Math-Bridge Exercise System
Transcript of Math-Bridge Exercise System
Exercises types in Math-Bridge
• Self assessment exercises• Multiple choice questions
• Single answer• Multiple answer
• Manually authored Fill-in-blank exercises• Multi-step• CAS evaluation• Exercise behavior graph defined manually• Feedback and hints defined manually
• Automatically generated Fill-in-blank exercises• Multi-step• Diagnosis powered by Domain Reasoners• Feedback and hints generated automatically• Supporting the learner on her own solution path
Exercises types: Self Assessment
• Solve a Self-assessment exercises on the paper• Compare your solution with the given model solution• Estimate the correctness on own solution
Exercises types: multiple choice
• Single or multiple answer exercises possible• Flag Feedback via coloring the chosen answers red or green, plus
correct/wrong symbols
Exercises types: multiple choice
• Flag Feedback in multiple answer choices can be mixed, since some answers can be correct, some others wrong
Exercises types: multiple choice• Exercise behavior in case of correct and wrong answer may differ
• Correct answer – exercise finished• Wrong answer – try again
Exercises types: fill in blank
• Use formula editor for entering answers• Flag Feedback is presented in a form of coloring and special correct/wrong symbols
Exercises with intelligent Feedback using CAS
• „Flag Feedback” (Correct/Wrong)• Matching exact answers, as well as semantically equivalent
Exercises with intelligent Feedback using CAS
• List of conditions on possible user answers are evaluated in a descending order
• First, the user answer is compared syntactically (literally) to the final correct solution
• If this condition is not satisfied, we compare it semantically
• Otherwise it is considered wrong
• Other conditions are possible matching against some typical wrong answers
Intelligent exercises using Domain Reasoners
• „Flag Feedback” (Correct/Wrong)• Matching various correct (expert) solution paths• Error Feedback for typical errors via matching buggy-rules
Intelligent Exercises using Domain Reasoners
• Generated Next-Step hints on student’s solution path• hints with increasing level of detail• Generated Worked out solutions
Further interactive Elements
• Arbitrary external multimedia can be integrated into the system• A web2.0-based Framework allows for communication of
integrated external content with the user model
Sample Exercise Graph
• Present Task• Enter Answer• Answer until Correct• Intermediate Correct
answers accepted• If final correct
answer entered the exercise terminates
Exercise System Hands-On
• Open a Course Book• Open a self assessment exercise
• Follow the instructions• Reflect on usefulness of such an exercise
• Open a multiple choice exercise• Solve the exercise correctly• Solve the exercise incorrectly to see different kinds of feedback
• Open a simple fill-in-blank exercise • Solve the exercise correctly• Several steps are allowed• Try incorrect steps to see different feedback• Try semantically equivalent steps
• Open a Domain Reasoner powered exercise• Solve the exercise using several steps• Use hints on several possible solution paths