Perceptions of Teaching and Learning Automata Theory in a College-Level Computer Science Course

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Perceptions of Teaching and Learning Automata
Theory in a College-Level Computer Science Course

• Phoebe Weidmann
• Oral defense of dissertation research
• Supervised by Dr. Bethel and Dr. Almstrum

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What is Automata Theory?

• Theory supporting Computer Science
• Study of computability
• Created by Noam Chomsky 1956
• Hierarchy of computational power (languages)

Regular
Context-free
Recursive
Recursively-enumerable
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What makes Automata Theory hard?
Alt(L) x ?y,n y?L, yn, ngt0,
ya1an, ?i ? n, ai??,
and xa1a3a5ak,
where k(if even (n) then n-1 else n)

Phoebe_Kay_Weidmann
Phoebe_Kay_Weidmann
Pob_a_edan
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Motivation

• Proven problematic in CS curriculum
• Required course in many CS degree programs
• Theory used throughout academia/industry
• Personal interest in theory
• Stable and common curriculum

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Purpose of research

• Identify good teaching practices
• Identify good learning practices
• Suggest improvements to teaching and learning

Suggestions for improving Teaching and
Learning Automata Theory
Case study of CS 341
Perceptions on teaching
Perceptions on learning
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Background literature

• Teaching Automata Theory (Rodger 1995, Berztiss
  1976)
• Computer Science curricula (CC2001, Shackelford
  1996)
• Lecture-style teaching (Felder 2000, Pollio 1996)
• Effective material use (Tuckman 1996, Ritter
  Lemke 2000)
• Student perceptions (Seymour Hewitt 2000,
  Margolis Fisher 2001)
• Instructor perceptions (Anyon 1981, Sadker
  Sadker 1995)
• Motivation (Boekaerts 2000, Potosky 2002)
• Theoretical models in Science and Education
• Intellectual maturity and Learning styles
• (Lawson 2000, Piaget, Vygotsky, Gagne,
  Meyers-Briggs, Felder-Silverman)

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Theoretical basis

• Pedagogical positivism
• Constructivist learning
• Positivist attitude toward instruction

Analysis of learning perceptions and performance (
3-part approach)
Instructor
Best practice instruction
Student population
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Emergent model
-Interactions -Grades
-Usage -Perceived helpfulness
-Rational behind use -Choice of usage
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Methodology

• Population
• 118 students, mostly seniors in CS degree
• 2 sections of CS 341, single instructor
• Techniques
• Interviews, surveys, observations,
  material analysis
• Data
• Transcriptions (3), surveys (3),
• field notes (2/week), artifacts collected

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Findings

• Effective practicesInstructor activities
• Overview lectures to begin course
• Use of programming projects
• Working examples in lecture
• Effective practicesStudent learning structures
• Discussion sessions focused on problem solving
• Examination reviews

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Findings

• Effective practicesMaterials
• Background material provided (with assessment)
• Lecture notes provided to students
• Providing voluntary practice problems
• Use of course webpage

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Findings

• Creating a more effective learning environment
• Better materials design
• Motivating good habits early
• Creating a better lecture environment
• Soliciting student feedback

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Problems with materials

• I don't know when to do informal homework. It
  would be nice to have a suggested schedule for
  the informal stuff. (survey 1 student 30)
• In class, I understand about 75 of lecture.
• But when I leave, only 15 stays with me, and Im
  
• completely lost. It seems easier when the teacher
  is
• there, but when Im on my own, its a lot
  harder.
• (survey 1 student 57)

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Perceptions of lecture notes

• What do you like about having the lecture notes?
• i can still take notes on the examples and other
  things, but I
• don't have to write down everything, and I
  don't have to worry about accidentally missing a
  few details, as well as the fact that its easier
  to make up for missing a day of class
• (survey 1 student 20)
• What do you dislike about having the lecture
  notes?
• They are incomplete. If you miss a lecture you
  may think that you have the material anyways, but
  it isn't true, the slides can be missing vital
  parts. (survey 1 student 37)

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Attendance lecture end (S1)
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Better materials design

• Student objectives should be clearly marked
• Solutions should wean students
• Complete solutions
• Scaffolded solutions
• Hint solutions
• Formatting should designate
• Complete information
• Information to be completed in lecture

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Example of scaffolded solution
Show that L anbn is not a regular language by
completing the partially worked out proof below.
We use the Pumping Lemma to show that Lanbn is
not regular. Let N be the constant from the
pumping lemma such that N ? xy and
waN/2bN/2. Case 1 y consists of only as.
Then when we pump y, the number of as will not
match the number of bs violating the condition
that the number of as and bs are equal.
Contradiction. Case 2 y consists of only bs.
(finish argument) Case 3 y is on the boundary of
as and bs. (finish argument)
Proof
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Example of hint solution
Show that L anbn is not a regular language by
completing the partially worked out proof below.
Hint
If you choose waN/2bN/2 your proof should have
three cases.
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Perception of examinations

