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Purpose: To analyse the potential impact of the adoption of technology as a tool for automating & reinforcing routines; supporting transformative and manipulative actions; and/or making tools and procedures visible and comprehensible.
A. Structure
References: 19, 20, 80
Sites, sections, pages:
- What is the focus:
- Mathematical resource sites containing atlases, libraries with or without interactive material, archives, dictionaries or mathematical enrichment like olympiad questions, puzzles or visual mathematics.
- A notice board site: … [mainly administration].
- Content sites with notes on specific topics or even an online book with hyperlinks, graphical illustrations and perhaps Java applets connected to a course.
- Exploration and demonstration sites containing mostly visual illustrations and animations in the form of Java applets, perhaps including other material, not necessarily connected to a traditional undergraduate mathematics topic. These sites include interactive as well as investigative (mostly geometry) sites.
- Sites containing exercises for practice and quizzes and normally used in connection with a teaching programme. Some of these sites contain exercises using a computer algebra system or some other similar software.
- Communication sites offering the opportunity for the mathematics community to share ideas, get answers to questions, provide links to resources, etc.
- A full course with content supplied and interaction taking place. In many of these courses, a VLE environment is used, sometimes linked to a resource site.
Referring to radar chart classification of online mathematics courses with six radials, each with a question to quantify a measure of quality of interaction or material:
- Interaction:
- Dynamics and Access: What is the frequency of access expected for success in the course?
- Assessment: How much of the assessment is done on the site?
- Communication: How much of the communication happens online?
- Material:
- Content: How much of the course content is on the site? [e.g., book, course information, course administration, lecture notes, study objectives]
- Richness: How many enriching components does the site have? [e.g., graphics, Java applets, slide presentations, video clips, sound clips, text communication]
- Independence: How independent is success in the course from face-to-face contact?
- Interface:
- Instructor facilitation: Are students able to share ideas with teachers electronically?
- Are there links to internet resources, including resource or textbook sites?
- Appropriate interface: Does presentation just resemble textbooks but with excellent graphics?
- Communication, interaction and collaboration: Is there synchronous or asynchronous communication through tools for co-construction of knowledge and sharing of ideas? [Synchronous could include voice and video conferencing, shared whiteboards and live presentation tools (e.g., tablet or electronic writing pad), application sharing, live assessment, chat rooms, web safari, and breakout rooms for smaller groups. Asynchronous, could include group project activity, assessments, surveys, votes. These may be completely open-ended or constrained. Ideally, course should be structured to necessitate communication.]
- Cognitive tools: Are there visualisation and information gathering tools; also animations [e.g., GIF or Java applets]?
- Which cognitive tools [e.g., glossary, calculator, workbook, calendar] are available to support learning?
- Which cognitive tools are available to support automating mathematical or statistical routines [i.e., drill-and-practice] ?
- Which cognitive tools are available to support transformative and manipulative actions oriented towards mathematics/numeracy [i.e., supporting individual sense-making and collective meaning] ?
- Which cognitive tools are available to support the focus on making tools and procedures themselves visible and comprehensible?
- Which cognitive tools are available to enable the automation of a new routine or construction of a new tool [i.e., creativity, new knowledge construction] ?
- Which cognitive tools are available to support data collection, analysis, and presentation [i.e., statistical tools] ?
- Are there links to internet resources, including resource or textbook sites?
- Communication :
- Does the lack of face-to-face contact result in a loss of interpersonal relations such as a sense of isolation?
- With asynchronous communication are there problems of:
- a lack of immediate feedback?
- students not checking in often enough?
- a long time necessary for discussion to mature?
- a sense of social disconnection experienced by students?
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