AOLA Framework for eLearning in Mathematics Education

Introduction

     The discussion of technology roles in mathematics and mathematics education (MME) is ongoing. No doubt that the benefits are welcoming, with some seeing more of what technology can do and should do.   In here, we believe that technology can and will enhance the learning process and the environment, especially at current time mathematics is not native to the Web yet. How this e-learning environment should be leveraged in both traditional and 'new' teaching practices, and how the augmented learning process with characteristics such as timeliness and availability would affect instruction design remain to be seen.   Nonetheless, it is time to act. We propose an e-Learning framework based on the simple idea of AOLA, that is, Author-Once-Learn-Anywhere. The AOLA framework offers a platform for teachers, learners and technology to co-exist in one environment, facilitating any-to-any (any2any) interaction that is crucial to the learning process. Note that the interaction is not limited to teachers-to-learners, but also, for example, learners-to-technology and vice versa. In 2007, the development of the language of AOLA - activityML begins.

     This website serves as the always-on dissemination channel for the development of this AOLA framework and its related technology. There are two tracks - one is the ePlatform, and the other is AOLA-related technology. The discussion of former can be found in this website also.  We will concentrate on the latter here.

Background

     In the 2nd ATCM (1997), one of the plenary speeches [Leong 1997] suggested that Internet technology was getting ready for mathematics on the Web as evident by the development of MathML and OpenMath [11]. The image format GIF provides one channel for mathematics symbols to be viewed, though not represented as native symbols, on the Web. At that time, as the Web entered into the Interactive Web Era [Chu, S., et. al., 2004], the challenges facing mathematics contents on the web were representations (basic and ad hoc) and presentations (e.g., expressions not as raster images). In the 3rd ATCM, Leong [9] provided his prediction of CAS (Computer Algebra System) for 2008. Two of the key points stated revolved around the dynamicity of mathematics contents (the need for ‘live math objects’), and the authoring of mathematics contents less the knowledge of some CAS language (the language should be hidden from the users - not to becoming another hurdle). At that time, the CAS engines, or compute engines in general, were not perceived as 'services' available on the Web but as an integral part of CAS. In the 4th ATCM, Lee (1999) strongly suggested the convergence of computers and graphic calculators will take pace. The performance limitation of handheld calculators will no longer be an issue as hardware technology can transform graphic calculator capability to parlay that of a computer with minimum disruption to learned processes, or a handheld computer of size comparable to that of the graphic calculator with connectivity to networks.

 When you are reading this, ATCM 2005, the tenth conference, has begun, and also a technology landscape begins to take shape. Internet technology, inclusive of Web technology, also has evolved since 1997. MathML 2.0 was released in 2001. Plug-ins (e.g., MathPlayer) or built-in capability (Amaya) enables standard web browsers to view mathematics expressions represented in MathML. Mathematics editors (e.g., MathCast) now can export MathML to be included in lessons, deployable as web pages. CAS’s are powerful, e.g., geometry objects can be manipulated in 2D and even 3D space, facilitated by faster and cheaper hardware. No doubt, mathematics objects are ‘alive’ within specific software environments.

     Conferences of similar nature as ATCM have tracks that deal with ‘live mathematics.’ One of the themes at ICTMT7 (The 7th International Conference on Technology in Mathematics Teaching) was ‘designing and using dynamic mathematics environments.’ There is also the International Conference on Technology in Collegiate Mathematics (ICTCM) where technology use is discussed. This topic has also been discussed in various publications [1][2][3][4]. In the 10th ATCM (here in Korea this December 2005), one of the plenary speeches will be discussing recent development on how mathematics can be ‘input’ – one of the major hurdles in authoring mathematics contents for the Web. No doubt it is a challenge to adopt technology in mathematics education. Nonetheless, unmistakably, these and other developments, studies and meetings are unrelenting efforts towards one common goal – enabling technology for learning and teaching mathematics.

AOLA Technology

Author-Once-Learn-Anywhere (AOLA) technology trends towards the e-Platform environement with seamless linking of different expressive language of mathematics education. Simply, AOLA requires

  1. Authoring tool of choice with ActivityML compliant,
  2. Open representation standard of one,
  3. Online manipulative environment for sharing, and,
  4. On-demand any2any integrative interaction.

Global Standards

Not many existing standards are gudiing the research and development of e-Learning environment. The DocBook is an attempt with SGML in the background pushing the publishing industry to adhere to one standards. Other standards that are needed, from a small scale, is the 'activity' template, We call this template or language the 'ActivityML.' We will explore this next.


Community Driven

The AOLA framework is community-based. Benefits obtained from the design can only be attributed to community contributions, leveraging expertises from different fields of mathematics and mathematics education. Thus, community-based technology must be designed to spawn communities, and to any2any link communities, and to co-exist in the same information infrastructure.


Resources
  • Electronic Proceedings of ATCM conferences (up to 2006) [2006] EPATCM's
  • Mathematics content by Professor Ivan Cnop [2005] 10th Anni. CD
  • www.mathforum.org
  • 10th Anniversary CD of past ATCM conferences 10th Anni. CD

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