An Exploratory Study of Attributes, Affordances, Abilities, and Distance in Children\u27s Use of Mathematics Virtual Manipulative iPad Apps

This exploratory qualitative study investigated the presence of and relationships among constructs that contribute to children\u27s 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\u27s 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\u27s interactions with educational technology tools, in particular literature concerning children\u27s interactions with mathematics virtual manipulative iPad apps

Learning Logic: A Mixed Methods Study to Examine the Effects of Context Ordering on Reasoning About Conditionals

Logical statements are prevalent in mathematics, the sciences, law, and many areas of everyday life. The most common logical statements are conditionals, which have the form “If H..., then C...,” where “H” is a hypothesis (or condition) to be satisfied and “C” is a conclusion to follow. Reasoning about conditionals is a skill that is only superficially understood by most individuals and depends on four main conditional contexts (e.g., intuitive, abstract, symbolic, or counterintuitive). The purpose of this study was to test a theory about the effects of context ordering on reasoning about conditionals. To test the theory, the researcher developed, tested, and revised a virtual manipulative educational mathematics application, called the Learning Logic App. This study employed a convergent parallel mixed methods design to answer an overarching research question and two subquestions. The overarching research question was “How does the order of teaching four conditional contexts influence reasoning about conditionals?” The two subquestions examined this influence on reasoning in terms of performance and perceptions. This study involved two phases. During Phase I, 10 participants interacted with the Learning Logic App in a clinical setting. The researcher used information gathered in Phase I to revise the Learning Logic App for Phase II. During Phase II, 154 participants interacted with the Learning Logic App in a randomly assigned context ordering in an online setting. In both phases, the researcher collected quantitative and qualitative data. After independent analyses, the researcher made meta- inferences from the two data strands. The results of this study suggest that context ordering does influence learners’ reasoning. The most beneficial context ordering for learners’ performance was symbolic-intuitive-abstract-counterintuitive. The most beneficial context ordering for learners’ perceptions was intuitive-abstract-counterintuitive-symbolic. Based on these results, the researcher proposed a new context ordering: symbolic-intuitive-abstract-counterintuitive-symbolic. This progression incorporates a catalyst at the beginning (symbolic context) which aids the learner in reassessing their prior knowledge. Then, the difficulty of the contexts progresses from easiest to hardest (intuitive-abstract-counterintuitive-symbolic). These findings are important because they provide an instructional sequence for teaching and learning to reason about conditionals that is beneficial to both learners’ performance and their perceptions

How Design Features in Digital Math Games Support Learning and Mathematics Connections

Current research shows that digital games can significantly enhance children’s learning. The purpose of this study was to examine how design features in 12 digital math games influenced children’s learning. The participants in this study were 193 children in Grades 2 through 6 (ages 8-12). During clinical interviews, children in the study completed pre-tests, interacted with digital math games, responded to questions about the digital math games, and completed post-tests. We recorded the interactions using two video perspectives that recorded children’s gameplay and responses to interviewers. We employed mixed methods to analyze the data and identify salient patterns in children’s experiences with the digital math games. The analysis revealed significant gains for 9 of the 12 digital games and most children were aware of the design features in the games. There were eight prominent categories of design features in the video data that supported learning and mathematics connections. Six categories focused on how the design features supported learning in the digital games. These categories included: accuracy feedback, unlimited/multiple attempts, information tutorials and hints, focused constraint, progressive levels, and game efficiency. Two categories were more specific to embodied cognition and action with the mathematics, and focused on how design features promoted mathematics connections. These categories included: linked representations and linked physical actions. The digital games in this study that did not include linked representations and opportunities for linked physical actions as design features did not produce significant gains. These results suggest the key role of mathematics-specific design features in the design of digital math games

