Tracking informal fraction knowledge and its correlates across first grade.

Abstract

Young children have informal knowledge of fractions before learning about fraction symbols in school. In the current study, we followed 103 children in the Mid-Atlantic United States from the fall to the spring of first grade to characterize the development of individual differences in early informal fraction knowledge, as well as its relation to other mathematical and cognitive skills. Most children in our sample showed some early fraction knowledge at the beginning of first grade, especially with nonsymbolic fractions and halving, and this knowledge improved over the school year without explicit instruction in fractions. However, there were large individual differences in early fraction knowledge at the start of first grade, which explained significant variance in math achievement at the end of first grade, even when controlling for whole number knowledge and a variety of cognitive skills. Start-of-year whole number knowledge, but not spatial scaling or proportional reasoning, also predicted early end-of-year fraction knowledge. These data can inform activities for learning in the early years to foster both early fraction and integer knowledge in parallel, which may better prepare students for later formal instruction in fractions.

From one half to 12th: acquisition of fraction writing in adult education program students and children

“…Throughout their lives, AEP-1 students also accumulated experiences with whole numbers in formal and informal contexts, which may support their performance in fraction tasks and limit the quantity and type of errors they make. Previous studies have shown that students' whole number knowledge predicts their performance in fraction tasks (e.g., Sidney & Alibali, 2017;Viegut et al, 2023). Future studies should investigate how whole number skills predict fraction skills in AEP-1 students, to identify pedagogical approaches that may support this particular group.…”

“…Both studies found that children read and write fractions as whole numbers, justifying our hypotheses. Finally, we predicted that informal numerical experiences (e.g., outside the school setting) may be associated with fraction writing skills based on previous studies on whole-number knowledge, which have shown that informal mathematics experience contribute to formal mathematics skills in general (e.g., Benavides-Varela et al, 2023;LeFevre et al, 2009;Levine et al, 2011;Napoli & Purpura, 2018;Ramani et al, 2015;Siegler & Ramani, 2009), and fraction skills, specifically (Viegut et al, 2023).…”

“…Mastering the ability to transcode fractions (i.e., converting one fraction notation to another, such as from a verbal form "one half" to a written form " 1 2 ", and vice versa) is an essential step in developing basic fraction knowledge. However, only a few studies have investigated fraction transcoding skills (Gelman, 1991;Saxe, 2005;Viegut, 2023). To date, no study has systematically analyzed the type of errors students make when converting the verbal representations of fractions to the common notation (i.e.,…”

“…In daily life, fractions are used by children and adults in different contexts, including talking about time (e.g., "a quarter after one", "três e meia [three and a half]") and money (e.g., "quarter dollar", "⅓ de desconto [⅓ discount]"), understanding and estimating quantities (e.g., "½ kg de carne [½ kg of beef]", "⅔ cup of flour", "half pizza") and solving ordinary problems (e.g., "how much should it cost to fill your car's tank if it is half full and a gallon of gas costs $3.25?"). Some studies have shown that preschool and 1 st -grade children-who have not yet learned about fractions in schools-can already reason about proportions using "half" as a boundary and link some unit fractions with the magnitude they represent (Hunting & Sharpley, 1988;Paik & Mix, 2003;Spinillo & Bryant, 1991;Viegut et al, 2023). Therefore, students may learn how to read and write fractions via daily life activities, even before formal educational experiences.…”