Papers by Stephen I Tucker
The Journal of Educational Research , 2018
This study focused on 18 students 4-5 years old in an urban full-day preschool program in the Mid... more This study focused on 18 students 4-5 years old in an urban full-day preschool program in the Mid-Atlantic region of the United States. Over the course of a month, students used a touchscreen tablet to interact with Fingu, an app designed to develop students' early number sense. Using backend data generated by the app, 8,153 individual task attempts were recorded. Multilevel growth modeling, with task attempts nested within students, was used to examine the extent to which students' speed of response and response accuracy changed over the course of the study, as well as whether any individual characteristics were associated with either speed or accuracy. Results indicate that, on average, students become both faster and more accurate. Girls were also found to be more accurate than boys, and older students were found to be both slightly slower to respond and less accurate.
Uses of Technology in Primary and Secondary Mathematics Education, 2018
Technologies such as touchscreen apps are increasingly popular in mathematics education. Research... more 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.
International Journal of Research in Education and Science, 2017
The purpose of this study was to examine patterns of mathematical practices evident during childr... more The purpose of this study was to examine patterns of mathematical practices evident during children’s interactions with touchscreen mathematics virtual manipulatives. Researchers analyzed 33 Kindergarten children’s interactions during activities involving apps featuring mathematical content of early number sense or quantity in base ten, recorded during one-to-one task-based interviews. Iterative analysis involved applying learning progression rubrics to video data, using hierarchical clustering to visualize the progressions via heatmaps with dendrograms, and returning to video data to investigate emergent patterns. Results indicated that overall, children’s mathematical practices aligned with research on development of mathematical understandings, but that individual children’s mathematical practices changed little within a given activity. The study extends existing research by shedding light on children’s interactions with touchscreen mathematics virtual manipulatives and supports the use of these analysis and visualization techniques.
Technology is an increasingly important component of education. Children's mathematical interacti... more Technology is an increasingly important component of education. Children's mathematical interactions with technology have become a focus of mathematics education research, but less research has investigated constructs that contribute to these mathematical interactions. Attributes of children and technology play a key role in mathematical interactions and both children and technology can modify attributes during these interactions. Grounded in the Artifact-Centric Activity Theory and linked to recent developments in research on technology in mathematics education, this qualitative study extended an earlier exploratory study to investigate attribute modification. In particular, this study examined patterns of attribute modification evident during fifth grade students' mathematical interactions with two mathematics virtual manipulative touchscreen tablet apps. Results included three categories related to attribute modification: (1) reactive attribute modification (linear progression or repeated repetition); (2) unperceived attributes and opportunities for proactive modification; and (3) proactive modification (seeking equilibrium, seeking disequilibrium, or seeking equilibrium and disequilibrium). Findings have implications for designers, teachers, and researchers of educational technology.
Multi-touch devices are becoming popular technology tools for use in mathematics education. Resea... more Multi-touch devices are becoming popular technology tools for use in mathematics education. Researchers have identified affordances of virtual manipulatives and have created cognitive design principles for mathematics apps. Emerging studies report some empirical evidence of connections between specific mathematics apps and student performance in mathematics. However, there are gaps in the current research, including a lack of in-depth analyses of children's interactions and strategies related to specific mathematics apps. Thus, the authors recommend a detailed examination of the nexus of mathematics, strategy, and technology in children's interactions with a virtual manipulative app for the iPad.
The purpose of this study was to explore the relationship between instructional modality used for... more The purpose of this study was to explore the relationship between instructional modality used for teaching fractions and third- and fourth-grade students’ responses and strategies to open-response fraction items. The participants were 155 third-grade and 200 fourth-grade students from 17 public school classrooms. Students within each class were randomly assigned to two instructional treatment groups: a virtual manipulatives representations (VMR) instruction group and a physical manipulatives and textbook representations (PMTR) instruction group. A conversion mixed methods analysis was used to examine quantitative and qualitative data. The quantitative analysis showed achievement outcomes were the same for both groups. The qualitative analysis revealed shifts in learning that were otherwise hidden with solely quantitative achievement results. Specifically, the results indicated VMR group success in understanding fractions as relationships and PMTR group success in maintaining conceptualization of the whole. Overall, the results of this study corroborate previous research indicating the importance of both types of instructional modalities, showing that virtual manipulatives and physical manipulatives are effective instructional tools with positive effects on student learning. The study expands existing research by offering an opportunity to explore the nuances of students’ fractions understanding and provide a window into students’ shifts in fraction learning.
Mathematics Education Research Journal, 2015
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, wall-mounted 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 touch-screen 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.
