Stephen I. Tucker

An Examination of Children’s Learning Progression Shifts While Using Touch Screen Virtual Manipulative Mathematics Apps

The purpose of this study was to examine shifts in young childrens 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, wall-mounted camera). Our results showed that it is possible to document evidence of shifts in childrens learning progressions while they are interacting with mathematics apps on touch-screen devices. Our results also indicated patterns in the childrens 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 childrens 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.

The Modification of Attributes, Affordances, Abilities, and Distance for Learning Framework and Its Applications to Interactions with Mathematics Virtual Manipulatives

While extensive research has examined the outcomes of interacting with virtual manipulatives, less research has focused on constructs and relationships among constructs involved in user-tool interactions. This chapter presents the Modification of Attributes, Affordances, Abilities, and Distance (MAAAD) for Learning framework, which conceptualizes the relationships among these constructs to describe user-tool interactions, including those involving virtual manipulatives. The framework is primarily grounded in theories of representation and embodied cognition, as user-tool interactions in mathematics involve internalizing and externalizing representations through physically embodied mathematical practices. In the framework, attributes, affordance-ability relationships, and distance are interrelated, and modification of one construct contributes to modification of the other constructs. Each attribute can contribute to many affordance-ability relationships and to distance. Attribute modification can change the approach or degree of affordance access and alter the degree of distance present, which can, in turn, lead to attribute modification. This chapter illustrates the constructs and relationships among constructs that form the framework in the context of user-tool interactions in mathematics. The chapter then applies the framework to examples of children’s interactions with mathematics virtual manipulative touchscreen tablet apps. The MAAAD for Learning framework has implications and applications relevant to theory, development, implementation, and research concerning technology tools, including virtual manipulatives.

Second-Graders' Mathematical Practices for Solving Fraction Tasks.

Abstract 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.

Heatmap and Hierarchical Clustering Analysis to Highlight Changes in Young Children’s Developmental Progressions Using Virtual Manipulative Mathematics Apps

The purpose of this study was to examine what patterns were revealed using heatmaps with hierarchical clustering to examine preschooler’s performance, speed, and developmental progressions in counting and seriation. The chapter describes a study conducted with 35 preschoolers who used six touchscreen virtual manipulative mathematics apps in two different learning sequences: counting and seriation. The analysis employed heatmaps coupled with hierarchical clustering to highlight changes in children’s performance, speed, and developmental progressions, between a pre- and post- assessment app after using two learning apps. This method allowed for analysis of individual and whole group data examining several tasks within each app and also several apps within each learning sequence. The analysis revealed different clusters of children grouped according to their developmental progressions which were related to incremental changes in performance and speed from the Pre to Post App use.

Applying the Modification of Attributes, Affordances, Abilities, and Distance for Learning Framework to a Child’s Multi-touch Interactions with an Idealized Number Line

Technologies such as touchscreen apps are increasingly popular in mathematics education. Researchers have begun to investigate children’s interactions with the apps, outcomes of using apps, and the characteristics that contribute to outcomes. This study applies the Modification of Attributes, Affordances, Abilities, and Distance (MAAAD) for Learning Framework to an 11 year-old child’s interactions with the mathematics app Motion Math: Zoom to evaluate the outcomes, contributors, and interactions. This framework accounts for relationships among attributes, affordance-ability relationships, and distance involved in interactions. Interacting with Motion Math: Zoom involves using multi-touch gestures to navigate an idealized number line with changeable interval scales. Findings indicate that the framework can contribute to research on the outcomes, contributors, and interactions, as well as linking the three.