Virtual math objects with pedagogical, mathematical, and cognitive fidelity

Bos, Beth

doi:10.1016/j.chb.2008.11.002

Cited by 25 publications

(22 citation statements)

References 14 publications

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“…These studies show the need for instruments for evaluating apps, especially instruments that emerge from studying apps. Bos (2009b) offers an instrument for determining the degree of fidelity on a three-point scale-low, medium, and high. Bos (2009a), Larkin (2015a), and Moyer-Packenham et al (2008) study the fidelity-pedagogical, mathematical, and cognitive fidelity-of technologybased learning tools.…”

Section: Selection Of Apps For Teaching Difficult Math Topicsmentioning

confidence: 99%

Selection of Apps for Teaching Difficult Mathematics Topics: An Instrument to Evaluate Touch-Screen Tablet and Smartphone Mathematics Apps

Namukasa

Gadanidis

Sarina³

et al. 2016

Mathematics Education in the Digital Era

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Manipulatives-including the more recent touch-screen mobile device apps-belong to a broader network of learning tools. As teachers continue to search for learning materials that aid children to think mathematically, they are faced with a challenge of how to select materials that meet the needs of students. The profusion of virtual learning tools available via the Internet magnifies this challenge. What criteria could teachers use when choosing useful manipulatives? In this chapter, we share an evaluation instrument for teachers to use to evaluate apps. The dimensions of the instrument include: (a) the nature of the curriculum addressed in the app-emergent, adaptable or prescriptive, and relevance to current, high quality curricula-high, medium, low; (b) degree of actions and interactions afforded by the app as a learning tool-constructive, manipulable, or instructive interface; (c) the level of interactivity and range of options offered to the usermultiple or mono, or high, moderate or low; and, (d) the quality of the design features and graphics in the app-rich, high quality or impoverished, poor quality. Using these dimensions, researchers rated the apps on a three-level scale: Levels I, II, and III. Few apps were classified as Level III apps on selected dimensions. This evaluation instrument guides teachers when selecting apps. As well, the evaluation instrument guides developers in going beyond apps that are overly prescriptive, that focus on quizzes, that are text based, and include only surface aspects of using multi-modality in learning, to apps that are more aligned with emergent curricula, that focus also on conceptual understanding, and that utilize multiple, interactive representations of mathematics concepts.

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Section: Selection Of Apps For Teaching Difficult Math Topicsmentioning

confidence: 99%

Selection of Apps for Teaching Difficult Mathematics Topics: An Instrument to Evaluate Touch-Screen Tablet and Smartphone Mathematics Apps

Namukasa

Gadanidis

Sarina³

et al. 2016

Mathematics Education in the Digital Era

View full text Add to dashboard Cite

show abstract

“…The cognitive fidelity as defined by Moyer-Packenham et al [14] is how well the math virtual tools reflect the user's cognitive actions while using them. While the cognitive fidelity as defined by Bos [33] is the concept better understood when the virtual object is acted on, it makes sense and adds depth of understanding and meaningful strategy to the concept, because of the action performed on it. However, Mayer [34] stated that the "generative cognitive processing occurs when a learner engages in deep processing in working memory in service of the learning goal, such as organizing the material and integrating it with prior knowledge".…”

Section: Cognitive Model Of Multimedia Learningmentioning

confidence: 99%

Interactive Virtual Reality Cognitive Learning Model for Performance Evaluation of Math Manipulatives

…¹

2012

JKAU Comp IT Sci

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Applications of virtual reality in E-Learning are gaining more popularity due to its interactive characteristics of virtual environments that can be offered. One unique example of this application is the use of virtual manipulatives, since they can be implemented on PCs economically for teaching students interactively in schools and universities. They enable students to learn mathematics thoroughly by easily providing computer-generated dynamic objects, allowing them to explore abstract mathematical concepts in a handson mode experince. In this paper, an implemented virtual reality based math virtual manipulatives is presented. A cognitive virtual reality learning model is also introduced. Performance evaluation of the virtual manipulatives, for several case studies, is achieved. Comparisons between the 2- Dimensions (2D) Java applets from National Library Virtual Manipulatives (NLVM) and the developed Java 3D Virtual Reality Math Manipulatives (VRMM) cases are performed. Results of the practical analysis for student grades show that VR enhances student learning of addition and subtraction operations in the VRMM, and it achieves superior results than the NLVM.

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“…Given this description, virtual manipulatives may be the same as virtual math objects or one type of math object because virtual manipulatives contain "multiple representations that are interactive and change with the given input." Although Bos (2009b) wrote, "Virtual manipulatives…are often mistaken as math objects…" (p. 522), the description of virtual math objects in these publications implies that virtual math objects and virtual manipulatives may be synonymous. Sedig and Liang (2006) describe computer-based mathematical cognitive tools (MCTs) as "a category of external aids intended to support and enhance learning and cognitive processes of learners.…”

Section: What Is the Difference Between Virtual Manipulativesmentioning

confidence: 99%

“…However, if learning objects include other tools, beyond those described in the study that do not fit the definition of a virtual manipulative, then learning objects and virtual manipulatives are not synonymous. Bos (2009b) writes about virtual math objects: "A math object enhanced with technology offers manipulations, multiple representations, multiple entry points, and provides opportunity to test, revisit, revise, and apply mathematical patterns" (p. 522). "The math object uses multiple representations that are interactive and change with the given input" (Bos 2009a, p. 110).…”

Section: What Is the Difference Between Virtual Manipulativesmentioning

confidence: 99%

“…Some of the terminology related to virtual manipulatives includes: cognitive technology tools (Pea 1985), learning objects (Kay 2012), virtual math objects (Bos 2009b), and computer-based mathematical cognitive tools (Sedig and Liang 2006). This similar terminology has led to confusion about virtual manipulatives.…”

Section: What Is the Difference Between Virtual Manipulativesmentioning

confidence: 99%

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