Overview of Project
1. Background
E-learning and e-assessment meet special challenges when it comes to the teaching of mathematical skills. Special tools and systems have been developed by the subject community to address these challenges, many of them—including the systems presented here—very sophisticated. However, the widespread adoption of these tools has been hindered by a lack of standards and interoperability.
We will extend and adapt existing mathematical e-learning tools and systems, developed by members of the project team, to make them interoperable with other components of a managed learning environment, as well as with one another. This will be done using and extending e-learning standards and web service protocols.
We will extend the following existing systems and make them interoperable:
• AiM and CABLE are self-testing and assessment systems based on server-side marking using computer algebra, allowing for testing of higher mathematical skills;
• METRIC is a self-testing and mathematical learning system based on client-side marking implemented in Java, allowing for scalability and use off-line.
• WaLLiS is an interactive learning environment that focuses on providing adaptive and intelligent feedback for mathematics questions.
• Moodle is a user-friendly VLE with an assessment system that we will extend.
These tools have already been proven at several institutions to provide great pedagogical benefit to the learning experience of students of mathematics and related disciplines, both in higher education and at the school-university interface.
2. Aims and Objectives
Our aim is to provide lecturers with convenient and easy-to-use tools to create computer aided assessment questions for mathematics and to integrate them as seamlessly as possible into their existing teaching practice.
In the field of mathematics, a would-be author of question items currently faces a number of problems. The only generally available, interoperable, standards-compliant authoring tools will allow her to create questions of a general type, such as multiple-choice, textual input or numerical input. However, they will not allow her to format mathematical expressions, or to generate such expressions from parameter sets, or to create items that assess student answers in the form of such expressions. The overall aim of the project is to solve these problems, by pooling and enhancing the non-generic solutions already developed by members of the team.
It is our aim that the tools we develop will be easy to integrate into existing e-learning environments and existing assessment systems. They should be easy to install, either by an individual lecturer or centrally by a whole institution.
A further aim of this project is to make it easier for developers of e-learning tools to equip their tools with the extra capabilities required for mathematics.
Our objectives are:
1. To develop a Web Service for the delivery of mathematical expressions. This service will be able to be called by any e-learning tool; it will respond appropriately to the capabilities of the user's browser and to his/her preferences, and will provide a choice of input tools (some of which have already been developed by members of the team). It will make available free-floating mathematical tools developed by team members, as well as fronts ends to server-side computer algebra systems.
2. To produce an XML specification to represent mathematical questions. The specification will reflect the particular nature of the subject: specifically, the need to assess student answers that are in the form of mathematical expressions. This will be implemented in AiM, CABLE and METRIC. We shall work closely with the MathML. OpenMath and IMS communities internationally.
3. To develop an authoring tool for mathematics question items, providing teachers with simple interfaces that allow questions to be written without the need to become familiar with the underlying formats. This tool shall accept plug-ins for various question types.
4. To develop a web services protocol with which existing assessment systems can communicate with our mathematical assessment engines to allow them to incorporate mathematical questions into their quizzes.
5. To develop tools with which lecturers can seamlessly integrate computer aided assessment questions into their traditional problem sheets.
3. Overall Approach
Strategy and structuring
The project is based around 5 existing and three new software packages. The existing packages are
• AiM
• CABLE
• METRIC
• Moodle
• WaLLiS
The three new packages to be developed by the project are
• a question authoring tool with plug-ins for different question types
• a web service for representing mathematics on the web
• a tool allowing lecturers to manage both their conventional assignment questions and their computer aided questions and to combine them seamlessly into problem sheets.
The project will tie these tools together by several web services protocols and interoperability specifications:
• a web service protocol for communication between assessment systems and question engines
• a syntax specification and web service protocol for communication with the service taking care of the presentation of mathematics on the web
• a specification for mathematical questions
This structure of working on 8 independent software projects, tied together by web services protocols and interoperability specifications makes management of this project easier as would otherwise be the case for a project with a geographically distributed team.
