A stratégiahasználat rugalmassága az alsó tagozatos matematikában: elemzés és fejlesztés

A neveléslélektan kutatói és a matematikát tanítók régóta hangsúlyozzák annak pedagógiai jelentőségét, hogy felismerjük és serkentsük a gyerekek önmaguk alkotta stratégiáinak rugalmasságát, ami fontos pillére az alsó tagozatos matematikatanítás innovatív megközelítésének. Készítettek és kipróbáltak olyan tananyagokat és fejlesztő programokat, amelyekkel ezt a fajta rugalmasságot kívánták növelni (lásd például Brownell, 1945; Freudenthal, 1991; Thompson, 1999; Wittmann és Müller, 1990-92). A múlt század végének számos reform-tantervében megjelenik a stratégia-rugalmasság kifejlesztésének pedagógiai értékéről alkotott meggyőződés

Evaluating the Effect of Labeled Benchmarks on Children’s Number Line Estimation Performance and Strategy Use

Some authors argue that age-related improvements in number line estimation (NLE) performance result from changes in strategy use. More specifically, children’s strategy use develops from only using the origin of the number line, to using the origin and the endpoint, to eventually also relying on the midpoint of the number line. Recently, Peeters et al. (unpublished) investigated whether the provision of additional unlabeled benchmarks at 25, 50, and 75% of the number line, positively affects third and fifth graders’ NLE performance and benchmark-based strategy use. It was found that only the older children benefitted from the presence of these benchmarks at the quartiles of the number line (i.e., 25 and 75%), as they made more use of these benchmarks, leading to more accurate estimates. A possible explanation for this lack of improvement in third graders might be their inability to correctly link the presented benchmarks with their corresponding numerical values. In the present study, we investigated whether labeling these benchmarks with their corresponding numerical values, would have a positive effect on younger children’s NLE performance and quartile-based strategy use as well. Third and sixth graders were assigned to one of three conditions: (a) a control condition with an empty number line bounded by 0 at the origin and 1,000 at the endpoint, (b) an unlabeled condition with three additional external benchmarks without numerical labels at 25, 50, and 75% of the number line, and (c) a labeled condition in which these benchmarks were labeled with 250, 500, and 750, respectively. Results indicated that labeling the benchmarks has a positive effect on third graders’ NLE performance and quartile-based strategy use, whereas sixth graders already benefited from the mere provision of unlabeled benchmarks. These findings imply that children’s benchmark-based strategy use can be stimulated by adding additional externally provided benchmarks on the number line, but that, depending on children’s age and familiarity with the number range, these additional external benchmarks might need to be labeled

Adapting strategy choices to situational factors: the effect of time pressure on children's numerosity judgement strategies

The present study investigated the effect of time pressure on 6th graders' (11-12 years old) numerosity judgement strategies under three different time pressure conditions. Time pressure was manipulated by varying the maximum presentation time of the stimuli on three different levels: 5 s in the severe, 10 s in the moderate, and 20 s in the low time pressure condition. Analysis of the results in terms of the theoretical framework of Lemaire and Siegler (1995) revealed an effect of increasing time pressure on several parameters of strategy use such as participants' strategy repertoire, relative frequency of strategy use and efficiency of strategy execution. Unexpectedly, we did not observe a significant decline in the adaptiveness of strategy choices as a function of item characteristics. Taken as a whole, these results indicate that children are already at a young age able to adapt their strategy use to the external demands of a task.Afdeling Didactiek. Departement Pedagogische wetenschappen. Centrum voor Instructiepsychologie en -technologie. Leuvens Instituut voor onderwijsonderzoek (LIVO)status: publishe

Estimation of 'real' numerosities in elementary school children

Groups of mathematically strong and weak second-, fourth- and sixth-graders were individually confronted with numerosities smaller and larger than 100 embedded in one-, two- or three-dimensional realistic contexts. While one third of these contexts were totally unstructured (e.g. an irregular piece of land jumbled up with 72 cars), another third had a clear structure (e.g. a 16x4 rectangular parking lot completely filled with 64 cars), and a last third had a "semi-structure" (e.g. the same 16x4 parking lot but with a number of cars missing). Besides analyzing the effects of different task and subject variables on pupils' accuracy and response-time data, the study involved an analysis of their estimation strategies, with an emphasis on multiplicative strategies that profited by some of the tasks' geometrical (semi-)structure. It was found that many children actually made use of such strategies, that using these strategies did however not always lead to accurate estimations, and that their frequency and efficiency increased with age.status: publishe

Analysing strategy use in terms of the four parameters of strategic competence : contributions from a numerosity judgement task

