The Stages of Student Mathematical Imagination in Solving Mathematical Problems

Abstract

This research is a qualitative study that aimed to describe the stages of students mathematical imagination in solving mathematical problems. There are three kinds of mathematical imagination in solving mathematical problems, namely sensory mathematical imagination, creative mathematical imagination and recreative mathematical imagination. Students can produce one kind of mathematical imagination or other kinds of mathematical imagination. Problem sheet is used as a supporting instrument to find out the stages of students mathematical imagination in solving problems. Three students are used as research subjects in whom students were able to produce their mathematical imagination in solving mathematical problems. The results showed that there are three stages of students mathematical imagination in solving mathematical problems, the first stage is sensory mathematical imagination, the second stage is creative mathematical imagination, and the last stage is recreative mathematical imagination.

Characteristics of Students Sensory Mathematical Imagination in Solving Mathematics Problem

“…Visual representation that done of subject in this case is a form of sensory mathematical imagination. It reinforced the opinion Wibowo & As'ari (2014) who said sensory mathematical imagination can be seen through appear of the idea based on students perception in solving mathematics problems. In line with that expressed by Currie & Ravenscroft (2002) that sensory imagination can appear through perception such as stimulus of the problem.…”

“…The based assumption is when students in face of mathematics problem, mathematical imagination can help thinking of students in finding solution ideas to solving the problem. Wibowo & As'ari (2014) divides three types of students mathematical imagination in solving mathematics problem, namely sensory mathematical imagination, creative mathematical imagination, and recreative imagination mathematical. Sensory imagination basically is perception such as the stimulation of problem (Currie & Ravenscroft, 2002).…”

“…This idea is a form of imagination that is appeared by students. Wibowo & As'ari (2014) said, sensory mathematical imagination can be seen through appear of the idea based on perception after receiving stimuli of the problem. How characteristics of students sensory mathematical imagination in solving mathematics problems?…”

Evidencias pedagógicas de gamificación: autoconstrucción y etnoculturalidad de aprendizajes matemáticos

“…En cierta medida, estos rasgos etnoculturales han brindado mejor adaptabilidad al problema (Lee, 2016;Viterbori et al, 2017), debido al potencial lúdico que representa desarrollar un problema desde el medio o recurso intercultural, lo que incrementó la posibilidad de aciertos luego del desarrollo del programa. En este caso, la flexibilidad cognitiva ha sido posible por el desarrollo de la capacidad de análisis en los niños del grupo experimental, lo cual confirma la teoría antepuesta sobre resolución de operaciones (D´Amore e Fandiño, 2013;D´Amore e Fandiño, 2006;D´Amore, 2006), y se ha influenciado en el pensamiento del estudiante con el fin de incrementar su imaginación sensorial y creativa para desarrollar soluciones inesperadas o lograr obtener resultados con mecanismos sin verticalidad (Wibowo et al, 2017).…”

“…La gamificación basada en etnoculturalidad ha demostrado que la internalización de procesos de resolución desde el uso de elementos culturales predispone las estructuras cuando se aplica la imaginación sensorial y creativa (Wibowo et al, 2017), en algunos casos el material autóctono proporciona libertad al estudiante, sobretodo porque permite alejarlo del desarrollo de esquemas de solución tradicional, para utilizar la lenguaje como aspecto sociocultural ISSN: 2225-7136(impresa)-2304-0335(en línea) primordial en el desarrollo de problemas en equipo (Planas, 2018;Ru-Fen, 2016), y en otro casos, se ha encontrado que los materiales didácticas estructurados como el Tangram, multibase y regletas son más efectivos si se asemejan más al origen cultural de los sujetos que los manipulan (Murillo, Román y Atrio, 2016).…”