv–xviii). Reston, VA: National Council of Teachers of Mathematics. Google Scholar - Kilpatrick, J., & Izsák, A. (2008). A history of algebra in the school curriculum. In C. E. Greenes & R. Rubenstein (Eds.),
*Algebra and Algebraic Thinking in School Mathematics, 70th Yearbook of the National Council of Teachers of Mathematics*(pp. 3–18). Reston, VA: NCTM. Google Scholar - National Mathematics Advisory Panel (2008).
*Foundations for Success: The Final Report of the National Mathematics Advisory Panel*. Washington, DC: U.S. Department of Education. Available from http://www2.ed.gov/about/bdscomm/list/mathpanel/index.html. - Ponte, J. P., Serrazina, L., Guimarães, H. M., Breda, A., Guimarães, F., Sousa, H., Graça Martins, M. E., & Oliveira, P. A. (2007, December).
*Programa de matemática do ensino básico.*Lisboa: Ministério da Educação. Available: http://www.dgidc.min-edu.pt/matematica/Documents/ProgramaMatematica.pdf. - Roberts, D. L. (2010). Interview with Izaak Wirszup.
*International Journal for the History of Mathematics Education*,*5*(1), 53–74. Google Scholar - Schmidt, W. H., & Houang, R. T. (2007). Lack of focus in the mathematics curriculum: Symptom or cause. In T. Loveless (Ed.),
*Lessons Learned: What International Assessments Tell Us About Math Achievement*(pp. 65–84). Washington, DC: Brookings Institution Press. Google Scholar - Yaroshchuk, V. L. (1969). A psychological analysis of the processes involved in solving model arithmetic problems. In J. Kilpatrick & I. Wirszup (Eds.),
*Problem Solving in Arithmetic and Algebra, Soviet Studies in the Psychology of Learning and Teaching Mathematics*(Vol. 3, pp. 53–96). Stanford, CA, & Chicago, IL: School Mathematics Study Group & Survey of Recent East European Mathematical Literature. Google Scholar