System ArchitectureThe LeActiveMath system architecture is composed of eight different components:
1) Front End - We envision that a mathematics student (or learner) will want to interact with an eLearning system both at school under guidance and at home in a less formal environment. Thus the interface a learner uses must provide for both, allowing them to work on school problems at home, share problem solving strategies with classmates, and always have the resources available that they need to support learning goals. The LeActiveMath front end allows a single workspace environment to support diverse types of interactions while all relevant knowledge is at the learner's fingertips, ready for exploration. The front end is directly connected to the Presentation System and Dictionary, which allow for the display of complex math formula.
2) Content Manager - This component allows for seamless interactions with a wide variety of objects a learner might need to work with. An element might be a definition, a proof, a mathematical formula, or an organized collection of these that form a lesson plan (a book). The content manager handles requests for these objects regardless of whether they are stored locally or remotely, or whether they are static or dynamically tailored to the current learner's environment or learning ability. The content manager also includes a mediator, which allows it to look for resources which are either currently unknown to the system, or which need to be requested by description rather than by name.
3) Tutorial Component - When a learner is trying to solve problems, whether in the classroom or at home, it is important that problems with the right amount of difficulty are posed by the system. The tutorial component consults two resources when selecting which problem to pose next: the content manager, which knows what problems are available and what the characteristics of each are, and the learner model, which knows the abilities of the learner and whether a particular problem would be too easy, too difficult, or just right.
4) Natural Language Dialogue Manager - When a learner is having trouble solving a particular problem, it is often useful to have a one-on-one tutor available who can point out errors in the learner's approach or reasoning, offer helpful suggestions, and help the learner try to reason the problem out for themselves. Natural language allows the learner to type in questions in regular language as well as mathematical formulas, and have the computer generate language-based responses and explanations based on reasoning automatically about the correctness or incorrectness of the learner's statements.
5) Learner Model - The learner model contains information about the learner's past progress during problems as well as an estimate of their current abilities at tackling a wide array of types of math problems. The learner model is initially created from either a sample test or a self-assessment, and subsequent attempts at solving problems are then used to modify relevant areas of the learner model by analyzing their performance. Additionally, the learner model in LeActiveMath will allow a learner or instructor to inspect and modify the model itself. A large amount of the system�s adaptability is derived from the learner model, as each model will reflect the diverse traits and abilities of each learner.
6) Assembling Tool - This tool allows the learner to 'bookmark' those items that were most helpful or interesting during the lesson interaction, allowing them to create a personalized 'book' containing the most interesting things they have learned. The learner can then reuse this individualized information in the future.
7) Concept Map Tool - This component allows the learner to visualize relationships between concepts that are not immediately obvious through the lessons themselves.
8) Siette Assessment Tool - Siette is a web-based tool for dynamically creating tests to assess the learner's performance. It adaptively poses problems to the learner, allowing for a more accurate assessment of their capability for problem solving.
Together, these components constitute a large, well-adapted architecture for adaptively teaching learners in multiple environments at their own pace.
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