• What would you have changed about the first exam?
• Nothing, I thought it was fair. (survey 2
  student 8)
• What would you have changed about the second
  exam?
• Instead of having out of the blue problems,
  could've had stuff that would make us feel like
  we did learn something from class. (survey 3
  student 4)

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Practice good performance

• Policy about examination questions
• So what I try to do now, is have the homeworks
  harder than the exam. (first interview with Dr.
  Quilt)
• Practice is critical
• That's the biggest thing I've played around
  with, is how to get them to understand from the
  beginning that if they don't do the problems on a
  regular basis they are not going to learn this
  stuff. There's no magicThe last year or so, I've
  done homeworks that I collect and grade, that
  don't count for a whole lot, because I can't be
  sure that people did the work on their own.
• (first interview with Dr. Quilt)

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98 completion of required homework
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Motivating good habits early

• First examination should be hard
• More practice problems for harder material
• Incentive to do voluntary work
• One question to appear on examination
• Extra credit
• Split passing standard
• Lectures will contain one examination problem

Pass homeworks
Pass examinations
Pass course


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Instructors view on use of examples

• I don't know how to teach abstract problem
  solving except you have to do a few and then ask
  people to practice. And it's very much like
  teaching art. You do a few and you ask people to
  practice and some people have talent and end up
  producing wonderful paintings and some people
  don't.
• (first interview with Dr. Quilt)
• How would you change the course?
• And this stuff is the most abstract, and so, I
  don't know, I'm thinking that I should try to get
  at least one more lecture, if I could push it one
  more lecture back, then maybe that would help
  because I could spend more time in class just
  doing more problems. (second interview with Dr.
  Quilt)
• How would you change the course?
• Make discussion sections required. Where we
  use lecture to present new material and we use
  the problem session, maybe we even require
  attendance or something, to just work problems.
  Because, the people seem to get a lot out of
  that.
• (third interview with Dr. Quilt)

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Students view on use of examples

• How would you change the course?
• Spend more time in class on harder examples that
  are similar to the ones on the exams. Most
  examples are simple so that we can understand
  but when exam time rolls around the problems will
  be much harder with less time to do.
• (survey 1 student 90)
• What do you like about CS 341?
• I can actually use this material in other
  classes, and the examples explain a lot (survey
  2 student 26)
• Why do you attend lecture at this point in the
  course?
• Teacher better explains the concepts with plenty
  of examples. (survey 3 student 15)

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Better lecture environment

• Create interactivity
• Work more problems during lecture
• Offset definitions to homeworks
• Use pro-active quizzes
• Teach problem solving realistically
• Instructor should think out loud
• Solution strategy, not just solution

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Pro-active quizzes

• What they are
• Problems that students must attempt to solve
• Problems will be worked during lecture
• Turned in at beginning of class for credit
• Benefits
• Encourages attendance
• Prepare for lecture strategy
• Encourages reflection

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Benefit of using surveys

• Students appreciate being heard
• Thank you for taking the time to evaluate our
  opinions on this course. (survey 3 student 38)
• Surveys provide basis for formative assessment
• Student performance typing (analysis)

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Student performance typing
Raw score

• 80
• Ultra
• performers

79-70 High performers
69-60 Average performers
? 59 Low performers
10 students
21 students
25 students
21 students
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Surveys and Typing
Ultra High Avg Low
Average age (years) 20.7 21.2 22.5 22.5
Repeating CS 341 0 5 17 35
Average PHL 313K grades 3.78 3.40 3.04 2.80
Average CS 336 grades 3.78 3.00 2.79 2.60
Average CS hours taken 8.5 7.7 8.1 8.4
Average total hours taken 13.1 13.5 13.0 12.5
Students working 60 45 46 55
Average hours/week worked 15-19 14-19 15-20 23-29
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Surveys and Typing
Ultra High Avg Low
Average age (years) 20.7 21.2 22.5 22.5
Repeating CS 341 0 5 17 35
Average PHL 313K grades 3.78 3.40 3.04 2.80
Average CS 336 grades 3.78 3.00 2.79 2.60
Average CS hours taken 8.5 7.7 8.1 8.4
Average total hours taken 13.1 13.5 13.0 12.5
Students working 60 45 46 55
Average hours/week worked 15-19 14-19 15-20 23-29
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Surveys and Typing
Ultra High Avg Low
(1) Equivalence Relation 100 95 83 80
(1) Converse 78 90 83 80
(1) Cardinality 100 90 88 95
(1) Set hierarchy 89 75 88 85
(2) NFSM 100 95 96 95
(2) Grammar production 78 60 58 65
(2) PDA 100 85 63 70
(3) Language classification 90 76 70 48
(3) Turing machine 40 33 26 29
(3) Reduction 20 19 26 22
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Surveys and Typing
Ultra High Avg Low
(1) Equivalence Relation 92 88 86 85
(1) Converse 92 88 86 85
(1) Cardinality 92 88 86 85
(1) Set hierarchy 92 88 86 85
(2) NFSM 93 80 72 77
(2) Grammar production 93 80 72 77
(2) PDA 93 80 72 77
(3) Language classification 50 43 41 33
(3) Turing machine 50 43 41 33
(3) Reduction 50 43 41 33
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Soliciting student feedback

