Math-Bridge Exercise System

1. Math-Bridge
Education Solution

2. EXERCISE SYSTEM OF
MATH-BRIDGE
Dr. Giorgi Goguadze

3. 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

4. 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

5. Exercises types: multiple choice
• Single or multiple answer exercises possible
• Flag Feedback via coloring the chosen answers red or green, plus
correct/wrong symbols

6. Exercises types: multiple choice
• Flag Feedback in multiple answer choices can be mixed, since
some answers can be correct, some others wrong

7. Exercises types: multiple choice
• Exercise behavior in case of correct and wrong answer may differ
• Correct answer – exercise finished
• Wrong answer – try again

8. 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

9. Exercises with intelligent Feedback using CAS
• „Flag Feedback” (Correct/Wrong)
• Matching exact answers, as well as semantically equivalent

10. 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

11. Intelligent exercises using Domain Reasoners
• „Flag Feedback” (Correct/Wrong)
• Matching various correct (expert) solution paths
• Error Feedback for typical errors via matching buggy-rules

12. Intelligent Exercises using Domain Reasoners
• Generated Next-Step hints on student’s solution path
• hints with increasing level of detail
• Generated Worked out solutions

13. 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

14. Structure of Interactive Exercises
• Exercise is a Graph of Tasks, Interactions and Transitions

15. Sample Exercise Graph
task
feedback2
Step wrong!
feedback3
All Correct!
Interaction intermediate answer
final answer
anything else
feedback1
Step Correct!
• Present Task
• Enter Answer
• Answer until Correct
• Intermediate Correct
answers accepted
• If final correct
answer entered the
exercise terminates

16. Different exercise graphs for the same problem
Calculate
(2x)'
You failed! Well done!
Calculate
2(x)'
Calculate
(2x)'
Calculate
(2x)'
Well done!Incorrect!
Incorrect!
2(x)'
2
2
2(x)'
2
2
default
default
default
default
Correct! Correct!

17. Exercise System Architecture
Tutorial
Component
Student
Model
Knowledge
Base
Exercise
Manager
User
Interface
Presentation
Engine
Presentation
Strategies
Tutorial
Strategies
Diagnoser
Exercise
GeneratorLocal Student
Model
Feedback
Generator
Query
Broker
Domain
Reasoner
Domain
Reasoner
CAS
strategy IDs
exercise
user input
event
user data
step result
strategy
user input query
resultdiagnosis
local data
feedback
exercise state
strategy
step
diagnosis
step presentation
Exercise
Subsystem

18. Thank you.
The Mathematical Bridge, Cambridge, England

19. 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