The University of Montana
Department of Mathematical Sciences

Technical report #20/2010

Commentary on the Cognitive aspects of Early Algebraization

Bharath Sriraman, The University of Montana, USA
Kyeong-Hwa Lee, Seoul National University, Korea

Abstract

In this commentary to the nine chapters in the cognitive section of early algebraization, we synthesize and critically discuss common themes found in them such as components of non-formal algebraic thinking, the purported dichotomy between arithmetic and algebra; meaningful arithmetic, and generalizing ability, among others using the frameworks of William Brownell, Ernst Haeckl and Jean-Baptiste Lamarck.

Keywords: abstraction; early algebraization; generalization; generalized arithmetic; recapitulation; cultural evolution; longitudinal algebra projects; history of mathematics

AMS Subject Classification: 97

Pre-print of Chapter to appear in J. Cai & E. Knuth (Eds). EARLY ALGEBRAIZATION-CURRICULAR, COGNITIVE AND INSTRUCTIONAL PERSPECTIVES. ADVANCES IN MATHEMATICS EDUCATION, VOLUME 2, SPRINGER SCIENCE, BERLIN/HEIDELBERG Pdf (58 KB)