Understanding Graphs: Modeling Processes, Prerequisites and Influencing Factors of Graphicacy

Die Fähigkeit, Visualisierungen von Daten zu verstehen, ist für Bildung, Arbeit und Leben im 21. Jahrhundert enorm wichtig geworden. In den meisten Fällen werden die Daten als Graphen visualisiert. Graphen stellen Mengen über eine "gepaart mit"-Beziehung dar, wobei größere Mengen durch längere Linien, höhere Balken oder mehr von einer anderen visuellen Dimension dargestellt werden. Trotz des Vorhandenseins von Graphen in allen Lebensbereichen haben groß angelegte Studien Bedenken hinsichtlich der Fähigkeit von Schülern und Schülerinnen, Graphen zu verstehen, geäußert. Im Vergleich zu den langen Traditionen der kognitiven psychologischen Arbeit in den Bereichen Lesen und Mathematik ist relativ wenig darüber bekannt, wie Individuen Graphen verstehen. Diese Arbeit entwickelt ein kognitiv psychologisches und psychometrisches Modell, das die zugrunde liegenden Verständnisprozesse, Voraussetzungen und Einflussfaktoren der Fähigkeit, Graphen zu verstehen, abbildet. Im Kapitel I verwies die Literaturrecherche auf zwei getrennte Forschungsstränge. Zum einen die Literacy-Forschung, die die Fähigkeit des Einzelnen beschreibt, realistische Probleme mit Graphen zu lösen (sog. Graphicacy-Forschung), und zum anderen die Forschung, die die zugrunde liegenden Prozesse des Graphenverstehens erklärt (sog. Graphenverstehensforschung). Um diese Forschungsstränge auf theoretischer und methodischer Ebene zu integrieren, wurde ein prozessorientiertes Modell der Graphicacy (eng. POMoG) entwickelt. Empirische Studien, die sich mit den verschiedenen Annahmen des POMoG, wurden in den Kapiteln II, III und IV vorgestellt. Kapitel II untersuchte den Einfluss von grundlegenden numerischen Fähigkeiten (eng. BNAs) auf die Graphenleseleistung. Der Einfluss von BNAs erklärt Verständnisprozesse, da die jeweiligen BNAs mit bestimmten Prozesskomponenten des Graphenlesens verknüpft werden können. Subtraktion, Zahlenstrahlschätzung und konzeptionelles Wissen über arithmetische Operationen wurden anhand von Testdaten von 750 Schülern aus der Sekundarstufe als Einflussfaktoren auf die Graphenleseleistung ermittelt. Subtraktion und Zahlenstrahlschätzung unterstützen einzelne Prozesskomponenten, während konzeptionelles Wissen bei der Anwendung effizienter Problemlösungsstrategien hilft. Kapitel III untersuchte den Zusammenhang zwischen Bearbeitungszeit, Text-Graphen-Übergängen und Verständniserfolg über Verständnisphasen hinweg. Text-Graphen-Übergänge können entweder als Integration von Informationen oder als Desorientierung interpretiert werden. In zwei Studien mit insgesamt 77 Studierenden wurde der Zusammenhang zwischen Bearbeitungszeit, Text-Graphen-Übergänge und Verständniserfolg untersucht. Die Ergebnisse zeigten, dass Bearbeitungszeit und Text-Graphen-Übergänge während der initialen Lesephase positiv und während der Aufgabenerledigungsphase negativ assoziiert sein können. Beim initialen Lesen bedeuten mehr Text-Graphen-Übergänge mehr Integration, während mehr Text-Graphen-Übergänge bei der Aufgabenbearbeitung auf Desorientierung hinweisen. Darüber hinaus moderiert das inhaltliche Wissen den Einfluss von Bearbeitungszeit auf den Verstehenserfolg während der initialen Lesephase und der Aufgabenerledigung. Dieser moderierende Effekt deutet darauf hin, dass inhaltliches Wissen entweder den anfänglichen Modellaufbau steuern oder den Schülern helfen kann, aufgabenrelevante Informationen zu finden. Kapitel IV untersuchte die Abhängigkeitsbeziehung zwischen Verständnisprozessen bei Verstehen von Text und Graphen. Zwei widersprüchliche Perspektiven über diese Abhängigkeitsbeziehung sind in der Literatur vorhanden. Die textzentrierte Perspektive besagt, dass das Verständnis des Graphen vom Verständnis des Textes abhängt. Die Mehrfachrepräsentationsperspektive besagt, dass das Verständnis des Textes und des Graphen getrennt voneinander Voraussetzung für ein integriertes Verständnis ist. Diese Perspektiven wurden mit den Antwortmustern von 50 Erwachsenen mit Hilfe der Wissensraumtheorie verglichen. Die Ergebnisse zeigten, dass die textzentrierte Perspektive eher für das Verständnis von Text und Graphen geeignet ist. Zusammenfassend lässt sich sagen, dass arithmetische Fähigkeiten, Zahlenstrahlschätzung, konzeptionelles Wissen über arithmetische Operationen sowie Inhaltswissen das Verstehen von Graphen über verschiedene zugrundeliegende Mechanismen beeinflusst. Entweder unterstützen sie Prozesskomponenten oder sie helfen bei deren Steuerung der Prozesskomponenten. Des Weiteren wurde gezeigt, dass Prozessmaßnahmen