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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.be:8081)

• (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 Maple’s 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

h> f:= `*`(op(combinat[randcomb]( \

[exp(-x), sin(2*x), cos(3*x)], 2))); t> Evaluate the following integral: p> Int(f_, x) forbid> int,Int s> [(ans)->`quiz/Testzero`(diff(ans, x)-f_),int(f, x)] sb> t> <b>Solution:</b> Use integration by parts. se> end>

1) choose an integrable function: e.g. sin(2x)cos(3x),

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*(1/2*cos(2*x)*cos(3*x)+3/4*sin(2*x)*sin(3*x))

Teacher’s 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.

Your last answer is: 2/5 cos(2 x) cos(3 x) + 3/5 sin(2 x) sin(3 x)

MarkMark

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Example 2: what the teacher types

• k> basis,easy

• v> 2

• t> Find a basis for V = {A in R^2x2 | AS[o]=S[o]A},with

• p> S[o] = matrix(2,2,[1,0,1,1])

• ap> A basis for V =

• c> set(matrix)

• h> ans_ := {matrix(2,2,[1,0,0,1]),matrix(2,2,[0,0,1,0])};

• s> [equal_bases, ans_]

• end>

1) keywords and value,

2) question and prompt

4) evaluation procedure

3) answer type

HTML elements

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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]])}

MarkMark

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Your last answer is: [ 1 0 ] [ 2 0 ] { [ ] , [ ] } [0 1 ] [ 2 2]

Teacher’s 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 (“c> flag”): give a warning without penalisation

• with a mathematical error:– give a warning

– give penalty (default: 20%)

– let the student try again

• “s> 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

a wrong type results in a warning

here an equation y = f(x) is expected ...

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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 teacher’s 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 student’s administration details

• Access to logfiles and statistics

• Organisation of surveys

• Password protection