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

Abstract

The objective of this study was to identify cognitive apprehensions used by fifth-and sixth-grade students (10-12-year-olds) when answering far generalization questions in two problems of visual pattern generalization. A total of 81 students solved two linear generalizing problems, presented in two different configurations, in a succession of figures (square tables or trapezoid tables). The results showed that students used different types of cognitive apprehensions to solve problems and that these apprehensions sometimes changed according to the configuration of the sequence of figures. This finding indicates that configurations could determine apprehensions used by students, which in some cases led to the emergence of algebraic thinking. In addition, difficulties in modifying apprehension and a lack of coordination between spatial and numerical structures could explain some students' difficulties in far generalization.

Relations between complexity and difficulty on repeating-pattern tasks in early childhood (Relaciones entre complejidad y dificultad en tareas con patrones reiterativos en la primera infancia)

“…So much so that different psychological tests involve a variety of patterning tasks as part of their study area (e.g., Kaufman & Kaufman, 1983;Raven et al, 1992;Wechsler, 1991). With regard to mathematics development, the literature documents a similar situation, with studies on number patterns (Baroody et al,2015;Zazkis & Liljedahl, 2002), growing/shrinking patterns (English & Warren, 1998;Papic, 2015), spatial/geometric patterns (Hendricks et al, 2006), repeating patterns (Rittle-Johnson et al, 2019;Threlfall, 1999), structural generalizations (determining pattern rules, Callejo et al, 2019;Economopoulos, 1998;Rivera, 2013;Zazkis & Liljedahl, 2002) or abstract language patterns (Fyfe et al, 2015).…”

“…Tanto es así, que diferentes test psicológicos incluyen una amplia variedad de tareas de reconocimiento de patrones de repetición como parte de su evaluación (por ejemplo, Kaufman & Kaufman, 1983;Raven et al, 1992;Wechsler, 1991). Con respecto al desarrollo matemático, la literatura documenta una situación similar, con estudios sobre patrones numéricos (Baroody et al,2015;Zazkis & Liljedahl, 2002), patrones de crecimiento/decrecimiento (English & Warren, 1998;Papic, 2015), patrones espaciales/ geométricos (Hendricks et al, 2006), patrones de repetición (Rittle-Johnson et al, 2019;Threlfall, 1999), estructuras generalizables (determinación de reglas en patrones, Callejo et al, 2019;Economopoulos, 1998;Rivera, 2013;Zazkis & Liljedahl, 2002) o patrones con lenguaje abstracto (Fyfe et al, 2015). La investigación empírica que se está llevando a cabo actualmente está proporcionando evidencias que indican que el conocimiento relacionado con los patrones de repetición puede desempeñar un papel fundamental en el rendimiento matemático y académico de los estudiantes.…”