Article

What Are Virtual Manipulatives?

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Abstract

As a result of innovations in technology, the prevalence of the Internet, and the increasing availability of computers in classrooms and homes, an enhanced approach for teaching and learning mathematics using manipulatives and computers is emerging. This new approach essentially creates a new class of manipulatives, called virtual manipulatives , as well as new capabilities, or toolkits, for computer programs that use visual representations. These new virtual manipulatives have all the useful properties of existing computer manipulatives while overcoming many of their disadvantages, yet very little is known or written about them. The purpose of this article is to establish a working definition of virtual manipulatives, highlight examples of virtual manipulatives on the Internet, and discuss their current and potential classroom use.

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... Furthermore, they can allow differentiation for the varied ability levels of the learners. Moyer et al. (2002) showed that VM were supporting children learning to work at their own pace. In addition, they argued that VM were great resources for classroom use because of their unique features to record and store user's movements online and their potential for alterations-such as size and colouring. ...
... However, there are a few discussions and studies on students' preference for using either physical, virtual or both VM and PM and their effectiveness when teaching mathematics in general (e.g., Day & Hurrell, 2017;Hunt et al., 2011;Moyer et al., 2002). Day and Hurrell (2017) showed that VM do not necessarily provide the same experience as concrete materials. ...
... They can provide a bridge between the concrete materials and other representations. On the other hand, Hunt et al. (201l) and Moyer et al. (2002) recommended VM to record and store users' movements, online and constant availability and their potential for flexible learning. However, a recent study by Đokić et al. (2022) showed that there was no difference in 4th graders (10-11 years old) students' 3D geometry achievement regardless of the learning support through either VM or PM. ...
Conference Paper
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This case study aims to describe the learning characteristics of a child and evaluate his preferences for using physical manipulatives (PM) and virtual manipulatives (VM) to solve fraction problems. The participant in this study was a fourth-grade child. The child was given similar problems to solve using PM and VM. Data sources were observations and interviewing the child during and after the tasks were completed. The results showed that the child engaged and preferred solving fraction problems using PM more than VM. The child stated that PM helped him quickly understand the relationship between various representations of fractions and model them using manipulatives. The VM did not help him solve the problems.
... Although generally the term 'virtual manipulative' is used to refer to any computer-generated image, they are typically available in two core representations. Moyer's (2002) research identifies static representations as mostly pictorial representations. Although static representations resemble the physical kind, they cannot be rotated, manipulated and manoeuvred. ...
... In comparison, the dynamic representations are visual images on a two-dimensional screen with the added advantage that they can be rotated. Moyer (2002) argues these representations are true virtual manipulatives as they offer an image of a threedimensional object. Although virtual manipulatives may at first glance appear similar and are often inscribed with the same names as the physical kind, they offer very different teaching and learning experiences. ...
... Teachers are now incorporating both virtual and physical manipulatives; however there remains an absence of theoretical and empirical grounds confirming which are more effective in mathematical teaching and learning (Moyer, 2002;McNeil and Jarvin, 2007). Educators are now expected to integrate technology into the delivery of mathematics lessons. ...
Conference Paper
Primary Postgraduate Certificate of Education (PGCE) teacher training courses are intense programmes of study that provide opportunities for trainees to develop and employ the more experiential aspects of classroom teaching such as making use of manipulatives. Manipulatives are tactile objects that can enrich instruction when handled. While there is a large body of complementary mathematical literature endorsing the use of manipulatives, some evidence exists within the literature that manipulatives are not used as effectively or as extensively as they could be. Little is known about how trainees conceive, use and apply manipulatives in the classroom. In response, this study explored eight primary PGCE trainee teachers’ experiences of using mathematical manipulatives as they develop their professional learning during placement. A mix of methods (survey, interviews and video recordings) was used over the course of one academic year. In order to understand the participants’ lived experiences, interviews were analysed using Interpretative Phenomenological Analysis (IPA). Overall, findings indicated a silent set of institutional rules at play as to how manipulatives are selected, introduced and utilised, reinforcing habitual practices such as assigning manipulatives solely to the pupils classified as requiring further support. Study data also revealed the sensory experiences of the manipulative were used as a ‘lifebuoy’ to bridge the social gap caused by grouping by ability. Significantly, this study revealed that although trainees are novices, they appeared to be expected to cope and navigate difficulties with mathematics teaching in isolation. Participants reported that they drew on support for manipulative use from learning theories, textbooks and their own experiences. Mismatches existed between perceptions and accounts of use, and although manipulatives have many affordances, it was taken for granted the manipulatives and the associated language assigned would be universally understood. This thesis concluded inquiry-based practices could help trainees challenge their traditional view of mathematics teaching and how manipulatives are assigned and used in the classroom. A balance has to be found between providing enough support to nurture trainees in becoming autonomous professionals and setting policies that prescribe practices.