je nach Verständnisphase unterschiedliche Verständnisprozesse anzeigen können. Schließlich ist das Verständnis von Graphen keine Voraussetzung für ein integriertes Verständnis von Text und Graphen. Die theoretischen, methodischen und praktischen Implikationen der Arbeit wurden in Kapitel V diskutiert.The ability to understand visualizations of data has become immensely important for education, work, and life in the 21st century. In most cases, data is visualized as a graph. Graphs represent quantities via a ‘paired with’ relation. Graphs represent greater quantities by longer lines, higher bars, or more of some other visual dimension. Despite the presence of graphs in all areas of life, large-scale studies have raised concerns about students’ ability to understand graphs. Compared to the long traditions of cognitive psychological work on reading and mathematics, relatively little is known about how individuals understand graphs. This thesis builds a cognitive psychological and psychometric model of the underlying comprehension processes, prerequisites and influential factors for individuals’ ability to understand graphs. A literature review revealed two separate research communities: first, literacy research describing individuals’ ability to solve realistic problems with graphs (i.e., graphicacy research), and second, research explaining the underlying processes behind graph comprehension (i.e., graph comprehension research). In Chapter I, a Process-Oriented Model of Graphicacy (POMoG) was developed to integrate these research communities on a theoretical and methodological level. Chapters II, III and IV presented empirical studies that address different assumptions of the POMoG. Chapter II investigated the influence of basic numerical abilities (BNAs) on graph reading performance. The influence of BNAs explains comprehension processes because specific BNAs can be linked to specific process components of graph reading. Subtraction, number line estimation, and conceptual knowledge about arithmetic operations were determined to be influencing factors based on test data from 750 students in secondary education. Subtraction and number line estimation facilitate unique process components, while conceptual knowledge helps students use efficient problem-solving strategies. Chapter III investigated the association between time-on-task, text-graph transitions and comprehension success across comprehension phases during the comprehension of a text and graph. Text-graph transitions can either be interpreted as the integration of information or as disorientation, the inability to find relevant information. The association between time-on-task, text-graph transition and comprehension success was examined in two studies with 77 university students in total. The results showed that time-on-task and text-graph transitions are positively associated during the initial reading phase and negatively associated during the task completion phase. Text-graph transitions indicate integration during initial reading and disorientation during task completion. Additionally, students’ content knowledge moderates the effect on time-on-task during initial reading and task completion. This moderating effect indicates that content knowledge can either control initial model construction or help students find task-relevant information. Chapter IV investigated the dependency relationships between comprehension processes in the comprehension of a text and graph. Two contradicting perspectives about these relationships are present in the literature. The text-centered perspective states that comprehension of the graph depends upon comprehension of the text, and the multiple-representation perspective states that comprehension of the text and graph separately are both prerequisites for integrated comprehension. These perspectives were compared to the response patterns of 50 adults using knowledge space theory. The results showed that the text-centered perspective is more applicable to text-graph comprehension. In sum, arithmetic fluency, number line estimation, conceptual knowledge about arithmetic operations, and content knowledge influence graphicacy via different underlying mechanisms. They either facilitate process components or help to control them. Further, it was demonstrated that process measures can be indicative of different comprehension processes depending on the comprehension phase. Finally, graph comprehension is not a prerequisite for integrated comprehension of a text and graph. The theoretical, methodological and practical implications of the thesis are discussed in Chapter V

