Curricular approaches to connecting subtraction to addition and fostering fluency with basic differences in grade 1 Baroody, Arthur J. Fact fluency Learning trajectories Part-whole relations Primary-grade mathematics curricula Subtraction-as-addition strategy Currículos de matemáticas Educación Primaria Estrategia de la sustracción como suma Fluidez informativa Relaciones parte-todo Aprendizaje Six widely used US Grade 1 curricula do not adequately address the following three developmental prerequisites identified by a proposed learning trajectory for the meaningful learning of the subtraction-as-addition strategy (e.g., for 13 – 8 think “what + 8 = 13?”): (a) reverse operations (adding 8 is undone by subtracting 8); (b) common part-whole relations (5 + 8 and 13 – 8 share the same whole 13 and parts 5 and 8); and (c) the complement principle in terms of part-whole relations (if parts 5 and 8 make the whole 13, then subtracting one part from the whole leaves the other part). Seis currículos ampliamente usados en Estados Unidos para primero de primaria no tratan adecuadamente tres prerrequisitos identificados por una trayectoria de aprendizaje propuesta para el aprendizaje significativo de la estrategia de sustracción como adición (ejemplo, para 13 – 8 piensa “¿qué + 8 = 13?”): (a) operaciones inversas (sumar 8 se deshace restando 8); (b) relaciones parte-todo comunes (5 + 8 y 13 – 8 comparten el mismo todo 13 y las partes 5 y 8) y (c) principio de complemento en relaciones parte-todo (si 5 y 8 dan el todo 13, al restar una parte al todo se obtiene la otra parte). 2016-03-28T08:37:07Z 2016-03-28T08:37:07Z 2016-03 info:eu-repo/semantics/article Baroody, A.J. Curricular approaches to connecting subtraction to addition and fostering fluency with basic differences in grade 1. PNA, 10(3): 161-190 (2016). [http://hdl.handle.net/10481/40449] 1887-3987 http://hdl.handle.net/10481/40449 eng PNA;10 http://creativecommons.org/licenses/by-nc-nd/3.0/ info:eu-repo/semantics/openAccess Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License Grupo de Investigación Didáctica de la Matemática: Pensamiento Numérico (FQM-193)