Transcript root question

On-Line Testing Center
Database Laboratories
Root Questions
Automating Homeworks
1
Tools for Increasing the
Efficiency of Teaching
1. Laboratories that give immediate,
accurate feedback for teaching SQL, e.g.
2. Automated homeworks that simulate the
effect of carefully graded “long-answer”
homework.
3. Lectures consisting of PowerPoint slides
with voiceover.
2
Productivity in Education
The education industry has a terrible
productivity-improvement record.
Using database courses as a focus, we
have developed a system, OTC (On-Line
Testing Center) that automates grading
and allows teaching effort to be reused.
3
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!
4
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?
5
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!
6
One Thing I’d Like to Do, but
Haven’t
Global, on-line TA system.
Students can ask questions about a
given course, via email.
They get fast email response.
A TA network is guided by a database
of previous questions and answers.
7
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.
8
Solution
Beer groups with at least
3 non-NULL bars and also
beer groups where the
manufacturer is Pete’s.
SELECT beer, AVG(price)
FROM Sells
GROUP BY beer
HAVING COUNT(bar) >= 3 OR
beer IN (SELECT name
FROM Beers
WHERE manf = ’Pete’’s’);
Beers manufactured by
Pete’s.
9
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.
10
OTC Laboratory
 Students get a description of a
schema and an English description of
several queries to write.
 Queries are sent to a database system
(Oracle or mySQL) for testing on a
preset, sample database.
11
OTC Laboratory --- (2)
 Three possible outcomes:
1. Syntactically incorrect --- they get the
feedback of the DBMS.
2. Semantically incorrect --- they get to see
what their query did on another sample
database and what it should have done.
3. Semantically correct --- they get credit for
the problem.
12
Creating an SQL Lab
1. Stem to describe the schema and queries.
2. CREATE TABLE statements to define the
schema.
3. INSERT statements for the test DB.
4. INSERT statements for the sample DB.
5. Reference queries for the correct
answers.
13
Other Labs
 Recently added: similar lab-creation
faciltities for:
1. Relational algebra.
2. JDBC.
3. XQUERY.
14
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.
15
Problem: Automate Construction
of Sample DB’s.
Queries involve particular constants.
Changing the constants in your
explanation doesn’t explain anything.
Example: “find all the bars in Boston.”
 The sample 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.”
16
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’.”
17
Example --- Continued
You need a “less than $5 – preserving”
transformation.
Example: p -> 2*p – 5.
18
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.
19
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.
20
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 ?
21
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.
22
Writing Root Questions --- (2)
For each wrong answer, write a choice
explanation that gives student a hint or
explanation of why it is wrong.
For the question as a whole, write a
question explanation.
23
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.
24
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 x minutes (instructor choice).
25
Student Responses
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.
26
Automatic Student Help
When a student submits work, they
immediately get the choice explanations
for those questions they get wrong.
After the due date, students can see
their assignments, with not only the
choice explanations but the question
explanations as well.
27
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 limit,
some students tried hundreds of times.
28
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?
29
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.
30
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?
31
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?”
32
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.
33
OTC Status
About 400 root questions, mostly on
databases, developed.
 Many have explanations included.
 Let’s face it: writing a root question
correctly is hard.
 But once done and debugged, it can be
used in many courses.
34
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).
35
OTC --- Winter, 2003
Supported CS245 (DB Implementation,
Hector Garcia) at Stanford.
Supported a CS145/245-like course at
North Carolina State (Rada Chirkova).
36
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).
37
OTC Status --- Fall 2003
New Sites: Penn State, U. Chicago,
Yale, U. Alabama, U. Karlsruhe, York
College/CUNY, U. Business & Econ.
(Athens).
38
OTC Development Team
The core software was developed by
Murty Valiveti and his team at Gautami
Software.
Alan Beck and Ramana Yerneni adapted
the OTC core for database instruction
and implemented a number of
important features.
39
Content Creators
Alan Beck: SQL, JDBC, and XQuery labs.
Austin Shoemaker: relational algebra lab.
Root-question developers: Foto Afrati,
Rada Chirkova, Mayur Datar, Prasanna
Ganesan, Wang Lam, Anand Rajaraman,
Jeff Ullman, Jennifer Widom, Ramana
Yerneni.
40
Find Out More
A tutorial for instructors is at
www-db.stanford.edu/~ullman/pub/otc.pdf
Demo site:
chub.stanford.edu:8181/CS145-demo/index.html
41