Proceedings of EdMedia: World Conference on Educational Media and Technology 2016, Jun 2016
Attributes are inherent traits in technology tools and their users. During user-tool interactions... more Attributes are inherent traits in technology tools and their users. During user-tool interactions, attributes are continually modified to bring the tool and user into alignment so the user can complete a desired task. The purpose of this study was to examine patterns of attribute modification as fifth grade students interacted with the mathematics virtual manipulative iPad apps Motion Math: Zoom and DragonBox Algebra 12+. Three categories of attribute modification were identified: 1) reactive attribute modification; 2) unperceived attributes and opportunities for proactive modification; and 3) proactive modification. The findings have implications for designers of educational technology, for teachers who integrate technology into their classrooms, and for researchers of educational technology.
International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives, Jul 2016
While extensive research has examined the outcomes of interacting with virtual manipulatives, les... more 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.
This study examined 32 second-grade children’s interactions with six virtual manipulative mathema... more This study examined 32 second-grade children’s interactions with six virtual manipulative mathematics apps on the iPad using a novel analysis approach called heatmap analysis. Mathematical topics of the six apps focused on understanding skip counting and place value concepts. Children interacted individually with the apps under the guidance of an interviewer during 30-40 minute clinical interviews. The heatmap analysis revealed patterns in children’s performance on the tasks and suggested individual cases for further analysis. For example, clusters of children showed high or low performance during the skip counting sequence. In the high-performing cluster, one child still struggled to monitor the skip counting process. In the low-performing cluster, one child showed growth on learning tasks but struggled on the assessments, which contained a different representation of the mathematical content and involved greater target numbers than in the learning app. There were fewer variations in place value task performance, but application of interaction techniques influenced children’s growth on one learning app. Although some children showed varying performance when encountering challenging mathematics content in the higher levels of one app, other children inefficiently interacted with the app and did not reach the more challenging content
The purpose of this study was to explore relationships between app affordances and user abilities... more The purpose of this study was to explore relationships between app affordances and user abilities in second graders' interactions with mathematics virtual manipulative touchscreen tablet apps. The research questions focused on varying manifestations of affordance–ability relationships during children's interactions with mathematics virtual manipulative touchscreen tablet apps. Researchers qualitatively analyzed video recordings and ethograms from clinical interviews of 33 second-grade children. Each 45-min clinical interview involved one child interacting with two sequences of mathematics virtual manipulative touchscreen tablet apps: one sequence focusing on place value concepts and the other sequence focusing on skip counting concepts. Results provided evidence of Moyer-Packenham and Westenskow's (Int J Virtual Pers Learn Environ 4(3):35–50, 2013) five affordance categories of virtual manipulatives. Approach to and degree of affordance access varied depending on a child's corresponding ability, and some children modified their affordance access as their ability changed. Results also indicated that outcomes of accessing an affordance also related to a child's ability. Context also influenced affordance access. These results imply that affordance–ability relationships are multifaceted. Overall, these results imply that is important to consider affordance–ability relationships in relation to mathematics education technology. Abstract and references only; please see journal/DOI for full article. affordance access as part of a continuous affordance–ability relationship that can lead to an array of outcomes depending on a child's corresponding ability. Thus, theoretical and empirical research should continue to explore the intricacies of these affordance–ability relationships. These results also have implications for practice, as those who design and implement educational technology tools should be aware of affordance categories and affordance–ability relationships when developing, choosing, and evaluating these tools and children's interactions with the tools. Importantly, these results indicate to researchers, designers, and implementers of educational technology that attributes of users, tools, and contexts will vary, prompting different mathematical learning experiences by users based on affordance–ability relationships.
This exploratory qualitative study investigated the presence of and relationships among construct... more This exploratory qualitative study investigated the presence of and relationships among constructs that contribute to children’s interactions with educational technology, leading to the development of the Modification of Attributes, Affordances, Abilities, and Distance (MAAAD) for Learning framework. For this study, each of 10 fifth-grade children participated in one individual video-recorded semistructured interview session, during which they interacted with two mathematics virtual manipulative iPad apps and responded to follow-up questions. Video recordings and observation field notes were analyzed for evidence of attributes, affordance-ability relationships, distance, and relationships among these constructs.
Constant comparative data analysis using memoing and eclectic coding provided evidence of the presence of each focus construct. Further analysis and interpretation, including quantization of qualitative data for visualization using novel rhombus plots, also led to the identification of emergent themes related to each construct and revealed relationships among the constructs. Emergent themes included categorization, alignment, and modification of attributes, variations and interrelationships among affordance-ability relationships, and the identification of and interactions among mathematical and technological distance. Furthermore, each construct related to each other construct. The evidence and interpretations led to the development of the MAAAD for Learning framework.
