JiTT in Calculus I

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JiTT in Calculus I

• Matt Richey
• Department of Mathematics

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FTC
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Math 120A, Spring 03

• Off-sequence calculussomewhat math-anxious
  students
• Few (probably no) future math majors.
• Several pre-meds
• Several future art, english, theater majors
• 2/3 female

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Why JiTT in Calculus?

• Students

• Dont prepare ahead of time
• Are reluctant to contribute
• Find the material difficult
• Dont know what the instructor expects

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Why JiTT in Calculus?

• Faculty

• Are over prepared
• Like to hear themselves talk.
• Find the material easy
• Dont know what the students understand

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Homework in Calculus

• Students do it the last minute
• Slow turn around (10 days!)
• Graded by other studentsquality of grading is
  variable
• Problems dont always match instructor
  expectations

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Doing Mathematics

• How mathematicians learn mathematics
• Work examplesmathematics is not a spectator
  sport
• Change things and see what happens
• Try different approaches to same idea
• Revisit ideaslearning is a spiral

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JiTT Goals in Calculus

• Encourage (force) students to prepare
• Make them do math before class!
• Give students a stake in the material so they
  contribute in class
• Make the class time more responsive to student
  needs, less scripted
• Increase the importance of homework
• Provide structure to the instructors sense of
  what is important

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JiTT Software

• Web-based
• Easy to use for students
• Easy to for instructors to prepare assignments
• Easy for IIT to support
• Automated grading and reporting

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JiTT in Calculus Barriers

• Mathematics as a language
• Difficult to typeset
• Hard to understand if not presented well
• Inputs are more complicated than outputs
• Multitude of problems types
• Graphical
• Numerical
• Symbolic
• Grading is difficult to automate

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Typesetting Solutions I

• Calculator representation
• (ab)2 or x33xex
• Easy for students to understand and use
• Not perfect for complicated expressions, e.g.

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Typesetting Solution II

• MathML
• Hyptertext markup language http//www.w3.org/Math
  
• Extremely flexible for presentation
• Not good for input.

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MathML Example
ltmathxmlns'http//www.w3.org/1998/Math/MathML'gt
ltmsupgt ltmfencedgt ltmrowgt
ltmigtalt/migt ltmogtlt/mogt ltmigtblt/migt
lt/mrowgt lt/mfencedgt ltmngt2lt/mngt
lt/msupgt lt/mathgt
Generated automatically. Dont need to type this!
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Software Solutions

• Does work
• MapleTA (MapleSoft)
• WebWork (Open Source)

• Dont work
• Generic web forms
• WebCT
• Cold Fusion

Not Designed for mathematics
Built to support mathematics
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MapleTA Advantages

• Good interface for students and instructors
• Uses the Maple engine and language
• well-know to math folk.
• Supports MathML and calculator representations
• Multiple question types
• Multiple choice
• Math Input
• Numeric
• Supports Maple graphics
• Automatic grading, reporting
• Excel downloads of gradebook

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Maple TA Disadvantages

• Less than great interface
• Awkward handling of class rosters
• Not great on essay questions
• Some bugs in first release
• Cost
• Slow turn-around for enhancements

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Strategy

• Daily MapleTA assignments
• Strict time limits
• Students accountable for attempting assignments
  but not accountable for score
• Use MapleTA to drive the course

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Strategy cont.

• Students engage in material before coming to
  classNose in the book
• Instructor responds to student work
• Class prep time focused on assignment
  preparation, not on lecture preparation
• Constantly remind students why we are using
  MapleTA/JiTT

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Practicalities

• No increase in time devoted to the course!

• Students
• Reduced book assignments.
• Strict time limit on each assignment (30 minutes)
• Faculty
• Development time per class cant exceed 1-2
  hours.
• Development replaces lecture preparationbetter
  be able to wing it in class!

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Assignment Design

• 5-10 questions each assignment
• New problems
• Variations on examples
• Verbatim problems from text
• Variety of types multiple choice, numeric,
  graphic
• Cover key points from section an outline for
  the section
• Not too hard they havent seen this before
• Nothing too fancy process is as important as
  productremember the goal is to engage the
  students

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Classroom Dynamic

• Staggered class time
• 45 minutes on last MapleTA assignment
• Focus on problems causing students difficulty.
• Ask students what they tried!
• Use MapleTA to structure presentationcover
  theory in the context of a problem
• 10 minutes looking ahead to next topic
• Outline key ideas
• Dont write on boardstudents will just copy it
  downuse technology (e.g. document camera).

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Student Response

• Most students attempted almost all the
  assignments
• Most didnt do well on the problemsnot a
  surprise
• They actually liked it
• Performance?
• No control, hard to say.

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Assessment 1One goal of MapleTA was to enable
you to come to class with some prior knowledge
of the topic. Was it successful in this way?
The Good

• Yes, I liked the overall idea of MapleTA.
• It was successful, but without too much prior
  knowledge they were really hard.
• I felt MapleTA was successful because then I had
  a idea of what would be discussed in class.
• Yes, it made you look at the book...and familiar
  with topics discussed in class.
• A lot, particularly if people were assigned to
  do the reading the should.

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Assessment 1One goal of MapleTA was to enable
you to come to class with some prior knowledge
of the topic. Was it successful in this way?
The Bad

• Yes, but many times I did not do well on MapleTA
  trying to learn it from the book but was easier
  after teacher's explanation.
• No, because the book was so difficult to
  understand and MapleTA just added to the
  confusion.
• ..many times I did not do well on MapleTA trying
  to learn it from the book but was easier after
  teacher's explanation.

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Assessment 2Another goal of MapleTA was to
provide you with more structure (what was
important, etc). Was it successful in this way?
The Good

• Yes, otherwise I would not have known what to
  focus on.
• Yes, it made a nice outline of the professor's
  expectations for certain sections.
• Yes, MapleTA was a way to force us to think
  about the problems without the pressure of having
  to get everything correct.
• YES! I thought that going over the MapleTA the
  next day was extremely helpful. Since we had
  worked through the problems the night before, I
  knew exactly where I was having trouble and could
  ask in class.

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Assessment 2Another goal of MapleTA was to
provide you with more structure (what was
important, etc). Was it successful in this way?
The Bad

• NOTHING HERE!

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Assessment 3A third goal of MapleTA was to help
your instructor use class time on problems and
issues that you are having trouble with. Was it
successful in this way?
The Good

• I think it was very helpful in the classroom it
  helped because there were problems set up and
  graded right away.
• I thought so. I thought class time was spent
  very efficiently.
• Yes, MapleTA was a very cool addition to class.
• Yes, it was very very very helpful SMILEY FACE.

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Assessment 3A third goal of MapleTA was to help
your instructor use class time on problems and
issues that you are having trouble with. Was it
successful in this way?
The Bad

• No, because we all had trouble on everything
  because we hadn't been taught it yet.
• Yes, would have liked more time with the
  homework problems....

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Instructor Response

• Liked itkept the instructor engaged
• Better contact with students, especially in the
  beginning
• A bit of a learning curve, but managed to keep
  prep time under control
• Annoying at timesmissed the old (boring)
  lecture

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Conclusions

• JiTT in Calculus is a success
• Easier second timeless development time
  (hopefully).
• Make expectations clear on the first day (and
  second, third,.)

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Unintended outcomes

• Expect to get to know your students earlier in
  the semester.
• More email contact with students.
• Learn about their weird sleep patterns.
• Think differently about calculus.

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On to MapleTA

• MapleTA on the web
• Student Assignments
• Assignment 2
• Assignment 16
• Practice Final