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Math4Mobile: Design & Implementation Challenges

Michal Yerushalmy & Arik Weizman

Calls are frequently heard for improving schooling by closing the gap between children’s life out-of-school and traditional learning styles, and by broadening the space and span for life-long learning opportunities. The Math4Mobile development endeavors to engage all students with mathematical ideas. It provides a collection of tools that could be included in a variety of activities to support students’ mathematical skills, conceptual understanding, and creative mathematical thinking.

Computerized tools have been shown to provide important support for achieving these goals. Three decades of using technology in mathematics education provide clear evidence that the tools designed to support a well-defined educational agenda were the most successful ones. In general, technology achieves its most important gains in settings in which it is available for long periods of time, and when it is designed to be incorporated regularly into the learning process. I suspect that an important reason for the slow pace of change in this area is that ubiquitous, long-term access to technology is yet to be achieved in most learning environments.

Given the high rate of increase in the number of mobile phone owners worldwide, the computational capability of most phones, and the widely available communication infrastructure, we have been looking for ways to turn the available and relatively cheap personal mobile technology into a relevant learning tool in and out of school.

Meeting the challenges of computation, communication, and usability

Understanding the computing potential: The Math4Mobile project has been developed based on VisualMath, which was found to be a successful technology-based curriculum for changing the ways students learn geometry, function-based school algebra, and calculus. The Math4Mobile project started as yet another cycle of development of already existing WEB tools, but working under the constraints of the new hardware and enablers has led us to ideas and challenges beyond hardware-related problems. To support cognitive empowerment for the learning of mathematical content, our first challenge was to plan a variety of well-recognized useful applications. Design decisions were to focus on:

  1. Applications that have already been recognized as successful in using technology for learning: Graph2Go, a graphing calculator that serves a wide range of users at different levels and in various fields of learning; Quad2Go, a dynamic geometry environment that allows constructing and analyzing while dynamically changing the various available quadrilaterals, mostly supporting primary school geometry.
  2. Applications that could be useful in motivating learning out of the classroom: Sketch2Go and Fit2Go, which support recording and mathematically analyzing temporal processes that students might face in a task out of class.
  3. Design applications supporting scientific inquiry; all applications designed to include embedded feedback in a variety of representations, to encourage observation of multiple examples, and at the same time to support the development of mathematical skills through intensive practice (for example, Solve2Go).
  4. Applications that first and foremost can be easily operated “on the go,” with a numeric keypad being the only necessary requirement, although navigation keys can also be used. Because typing mathematical signs and expressions can be extremely tedious, our design strategy is to provide ready to work but easy to alter mathematical objects such as expression or equation clusters, iconic graphs, geometric shapes, etc.
  5. Applications that are appropriate to use by children and that comply with hardware, resources, and infrastructure constrains. Our intention is to develop for everyone, closing rather than widening the social gaps in the process. Thus, we plan for minimal air time and the lowest possible end, and for widely used hardware that does not require compromising on essential learning goals. We chose J2ME as the development language because it supports the visual mathematical representations assumed to be essential for conceptual learning and design that works for users of small screens.

Understanding the communication potential: According to social-cultural theories of learning, collaborative thinking is an essential component of scientific inquiry. Whereas the social studies and humanities are better known for providing opportunities for sharing, mathematics is assumed to be practiced and developed individually. The choice of mobile phones provides an opportunity to create incentives for collaboration that are authentic learning processes for a community of math learners at all levels. We examine designs of three types of communication:

  1. Each Math4Mobile application includes Phone 2 Phone collaboration via SMS center. Students can use it to share their work, post it to receive critical comments from their peers, analyze and propose improvements of others’ work, and submit their work to the teacher.
  2. We identified two challenges for our future development work: multi-user communication, where users can share their work interactively, and communication between phones and computers. Advancing in this direction, we developed the Click2Go Classroom Interaction System, currently piloted in schools. Click2Go allows students to use the local communication infrastructure to respond to teachers’ prompts and present the collated students’ responses to promote whole-group discussion.
  3. Another channel of communication, the Augmented Textbook, works with the Math4Mobile application to augment paper textbooks with mobile applications that include interactive diagrams, a counterpart to printed diagrams.

