\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2015b.00594}
\itemau{Fujita, Taro; Yamamoto, Shinya}
\itemti{The development of children's understanding of mathematical patterns through mathematical activities.}
\itemso{Res. Math. Educ. 13, No. 3, 249-267 (2011).}
\itemab
Summary: In this paper we report how children (aged 8) developed their mathematical understanding through number tasks based on the Fibonacci sequence (Bamboo numbers) used in the context of a substantial learning environment (SLE), which is designed to be mathematically rich, have a clear purpose and give opportunities to utilise mathematical thinking. The flexible nature of the SLEs makes it possible for teachers and children to explore various mathematical patterns. To capture children's activities when working within SLEs, we make particular reference to {\it J. Pegg} and {\it D. Tall}'s work [ZDM, Zentralbl. Didakt. Math. 37, No. 6, 468--475 (2005; ME 2006a.00169)], and consider a theoretical framework based on the SOLO taxonomy and the developmental process of understanding mathematical concepts. It was found that the key progression to be made through learning using our Bamboo number-based SLEs is from multi-structural to relational levels. It was also suggested that it is difficult for many children to understand the structural aspects of number patterns.
\itemrv{~}
\itemcc{F32 C32}
\itemut{substantial learning environment; number patterns; mathematical activities}
\itemli{doi:10.1080/14794802.2011.624730}
\end