Children’s Conceptions of Area Measurement and Their Strategies for Solving Area Measurement Problems

Abstract

This study investigated children's understanding of area measurement, including the concept of area and the area formula of a rectangle, as well as their strategic knowledge for solving area measurement problems. Twenty-two fourth-graders from three classes of a public elementary school in Taipei, Taiwan, participated in a one-on-one interview. Results show that the children who had a good understanding of the concept of area and the area formula (by using the property of multiplication) exhibited competency in identifying geometric shapes, using formulas for determining areas, and self-correcting mistakes. The children who had a good understanding of multiplication underlying the area formula, but misunderstood the concept of area, showed some ability to use area formulas. Conversely, the children who were unable to interpret the property of multiplication underlying the area formula irrespective of their conceptions of area exhibited the common weaknesses in identifying geometric shapes and differentiating between area and perimeter.

Procedimientos Utilizados por Estudiantes de 13-14 Años en la Resolución de Tareas que Involucran el Área de Figuras Planas

“…Diversos estudios (D'AMORE;FANDIÑO, 2007;HUANG;WITZ, 2013;KOSPENTARIS;SPYROU;LAPPAS, 2011;ZACHAROS, 2006) han mostrado que un gran ISSN 1980-4415 DOI: http://dx.doi.org/10.1590/1980 número de estudiantes, tanto de educación primaria como de secundaria y bachillerato, poseen una comprensión limitada del área, vinculándola únicamente con el uso de cálculos que aplican de forma memorística. Esto puede ser porque los estudiantes no comprenden el significado de las fórmulas, ni cómo éstas se originan (D'AMORE;FANDIÑO, 2007).…”

“…El uso de los diferentes SP del área se ve restringido por el conocimiento de la fórmula del área de cuadrados y triángulos. De esta manera, se confirman resultados de investigaciones anteriores (D'AMORE;FANDIÑO, 2007;HUANG;WITZ, 2013;KOSPENTARIS;SPYROU;LAPPAS, 2011;ZACHAROS, 2006), que concluyen que el desempeño de los estudiantes queda limitado casi exclusivamente por el uso de cálculos y fórmulas, aun cuando no se precisa de éstos.…”

Analysing Mathematical Abilities of High School Graduates

“…Faulkenberry (2003) suggests that conceptual knowledge is rich with relations, and refers to the basic mathematics constructs and relations between the ideas that illustrate mathematical procedures, and gives it a For instance, in understanding of area measurement, procedural fluency, and reflections on the accuracy of solutions for measuring areas, represents higher-order thinking skills (Lehrer, 2003). While investigating children's conceptions of Area Measurement and their strategies for solving Area Measurement problems, Huang, Witz (2012) found that children who had a good understanding of the concept of area and the area formula (by using the property of multiplication) exhibited competency in identifying geometric shapes, using formulas for determining areas, and self-correcting Many mathematics skills are involved in problem-solving. However, large numbers of students have not acquired the basic skills they need in mathematics.…”

A Learning Progression for Geometrical Measurement in One, Two, and Three Dimensions

“…(2) Assigns meaning to numerical quantities (i.e., numbers) for the length and width of 2-D figures (Reynolds & Wheatley, 1996); thus, relates the numbers to symbolic representations of geometric properties and formulas for (surface) area measurement and unit conversion (Battista, 2004;Huang & Witz, 2013). Battista, 2004;Reynolds & Wheatley, 1996) or in finding the areas of irregular 2-D figures.…”