Flexibility and coordination among acts of visualization and analysis in a pattern generalization activity

Working With Patterns Through Chess-Based Problems. Strategies and Reasoning Levels of Primary School Students.

“…One aspect to highlight is that the more complex the strategy used, the less visual support the students needed. The variety of strategies found, some of them different from those found in previous literature, is a sign that the activities allow for different ways of solving them, an aspect that favours flexibility (Nilsson & Juter, 2011).…”

“…An important aspect of generalisation is flexibility in strategy use, i.e. the ability to replace one strategy with another when a task demands change (Nilsson & Juter, 2011). There is some research that supports the treatment of Algebra based on pattern generalisation (Molina, 2009;Radford, 2010) from Primary Education.…”

Cognitive apprehension in visual pattern generalization problems / Aprehensión cognitiva en problemas de generalización de patrones visuales

“…Los problemas de generalización de patrones se han estudiado desde diversas perspectivas: las estrategias que los estudiantes utilizan (Rivera & Becker, 2011;Stacey, 1989) y su flexibilidad de uso (Callejo & Zapatera, 2014;Nilsson & Juter, 2011), las características del proceso de generalización (García-Cruz, 1998;Rivera & Becker, 2007), la dimensión semiótica en la expresión de la generalidad (Radford, 2014), la emergencia del pensamiento algebraico temprano (Radford, 2014;Vergel, 2015) y la transición desde la identificación del patrón de crecimiento o relación recursiva a la relación funcional para expresar esta función (Carraher, Martinez, & Schliemann, 2008;Martinez & Brizuela, 2006). Además, diversos estudios muestran que los estudiantes logran identificar mejor las relaciones funcionales en secuencias de patrones visuales que en secuencias numéricas, puesto que las estrategias visuales son más potentes, especialmente cuando comprenden la multiplicación como grupos de (Lannin, 2005;Rivera & Becker, 2011).…”

“…Pattern generalization problems have been studied from different perspectives: students' different strategies (Rivera & Becker, 2011;Stacey, 1989) and the flexibility of their use (Callejo & Zapatera, 2014;Nilsson & Juter, 2011); the characteristics of the process of generalization (García-Cruz, 1998;Rivera & Becker, 2007); the semiotic dimension in the expression of generality (Radford, 2014); the emergence of early algebraic thinking (Radford, 2014;Vergel, 2015); and the transition from the identification of the growth pattern or recursive relation to the functional relationship to express this function (Carraher, Martinez, & Schliemann, 2008;Martinez & Brizuela, 2006). Moreover, several studies show that students succeed better at identifying functional relationships when presented with visual pattern sequences than with numerical sequences, since visual strategies are more powerful, especially when students understand multiplication as groups of (Lannin, 2005;Rivera & Becker, 2011).…”

Middle school students’ patterning performance on semi-free generalization tasks

“…Children and adults have been documented as having a natural disposition toward pattern generalization ("PG;" Cadez & Kolar, 2015;Jurdak & El Mouhayar, 2014;Nilsson & Juter, 2011;Rivera, 2013;Tanisli & Özdas, 2009;Walkowiak, 2014;Wilkie, in press). PG is an ability that involves constructing and justifying a well-defined mathematical structure for a given set of initial cues or particular cases.…”