... The virtual manipulative was originally defined as an "interactive, Web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge", and they are often modeled after concrete manipulatives (Moyer et al., 2002). Bouck and Flanagan (2010) extended its definition as a computer-based simulation of physical manipulatives that is accessed through the Internet or computer software. ...
... Due to these attributes, VMs have been widely adopted in science classrooms to enhance students' deep comprehension of scientific knowledge. Through the affordances of VMs, students can extensively manipulate and even alter representations to explore concepts and construct meanings, as explained by Moyer et al. (2002). VMs provide students with the capacity to observe the consequences of their actions. ...
Article
Digital instructional tools, such as virtual manipulatives, have been widely adopted as an enhanced approach to inquiry-based learning. However, the optimal ratio of mobile devices to students in instructional settings remain controversial. This research introduced a counterbalanced quasi-experiment to compare the learning performance and group-process satisfaction (GS) of primary school students under various settings of mobile device-student ratios (1:1 or 1:m) and external scripts (ES, with or without). A total of 128 sixth graders (11 drop-outs in the second-round experiment) in four elementary-school classes adopted physics simulations on tablet PCs as virtual manipulatives (VMs). Group worksheets and posttests were administered during and after the inquiry process to assess students’ inquiry performance and knowledge acquisition. The analyses revealed that students under the 1:m condition significantly outperformed their peers in the 1:1 condition in both subterms, concept understanding (CU) and problem-solving (PS), but no significant difference was found in knowledge acquisition (KA). ES showed no effect on students’ learning performance. VMs that students used in collaborative tasks operated separately on each tablet PC, which may have distracted learners’ joint attention. Hence, the collaboration patterns were observed and discussed. Four potential collaboration patterns are discussed at the end of this paper.
... Χρησιμοποιώντας υπολογιστές, iPads ή ανάλογες συσκευές οι μαθητές εξερευνούν και κατασκευάζουν μαθηματικές έννοιες και ιδέες μέσα σε ψηφιακά περιβάλλοντα (Satsangi & Miller, 2017). Με άλλα λόγια, είναι τρισδιάστατες ηλεκτρονικές προσομοιώσεις φυσικών αντικειμένων, όπως base 10 blocks, γεωμετρικά στερεά κ.ά., που εμφανίζονται σε μια οθόνη ενός ηλεκτρονικού υπολογιστή και μπορούν να μετασχηματιστούν και να τροποποιηθούν με πολλούς τρόπους από το χρήστη (Clements & McMillen, 1996, Moyer, et al., 2002Bouck & Flanagan, 2010). Τα τελευταία χρόνια, μάλιστα, αναδύθηκε και μια νέα μορφή ηλεκτρονικών εικονικών αντικειμένων μέσα από εφαρμογές κινητών συσκευών (app-based manipulatives) (Bouck, Chamberlain & Park, 2017). ...
... (Clements & McMillen, 1996). Ένα σημαντικό αναπαραστάσεις και προσφέρουν τη δυνατότητα αποθήκευσης του έργου του μαθητή (Clements & McMillen, 1996, Moyer et al., 2002Moyer et al., 2005). Επιπλέον, έχει υποστηριχθεί πως μειώνουν το γνωστικό φορτίο των μαθητών με αναπηρίες (Suh & Moyer, 2008). ...
Thesis
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The present study attempted to examine an alternative way of representing mathematical word problems. The study’s objective was to assess the cognitive scheme in compare addition and multiplication problem solving, through video representation. The research sample was constituted from 30 students with Specific Learning Disabilities, who were asked to solve math problems in two phases. During the first phase, word problems were represented through text, while during the second phase word problems were represented using video technology via an iPad. Students’ performance was tested before and after the video use and a statistical analysis was performed. The results showed that video use for representing compare addition and multiplication word problems was effective, as most of the students improved significantly, as illustrated by their performance.
... Salah satu definisi dari virtual manipulative (VM) adalah sebagai berikut: "In our view, a virtual manipulative is best defined as an interactive, Web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge" (Moyer, Bolyard, & Spikell, 2002). Artinya, VM dapat dipahami sebagai sebuah media pembelajaran matematika yang berbasis web, interaktif, serta dinamis. ...