MAD Learn: An Evidence-based Affordance Framework to Assessing Learning Apps

Existing recommendations about how to select or design mobile applications (apps) for learning have been heavily relied on customer and teacher reviews, designer descriptions, and educational theories. There is a lack of evaluation frameworks that are informed by research evidence of how different children interact and use apps. The first version of an evidence-based framework, coined as MAD learn, is presented detailing affordances that hinder or help children’s learning, as emerged from relevant studies. To encourage further studies in the field, not only by researchers but also designers and practitioners, a methodological approach to iteratively assess the affordances of mobile apps is also introduced. This is based on (a) visualising the learning design and learning components of a given app and (b) analysing the screen and audio recordings of children’s interactions with apps. The proposed approach has been tested with 17 children 5-6 years old who interacted with a maths app. The analysis captured patterns of actual usage, including time spent on different activities, completion rates, communication instances, and number and type of mistakes. Insights revealed that certain design affordances, including instructions, feedback, and help-on-demand, were differently perceived by children, in some cases helping learning while, in others, hindering it

Eliciting preschoolers’ number abilities using open, multi-touch environments

Research has highlighted the potential of digital technology to support the development of children’s number sense abilities. However, the main focus of such research has been on apps affording directed interactions, where only one solution strategy is available, and it has targeted mostly cardinality. Little is known, in these terms, about task design and implementation in more open environments where several different solution strategies are available. To explore this direction, we chose to study TouchCounts, an open environment that combines multi-touch affordances with aural, visual and symbolic ones as well. Using tasks that were designed to address different number sense abilities, we experimented with 4-year-old preschoolers. In this paper we present two tasks, their expected potential with respect to strengthening number sense abilities, and analyses of data collected during the preschoolers’ interactions with TouchCounts. The analyses reveal that the children used different strategies in response to the two tasks, and that a broad range of abilities related to number sense were elicited, including both cardinality and ordinality. An important contribution of this study is also a theoretical framework capable of identifying children’s learning in a multi-touch environment

Children\u27s Mathematical Engagement Based on Their Awareness of Different Coding Toys\u27 Design Features

Tangible coding toys have been promulgated as useful learning tools for young children to learn computer science and mathematics concepts and skills. Although research shows coding toys can support mathematics for early childhood aged children, little is known about the specific design features of coding toys that afford mathematical thinking concepts and skills to young children. The purpose of this study was to examine kindergarten-aged children’s awareness of the design features in coding toys and to understand how those design features afford children’s engagement with mathematics. The dataset used for this study was collected as part of design-based research NSF project (award #DRL-1842116). I used a multi-phased qualitative analysis with a total of 42 hours of video data of 106, 5- to 6-year-old children engaging in coding toy tasks with four coding to answer the three research questions which were focused on perception of design features, mathematical engagement, and how different design features could afford mathematics. Results indicated that (a) children used and perceived the grid square and command arrow design features frequently, while other design features were used moderately or rarely; (b) children engaged in a variety of mathematical concepts and skills in five main categories of mathematical topics: spatial reasoning, geometry, comparison, measurement, and number; and (c) the relationship between design features affording mathematics varied depending on the coding toy. This research highlights the importance of specific design features to afford certain mathematical concepts and skills. These findings have important implications as early childhood educators explore ways to implement coding toys to support mathematics and computer science concepts, researchers conduct studies to better understanding how coding toys support mathematics and computer science learning, and commercial companies design new coding toys to fill the needs of educators and parents

Can Maths Apps Add Value to Young Children's Learning? A Systematic Review and Content Analysis

Educational maths applications (apps) are an emerging trend in children’s learning environments aiming to raise their mathematical attainment. However, with over 200,000 educational apps available within the App Store (Apple, 2014), deciding which apps to use poses a significant challenge to teachers, parents, and policy makers. The current study aimed to advance our understandings of whether and how educational maths apps can support children’s learning, as well as outline gaps in current research evidence and practice. In doing so, the current study included: / • A systematic review (Part 1) to synthesise the current evidence on educational maths apps for young children in the first three years of compulsory school (e.g., ages 4-7 years in England; ages 5-8 years in the USA). / • A content analysis (Part 2) to examine the content and design features of different educational maths apps and how they may support children’s learning

The Effects of Isolated Affordances on Preschool Counting Improvement when Using a Digital Coloring App

