On-Line Testing Center

1. On-Line Testing Center Database Laboratories Root Questions Automating Homeworks

2. The Story • Centered around the database course sequence, we have developed tools for increasing the efficiency of teaching. • Laboratories that give immediate, accurate feedback for teaching SQL, etc. • Automated homeworks that simulate the effect of carefully graded “long-answer” homework.

3. Productivity in Education • The education industry has a terrible productivity-improvement record. • Not only are database systems essential for delivering improvements, but the DBMS courses serve as a wonderful example of how new technology can impact education.

4. Comparison: Versus Telecom • Tuition 3-min LD call Ratio • 1959 $ 1,200 $3.00 400 • 2004 $30,000 $0.15 200,000 In 45 years, high-end college tuition has gotten 5000 times more expensive relative to a long-distance phone call!

5. But Isn’t … ? • The telecom industry is arguably the best example of the use of technology to reduce costs. • How about the much-maligned US Post Office?

6. Comparison: Versus Post Office • Tuition Airmail Stamp Ratio • 1959 $ 1,200 $0.08 15,000 • 2004 $30,000 $0.37 81,000 In 45 years, high-end college tuition has gotten 5.4 times more expensive relative to a stamp!

7. Our Assumptions • Pure on-line education is failing. • 4-year, residential education has great value. • We can make instructors and TA’s more efficient through automation. • We can give course staff the time to do what they do best: individual, informal instruction.

8. The Database Course as an Example • How a DB course could be automated: • Lectures --- extended textbook. • On-line, instant-help desk. • Programming laboratory. • Homework and exams. • Similar requirements for any programming course; 1, 2, 4 for any course.

9. Lectures • We have PowerPoint slides with voiceover for an introductory DB course. • Intended use: play for 50-60% of the lecture; use the rest of the time for discussion. • Pace is critical --- stop for class thought after each slide.

10. Beer groups with at least 3 non-NULL bars and also beer groups where the manufacturer is Pete’s. Beers manu- factured by Pete’s. Solution SELECT beer, AVG(price) FROM Sells GROUP BY beer HAVING COUNT(bar) >= 3 OR beer IN (SELECT name FROM Beers WHERE manf = ’Pete’’s’);

11. Help Desk • “To be done.” • Scale is important. With 1500 students/year, we can afford a 24/7 TA answering queries by email. • Vital for any course involving programming --- so students don’t get stuck on “Oracle says ‘semicolon missing’; what does that mean?”

12. Help Desk --- (2) • Technology boost: customer-support software. • Need to accumulate knowledge about tricky points and errors in assignments and material. • Need fast keyword search: • Find on-line guides to assist TA in responding to a specific question.

13. Laboratory Assignments • Conventional SQL homework: “Here is a database; write these queries in SQL.” • TA’s look at SQL answers and try to figure out whether the queries do what they’re supposed to do. • Rate of regrades tells me this task is too hard to get right.

14. OTC Laboratory • OTC (On-line Testing Center) solves this problem by: • Giving students a description of a database schema. • Asking them to enter certain SQL queries. • Telling them whether their query is syntactically-wrong, syntactically-correct- but-gives-the-wrong-result, or correct.

15. Behind the Scenes • OTC uses an Oracle DBMS, in which the schema for each assignment is held, along with carefully selected tuples to populate the relations. • Relations must expose common errors.

16. Behind the Scenes --- (2) • Queries are passed to Oracle via JDBC, and checked for syntax errors. • We create an instance of the generic query interface (sqlplus) only if the student requests help locating syntax errors.

17. Behind the Scenes --- (3) • Syntactically correct queries are executed on the sample database. • Answers are checked for the presence of certain strings and the absence of others. • Almost certainly catches wrong answers; always accepts right answers.

18. Creating a Lab • Interface allows designer to specify: • The stem (informal description of the schema and the queries to be written). • Reference queries used to generate the correct tuples for each query. • INSERT statements to initialize the database.

19. Other Labs • Recently added: similar lab-creation faciltities for: • Relational algebra. • JDBC. • XQUERY.

20. Policy Issues • The lab is set up so students may submit a query as many times as they like. • Once correct, a query can be stored and the next one worked on.

21. Feedback on Labs • An unsolved problem is how to give students advice when their query is syntactically correct but semantically incorrect. • Showing them the test database is a bad idea, because they can then tailor their query to the data.

22. Probable Architecture • Create “shadow database” isomorphic to the test database, but with other values. • Use “lineage tracing” to determine where an incorrect tuple or missing correct tuple comes from. • Express the problem in terms of the shadow DB.

