Papers by Jessica Shumway
This study examined 371 third and fourth grade students’ fraction pictorial representations for e... more This study examined 371 third and fourth grade students’ fraction pictorial representations for evidence of whole number bias. Students exhibited difficulties in developing and using fractional representations. Four areas of whole number bias were identified in the students’ representations; naming fractions, partitioning, comparing fractions, and developing equivalence. Introduction Many students struggle with the development of fraction understanding. Fractions, unlike whole numbers, describe a relationship instead of a discrete quantity (Smith, 2002; Van de Walle, 2004). Students’ tendency to incorrectly use whole number schemes to interpret fractions is called “whole number bias” and often results in the development of fraction misconceptions (Ni & Zhou, 2005). As students seek to understand new concepts, they develop internal representations which become fundamental to how the students understand and use the new concepts (NCTM, 2000). Students’ drawn pictorial representations s...
Australian primary mathematics classroom, 2016
An investigation of how an app can influence children's mathematical learning in different wa... more An investigation of how an app can influence children's mathematical learning in different ways. Suggestions are made on several aspects teachers may consider when selecting apps for students.
The purpose of this study was to examine shifts in young children’s learning progression levels w... more The purpose of this study was to examine shifts in young children’s learning progression levels while they interacted with virtual manipulative mathematics apps on touch-screen devices. Researchers developed learning progressions to analyze video data of the interviews. Our results showed that it is possible to document evidence of shifts in children’s learning progressions while they are interacting with mathematics apps and indicated patterns in the children’s interactions that were related to the shifts in their learning progression levels. Design features such as an open-ended number of tasks with a variety of representations and tasks at varying levels of difficulty led to children refining their understanding and shaping their concept image of mathematical ideas resulting in incremental shifts in learning
International Journal for mathematics teaching and learning, 2016
The purpose of this study was to identify and describe students’ use of number sense as they solv... more The purpose of this study was to identify and describe students’ use of number sense as they solved story problem tasks. Three 8- and 9-year-old students participated in clinical interviews. Through a process of holistic and qualitative coding, researchers used the number sense view as a theoretical framework for exploring how students’ number sense was reflected in their numerical reasoning and verbal explanations of strategies for solving story problems. The results suggest that students’ coordination of number sense constructs affords flexibility in problem-solving and deeper understanding of place value. Implications for classroom practice and mathematics education research are discussed.
International Journal for mathematics teaching and learning, 2018
The purpose of this study was to explore the variations in students’ achievement on computational... more The purpose of this study was to explore the variations in students’ achievement on computational fluency assessments and variations in strategies for solving computation problems. Computational fluency was defined as a student’s ability to compute flexibly, accurately, efficiently, and appropriately. Sevenand eight-year-old students completed four paper-pencil assessments and participated in four interviews about their strategies for solving computation problems. Researchers used a mixed methods design using test scores and interviews that measured six students’ development of computational fluency at four time points over nine weeks. The results showed that there was variation in students’ assessment scores and strategy use, and the quantitative and qualitative data converged or diverged at various measurement points. The divergent results highlighted a trend of improved strategy use in the interviews parallel to a decrease in test scores. Implications for mathematics teachers are...
The Journal of Computers in Mathematics and Science Teaching, 2018
Functional near-infrared spectroscopy (fNIRS) is an easy to use neuroimaging technique that is po... more Functional near-infrared spectroscopy (fNIRS) is an easy to use neuroimaging technique that is portable and maintains a liberal tolerance to movement. As such, fNIRS represents an ideal tool to observe children’s neural activity as they engage in real-world classroom activities, such as the interaction with digital math apps on an iPad. Here, we provide the results of an initial hypothesis-generating pilot study designed to assess patterns of cortical activity that occur when children interact with digital math apps, that contained virtual manipulatives, on a touch-screen device. Our results highlight cortical activity within the bilateral intraparietal sulci and dorsolateral prefrontal cortices as children interacted with three different digital math apps, but not during rest. Our results provide valuable proof-of-concept that fNIRS may be used to assess math-related cortical activity during children’s naturalistic use of digital math apps on a touch-screen device
Australian primary mathematics classroom, 2016
Teachers increasingly use virtual manipulatives and other apps on touch-screen devices (e.g., iPa... more Teachers increasingly use virtual manipulatives and other apps on touch-screen devices (e.g., iPads) in an effort to help students understand mathematics concepts. However, students experience these apps and their affordances in different ways. The purpose of this article is to inform teachers’ decisions about app implementation in the classroom through discussion of four case studies illustrating ways children interacted with the app Motion Math: Zoom, and how these interactions revealed, concealed, and developed children’s mathematical understanding. These results suggest that mathematics virtual manipulative apps on touch-screen devices can be useful tools when thoughtfully implemented.
International Group for the Psychology of Mathematics Education, 2011
Teacher Educator’s questioning strategies are essential in maintaining the level of cognitive dem... more Teacher Educator’s questioning strategies are essential in maintaining the level of cognitive demand of tasks for preservice teachers’ learning of mathematics for teaching. Classroom discourse has been known to maintain the level of cognitive demand of tasks. However, qualitative differences exist in the use of discourse. This study focuses on comparing instructors’ questioning strategies with two groups of preservice elementary teachers using the same cognitively challenging task on surface area, where in one group the level of the cognitive demand of the tasks is maintained while in the other it is lowered. We highlight effective questioning strategies during whole group discussion.
Journal of Education, 2013
The study reported here examined virtual manipulatives as an instructional treatment in 17 third-... more The study reported here examined virtual manipulatives as an instructional treatment in 17 third- and fourth-grade classrooms. Students were randomly assigned to two treatment groups: texts and physical manipulatives (PM), and virtual manipulatives (VM). Results revealed no significant differences in achievement between the treatments. Additional results showed that objective ability predicted fraction achievement; virtual manipulative use can be modulated by test question type (e.g., symbolic vs. pictorial); percentage of class time using representations differed between VM and PM classrooms; and percentage of class time spent using representation types differed, potentially providing differential opportunities to learn.
Computers in Human Behavior, 2016
The purpose of this study was to examine shifts in young children's learning progression levels w... more The purpose of this study was to examine shifts in young children's learning progression levels while they interacted with virtual manipulative mathematics apps on touch-screen devices. A total of 100 children participated in six mathematics learning sequences while using 18 virtual manipulative mathematics touch-screen apps during clinical interviews. Researchers developed a micro-scoring tool to analyze video data from two camera sources (i.e., GoPro camera, wallmounted camera). Our results showed that it is possible to document evidence of shifts in children's learning progressions while they are interacting with mathematics apps on touchscreen devices. Our results also indicated patterns in the children's interactions that were related to the shifts in their learning progression levels. These results suggest that an open-ended number of tasks with a variety of representations and tasks at varying levels of difficulty led to children refining their understanding and shaping their concept image of mathematical ideas resulting in incremental shifts in learning. The results of this study have important implications about how mathematical tasks in touch-screen apps may prompt children's incremental learning progression shifts to occur, and thereby promote opportunities for learning. We propose that design features in mathematics apps can be created to support and encourage these learning shifts.
International Journal of Education in Mathematics, Science and Technology, 2016
This article may be used for research, teaching, and private study purposes. Any substantial or s... more This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden.
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Papers by Jessica Shumway