Measurement and Geometry in Upper Primary School

The relation between creativity and students’ performance on different types of geometrical problems in elementary education

“…Closedended non-routine problems require students to apply existing knowledge of facts and procedures to a novel problem not encountered before, for example when students are asked to draw a floor map of a still-life painting (Schoevers et al, 2020b). While this novel problem is conceptually similar to a routine block construction problem, the novel problem requires students to figure out how to apply their knowledge and skills to make the map (Gravemeijer et al, 2007). An example of an open-ended non-routine problem is a multiple solution task in which students have to compare different plane figures (e.g., isosceles triangle, right-angled triangle, square) and are invited to give multiple answers to the question of how the plane figures differ from each other.…”

“…For example, a target figure, such as a block construction, needs to be stored temporarily in memory in order to mentally rotate the construction to see how it would look from another perspective. In addition, general mathematical ability should be taken into account, since basic mathematical procedures and knowledge about, for example, numbers, proportions and measurement, can be used to solve geometrical problems (Gravemeijer et al, 2007). Gender might also play a role.…”

“…Geometry education aims to teach students to understand, explain and predict geometric phenomena, to reason spatially, and to order and organize spatial situations. For example, it is considered important that students be able to draw a map or to reason about the effect of the height of the sun on the length of the shadow (Gravemeijer et al, 2007). Typical topics in geometry in the upper grades of elementary school are (1) 'spatial sense', including localizing, taking a standpoint and navigation, (2) 'plane and solid figures', including spatial properties and relations between figures, operations, transformations and constructions, and (3) 'visualization and representation', including representations of two-dimensional and three-dimensional reality (Gravemeijer et al, 2007).…”

Algorithms . . . Alcatraz: Are children prisoners of process?

“…Goutard's short article discussed above implies that students who have a conceptual understanding of the mechanics of an operation (in this case division) are well placed to learn how to use an algorithm at a later time, if indeed they need to do so. This is supported by Gravemeijer and van Galen (2003) who said that teaching an algorithm without understanding results in isolated and unconnected knowledge which is only useful to students in familiar situations and which they find difficult to apply more widely.…”

Estudio comparativo de cálculo mental y escrito en tercer ciclo de educación primaria

“…Desde entonces, han sido muy numerosos los autores que han analizado el insuficiente sentido pedagógico que los algoritmos tradicionales tienen en la actualidad (Martínez Montero, 2011), los errores conceptuales que pueden causar los algoritmos tradicionales de las cuatro operaciones básicas (Van de Walle et al, 2020), además de la posibilidad de ser sustituidos por el cálculo mental para números pequeños y el uso de la calculadora para números grandes (Gómez Alfonso, 1988;Maza, 1989;1991). Otros autores consideran que la enseñanza de los algoritmos escritos verticales podría debilitar el aprendizaje significativo del estudiante (Gravemeijer y Van Galen, 2003;Heirdsfield y Cooper, 2004;Kamii y Dominick, 1998). Gallardo Romero (2014), realiza un análisis de la situación actual de los algoritmos tradicionales y su uso en la escuela, así como las tendencias en la enseñanza del cálculo aritmético elemental y las formas propias que ingenian los estudiantes para facilitar la resolución de las operaciones, sobre todo cuando presentan dificultades en el aprendizaje de estos algoritmos.…”