The strong reliance on web service protocols and interoperability specifications however serves another purpose: it will make it possible for other mathematical software, not included in this project, to achieve interoperability with our tools by implementing the same protocols and specifications.
Scope and boundaries
The project is focused on the development and implementation of standards, services and implementations for authoring and deploying question test items in mathematics. Within this, our central concern is mathematical expressions: their generation, rendering and comparison as mathematical objects. The project is not concerned with wider e-learning issues in mathematics, such as microworlds, intelligent tutoring, course management or assessment of sustained mathematical argument.
Neither is the project committed to dealing with the issue of graphics in question tests. This issue has, however, been addressed by several of the individual team members in their non-generic projects, and the work may reveal opportunities to build on these achievements. Any such opportunities will be taken advantage of if time, and other project commitments, allows it.
Important issues and critical success factors
Interoperability lies at the heart of the project's aims, and indeed a large mid-project milestone has been scheduled that consists in demonstrating interoperability among all components developed thus far. Achieving interoperability is central to the project's success, as is compliance with existing and emerging standards (for example, those for QTI in general).
Of at least equal importance is ease of use. Since the project's overall aim is to enable colleagues to create mathematical question test items without becoming expert programmers, the ensemble of services, standards, implementations and authoring tools that the project produces must be usable in a natural and intuitive way, and without extensive training. Also, at the learner's end, the project's implementations must generate questions that are themselves easy to use. In particular, questions must test, as far as possible, the learner's knowledge of mathematics only, and not of specialised, non-intuitive notations and conventions.
Pedagogical soundness cannot be directly guaranteed, because it is always possible to use good tools badly. Nonetheless, the project's deliverables must lend themselves to pedagogically sound use. Specifically, they must enable the creation of cognitively rich question items that assess as many aspects as possible of mathematical thinking, at as many levels as possible in a Bloom-type taxonomy of objectives. Cognitive richness must come without a major cost in interoperability or ease of use, and must not require the author to acquire arcane expertise. It must manifest itself in tasks for the learner whose richness of challenge lies solely in their mathematical content, and not in any fresh computational or user interface problems.
Overview of Project
1. Background
E-learning and e-assessment meet special challenges when it comes to the teaching of mathematical skills. Special tools and systems have been developed by the subject community to address these challenges, many of them—including the systems presented here—very sophisticated. However, the widespread adoption of these tools has been hindered by a lack of standards and interoperability.
We will extend and adapt existing mathematical e-learning tools and systems, developed by members of the project team, to make them interoperable with other components of a managed learning environment, as well as with one another. This will be done using and extending e-learning standards and web service protocols.
We will extend the following existing systems and make them interoperable:
• AiM and CABLE are self-testing and assessment systems based on server-side marking using computer algebra, allowing for testing of higher mathematical skills;
• METRIC is a self-testing and mathematical learning system based on client-side marking implemented in Java, allowing for scalability and use off-line.
• WaLLiS is an interactive learning environment that focuses on providing adaptive and intelligent feedback for mathematics questions.
• Moodle is a user-friendly VLE with an assessment system that we will extend.
These tools have already been proven at several institutions to provide great pedagogical benefit to the learning experience of students of mathematics and related disciplines, both in higher education and at the school-university interface.
2. Aims and Objectives
Our aim is to provide lecturers with convenient and easy-to-use tools to create computer aided assessment questions for mathematics and to integrate them as seamlessly as possible into their existing teaching practice.
In the field of mathematics, a would-be author of question items currently faces a number of problems. The only generally available, interoperable, standards-compliant authoring tools will allow her to create questions of a general type, such as multiple-choice, textual input or numerical input. However, they will not allow her to format mathematical expressions, or to generate such expressions from parameter sets, or to create items that assess student answers in the form of such expressions. The overall aim of the project is to solve these problems, by pooling and enhancing the non-generic solutions already developed by members of the team.
It is our aim that the tools we develop will be easy to integrate into existing e-learning environments and existing assessment systems. They should be easy to install, either by an individual lecturer or centrally by a whole institution.
A further aim of this project is to make it easier for developers of e-learning tools to equip their tools with the extra capabilities required for mathematics.
