How many apples make a quarter? The challenge of discrete proportional formats

From Non-symbolic to Symbolic Proportions and Back: A Cuisenaire Rod Proportional Reasoning Intervention Enhances Continuous Proportional Reasoning Skills

“…Together, these studies suggest that improvements in one format should also be reflected in other formats due to proportional magnitudes being processed in an amodal manner. However, this conclusion is difficult to reconcile with the persistent decrements in performance found in non-symbolic discrete formats (Jeong et al, 2007;Begolli et al, 2020). An alternative line of research (Boyer and Levine, 2015;Hurst and Cordes, 2018;Abreu-Mendoza et al, 2020) suggests priming continuous proportional reasoning immediately before discrete stimuli mitigates the challenges of discrete proportional reasoning.…”

Fraction Symbols and their Relation to Conceptual Knowledge

“…Thus, to describe the visual representations, it is necessary for researchers to distinguish between fractions of continuous versus discrete quantities. Visual representations of continuous quantities have been referred to as area models (e.g., Fuchs et al, 2017;Roesslein & Codding, 2019), discretized models (Begolli et al, 2020) continuous models (Newstead & Murray, 1998) and part-whole models (Misquitta, 2011). The area model label is limited because it precludes representations of linear or volumetric quantities.…”

“…For example a circle showing 3 out of 4 sections shaded or a beaker that is filled to the 3 rd of 4 tick marks both refer to the fraction Some visual fraction representations are more difficult for students to name than others (Behr et al, 1983;Brousseau et al, 2004;Charalambous & Pitta-Pantazi, 2007). For example, students aged 7 to 12 were more successful identifying equivalent fractions when they compared part-whole representations (i.e., 3 out of 4 sections of a rectangle coloured) than comparing discrete representations (i.e., 3 out of 4 balls) (Begolli et al, 2020). Students in fourth and fifth grade were more successful mapping visual representations of unit fractions presented as partwhole area models (rectangles and circles) than those presented as continuous number line models (Tunç-Pekkan, 2015).…”

“…The fraction mapping task was a novel iPad app developed to allow students to show how to accurately they could connect the three forms of mathematical discourse: visual representations, symbols, and words. To control for any effect of representation type, the mapping task included an equal number of part-whole models (e.g., area and volume representations) and discrete models (Begolli et al, 2020;Bruce et al, 2013;Hebert & Powell, 2016;Rau & Matthews, 2017).…”

A Importância da Explicitação da Correspondência Um para Muitos na Resolução de Problemas de Estrutura Multiplicativa

“…ISSN 1980-4415 DOI: http://dx.doi.org/10.1590/1980 ou grandes (de três ou mais dígitos) surgem como um dos aspectos mais investigados na literatura, sobretudo em pesquisas sobre o conceito de proporção, como é o caso do estudo clássico de Piaget, Grize, Szeminska e Bang (1968) cujo principal resultado foi que as crianças tinham um melhor desempenho em tarefas com quantidades contínuas do que com quantidades discretas. Resultado semelhante foi obtido em diversas pesquisas (BEGOLLI et al, 2020;BOYER;LEVINE, 2015;HURST;CORDES, 2018;JEONG;HUTTENLOCHER, 2007;SPINILLO;BRYANT, 1999) que, de modo geral, revelaram que crianças da Educação Infantil e de Anos Iniciais do Ensino Fundamental apresentavam mais dificuldades em lidar com a proporção quando as quantidades eram discretas do que quando as quantidades eram contínuas.…”