Alice Interactive Mathematics 1 Maple as a Tool for Selfstudy and Evaluation

Alice Interactive Mathematics 2 N. Van den Bergh, T. Kolokolnikov Ghent University Belgium

Alice Interactive Mathematics 3 Maple as a Tool for Selfstudy

Alice Interactive Mathematics /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

Alice Interactive Mathematics 5 Results Students “like to do linear algebra” Marks of the pilot group comparable to those of the regular students

Alice Interactive Mathematics /1999: introduction of selfstudy for linear algebra, calculus and theoretical mechanics : integration in the final exam + decoupling of the selfstudy (ALICE) and evaluation (AIM) modules

Alice Interactive Mathematics 7 Maple as a Tool for Evaluation

Alice Interactive Mathematics 8 AIM web server ( (password protected) web-interface for both student and teacher using Maple for the development and evaluation of randomised tests with a mathematical content

Alice Interactive Mathematics 9 Features

Alice Interactive Mathematics 10 it is free

Alice Interactive Mathematics 11 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

Alice Interactive Mathematics 12 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> Solution: 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

Alice Interactive Mathematics 13 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) Mark

Alice Interactive Mathematics 14 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

Alice Interactive Mathematics 15 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:

Alice Interactive Mathematics 16 what the student sees... Question 1 (2 marks) Find a basis for V = { A in R 2x2 ¦ AS 0 = S 0 A } with [ 1 0 ] S 0 = [ ] [ 1 1 ] A basis for V = {matrix([[1,0],[0,1]]),matrix([[2,0],[2,2]])} Mark

Alice Interactive Mathematics 17 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.

Alice Interactive Mathematics 18 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)

Alice Interactive Mathematics 19 Answer types Built-in Free

Alice Interactive Mathematics 20 Built-in default = no type controle constant = numeric controle multiple-response multiple-choice

Alice Interactive Mathematics 21 Free a wrong type results in a warning here an equation y = f(x) is expected...

Alice Interactive Mathematics 22 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.

Alice Interactive Mathematics 23 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

Alice Interactive Mathematics 24 Web-interface: Editing question and quiz files Entering student’s administration details Access to logfiles and statistics Organisation of surveys Password protection