... Untuk melihat contoh koleksi VM, banyak penelitian yang menyarankan untuk melihat di National of Virtual Manipulatives (http://nlvm.usu.edu/en/nav/vlibrary.html) yang disusun oleh Utah State University (Durmus, & Karakirik 2006;Moyer, Bolyard, & Spikell, 2002 (Garzón & Bautista, 2018;Leitze & Kitt, 2000). ...
... Discussion: It could be indicated that virtual manipulatives can be regarded as an important tool in teaching algebraic concepts. Moyer, Bolyard, and Spikell (2002) stated that virtual manipulatives provide students with the opportunity to manipulate them through different representations while discovering the meanings of mathematical concepts and constructs. ...
... It has been suggested by the participants that some of the virtual manipulative is incomplete or narrow and at the same time can lead to confusion. In parallel with this finding, Moyer et al. (2002) indicated some computer-based tools is only visual and they are not enough for providing the manipulation. It is also stated that some of the virtual manipulatives used by the participants in the study will not be sufficient for building mathematical knowledge and concepts. ...
Article
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The purpose of the study was to investigate preservice mathematics teachers' using of virtual manipulatives to teach algebra through a lesson study. 17 preservice mathematics teachers voluntarily participated in the study. Phenomenological approach has been used as a qualitative method of research. The preservice mathematics teachers created lesson plans about the middle school algebra topics using virtual manipulatives. Interviews were used as a way to collect data to gain information about their using of virtual manipulatives to teach algebra. The findings of the study showed that preservice mathematics teachers revealed positive and negative decisions about algebra teaching by using virtual manipulatives and they found the most of the virtual manipulatives effective in exploring and visualizing algebraic relations. As a result, the lesson study has played an important role in preservice teachers' preparing a lesson plan for teaching algebra and integrating the virtual manipulatives into the stages of a lesson plan.
... Dans cette introduction nous précisons le contexte et les objectifs de cette recherche. La manipulation dans l'apprentissage des mathématiques, que ce soit dans un environnement réel ou virtuel, est un élément important dans l'apprentissage des mathématiques [2,3]. La résolution de problèmes continue d'occuper une place centrale dans le curriculum français [4,5]. ...
Article
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Des recherches ont montré l’intérêt et les limites de la manipulation dans l’enseignement des mathématiques [1]. Dans le contexte de l’apparition d’environnements virtuels et de la place centrale de la résolution de problèmes, nous étudions la manipulation virtuelle, dans la résolution de problèmes ouverts de mathématiques, dans l’environnement ANIPPO, par des élèves de la fin de l’école primaire. La méthodologie permet de comparer un groupe expérimental dans l’environnement ANIPPO avec un groupe de contrôle dans l’environnement traditionnel. Nous décrivons le cadre théorique des problèmes ouverts, des registres de représentations sémiotiques, de la collaboration et de la motivation. Nous précisons comment les résultats de la pré-expérimentation montrent les difficultés des apprentissages dans un environnement virtuel a-didactique et influencent les conditions de l’expérimentation à venir, pour l’appropriation de l’environnement ANIPPO, la prise en compte des procédures des élèves et la progressivité des problèmes à résoudre.
... Our work contributes to research attempting to compare children's use of tangible and virtual manipulatives in math education [9, 58,63]. Unlike prior work, however, our AR approach afforded the opportunities to compare the two modalities in the same mixed-reality environment. ...
... In fact, the theoretical foundations of manipulative date back to the past (Bruner, 1966;Dienes, 1973;Piaget;1965). These dynamic objects that provide a good opportunity for the creation of mathematical knowledge can be both concrete (tactile, real, sensory, real) manipulatives (Clements, 1999) and virtual (interactive, web-based visual) manipulatives that support the transition between visual representations and soft information (Moyer, Bolyard & Spikell, 2002;Volk, Cotič, Zajc & Starčič, 2017). In some studies, that compared the effects of concrete and virtual manipulatives on academic achievement, a significant difference was found between both types of manipulatives (Gülkılık, 2013;Lee & Chen, 2015;Ross, 2008;Suh, Moyer & Heo, 2005;Şahin, 2013;Takahashi, 2002;Yolcu, 2008). ...