The other art of computer programming: A visual alternative to communicate computational thinking

The thesis will explore the implications of teaching computer science through visual communication. This study aims to define a framework for using pictures within learning computer science. Visual communication materials for teaching computer science were created and tested with Year 8 students. Along with a recent commercial and political focus on the introduction of coding to adolescents, it appears that the computer industry has a large shortfall of programmers. Accompanying this shortfall is a rise among adolescents in the preference for visual communication (Brumberger, 2011; Coats, 2006; Oblinger et al., 2005; Prensky, 2001; Tapscott, 1998) while textual communication currently dominates the teaching materials in the computing discipline. This study looks at the learning process and utilises the ideas of Gibson, Dewey and Piaget to consider the role of visual design in teaching programming. According to Piagetian theory Year 8 is the time a child begins to understand abstract thought. This research investigated through co-creation and prototyping how to creatively support cognition within the learning process. Visual communication theories, comprising the fields of graphic and information design, were employed to communicate computer science to approximately 60 junior high school students across eight schools. Literature in a range of visual communication fields is reviewed along with the psychology of perception and cognition to help create a prototype lesson plan for the target audience of Year 8 students. The history of computer science is reviewed to illustrate the mental imagery within the discipline and also to explore computational thinking concepts. These concepts are . . . the metaphors and structures that underlie all areas of science and engineering (Guzdial, 2008). The participants’ attitudes increased toward learning programming through visual communication. Quantitative questionnaires were used to gather data on cognition and measure the effectiveness of the learning process. Thirteen hypotheses were established concerning learning programming through pictures from the quantitative data. Focus groups further triangulated data gathered in the quantitative stage. Approximately seventy percent of the participants understood seventy percent of the information within the instrumentation. Models of intent to learn programming through pictures were established using structural equation modelling (SEM). Outcomes of the exegesis are a framework for using pictures that demonstrates computational thinking and explains the research

Education on the Gis Frontier: Cybergis and Its Components

Geographic information systems (GIS) are a fundamental information technology. Coupled with advancing developments in spatial analysis through geographic information science (GISci), the capabilities and applications of GIS and GISci continue to rapidly expand. This expansion requires practitioners to have new skills and competencies, especially in computer science and programming. One developing framework for GIS’ future is that of Cyber Geographic Information Systems (CyberGIS), which fuses the technical capabilities of advanced cyber-infrastructure, like cloud and server computing, with the spatial analysis capabilities of GIS. This structure of GIS requires further computer science and programming abilities, but how GIS practitioners use and value the variant components within CyberGIS is unknown. This gap makes teaching and preparing students on the CyberGIS frontier difficult. The GIS skillset is in an ever-present state of re-imagination, but with the growing prominence of CyberGIS, which seeks to capitalize on advanced computing to benefit analysis in GIS, the need for an understanding of educational implications continues to grow. This dissertation uses a mixed-methods approach to explore how CyberGIS functions academically. First, I explore how university geography departments in the U.S. integrate computer science and programming skills in their undergraduate geography and GIS degree programs by reviewing degree requirements in highly-ranked departments. Few departments require computer science or programming courses for undergraduate degrees. Then, I explore the nature of knowledge and skills in CyberGIS using machine reading and q- methodology to explore viewpoints of how key CyberGIS skills function. The three viewpoints I identify reveal highly conflicting mindsets of how GIS functions. Finally, I use syllabi from different GIS programming and computer science courses to identify common topics, course structures, and instructional materials across a broad sample of courses. Three major topic foci emerged, including GIS scripting with Python, web-enabling GIS with JavaScript and HTML, and geodatabase manipulation with SQL. Some common instructional materials exist, but syllabi show little consistency in their curriculum focus and instructional design within or across topics relating GIS programming and computer science. There is little consistency or emphasis in current educational efforts concerning computer science and programming and how they function in building competencies required in CyberGIS. While CyberGIS promises advanced computing capabilities using complex systems, the fractured and uneven nature of basic computer science and programming instruction in GIS indicates that to achieve a Cyber-enabled GIS future, a much larger chasm between GIS and computer science must be bridged

Score Reporting Research and Applications

Score reporting research is no longer limited to the psychometric properties of scores and subscores. Today, it encompasses design and evaluation for particular audiences, appropriate use of assessment outcomes, the utility and cognitive affordances of graphical representations, interactive report systems, and more. By studying how audiences understand the intended messages conveyed by score reports, researchers and industry professionals can develop more effective mechanisms for interpreting and using assessment data. Score Reporting Research and Applications brings together experts who design and evaluate score reports in both K-12 and higher education contexts and who conduct foundational research in related areas. The first section covers foundational validity issues in the use and interpretation of test scores; design principles drawn from related areas including cognitive science, human-computer interaction, and data visualization; and research on presenting specific types of assessment information to various audiences. The second section presents real-world applications of score report design and evaluation and of the presentation of assessment information. Across ten chapters, this volume offers a comprehensive overview of new techniques and possibilities in score reporting

Score Reporting Research and Applications

Score reporting research is no longer limited to the psychometric properties of scores and subscores. Today, it encompasses design and evaluation for particular audiences, appropriate use of assessment outcomes, the utility and cognitive affordances of graphical representations, interactive report systems, and more. By studying how audiences understand the intended messages conveyed by score reports, researchers and industry professionals can develop more effective mechanisms for interpreting and using assessment data. Score Reporting Research and Applications brings together experts who design and evaluate score reports in both K-12 and higher education contexts and who conduct foundational research in related areas. The first section covers foundational validity issues in the use and interpretation of test scores; design principles drawn from related areas including cognitive science, human-computer interaction, and data visualization; and research on presenting specific types of assessment information to various audiences. The second section presents real-world applications of score report design and evaluation and of the presentation of assessment information. Across ten chapters, this volume offers a comprehensive overview of new techniques and possibilities in score reporting