Counting is an important preschool math skill that is necessary for building a strong foundation in mathematics. Previous research has demonstrated that guided counting activities can improve counting ability in preschoolers and that drawing on paper while learning can deepen processing, but research has not included digital drawing as a potential means of deepening processing while children count. This study developed a novel touch-screen app, which used a guided coloring activity to encourage effective counting skills and serve as a home numeracy tool that could be employed by all parents, including those with math anxiety. To evaluate the benefits of individual affordance features, three- and four-year-olds (n = 61) were assigned to one of six training conditions: active areas, simultaneous linking, combined (active areas and simultaneous linking), non-affordance control, non-counting control, or non-coloring control. During training, children were instructed to color specific quantities of dots using a touch-screen tablet. In the active areas condition, children were only able to color within the bounds of one dot at a time (the “active” dot), which started on the left and moved sequentially to the next dot until all dots had been colored. In the simultaneous linking condition, children heard the number name of each dot while they were coloring that dot, but could color anywhere on the screen. The combined affordance condition incorporated the features of the active areas condition and the simultaneous linking condition: children were restricted to coloring only in the active dot, and they heard the number name of that dot while coloring. Control conditions included no added affordances. All children completed a counting pre-test before training and a counting post-test following training. After one session of training, the activity was not found to be effective in improving counting ability in preschoolers, nor were there differences across the conditions. However, parents did perceive the activity to be educational, and neither parents’ math attitudes nor parents’ math anxiety predicted their perceptions of the activity. This suggests that a similar activity could provide a method for parents, including those with higher levels of math anxiety, to increase the frequency of math activities in their home environments. These findings also indicate that parents need support in determining which activities are truly educational for their children

Opening doors: a collective case study of integrating technology in the preschool through 3rd grade classroom in a developmentally appropriate way

Children today are growing up in a technology-saturated world and yet early childhood teachers do not typically include technology in their classrooms, or if they do, they include it inappropriately. The literature states that integrating technology in early education can yield many benefits, but many teachers of young children avoid using technology because they do not know how to incorporate it appropriately. This dissertation is an exploratory observational study of early childhood teachers (preschool through third grade) who integrate technology in their programs in developmentally appropriate ways. This study involved three classroom teachers who were identified as model teachers at integrating technology in their classrooms: a preschool teacher and two kindergarten teachers. The study was guided by the recommendations from the National Association for the Education of Young Children (NAEYC) and the Fred Rogers Center for Early Learning and Children\u27s Media at Saint Vincent College (2012) position statement for early childhood teachers in the appropriate use of technology and digital media in the early childhood classroom. In this exploratory collective case study, visits to the classrooms were conducted several times and observations were performed. Checklists and field notes were used to record the findings. The teachers were interviewed before and after the observations to create a clearer picture of the classroom practices. This resulted in three cases that can serve as examples for teachers on how to integrate technology in the early childhood classroom in a developmentally appropriately way for young children. This study also provides recommendations for teachers who want to provide children with digital learning tools that can extend, enrich, and scaffold their learning. This study contributes four conclusions and five recommendations to guide teachers in integrating technology in a developmentally appropriate way for young children

An Explanatory Sequential Mixed Methods Study of the School Leaders’ Role in Students’ Mathematics Achievement Through the Lens of Complexity Theory

School leaders are expected to make decisions that improve student mathematics achievement. However, one difficulty for school leaders has been the limited amount of research concerning content-specific (e.g., mathematics) school leadership and its effects on student achievement. School leaders do not make decisions in isolation; rather, they make decisions as part of a complex adaptive system (CAS), as proposed by complexity theory. The purpose of this study was to explore the role the school leader plays in students’ mathematics achievement through the lens of complexity theory. The researcher collected survey data from K-12 school leaders and conducted focus group interviews to answer the research questions. The researcher found a significant regression equation predicting the school-wide average SAGE mathematics proficiency scores based on several characteristics of the school leader and student demographics. Distinctive patterns emerged in the decisions and actions made by school leaders based on school-wide SAGE mathematics proficiency. Results suggest that the school leaders’ first role in promoting higher student mathematics achievement is to directly and indirectly facilitate a shared vision of mathematics education between stakeholders in the CAS. The school leader’s second role is to actively work to recruit and retain the highest quality teachers possible