Conference Paper

Quadratic: Manipulating algebraic expressions on an interactive tabletop

Authors:
To read the full-text of this research, you can request a copy directly from the author.

Abstract

This paper introduces Quadratic---a virtual manipulative for two people to explore algebraic expressions on an interactive tabletop. Users assemble rectangles out of fundamental components: 1, x, and x2. As the area of a rectangle is both the product of its sides and the sum of its components, users can explore how the product of two linear expressions (the rectangle's sides) equals a quadratic equation (the rectangle's area). This virtual manipulative adds several important features to the previously existing physical manipulative: 1) negative pieces; 2) multiple palettes; 3) multiple linked representations between the visual elements, the equivalent algebraic expression, and the graph of that expression; 4) the ability to provide feedback on posed challenges.

No full-text available

Request Full-text Paper PDF

To read the full-text of this research,
you can request a copy directly from the author.

... By designing for these mechanisms one can achieve higher collaborative outcomes [34]. For example, while working together and sharing insights and problems with each other, the peers might benefit from a reflection tool [76]. ...
Article
Collaboration and engagement while coding are vital elements for children, yet very little is known about how children's engagement and collaboration impact their attitudes toward coding activities. The goal of the study is to investigate how collaboration and engagement moderate children's attitudes about coding activities. To do so, we designed an study with 44 children (between 8 and 17 years old) who participated in a full-day coding activity. We measured their engagement and collaboration during the activity by recording their gaze, and their attitudes in relation to their learning, enjoyment, team-work and intention by post-activity survey instruments. Our analysis shows that there is a significant moderating effect of collaboration and engagement on children's attitudes. In other words, highly engaging and collaborative coding activities significantly moderate children's attitudes. Our findings highlight the importance of designing highly collaborative and engaging coding activities for children and quantifies how those two elements moderate children's attitudes.
... Examples for using tangibles for math learning have been provided by Falcaō et al. [6], Girouard et al. [7], Manches and O'Malley [14], and Marichal et al. [15], amongst many others. Others, like Rick [22], have incorporated touch to be able to directly manipulate math objects presented on a screen. Research about how tangibles can support learning or how learning theories can inform tangible development has for example been presented by the "Tangible Interaction Framework" by Hornecker and Buur [9] or the "Tangible Learning Design Framework" by Antle and Wise [1]. ...
Article
Full-text available
While manipulatives have played an important role in children’s mathematics development for decades, employing tangible objects together with digital systems in the classroom has been rarely explored yet. In a transdisciplinary research project with computer scientists, mathematics educators and a textbook publisher, we investigate the potentials of using tangible user interfaces for algebra learning and develop as well as evaluate a scalable system for different use cases. In this paper, we present design implications for tangible user interfaces for algebra learning that were derived from a comprehensive field study in a grade 9 classroom and an expert study with textbook authors, who also are teachers. Furthermore, we present and discuss the resulting system design.
... Examples for using tangibles for math learning have been provided by Falcāo et al. [5], Girouard et al. [6], Manches and O'Malley [12], and Marichal et al. [13], amongst many others. Others like Rick [19] incorporate touch to be able to directly manipulate math objects presented on a screen. Research about how tangibles can support learning or how learning theories can inform tangible development is for example presented by the "Tangible Interaction Framework" by Hornecker and Buur [7] or the "Tangible Learning Design Framework" by Antle and Wise [1]. ...
Preprint
Full-text available
This workshop position paper presents ongoing research on using smart tangible objects for algebra learning. While mathematical manipulatives have played an important role in children's mathematics development for decades, employing tangible objects in the classroom has been rarely explored yet. In our work, we investigate the potentials of using smart objects for algebra learning. Our smart tiles are based on traditional algebra tiles, passive mathematical manipulatives used in many schools in Northern America, and we currently extend these by 1.) multimodal input and output capabilities, 2.) dynamic constraints and 3.) adaptivity and feedback. In this paper, we give an overview on the overall system concept, the interaction with the tangible objects and their current design, as well as on the potentials of actuated smart objects for future interaction.
... Then there are tabletop applications that focus on learning numbers and sorting (Khandelwal and Mazalek, 2007) and concept mapping (Son Do-Lenh et al., 2009). Quadratic (Rick, 2010) is another educational Tabletop application which allows learners to explore algebraic expressions on a tabletop. Bryce and Robertson (1985) observed that in majority of the schools the assessment of science lab work is nonhands in nature with much more focus on the report writing skills. ...
Conference Paper
Full-text available