Article
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The purpose of this study is to examine the effect of using concrete and virtual manipulatives relevant fractions subject to 3rd grade students' understanding of fractions and motivation towards mathematics lessons. The study group consists of 61 students studying in three different classes at the 3rd grade level of a private primary school in Turkey. A quantitative research method, pretest and posttest, and a quasi-experimental research design including two experimental and one control group were adopted. The study was carried out by the experimental-1 group with concrete manipulative-assisted training, the experiment-2 group with virtual manipulative-assisted training, and the control group with the traditional teaching in the mathematics curriculum. Data collection tools were the Fraction Comprehension Test (FCT) developed originally with a cronbach alpha reliability coefficient of 0.874 and the Mathematics Lesson Motivation Scale (MLMS) for primary schools was used. One-way MANOVA was used for analysing the data. As far as the research findings; using manipulatives makes a statistically significant difference in the understanding of fractions of 3rd grade students (F(2-60) = 9.171, p<.05), but it was detected that there was not statistically important difference (F(2-60)= 0.163, p>.05) in motivation for mathematics lessons. It is seen that 24% of the change in comprehension is caused by using manipulative. Concrete manipulative use and virtual manipulative use have no superiority in terms of both fraction comprehension and mathematics motivation when compared to each other. It can be suggested that using manipulatives as complementary to each other may give better results.
... A further advantage of computerized training format is the provision with immediate feedback. Different researchers also highlighted more pragmatic advantages of computerized trainings, such as availability and ease of running the intervention (Manches, O'Malley, & Benford, 2010;Moyer, Bolyard, & Spikell, 2002). ...
Thesis
Early mathematical abilities, developed prior the onset of formal instruction, have been identified as a strong predictor of later mathematical achievement and numeracy, which goes along, in turn, with a variety of different life outcomes. Hence, unravelling the cognitive abilities associated with successful mathematical development is an important effort in the field of numerical cognition and developmental psychology. Abilities that are identified as predictors of mathematical development are potentially vital key targets of early interventions. By fostering these key abilities, children’s mathematical development should be positively influenced. The present thesis pursues two major aims. The first aim is to identify key predictors of mathematical development. More precisely, the present thesis studies whether spatial skills fall within the category of key predictors in young children. Findings illustrate that different aspects of spatial skills emerge as strong predictors of mathematics (study I). Findings further highlight, that spatial skills hold a pivotal role for mathematical skills with a prominent verbal component (study II). The second aim is concerned with the elaboration and scientific investigation of the effects of early interventions. A distinguishing feature of the present thesis is, that it is set in the Luxembourgish school setting. The latter is characterized by its heterogeneous student population from diverse language backgrounds. According to current statistics, around two-third of the children who attend Luxembourgish fundamental school do not speak Luxembourgish as a first language at home. Hence, an important number of children are not fluent in the language of instruction in preschool. Therefore, a central concern was to develop and implement early interventions that face the challenges posed by a multilingual school setting. For this reason, the language-neutral early mathematics training tool “MaGrid” was developed. MaGrid sets out to overcome the language-barrier in early mathematics education. On the content side, it encompasses a vast amount of number-specific and spatial training tasks. In the context of the present thesis two intervention studies (study III and study IV), including this tool, were run and yielded promising results. Results of these studies further add to unravelling the relation between spatial skills and mathematics and answering the question, whether the (early) road to mathematics is spatial indeed.
... On the other hand, there exist several studies, such as [22], about the application of the dual coding in mathematics and its good results. Finally, other techniques for teaching mathematics with different technologies are presented by very renowned researchers in this area [23][24][25][26][27][28][29]. ...
Article
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This study aims to implement and evaluate a methodological proposal using the hologram as a teaching medium for the learning of concepts related to areas and volumes of geometrical bodies. The study has been carried out with a sample of 78 students in the third year of secondary education from a privately-owned but state-funded school in Madrid. Thirty-five students who have been taught traditionally formed the control group, and 43 formed the experimental group in which the methodology was implemented. To evaluate its goodness, we have used the Student's t-test to assess the existence of significant differences between both groups. The results reported by the test show that there is a difference of 3.9 points between the scores of both groups which is significant at the level of 0.05. In addition, the user experience in the experimental group has also been evaluated to assess the students’ opinions of the hologram in the learning process. The overall results have assisted us in corroborating the efficacy of the hologram as a teaching medium.
... It provides multiple learning options, such as multimedia that are new ways to engage students and virtual learning environments. One of them is virtual manipulative, which is an 'interactive, web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge' [26]. In recent years, new technologies are developing with the potential such as interactive games, AR, robotics technology and mobile computing and communication [27]. ...