The results of the study suggest that the MAAAD for Learning framework models relationships among attributes, affordance-ability relationships, and distance in the context of user-app interactions. The framework could serve as a tool for app developers designing apps, educators using apps to support children’s learning, and researchers characterizing user-app interactions and the outcomes of those interactions. The constructs, relationships, and framework identified in this study advance the literature on children’s interactions with educational technology tools, in particular literature concerning children’s interactions with mathematics virtual manipulative iPad apps.
The Journal of Men's Studies, Mar 2015
Male preservice elementary teachers often receive special attention. However, identities consist ... more Male preservice elementary teachers often receive special attention. However, identities consist of many complex components. Constant comparative methodology revealed emergent themes of privilege and disadvantage linked to gender, religion, and ethnicity in this exploratory examination of the stories of three male preservice elementary teachers. The men demonstrated varying awareness of their hybrid identities and associated privileges and disadvantages. The participants found privileges and disadvantages related to their gender, but members of religious and ethnic minority groups perceived significant disadvantages of those aspects of their identities. Findings suggest that preservice male teachers’ identities are more complex than gender alone, that being in multiple minority groups may compound challenges for preservice male teachers, and that teacher training alone may not sufficiently address issues of identity.
Journal of Computers in Mathematics and Science Teaching, 2015
This paper discusses changes in young children’s learning performance and efficiency during clini... more This paper discusses changes in young children’s learning performance and efficiency during clinical interviews in which each child interacted with a variety of virtual manipulative mathematics apps on iPads. Researchers interviewed 100 children ages 3 to 8 using a protocol format with two pre-assessment apps, four learning apps, and two post-assessment apps. Data were gathered quantitatively and qualitatively, using wall and screen-capture videos, pre and post assessments of performance, and time-stamping to record efficiency. Following 30-40 minute interviews where children interacted individually with the mathematics apps, results showed that children in the Preschool group increased efficiency while maintaining performance, children in the Kindergarten group increased performance while maintaining efficiency, and children in the Grade 2 group increased their performance and efficiency in skip counting, but not in place value. Overall, children in different age groups responded in different ways to the apps and some apps had a greater influence on children’s learning performance and efficiency than others. To conduct this study, researchers created a variety of research tools that were not readily available because research on children’s interactions with touch-screen-based virtual manipulative mathematics apps is still in its infancy. The paper describes the processes our research team used to develop new tools for novel and unique research situations.
Proceedings of the Joint Meeting of PME 38 and PME-NA 36, 2014
Australian Primary Mathematics Classroom, Mar 2014
*Article and free activity materials available upon request.* In this hands-on activity, students... more *Article and free activity materials available upon request.* In this hands-on activity, students reason with linked concrete, pictorial, and symbolic models to make sense of fraction concepts from the Common Core State Standards, including representation, equivalency, addition, and comparison.
Investigations in Mathematics Learning, 7 (1), 2014
Recently, over 40 states in the United States adopted the Common Core State Standards for Mathema... more 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.
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Papers by Stephen I Tucker
Constant comparative data analysis using memoing and eclectic coding provided evidence of the presence of each focus construct. Further analysis and interpretation, including quantization of qualitative data for visualization using novel rhombus plots, also led to the identification of emergent themes related to each construct and revealed relationships among the constructs. Emergent themes included categorization, alignment, and modification of attributes, variations and interrelationships among affordance-ability relationships, and the identification of and interactions among mathematical and technological distance. Furthermore, each construct related to each other construct. The evidence and interpretations led to the development of the MAAAD for Learning framework.
The results of the study suggest that the MAAAD for Learning framework models relationships among attributes, affordance-ability relationships, and distance in the context of user-app interactions. The framework could serve as a tool for app developers designing apps, educators using apps to support children’s learning, and researchers characterizing user-app interactions and the outcomes of those interactions. The constructs, relationships, and framework identified in this study advance the literature on children’s interactions with educational technology tools, in particular literature concerning children’s interactions with mathematics virtual manipulative iPad apps.
Constant comparative data analysis using memoing and eclectic coding provided evidence of the presence of each focus construct. Further analysis and interpretation, including quantization of qualitative data for visualization using novel rhombus plots, also led to the identification of emergent themes related to each construct and revealed relationships among the constructs. Emergent themes included categorization, alignment, and modification of attributes, variations and interrelationships among affordance-ability relationships, and the identification of and interactions among mathematical and technological distance. Furthermore, each construct related to each other construct. The evidence and interpretations led to the development of the MAAAD for Learning framework.
The results of the study suggest that the MAAAD for Learning framework models relationships among attributes, affordance-ability relationships, and distance in the context of user-app interactions. The framework could serve as a tool for app developers designing apps, educators using apps to support children’s learning, and researchers characterizing user-app interactions and the outcomes of those interactions. The constructs, relationships, and framework identified in this study advance the literature on children’s interactions with educational technology tools, in particular literature concerning children’s interactions with mathematics virtual manipulative iPad apps.