SECOND-GRADERS' MATHEMATICAL PRACTICES FOR SOLVING FRACTION TASKS.

Moyer-Packenham, Patricia S.; Bolyard, Johnna J.; Tucker, Stephen I.

Recently, over 40 states in the United States adopted the Common Core State Standards for Mathematics (CCSSM) which include standards for content and eight standards for mathematical practices. The purpose of this study was to better understand the nature of young children's mathematical practices through an exploratory examination of the practices of a group of second-grade students engaged in several mathematical tasks focused on rational number concepts. Twenty-five second-grade students completed three fraction tasks in structured clinical interviews. The interviews and student work were analyzed using an interpretational analysis to examine the data for constructs, themes, and patterns that were useful in explaining children's mathematical practices. The results reveal that children used a variety of mathematical practices during the interviews to respond to the mathematical problems presented. Children's mathematical practices were both a product that they used to solve the mathematical situations, and a process that was developing during the interactions of the interview. The findings lead to new insights about how mathematical practices develop and what promotes their development. A decade ago, the RAND Mathematics Study Panel (2003) identified mathematical practices as highly important and suggested that a better understanding of the nature of mathematical practices had the potential to have significant impacts on the improvement of student learning. One particular concern of the panel was that mathematical practices are often left implicit in curriculum and standards documents, which can lead to them being overlooked during instruction. Another concern was that there were many unanswered questions about mathematical practices, which has led to them being misunderstood by teachers and curriculum developers. In 2010, the Common Core State Standards for Mathematics (CCSSM) brought mathematical practices to the fore by laying out eight Standards for Mathematical Practice (National Governor's Association Center for Best Practices, 2010). These practices are: a) make sense of problems and persevere in solving them; b) reason abstractly and quantitatively; c) construct viable arguments and critique the reasoning of others; d) model with mathematics; e) use appropriate tools strategically; f) attend to precision; g) look for and make use of structure; and, h) look for and express regularity in repeated reasoning. The CCSSM note that "The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students" (National Governor's Association Center for Best Practices, 2010, p. 6). In the CCSSM documents, descriptions are provided for each of the eight mathematical practices. But what do mathematical practices "look like" when students are employing them during mathematical tasks? Are there some mathematical practices that are more common or well-developed in children from an early age and other mathematical practices that take a great deal of time and experience to develop? While there are large bodies of research focused on specific mathematical content domains (e.g., number operations, fractions, geometry), there are virtually no studies that place emphasis on examining students' mathematical practices as defined in the CCSSM. The present study sought to begin the conversation on the CCSSM's Mathematical Practices that are employed by children during mathematical tasks. The purpose of this study was to better understand the nature of young children's mathematical practices through an exploratory examination of the practices of a group of second-grade students engaged in several mathematical tasks focused on rational number concepts.

FRACTIONS; MATHEMATICS teachers; MATHEMATICS students; MATHEMATICS education; MATHEMATICAL ability

Investigations in Mathematics Learning, 2014, Vol 7, Issue 1, p54

1947-7503

Academic Journal

10.1080/24727466.2014.11790338