... Bolyard, and Spikell 2002). VMs are found in a variety of platforms (e.g., Java®, HTML5, Flash®, cdf, GeoGebra tube, etc.) and as apps for tablets (e.g., iPad® and Android™).VMs can be used to address issues of inequity among students and make higher levels of mathematics more accessible to all students (e.g., the ability to off-load calculations or drawings to some VMs thus enables students to focus on content). ...
Article
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Guiding questions and a task-analysis framework support teachers in using virtual manipulatives to enhance student understanding.
... However, it should not be forgotten that this situation basically requires pre-service teachers to have a computer, phone, or tablet. Moreover, virtual material integration does not necessarily guarantee effective online learning environments (Hunt et al., 2011) but, nonetheless, they have a potential to helplearners make practices out of class hours and learn actively by engaging with them (Moyer et al., 2002). They can also be used not only to reinforce conceptual understanding, but also to evaluate students, encourage them to work together, or reflect on their own learning (Clements & McMillen, 1996). ...
... In a similar vein, virtual manipulatives have been proposed [12]. They are a new class of manipulatives for computer programs that use visual representations and include static and dynamic visual representations of concrete manipulatives. ...
Chapter
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The digital revolution has deeply transformed the educational materials, especially for children, in a pathway going from physical objects to digital ones. In this paper, after delineating some relevant milestones in this route, one further step is delineated which proposes multisensory materials for learning. These kind of materials keep the main advantages of physical educational materials and marry them with the ones derived from the digital world. Then, an example of multisensory materials for learning is introduced: STTory, which is dedicated to multisensory storytelling, together with results about one study on this material which indicate that introducing multisensory elements in digital materials has positive effects on learning in children. Multisensory educational materials provide multimodal input for learning individual, enriching learning environments and educational scenarios.
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It is an increasingly common phenomenon that elementary school students are using mobile applications (apps) in their mathematics classrooms. Classroom teachers, who are using apps, require a tool, or a set of tools, to help them determine whether or not apps are appropriate and how enhanced educational outcomes can be achieved via their use. In this article we investigate whether Artifact Centric Activity Theory (ACAT) can be used to create a useful tool for evaluating apps, present a review guide based on the theory and test it using a randomly selected geometry app [Pattern Shapes] built upon different (if any at all) design principles. In doing so we broaden the scope of ACAT by investigating a geometry app that has additional requirements in terms of accuracy of external representations, and depictions of mathematical properties (e.g. reflections and rotations), than is the case for place value concepts in [Place Value Chart] which was created using ACAT principles and has been the primary app evaluated using ACAT. We further expand the use of ACAT via an independent assessment of a second app [Click the Cube] by a novice, using the ACAT review guide. Based on our latest research, we argue that ACAT is highly useful for evaluating any mathematics app and this is a critical contribution if the evaluation of apps is to move beyond academic circles and start to impact student learning and teacher pedagogy in mathematics. Free Online version available = https://protect-au.mimecast.com/s/4ZGUC2xZzgHWA8B6HB_fFm?domain=em.rdcu.be
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Chapter
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Chapter
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Chapter
We consider how dynamic diagrams can be used to model multiplication and division. This chapter begins with a review of how multiplication is conceptualized in elementary mathematics education. We consider the affordances of familiar representations of multiplication (e.g., repeated addition, the area representation) and highlight aspects of arithmetic (e.g., multiplication with signed numbers) that are difficult for them to represent. Next, we develop geometric models of multiplication and division by adapting compass-and-straightedge procedures to dynamic geometry. We argue that dynamic diagrams can model multiplication and division as continuous scaling operations on directed lengths, and we consider how dynamic diagrams could be used as virtual manipulatives in pre-service teacher education.
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The 7th International Conference of the Immersive Learning Research Network (iLRN 2021) is an innovative and interactive virtual gathering for a strengthening global network of researchers and practitioners collaborating to develop the scientific, technical, and applied potential of immersive learning. It is the premier scholarly event focusing on advances in the use of virtual reality (VR), augmented reality (AR), mixed reality (MR), and other extended reality (XR) technologies to support learners across the full span of learning—from K-12 through higher-education to workbased, informal, and lifelong learning contexts. Following the success of iLRN 2020, our first fully online and in-VR conference, this year’s conference was once again based on the iLRN Virtual Campus, powered by ©Virbela, but with a range of activities taking place on various other XR simulation, gaming, and other platforms. Scholars and professionals working from informal and formal education settings as well as those representing diverse industry sectors are invited to participate in the conference, where they may share their research findings, experiences, and insights; network and establish partnerships to envision and shape the future of XR and immersive technologies for learning; and contribute to the emerging scholarly knowledge base on how these technologies can be used to create experiences that educate, engage, and excite learners.