Our objectives are:
1. To develop a Web Service for the delivery of mathematical expressions. This service will be able to be called by any e-learning tool; it will respond appropriately to the capabilities of the user's browser and to his/her preferences, and will provide a choice of input tools (some of which have already been developed by members of the team). It will make available free-floating mathematical tools developed by team members, as well as fronts ends to server-side computer algebra systems.
2. To produce an XML specification to represent mathematical questions. The specification will reflect the particular nature of the subject: specifically, the need to assess student answers that are in the form of mathematical expressions. This will be implemented in AiM, CABLE and METRIC. We shall work closely with the MathML. OpenMath and IMS communities internationally.
3. To develop an authoring tool for mathematics question items, providing teachers with simple interfaces that allow questions to be written without the need to become familiar with the underlying formats. This tool shall accept plug-ins for various question types.
4. To develop a web services protocol with which existing assessment systems can communicate with our mathematical assessment engines to allow them to incorporate mathematical questions into their quizzes.
5. To develop tools with which lecturers can seamlessly integrate computer aided assessment questions into their traditional problem sheets.
3. Overall Approach
Strategy and structuring
The project is based around 5 existing and three new software packages. The existing packages are
• AiM
• CABLE
• METRIC
• Moodle
• WaLLiS
The three new packages to be developed by the project are
• a question authoring tool with plug-ins for different question types
• a web service for representing mathematics on the web
• a tool allowing lecturers to manage both their conventional assignment questions and their computer aided questions and to combine them seamlessly into problem sheets.
The project will tie these tools together by several web services protocols and interoperability specifications:
• a web service protocol for communication between assessment systems and question engines
• a syntax specification and web service protocol for communication with the service taking care of the presentation of mathematics on the web
• a specification for mathematical questions
This structure of working on 8 independent software projects, tied together by web services protocols and interoperability specifications makes management of this project easier as would otherwise be the case for a project with a geographically distributed team.
The strong reliance on web service protocols and interoperability specifications however serves another purpose: it will make it possible for other mathematical software, not included in this project, to achieve interoperability with our tools by implementing the same protocols and specifications.
Scope and boundaries
The project is focused on the development and implementation of standards, services and implementations for authoring and deploying question test items in mathematics. Within this, our central concern is mathematical expressions: their generation, rendering and comparison as mathematical objects. The project is not concerned with wider e-learning issues in mathematics, such as microworlds, intelligent tutoring, course management or assessment of sustained mathematical argument.
Neither is the project committed to dealing with the issue of graphics in question tests. This issue has, however, been addressed by several of the individual team members in their non-generic projects, and the work may reveal opportunities to build on these achievements. Any such opportunities will be taken advantage of if time, and other project commitments, allows it.
Important issues and critical success factors
Interoperability lies at the heart of the project's aims, and indeed a large mid-project milestone has been scheduled that consists in demonstrating interoperability among all components developed thus far. Achieving interoperability is central to the project's success, as is compliance with existing and emerging standards (for example, those for QTI in general).
Of at least equal importance is ease of use. Since the project's overall aim is to enable colleagues to create mathematical question test items without becoming expert programmers, the ensemble of services, standards, implementations and authoring tools that the project produces must be usable in a natural and intuitive way, and without extensive training. Also, at the learner's end, the project's implementations must generate questions that are themselves easy to use. In particular, questions must test, as far as possible, the learner's knowledge of mathematics only, and not of specialised, non-intuitive notations and conventions.
Pedagogical soundness cannot be directly guaranteed, because it is always possible to use good tools badly. Nonetheless, the project's deliverables must lend themselves to pedagogically sound use. Specifically, they must enable the creation of cognitively rich question items that assess as many aspects as possible of mathematical thinking, at as many levels as possible in a Bloom-type taxonomy of objectives. Cognitive richness must come without a major cost in interoperability or ease of use, and must not require the author to acquire arcane expertise. It must manifest itself in tasks for the learner whose richness of challenge lies solely in their mathematical content, and not in any fresh computational or user interface problems.
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