Maple as a Tool for Selfstudy and Evaluation

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Maple as a Tool for Selfstudy and Evaluation
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N. Van den Bergh, T. Kolokolnikov

• Ghent University
• Belgium

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Maple as a Tool for Selfstudy
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• 1996/1997 launch of ALICE (Active Learning in a
  Computer Environment) for linear algebra
• target pilotgroup of civil engineers with a
  traditionally weak mathematical background
• software collection of hyperlinked Maple
  worksheets, worked out exercises and short
  pencil and paper tests

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Results

• Students like to do linear algebra
• Marks of the pilot group comparable to those of
  the regular students

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• 1998/1999 introduction of selfstudy for linear
  algebra, calculus and theoretical mechanics
• 1999-2000 integration in the final exam
  decoupling of the selfstudy (ALICE) and
  evaluation (AIM) modules

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Maple as a Tool for Evaluation

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AIM web server(http//allserv.rug.ac.be8081)

• (password protected) web-interface for both
  student and teacher
• using Maple for the development and evaluation of
  randomised tests with a mathematical content

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Features
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• it is free

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• it is fast
• it uses Maples powerful symbolic manipulation
  engine for the evaluation of non-numeric answers
• it provides decent representation of formulas,
  without MathML or Techexplorer
• it delivers individualised tests
• it is highly flexible in question format
• it allows for giving partial marks and referring
  to sub-questions

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Example 1 what the teacher types
1) choose an integrable function e.g.
sin(2x)cos(3x),

• hgt f (op(combinatrandcomb( \
  exp(-x), sin(2x), cos(3x), 2)))
• tgt Evaluate the following integral
• pgt Int(f_, x)
• forbidgt int,Int
• sgt (ans)-gtquiz/Testzero(diff(ans,
  x)-f_),int(f, x)
• sbgt
• tgt ltbgtSolutionlt/bgt Use integration by parts.
• segt
• endgt

2) type question,
4) and provide some feedback
3) evaluate the answer,
HTML elements
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what the student sees ...
Question 1 (1 marks) Evaluate the
following integral /
sin(2 x) cos(3 x) dx
/ Answer
4/5(1/2cos(2x)cos(3x)3/4sin(2x)sin(3x))
Your last answer is 2/5 cos(2
x) cos(3 x) 3/5 sin(2 x) sin(3 x)
Mark
Teachers answer is - 1/10 cos(5
x) 1/2 cos(x) Your mark for this question is 1
out of 1 .Solution Use integration by parts.

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Example 2 what the teacher types

• kgt basis,easy
• vgt 2
• tgt Find a basis for V A in Rltsupgt2x2lt/supgt
  ASoSoA,with
• pgt So matrix(2,2,1,0,1,1)
• apgt A basis for V
• cgt set(matrix)
• hgt ans_ matrix(2,2,1,0,0,1),matrix(2,2,0,0,
  1,0)
• sgt equal_bases, ans_
• endgt

1) keywords and value,
HTML elements
2) question and prompt
3) answer type
4) evaluation procedure
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Example of an evaluation procedure

• equal_bases proc(A,B) nops(A)nops(B) and
  rank(matrix(map(convert, op(B), op(A),
  vector))) rank(matrix(map(convert, op(A),
  vector)))end

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what the student sees ...
Question 1 (2 marks) Find a basis for V
A in R2x2 AS0 S0A with 1 0
S0 1 1
A basis for V
matrix(1,0,0,1),matrix(2,0,2,2)

Mark
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Your last answer is 1 0
2 0 ,
0 1 2 2
Teachers answer is 0 0
1 0 ,
1 0 0 1
Correct! Your mark for this question is 2 out of
2.
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Dealing with errors ...

• with incorrect syntax or incorrect Maple type
  (cgt flag) give a warning without penalisation
• with a mathematical error
• give a warning
• give penalty (default 20)
• let the student try again
• sgt flag allows for dynamic feedback depending
  on the form of the answer
• access to standard answers after the deadline,
  with additional comments (static or dynamic)

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Answer types

• Built-in
• Free

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Built-in

• default no type controle
• constant numeric controle
• multiple-response
• multiple-choice

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Free
here an equation y f(x) is expected ...
a wrong type results in a warning
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Individualised questions

• Questions are collected in a database and can be
  tagged with an arbitrary number of keywords,
  indicating subject and/or difficulty level.
• Quizzes are built out of the database using
  arbitrarily specifiable selection criteria.
• The degree of randomisation of questions, as well
  as of individual (e.g. numeric) question
  components is only restricted by the teachers
  imagination
• Tests can be delivered to registered students on
  the basis of a fixed random generator seed, or
  can be completely randomised for non-registered
  students.

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Marking and statistics

• Marking scheme freely specifiable
• Possibility of deadline
• no access to solutions before the deadline
• answers can be modified (with possible
  penalisation) before the deadline
• teacher can always modify answers and
  penalty-marks.
• Automatic generation of logfiles, statistics,
  grade reports

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Web-interface

• Editing question and quiz files
• Entering students administration details
• Access to logfiles and statistics
• Organisation of surveys
• Password protection