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Virtual manipulatives are a form of technology that support the mathematics teaching and learning of students with high-incidence and low-incidence (or extensive support needs) disabilities. The purpose of this chapter is to present virtual manipulatives as an assistive technology. Access to and use of virtual manipulatives have increased over the last decade, resulting in virtual manipulatives serving as a modern assistive technology to support students with a wide range of disabilities in mathematics. This chapter will present an overview of virtual manipulatives as assistive technology for students with disabilities and the research base supporting the effectiveness of this technology.
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E-learning has become an important part of our educational life with the development of e-learning systems and platforms and the need for online and remote learning. ICT and computational intelligence techniques are being used to design more intelligent and adaptive systems. However, the art of designing good real-time e-learning systems is difficult as different aspects of learning need to be considered including challenges such as learning rates, involvement, knowledge, qualifications, as well as networking and security issues. The earlier concepts of standalone integrated virtual e-learning systems have been greatly enhanced with emerging technologies such as cloud computing, mobile computing, big data, Internet of Things (IoT), AI and machine learning, and AR/VT technologies. With this book, the editors and authors wish to help researchers, scholars, professionals, lecturers, instructors, developers, and designers understand the fundamental concepts, challenges, methodologies and technologies for the design of performant and reliable intelligent and adaptive real time e-learning systems and platforms. This edited volume covers state of the art topics including user modeling for e-learning systems and cloud, IOT, and mobile-based frameworks. It also considers security challenges and ethical conduct using Blockchain technology.
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Background Virtual manipulatives (VMs) are increasingly adopted in inquiry activities. However, the effects of the ratio of mobile device‐based VMs to students and external scripts (a guiding structure for prompting group process) provision on group interaction has not been detailed. Objectives This study proposed four different technology affordance conditions for collaborative inquiry learning: 1:1 device‐student ratio (one tablet per student) with external scripts, 1:m ratio (one tablet per group) with external scripts, 1:1 ratio without external scripts, and 1:m ratio without external scripts. The purpose of this study is to identify the effect of technology affordances on group behavioural patterns during collaborative inquiry learning. Methods The research participants were 21 fifth‐grade students from 4 classes (totalling 130 students) in a public elementary school. Students' collaborative inquiry behavioural patterns were video‐recorded during three themed inquiry activities. To identify the behavioural patterns of groups, this study developed an action‐oriented coding scheme for collaborative inquiry learning emphasizing and coded student actions during cooperation. Through lag sequential analysis and dialog content analysis, the behavioural transition modes of groups were obtained. Results The results show that device‐student ratios and external scripts affect behavioural patterns through resource coordination, information interaction, collaborative atmosphere, and task awareness. Implications In mobile device‐support collaborative inquiry learning, the 1:m device‐student ratio yielded more exchanges to test and apply new constructions than that of the 1:1 ratio. External scripts were more applicable to the 1:m condition than to the 1:1 condition.
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Embodied learning tools (ELTs), such as building and manipulating models, bolster students’ learning of spatially demanding science content, such as stereochemistry. However, studies comparing the effectiveness of virtual to physical ELTs on student learning are limited. This study compares online instruction using a virtual ELT, virtual models, to a physical ELT, physical models, on organic chemistry students' stereochemistry understanding. Furthermore, it identifies which tool promotes the transfer and application of spatial science content to higher order concepts, such as reaction mechanisms. Lastly, the role of students' spatial skills is considered. To assess the magnitude of the effect of each tool, two control groups were included, a text-based instruction and a no instruction group. Results revealed that the physical model group showed greater stereochemistry understanding compared to the no instruction group, while there was no difference between the virtual model and the no instruction groups. When asked to apply their knowledge to reasoning about reaction mechanisms, the physical model group outperformed the virtual model group and both control groups. Students' spatial skills did not influence their understanding of either concept in any learning condition. These results suggest that regardless of spatial skills, physical ELTs may provide the necessary scaffolding for students to learn spatially demanding science content, whereas virtual ELTs are no more effective than receiving no formal instruction. Furthermore, physical ELTs may be more effective than virtual ELTs in facilitating the application of that knowledge to more complex concepts. These findings have broad implications for online science pedagogy.