En el presente trabajo se analizan tres estudios basados en el marco teórico de Lemaire y Siegler (1995) para el análisis del uso de estrategias en el contexto de una tarea de juicio de cantidad (numerosity). Este marco distingue entre cuatro diferentes parámetros de la competencia estratégica: el repertorio, la frecuencia, la eficiencia y la adaptabilidad. En el Estudio 1, se aplicó este marco para el análisis de los cambios evolutivos en las estrategias sobre juicios de cantidad. En el Estudio 2, se analizó la contribución de la inteligencia en estos cuatro parámetros y se evaluó en qué medida el suministro de información podría conducir a una mejora en uno o más de estos parámetros. En el Estudio 3, se investigó si las variaciones en el contexto de la tarea darían lugar a alteraciones en uno o varios de estos parámetros. Al final de este trabajo, reflejamos la amplia aplicabilidad de este marco teórico y los resultados que la investigación ha proporcionad

ANALIZANDO EL USO DE ESTRATEGIAS EN TÉRMINOS DE CUATRO PARÁMETROS DE LA COMPETENCIA ESTRATÉGICA: CONTRIBUCIONES DE UNA TAREA DE JUICIO DE CANTIDAD

The present paper discusses three studies that all relied on Le-maire and Siegler's (1995) theoretical framework for analyzing people's strategy use in the context of a numerosity judgment task. This framework distinguishes between four different parameters of strategic competence: repertoire, frequency, efficiency and adaptivity. In Study 1, we applied this framework for studying developmental changes in children's numerosity judgment strategies. In Study 2, we analysed the contribution of intelligence on these four parameters and assessed the extent to which the provision of feedback could lead to an improvement in one or more of these parameters. In Study 3, we investigated whether variations in the task context would lead to alterations in one or several of these parameters. At the end of the paper, we reflect on the broader applicability of this theoretical framework and the research findings that it has yielded.En el presente trabajo se analizan tres estudios basados en el marco teórico de Lemaire y Siegler (1995) para el análisis del uso de estrategias en el contexto de una tarea de juicio de cantidad (numerosity). Este marco distingue entre cuatro diferentes parámetros de la competencia estratégica: el repertorio, la frecuencia, la eficiencia y la adaptabilidad. En el Estudio 1, se aplicó este marco para el análisis de los cambios evolutivos en las estrategias sobre juicios de cantidad. En el Estudio 2, se analizó la contribución de la inteligencia en estos cuatro parámetros y se evaluó en qué medida el suministro de información podría conducir a una mejora en uno o más de estos parámetros. En el Estudio 3, se investigó si las variaciones en el contexto de la tarea darían lugar a alteraciones en uno o varios de estos parámetros. Al final de este trabajo, reflejamos la amplia aplicabilidad de este marco teórico y los resultados que la investigación ha proporcionado

Anales de psicología

Resumen tomado parcialmente de la revista.- El artículo forma parte de un monográfico de la revista dedicado a Psicología de las MatemáticasEn el presente trabajo se analizan tres estudios basados en el marco teórico de Lemaire y Siegler (1995) para el uso de estrategias en el contexto de una tarea de juicio de cantidad (numerosity). Este marco distingue entre cuatro diferentes parámetros de la competencia estratégica: el repertorio, la frecuencia, la eficiencia y la adaptabilidad. En el primer estudio se aplicó este marco para el análisis de los cambios evolutivos en las estrategias sobre juicios de cantidad. En el segundo estudio, se analizó la contribución de la inteligencia en estos cuatro parámetros y se evaluó en qué medida el suministro de información podría conducir a una mejora en uno o más de estos parámetros. En el tercer estudio se investigó si las variaciones en el contexto de la tarea dan lugar a alteraciones en uno o varios de estos parámetros. Al final de este trabajo, se refleja la amplia aplicabilidad de este marco teórico y los resultados que la investigación ha proporcionado..MurciaConsejería de Educación, Formación y Empleo. Biblioteca; Avda. de la Fama, 15; 30006 Murcia; +34 968279685; +34 968279835; [email protected]

Measurement, development, and stimulation of computational estimation abilities in kindergarten and primary education: A systematic literature review

For several decades computational estimation is seen as an important topic in primary mathematics education. While previous narrative literature reviews on computational estimation summarized the available research on computational estimation abilities in students and adults, the present systematic literature review focuses on the measurement, development, and stimulation of computational estimation abilities in kindergartners and primary school children. Reviewing 28 studies revealed that these abilities were mostly investigated from 8-years old onwards by using a variety of measures. Age-related improvements in estimation performance and strategy use were observed in most studies. Only very few studies addressed the targeted stimulation of computational estimation abilities. The current review identified several gaps in the research literature, such as the absence of studies investigating the relationship between computational estimation performance and other basic numerical and mathematical abilities in children, and the paucity of longitudinal studies on the development of computational estimation ability.status: publishe