From arithmetic to algebra. A sequence of theory-based tasks. (English)

Czarnocha, Bronislaw (ed.) et al., The creative enterprise of mathematics teaching research. Elements of methodology and practice ‒ from teachers to teachers. Rotterdam: Sense Publishers (ISBN 978-94-6300-548-7/hbk; 978-94-6300-547-0/pbk; 978-94-6300-549-4/ebook). 425-443 (2016).

Summary: The chapter deals with language in the mathematics classrooms, especially with mathematics remedial classrooms. It presents an unusual example of integrating two independent theories, the {\it A. Sfard} [Educ. Stud. Math. 22, No. 1, 1‒36 (1991; ME 1992a.03697)] theory of reification and {\it R. G. Shepard} [J. Math. Behav. 12, No. 3, 287‒93 (1993; ME 1995c.01410)] and {\it T. J. Shuell} [“Phases of meaningful learning", Rev. Educ. Res. 60, No. 4, 531‒547 (1990; \url{doi:10.3102/00346543060004531})] integrated theory of cognitive development and writing categories. In the first cycle it’s the TR Design Type A, from Practice; it uses problem types designed through practice and supports itself by a standard yet simple statistical analysis.