23. Why It’s Not That Simple • Queries involve particular constants. • Changing the constants in your explanation doesn’t explain anything. • Example: “find all the bars in Boston.” • The shadow DB better not change ’Boston’ in tuples or you’ll be explaining: “if the DB contains (’Joe’’s Bar’, ’Miami’) you need to produce ’Joe’’s Bar’ in your answer.”

24. A Harder Example • Consider query: “find all the beers Joe’s Bar sells for less than $5.” • You can’t change prices in tuples like (’Joe’’s Bar’, ’Bud’, 4.00) randomly, or you’ll give advice like “if the DB contains (‘Joe’’s Bar’, ‘’Coors’, 6.50), you need to produce ’Coors’.”

25. Example --- Continued • You need a “less than $5 – preserving” transformation. • Example: p -> 2*p – 5.

26. Automating Homework • The heart of OTC is a system for automating homeworks and exams. • Goal 1: Encourage students to work “long-answer” problems for themselves. • Goal 2: Inhibit cheating. • Goal 3:Eliminate the drudgery of grading, while still giving students feedback.

27. Modeling “Long-Answer” Questions with Multiple-Choice • Here is a typical “long-answer” question we might ask in a DB course: Relation R consists of the following tuples, and relation S has the following tuples. Compute the join of R and S.

28. Root Questions • A root question is a multiple-choice question with several right and many wrong answers. • Example: Relation R consists of the following tuples, and relation S has the following tuples. Which of these tuples is in the join of R and S ?

29. Writing a Root Question • The question-designer provides several correct answers. • In our example, each tuple of the join could be one correct answer. • Many wrong answers are also provided. • Here, any tuple of the correct length that is not in the join could be used.

33. Assigning Root Questions • The instructor develops an assignment consisting of several root questions. • 4-6 seems to be the right number --- we’ll see why. • Students take the assignment as many times as they like and are encouraged to get a perfect score. • Only the final score counts.

34. Assigning Root Questions --- (2) • Each time the student opens the assignment, they are given the same questions, but with a different choice of one correct and three incorrect answers, in random order. • To prevent rapidfire guessing, the student may open an assignment only once per 15 minutes.

35. Student Responses • Ideally, students open the assignment and see if they can work their particular instances of the root questions. • If they can work a question instance, they probably understand it. • If not, they need to study the subject.

36. Student Responses --- (2) • Each root question suggests a conventional, “long-answer” question, that the student should work. • Example: for the join question, they may as well compute the entire join. • With the join tuples listed on scratch paper, they can quickly solve any instance of the root question.

41. How Many Questions? • We recommend 4-6 questions per assignment. • Fewer than 4 encourages students to guess; too many questions runs the risk a student will miss one for carelessness. • When first given at Stanford with no 15-minute rule, some students tried hundreds of times.

42. Comparison • There is a simpler scheme used in courses like physics, where questions are parametrized, and the correct answer computed by a formula. A weight of $w kilograms is dropped from height $h. How long does it take the weight to reach the ground?

43. Comparison --- (2) • Question is generated by choosing random values of the parameters, and the answer checked against the result of the formula. • Root questions simulate this question type by selecting many parameter values and asking for a correct pairing of parameters and result.

44. Comparison --- (3) • Example: A weight of w kilograms is dropped from height h. For which of the following triples (w, h, t ) is t the time it takes the weight to reach the ground?

45. Comparison --- (4) • In the database domain, many kinds of questions cannot have their answer computed by arithmetic formula: • “Which of these functional dependencies follows from the given FD’s?” • “Which of these schedules is serializable?” • “For which relation sizes is query plan A better than plan B?”

46. Comparison --- (5) • If you are willing to write a program to (say) test serializability, you can write a program that generates a root question with lots of serializable and lots of unserializable schedules. • The output of this program can be input automatically to OTC.

47. OTC Status • About 300 root questions, mostly on databases, developed. • Let’s face it: writing a root question correctly is hard. • But once done and debugged, it can be used in many courses.

48. OTC History --- Spring, Fall, 2002 • One assignment in Stanford CS347 (Transaction-Processing and Distributed Databases) supported, Spring 2002. • CS145 (Intro. DB course at Stanford) supported in Fall, 2002. • 2 Lab assignments, 11 root-question assignments, midterm (not root questions).

49. OTC --- Winter, 2003 • Supported CS245 (DB Implementation, Hector Garcia) at Stanford. • Supported a CS145/245-like course at North Carolina State (Rada Chirkova).

50. OTC Status --- Spring 2003 • Supported CS145, CS347, and CS345 (DB Theory) at Stanford. • Continued support at NC State. • Supported CS145-like courses at UC Santa Cruz (Arthur Keller) and Univ. of Leipzig (Erhard Rahm). • Supported a Discrete Math course at NTU Athens (Foto Afrati).