Tools for Presenting and Evaluating Mathematics Online

1. Tools for Presenting and Evaluating Mathematics Online Ajnu Jacob, Travis Miller and Sean Scott of

2. Overview • Maple T.A. progress report • Adaptive Questions • Maple worksheets & MapleNet

3. What is Maple T.A.? • Amathematically intelligent assessment system • Supports multiple question types • Algorithmic templates for questions • Grade management

4. Algorithmic variables • Variables can be assigned random values • set a range such as x from [-1,1] in 0.01 increments • select an object from a (weighted) list • create a matrix with a certain rank • a set of plots • Impose conditions • x > y or (x+y) > 0 • rank ≠ 0

5. Question Database • Managed (mostly) by MFCF • Several master repositories in different disciplines • Several thousand questions and growing

6. Question Database • Every question is tagged with its location in the database • Question attributes can be assigned, e.g. difficulty, course, keywords, etc.

7. Assignments • Several types available • Allows question “pools” • Controlled access with proctoring • Includes a “proctored” browser option

8. Usage • Assignments Finished : 2010 95,906 2011 174,047 2012 198,224

9. Math Readiness Test • 1500 students using the system in a 6 hour period • Repeated the next night in Engineering • Didn’t even break a sweat.

10. Availability • Paid for by Mathematics, Engineering & Science faculties. Free for all courses in those faculties • Other faculties pay a per-student charge • Course setup, training documentation and “getting started” support provided by MFCF

11. Adaptive Questions

12. Features • Deepens student comprehension • Guidance for those who give incorrect response to a question. • Walk the student through the problem one step at a time. • Increases understanding of concepts. • Let the student try a simpler version of the question before retrying the original problem.

13. Features • Instructors can control the behavior of the question • Number of attempts at each stage. • Credit the student gets for incomplete answers and penalty for repeated attempts. • If the correct answer should appear after the problem has been attempted max times. • When to move on to the next question in the assignment.

14. Implementation • Drill down (easy to hard) • Drill up (hard to easy) • Multiple attempts • Additional hints • Decreasing grades • Partial grading

15. Self Evaluation

16. Self Evaluation

17. Self Evaluation

18. Self Evaluation

19. Self Evaluation

20. Self Evaluation

21. Self Evaluation

22. Maple Worksheets &MapleNet

23. Key Features • Users Do Not Need to Understand Maple • Work shifted from users onto developers. • Easy to use. • Easy to redistribute.

24. Key Features 2) User Input with Automatic Calculations Video:Partial Differentials and Tangents Part 1

26. Key Features 3) 3D Plots, and Animations Video: • Partial Differentials and Tangents Part 2 • Parameterization • Hooke’s Spring Law

29. Key Features 4) Interactive Practice with Randomization Video: System of Equations

31. Key Features 5) MapleNet Online Viewing Video: Quadric Surfaces

33. Recap Advantages • Interactive and Fun • Users do not need to understand, own, or install Maple • One worksheet = hundreds of examples • Dynamic solution feedback • Possible replacement for textbooks?

34. Recap Advantages • MapleNet online viewing and integration with D2L. • Server does the work, not the client. • Easy to modify and redistribute.

35. Statistics • Average about one week to create a worksheet. (12-16 worksheets per co-op per term) • One day to create a video version. • Currently have 15+ worksheets online.

36. Possible Uses • Calculus • Algebra • Statistics • Physics • Economics • Chemistry • Biology

37. Questions?