Understanding the Usability Potential: Pilot experiments involving teachers in schools and pre-service teachers were part of our development work. In each experiment we designed activities relevant to the curricular agenda. The learning was recorded and analyzed, and usually the results showed the direction of required improvements of the application. After analyzing the learning and teaching opportunities, we design scenarios that can be relevant to the following pedagogical and technological variables:

  • Space: activity suited for use in class, in and around school, or anywhere
  • Size: to be used by an individual student, in collaboration in a small group, in the course of a whole-class discussion
  • Learning mode: exploring, practicing skills, or solving problems
  • Teacher’s role: teachers could use the tools and the activity to deliver instruction, moderate group collaboration, assess individual performance, or observe student activities out of the classroom
  • Means of use: online, offline, asynchronous, synchronous
  • Infrastructure media components available (ubiquity): the ideal setting for the activity also includes, in addition to the personal mobile phone, a “smart board,” a website, a desktop application, and an augmented textbook
  • Phone resources: camera, calculator, stop watch, dedicated applications

Educational impact: Patterns, scalability, and sustainability

Since 2008/2009, downloads range from hundreds to thousands monthly, the more frequently downloaded being Graph2Go and Solve2Go. Most applications can be downloaded from the site free of charge. There are many options to download the applications from a variety of sites that adopted them as favorite educational resources. The applications also spread virally. We therefore assume that the above figures are only partial.

The geographic breadth spans the globe and includes India with thousands of downloads yearly, and African countries (Cote D’Ivoire, South Africa, Ghana, Nigeria, Mozambique), South American countries (Argentina, Mexico), and Asian countries (Bangladesh, Pakistan, the Philippines) with hundreds of downloads a year. Clearly, the development is attractive, sought after, and useful in rural locations and in less developed communities.

Users: We suspect that the applications are being used by students in a wide range of ages and settings. We learn from teachers around the globe who occasionally write to us about their use of the applications in their schools, from teachers’ centers using the applications for professional development at teachers’ workshops, from secondary and higher education students reporting and asking for further improvements, and from resources being created for Math4Mobile independently by users.

Development challenges

The lack of standards has been a major difficulty. Several years ago Symbian and J2ME were supported by the majority of mobile phones. This is not the case anymore, and since 2010 the market share of Android and iPhone systems keeps growing. This continuing fragmentation is a major obstacle for the scalability and sustainability of the development. It requires constant investment in parallel development (different languages and mathematical packages) for a variety of systems and hardware, that have different capabilities even when operating under similar system. It also requires software verifications and quality assurance that are not easy to do in educational environments.

Developing high-quality applications is relatively expensive. Math4Mobile, an innovative experiment, has been developed in an academic R&D center by faculty and students. To scale it up, it requires economical models that would support free personal use and also provide sustained support for further development and implementation.

Designing human-computer interfaces that take into account the yet unknown health effects of extensive use of mobiles by children. For example, current design is aimed at maximizing offline use.

Investing in a variety of application types such as games and location-based applications that have been shown to be important for learning.

Pedagogical challenges

At present, educational systems own the hardware and software required for learning. Mobile personal phones are a different ball park, in which the centralized models do not seem to work well.

Taking into account the new meaning of students working with their own personal tool is a challenge. A major threat to teachers is the misuse of the communication tools during school time. Another threat is use of applications that students upload to their mobiles (or of resources such as video clips) that interrupt class work. Yet another popular use that can be interpreted as misuse of a cell phone in a classroom setting is recording with the camera and mailing paper resources. It requires imagination and creativity to turn these affordances into constructive learning situations. Projects that involve children in the design could be important in establishing new learning norms.

Tools should support teachers in managing the load of students’ personal work. Following the first design experiment, a full archive system was developed for each application. It was required because the traffic of work sent by SMS between students and the teacher was enormous. The development of Click2Go, which collects and organizes personal data on a server that can be accessed by the teacher, is another model for organizing assessment. Further enhancement of ubiquity that would easily make the same applications work with a variety of media is essential.

Math4Mobile provides and updates activities and teaching ideas at its site. We hope to create professional development models using new means that assume the active involvement of such media as blogging, mobile communication, and sharing mLearning scenarios used around the world throughout social networks. We continue developing instructional materials to be used with existing curricular standards and platforms that allow phone users to communicate with colleagues and mentors worldwide, even when they have no access to computers (as we recently prototyped in India with www.mobilegurukul.org).

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