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Soft skills training is considered important for employees to be successful at work. Several companies are offering immersive virtual soft skills training with head-mounted displays. The main contribution of this paper is to provide an overview of the research literature within the field of using immersive virtual soft skills learning and training of employees. The results of this preliminary scoping review show that there is a lack of research literature and empirical studies within this topic.
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The duo of artefacts is a simplified model of the complex systems of various manipulatives (either tangible or virtual) that mathematics teachers and their students use in classrooms. It offers a means to study the complexity of the interweaving of the tangible and of the digital worlds in the teaching and learning processes. A duo of artefacts is defined as a specific combination of complementarities, redundancies and antagonisms between a tangible artefact and a digital artefact in a didactical situation. It is designed to provoke a joint instrumental genesis regarding both artefacts, and to control some of the schemes and mathematical conceptualizations developed by pupils during its use. This article exemplifies the model of a duo of artefacts, in the case of the pascaline and the e·pascaline for the learning of place-value base 10 notation of numbers. It details the design process of the e·pascaline (given the pascaline and its complementarities, redundancies and antagonisms), resulting from feedback of the digital environment and haptic properties of the tangible one. It provides examples of the evolution of pupils’ conceptions of numbers when using the duo. It also shows how teachers transform the duo into a system of instruments, allowing them to manage the problem-solving strategies of their students, providing them with one or the other artefact, playing with their complementarities and antagonisms.
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No artigo, apresentam-se resultados de uma investigação que teve por objetivo verificar como estudantes de um mestrado resolviam uma situação-problema para construir o artefato Geoplano Octododecágono e resolver um problema de geometria plana utilizando registros figurais. Após a resolução do problema e a construção desse objeto, os estudantes o utilizaram, juntamente com atilhos elásticos, para obter soluções de uma das investigações. A partir desse registro, iniciou-se o desenvolvimento de habilidade visual, a qual continuou com o segundo tipo, no software GeoGebra. Concluiu-se que a didática envolvida no Espaço de Trabalho Geométrico – ETG organizado, envolvendo o professor, alunos e uma instituição de ensino superior, permitiu, a partir desses tipos de registros figurais, desenvolver visualização como constructo mental.
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Place value is a challenging concept in children’s developing understanding of number. In this study we examine how first-grade children’s developing understanding interacts with representations of place value in a virtual game. We examined the comments and strategies children produced during the game, particularly attending to those that exhibited emerging knowledge about base-10 structure. Both behaviors were then examined in relation to children’s performance on a grade-specific pre- and posttest. Not surprisingly, children who made comments about tens during the game showed greater pre-to-posttest gains than those who did not. Less expectedly, children whose strategies relied exclusively on counting, but were prone to errors, showed gains in performance when compared to accurate counters. Implications are discussed in terms of the affordances of virtual manipulatives, especially when learners lack some necessary skills to succeed.
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Virtual manipulatives provide benefits to students as they encounter the Common Core State Standards for Mathematics content and practice standards. The National Library of Virtual Manipulatives provides an abundant supply of virtual manipulatives for all K-12 grades and mathematics content areas. Specifically, in this chapter, the authors explore the use of Algebra Balance Scale manipulatives in a middle school mathematics classroom. Using virtual manipulatives increases understanding of the equal sign, algebraic symbols, and increases procedural and conceptual knowledge. In this chapter, the authors demonstrate how using virtual manipulatives helped middle school students to meet grade level content standards for solving equations in one variable. Additionally, practice standards, such as making sense of problems and persevering to solve them, modeling with mathematics, and using tools strategically through the use of virtual manipulatives are addressed. They conclude by considering practical issues related to incorporating virtual manipulatives in mathematics classrooms.
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The study presents results of a tablet-based math game intervention to enhance early numeracy skills of children in Tanzania. Standard level 1 children (n = 122), attending a rural primary school, were randomly allocated to either intervention or control group. The intervention group participated in a daily intervention session for 46 days. Children’s performances in number identification, quantity discrimination, addition, subtraction, and missing number tasks were measured before and after the intervention with randomly selected children from both groups (treatment = 30, control = 31). Score gains in the intervention group were substantially greater than those in the control group. In particular, statistically significant effects of the intervention were identified in quantity discrimination, addition, and subtraction tasks. Item-level analyses using Item Response Theory showed that addition and subtraction items involving regrouping and most missing number items were too difficult even after the intervention. The study also identified which games were played the most or least during the sessions from play-log data and analyzed associations between children’s test performances and gameplays.