Within the context of Roger’s Diffusion of Innovation theory we propose a pedagogical framework for attributes that can significantly affect student adoption of collaborative learning environment like multi-user, multi-touch tabletop. We investigated the learning outcomes of secondary school students in India collaboratively using OLabs on a tabletop (EG1 = 30) vs. individually using at desktops (EG2 = 92). We analyzed the nature of communication, touch and non-touch gesture actions, position around the tabletop, focus group interviews, and pre and post test scores. Using Bass model the study also accounts for the inter influence of related group of potential adopter teachers who are likely to exert positive influence on students. The results revealed that learning outcomes on tabletop are strongly associated with innovation attributes like Relative Advantage, Compatibility, Ease of Use, Perceived Enjoyment, Perceived usefulness and Teachers support. Overall students expressed much more positive attitude to adopt tabletop technology for learning vs. desktop. We find that the mean group performance gain is significant with collaboration using tabletop and significantly greater than the group using desktops. We also find that the group interactions with the tabletop area significant factor that contributes to the group’s average performance gain. However, the total time spent in while using the tabletop is surprisingly not a significant factor in the performance gain. Our findings contribute to the design of new pedagogical models for science learning that maximizes the collaborative learning potential of tabletops.
... Studies have suggested that interactive tabletops have the potential to be productive tools for collaboration and learning [2,10,14,17]. Specific applications have included: biodiversity, reading, fractions, the physics of light, quadratic equations, language learning, and genomics [5,9,11,13,14,17,18]. ...
Conference Paper
Full-text available
In this paper we describe NetTango, an agent-based modeling environment designed for elementary school students to use on a multi-touch tabletop surface. We review literature on the use of interactive tabletops for learning and present examples from an exploratory study that we conducted with 28 children (ages 6--10). We also discuss two design challenges that emerged during our study and consider possible solutions.
Conference Paper
In this paper we describe the design and implementation of a tangible balance beam that we created for early algebra education. We also present data from an exploratory study with seven children (ages 9--10 years) in a local elementary summer school classroom. Our results provide insight into how students solve algebra problems using our tangible interface, how they coordinate multiple representations (both digital and physical) in the problem solving process, and how they understand the concept of algebraic equality in this context. The data suggests that our interface helps students think about equations in a relational context, which has been shown to be an important skill for understanding more advanced concepts in algebra. Whether or not the combination of physical and digital representations provided by our interface helps students apply this relational understanding to equations written using standard algebraic notation is an open question that we hope to investigate in future work.
Article
Full-text available
The abstract for this document is available on CSA Illumina.To view the Abstract, click the Abstract button above the document title.
Article
Full-text available
This paper presents a study that investigated collaborative activity in a tangible tabletop environment to support learning about the physics of light. In co-located groups of three, children performed exploratory activities, using tangible artefacts, to find out about light. Analysis suggests that the environment can support various collaborative activities, but of central interest, demonstrated the role of peer interference in learning activities. Verbal negotiation and synchronization of actions emerged as conflict-resolution strategies and an implicit agreement by the children for sharing the physical and virtual resources of the system was noticed. The physicality and 'present at hand' nature of the input devices contributed to balanced levels of participation, particularly through action. Overall, the interference-prone tabletop environment contributed to creating a highly collaborative environment in which individual exploration was discouraged, leading the group through a productive process of collective exploration and knowledge construction.
Article
Full-text available
This article introduces medium-based design—an approach to creating exploratory learning environments using the method of extending a medium. First, the character-istics of exploratory learning environments and medium-based design are described and grounded in related work. Particular attention is given to extending a medium— medium-based design's core method. Then, the product and process of two envi-ronments are detailed to show how medium-based design enables the creation of ex-ploratory learning environments. Finally, a study compares medium-based design to a conventional design process to test the hypothesis that medium-based design is partic-ularly effective in creating exploratory learning environments.
Article
Full-text available
New technologies, such as multi-touch tables, increasingly provide shareable interfaces where multiple people can simultaneously interact, enabling co-located groups to collaborate more flexibly than using single personal computers. Soon, these technologies will make their way into the classroom. However, little is known about what kinds of learning activities they will effectively support that other technologies, such as mobile devices, whiteboards, and personal computers, are currently unable to do. We suggest that one of the most promising uses of shareable interfaces is to support learning through exploration and creation. We present our work on DigiTile as a case study of how shareable interfaces can enable these forms of learning by doing. We demonstrate how DigiTile supports collaboration, present a field study on its learning benefits, and show how it can fit into a larger computing ecology.
Concrete' manipulatives, concrete ideas Contemporary Issues in Early Childhood
  • D H Clements