• Use of surveys
• Psychologically motivating to students
• Formative assessment for teaching
• Lecture pacing
• Effective student learning
• Examination question preparation
• Recognition of problem population (background)

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Contributions

• Pedagogical positivism
• Research methodology for college level courses
• Listing of effective practices for Automata
  Theory
• Suggestions for better learning environment
• Create a more dynamic lecture
• Motivate good learning habits early
• Take a more algorithmic approach to abstraction

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Suggestions for future research

• Quantitative investigation of suggestions
• Study class again after admissions filter
• Study elective offering of Automata Theory
• Test intellectual maturity of in-coming students
• Use pedagogical positivism to study other courses

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Thank you
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SIGCSE survey results

• 48 respondents
• 92 reported offering AT
• 56 required course
• 71 stated course was upper division
• 27 average class size

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SIGCSE survey results (AT req)

• (48) 27 respondents
• (92) 100 reported offering AT
• (56) 100 required course
• (71) 81 stated course was upper division
• (27) 29 average class size

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SIGCSE survey results (cont)

• Trends
• 31 stated nearly all students pass
• 14 stated students have trouble passing
• 32 stated students find AT difficult
• 38 stated students question utility of AT
• 2 stated students would not take

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SIGCSE survey results (AT req)

• Trends
• (31) 37 stated nearly all students pass
• (14) 25 stated students have trouble passing
• (32) 48 stated students find AT difficult
• (38) 48 stated students question utility of AT
• (2) 4 stated students would not take

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Research Questions

1. How do instructor perceptions shape teaching and
   learning in Automata Theory?
2. How do student perceptions shape teaching and
   learning in Automata Theory?
3. How do materials used in Automata Theory help or
   hinder teaching and learning?

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Models influence on research design and data
analysis

• Interview questions
• Focus on bullets
• Analysis
• Report when bulleted items appear in transcripts
• Influence of bulleted items on course design
• Influence of bulleted items on student
  expectations and assessment

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Models influence on research design and data
analysis

• Survey items
• Focus on bullets
• Analysis
• Report when bulleted items appear in surveys
• Influence of bulleted items on perceptions
• Influence of bulleted items on performance in
  course

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Models influence on research design and data
analysis

• Analysis
• Report on bulleted items
• Clarity suggestions
• Student opinions
• Student usage
• Instructor rationale for inclusion
• Researcher opinion

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Models influence on research design and data
analysis

• Observations
• Interactions
• Student surveys
• Usage
• Perceived helpfulness
• Instructor interview
• Rationale behind use
• Choice of usage
• Artifacts
• Grades
• Analysis
• Combined with other data

Students
-Interactions -Grades
Instructor
-Usage -Perceived helpfulness
-Rational behind use -Choice of usage
Materials
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Pedagogical positivism vs. Constructivism

• Constructivism
• Epistemology based on individual learning
• Does not address teaching
• Use definition as is
• Constructionism
• Teaching methodology based on constructivist
  learning
• No definition of best practice
• Implied best practice when most students learn

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Pedagogical positivism vs. Constructivism
Pedagogical positivism
Define learning as performance experience in
course
Learning (Constructivist)
Teaching (Constructionist)

Make explicit definition of best practice
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Automata Theory then and nowLIN 340 vs. CS 341
vs. Dr. Quilt

• LIN 340
• 863 samples
• F 1998 S 2000
• CS 341
• 717 samples
• F 2000 S 2002
• Dr. Quilts class
• 502 samples
• F 2000 S 2002

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Other required courses

• Data from 00-02
• PHL 313K
• 1997 samples
• M 408C
• 1565 samples
• CS 307
• 2752 samples
• CS 336
• 1047 samples
• CS 341
• 717 samples