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In scientific inquiry learning, manipulatives have been widely utilized as learning resources. Studies have explored the advantages of virtual manipulative (VM) for conceptual understanding and knowledge construction in science education. However, research on the mental engagement and perception of students during collaborative learning under different modalities of using VM remains rare. In this study, we designed a virtual lever manipulative (VLM) and three modalities of using VLM in a primary science course: one VLM per student, one VLM per group, and one VLM per class. There were 80 fifth graders from three classes who participated in this quasi-experimental study. They were asked to complete a group worksheet during collaborative learning activities. Cognitive load, as well as flow experience, was invested through a questionnaire survey after the learning activities. Task involvement was calculated by using the mental effort dimension of cognitive load and post-test scores. The findings indicate that class B (one VLM per group) gained the highest scores in group worksheet and the post-test 1 week later, followed by class C (one VLM per class) and class A (one VLM per student). Class B had the highest level of task involvement, as they had a shared screen among group members. In contrast, class A had a relatively low task involvement and spent more time checking consistency. Besides, both classes A and B had a higher sense of flow experience than class C. Class C experienced a traditional teaching method and less interaction with learning materials, leading to a lower level of flow experience and moderate task involvement.
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This article examines the role that replication research has played in the development and refinement of mathematics interventions for learners with extensive support needs. By highlighting 16 research studies, we seek to inform stakeholders of lessons learned and knowledge gained through replication. These studies show that when given high-quality instruction in the area of mathematics, students with extensive support needs can make great gains in their early number sense and problem-solving skills. Further, social validity data indicate teachers improved their implementation of systematic instruction as a result of using scripted curricula and transferred their skills to other content and skill areas. Implications for practice and policy are discussed, as well as a call for future research.
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This paper offers insight into teachers’ perspectives on the role of manipulatives in the mathematics classroom on either side of the primary to post-primary transition (sixth class teachers in Irish primary schools and first year mathematics teachers in post-primary schools) to examine if discontinuities exist around their usage. The transition from primary to post-primary education is considered the most difficult of all educational transitions that students face, with negative effects more pronounced in the subject of mathematics. A questionnaire involving several open-ended questions was distributed to teachers teaching students in the final year of primary school and teachers teaching mathematics to students in the first year of post-primary education. Results of the qualitative data analysis reveal insights into teachers’ perceptions of the benefits, supports and obstacles to manipulative use. It reveals that, in general, teachers on either side of the boundary crossing are in agreement regarding the perceived benefits of using manipulatives and also the potential factors that inhibit their usage. On the other hand, their opinions regarding the factors that support the use of manipulatives are more divergent.
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This paper reports on how the affordances of the app Math Shake reshaped the learning experience—an aspect of a research project examining the ways mobile technologies are used in primary-school mathematics. Students used different digital tools within the app to solve word problems, while the affordances, including simultaneous linking, focussed constraint, creative variation, dynamic and haptic, made the learning experience different from when using pencil-and-paper technology. However, while the affordances of the mobile technologies are important, the teacher’s pedagogical approach was also influential in the learning.
Virtual Manipulatives: A New Tool for Hands-On Math
  • J Spicer
Spicer, J. "Virtual Manipulatives: A New Tool for Hands-On Math." ENC Focus 7 (4) (2000): 14-15. v
Serendipity in Interactive Mathematics: Virtual (Electronic) Manipulatives for Learning Elementary Mathematics
  • L O Cannon
  • E R Heal
  • R Wellman
Cannon, L. O., E. R. Heal, and R. Wellman. " Serendipity in Interactive Mathematics: Virtual (Electronic) Manipulatives for Learning Elementary Mathematics. " Journal of Technology and Teacher Education, Proceedings of the Society for Information Technology and Teacher Education. San Diego, Calif.: February 2000.
Journal of Technology and Teacher Education, Proceedings of the Society for Information Technology and Teacher Education
  • L O Cannon
  • E R Heal
  • R Wellman
Cannon, L. O., E. R. Heal, and R. Wellman. "Serendipity in Interactive Mathematics: Virtual (Electronic) Manipulatives for Learning Elementary Mathematics." Journal of Technology and Teacher Education, Proceedings of the Society for Information Technology and Teacher Education. San Diego, Calif.: February 2000.