Math-BridgeEducation Solution

EXERCISE SYSTEM OF MATH-BRIDGE

Dr. Giorgi Goguadze

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

Structure of Interactive Exercises

• Exercise is a Graph of Tasks, Interactions and Transitions

Sample Exercise Graph

• Present Task• Enter Answer• Answer until Correct• Intermediate Correct

answers accepted• If final correct

answer entered the exercise terminates

Different exercise graphs for the same problem

Exercise System Architecture

Thank you.

The Mathematical Bridge, Cambridge, England

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