Investigating secondary students beliefs about mathematical problem-solving

Abstract

Many studies over the past thirty years have highlighted the important role of students' beliefs for successful problem solving in mathematics. Given the recent emphasis afforded to problem solving on the reformed Irish secondary school mathematics curriculum, the main aim of this study was to identify Irish students' (n = 975) beliefs about the field. A quantitative measure of these beliefs was attained through the use of the Indiana Mathematical Belief Scale, an existing thirty item (five scale) self-report questionnaire. A statistical analysis of the data revealed that students who were further through their secondary education had a stronger belief that not all problems could be solved by applying routine procedures. In contrast, the same students held less positive beliefs than their younger counterparts that they could solve time-consuming problems and that conceptual understanding was important. The analysis also indicated that gender had a significant impact on three of the five belief scales.

Mathematics as a gendered subject: a deeper insight into students’ attitudes in Irish post-primary schools

“…As such, while the reform encourages the collaborative and realistic approaches described in feminist mathematics pedagogy (Anderson 2005;Spielman 2008), it is evident that girls are still struggling with lower confidence in having to implement a scientific problem-solving approach. This is further supported by Prendergast et al (2018), who found that, in Ireland, female students had lower belief in their ability to solve time-consuming problems than their male peers and had lower levels of belief that effort could increase mathematical ability. This could be considered one of the factors in the continually negative attitudes of females to mathematics, despite the increase of more modern, inclusive methodologies.…”

Estrategias resolutivas de Allan Schoenfeld y la solución de problemas matemáticos de alta demanda cognitiva en estudiantes de cuarto año de secundaria de un colegio ubicado en el distrito de Magdalena del Mar de Lima Metropolitana

“…Al contextualizar los problemas, Prendergast et al, (2018) sugiere que las creencias de los estudiantes sobre la utilidad del curso tienen relación con su desempeño en la resolución de problemas por lo que deja en claro que existe un vínculo entre las creencias de los estudiantes sobre la resolución de problemas en matemáticas y su desempeño en la materia. La gran mayoría de estudiantes manifiesta ciertas creencias según como haya sido su experiencia en años anteriores, según como lo han experimentado sus padres o incluso sus mismos docentes.…”

“…Desde muchos años, existe una creciente preocupación ya generalizada porque la resolución de problemas sea una actividad del pensamiento como resultado del análisis-razonamiento y no una mera aplicación repetitiva y mecánica de algoritmos con la única intención de obtener un resultado sin el debido tiempo de razonar si dichos procedimientos responden a la solución del problema (Prendergast et al, 2018;Lane et al, 2016;Gijsbers et al, 2019). En la mayoría de los casos se ve que se trata de una mera aplicación de algoritmos repetidos sin operacionalizar las situaciones problemáticas de la vida real donde se pueda medir las competencias interpretativas y argumentativas de las mismas.…”

Success Indicators of Mathematical Problem-Solving Performance Among Malaysian Matriculation Students

“…Students believe that attempts to study can motivate them to successfully solve mathematics problems (Prendergast et al, 2018).…”