Understanding Public School Accountability Report Design

From the passing of No Child Left Behind (NCLB) through to the signing of the Every Student Succeeds Act (ESSA), all states receiving federal funds must have been required to publicly report on the quality of their schools. In this article, I look at the role of these reports in the broader system of public school accountability, specifically working to untangle the complex interaction between content and form. Drawing on an interdisciplinary body of work in education policy and data visualization and design, I argue that these reports – and more importantly, their visual design – serve as a lynchpin of contemporary school accountability and deserve considerably more attention from both policymakers and practitioners

Mathematical practices: their use across learning domains in a tertiary environment

This research presents a case study at a South African University, involving students who had studied mathematics in a pre-undergraduate Foundation Programme (FP) and who were currently in their first year of study in Information Technology (IT) at the same institution. The study investigated a possible relationship between the teaching approach used in the FP mathematics classroom and the extent of students’ abilities to use important mathematical practices, such as using procedures flexibly; using representation; understanding/explaining concepts; questioning; justifying claims; disagreeing; strategising; and generalising, in an undergraduate IT context. Focus group interviews and task-based interviews were used to answer three related questions: “To what extent are students aware of differences in teaching approaches between FP mathematics and undergraduate study?”; “To what extent do students believe that their experiences of the teaching approaches in the Foundation Programme mathematics class have helped them in undergraduate study in other courses?”; and “In what ways are the mathematical practices taught in the Foundation Programme used in undergraduate study in IT?” A bricolage of learning theories was used as a framework for understanding the possible relationships between teaching approach, development of mathematical practices and learning transfer. The students in the focus groups described the teaching approach used in the FP mathematics classes as studentcentred, whereas many of the undergraduate IT lectures and tutorials were described as teachercentred. The students felt that the approach used in the FP mathematics classroom was beneficial to further study, in that it taught them how to become responsible for their own learning and brought about deep understanding of the mathematical concepts learned in the FP. The task-based interviews showed that all students used mathematical practices to solve IT problems to a greater or lesser extent. The use of these mathematical practices was best understood as being influenced by all past cognitive, social and cultural experiences, and was therefore not a case of “transfer” in the traditional sense of the word. Instead, the use of mathematical practices could be described as an extreme case of “cognitive accommodation” from a cognitive constructivist perspective, or a case of “generality” from a situative perspective. Furthermore, an inter-relationship emerged between student-centred teaching, students’ productive disposition towards mathematics, and the extent of “transfer” of mathematical practices to the IT domain. This interesting relationship warrants further investigation

Re-designing Design and Technology Education: A living literature review of stakeholder perspectives

Created following the amalgamation of several individual subject disciplines, in England, design and technology is in decline. Debates about its purpose and position have taken place since its inception but arguably these have not transferred into a rigorous research base. There is a growing body of scholars exploring the field, but with the decline of the subject, so the community working and investigating it is also diminished. Without a strong foundation, the actions of the few may not carry sufficient weight to generate full and meaningful debate that would influence those with the power to change policy on curriculum and lead to innovation. If we are to have any hope of reversing the subject’s deterioration, we must do something bold and significant. While an awareness of the subject’s history and its evolution is integral to our understanding of how and why we are where we are, merely reflecting on the past will do little to help the subject move forward. Hence, the principal aim of our research is to explore what a re-designed design and technology could look like. To achieve this, this study draws on different stakeholders’ visions of how they perceive the subject’s future

CAMAU Project: Research Report (April 2018)

‘Learning about Progression’ is a suite of research-based resources designed to provide evidence to support the building of learning progression frameworks in Wales. ‘Learning about Progression’ seeks to deepen our understanding of current thinking about progression and to explore different purposes that progression frameworks can serve to improve children and young people’s learning. These resources include consideration of how this evidence relates to current developments in Wales and derives a series of principles to serve as touchstones to make sure that, as practices begin to develop, they stay true to the original aspirations of A Curriculum for Wales – A Curriculum for Life. It also derives, from the review of evidence, a number of fundamental questions for all those involved in the development of progression frameworks to engage

CAMAU Project: Research Report (April 2018)

‘Learning about Progression’ is a suite of research-based resources designed to provide evidence to support the building of learning progression frameworks in Wales. ‘Learning about Progression’ seeks to deepen our understanding of current thinking about progression and to explore different purposes that progression frameworks can serve to improve children and young people’s learning. These resources include consideration of how this evidence relates to current developments in Wales and derives a series of principles to serve as touchstones to make sure that, as practices begin to develop, they stay true to the original aspirations of A Curriculum for Wales – A Curriculum for Life. It also derives, from the review of evidence, a number of fundamental questions for all those involved in the development of progression frameworks to engage