Maple T.A. in Mathematical Education of Engineers in Austria...Maple T.A. in Mathematical Education...
Transcript of Maple T.A. in Mathematical Education of Engineers in Austria...Maple T.A. in Mathematical Education...
Maple T.A. in Mathematical Education of Engineers in Austria
F. Breitenecker, A. Körner, S. Winkler Vienna University of Technology
Institute for Analysis and Scientific Computing
Felix Breitenecker
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Vienna University of Technology
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Vienna University of Technology
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Vienna University of Technology
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Vienna University of Technology
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• Since 1814
• 4.500 staff
• 28.000 students
• 5.400 students for 2014
Vienna University of Technology: • > 3.400 staff for research • 8 faculties Faculty of Mathematics and Geoinformation: • > 300 staff Institute for Analysis and Scientific Computing • 60 staff Research Group Mathematical Modelling and
Simulation • 3 staff
Vienna UT, Institute ASC, RG MMS
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Problem 1
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Knowledge Test
Problem 2
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Problem 3
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Skills
Understanding
• Refresher Course Mathematics
• Blended Learning
• Continuity in first semesters
Solution Approach
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• Computer Algebra System Maple • Maple T.A.: Testing and Assessment via Web • Usage in USA, partly in Europe • Examples: standardised Databank • Alternative Platforms: Moodle Math.EL System RWTH Aachen Extension of MMT (Mathematics, Modelling and Tools)
Why Maple T.A.?
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Result 1
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Knowledge Test Final Test
Results 2
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Result 3
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Skills
Understanding
Skills
Understanding
• Maple T.A. used since 2006/2008
• 2 part-time staff: Administration and Content Adviser
• 3 part-time Tutors: Example Development • Around 820 examples:
• Refresher course level: 120 • Basic mathematical level: 200+230 • Advanced mathematical level: 270
Facts
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Evolution using Maple T.A.
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• Refresher Course Mathematics
• Mathematics 1 for electrical engineers • Mathematics 2 for electrical engineers
• Examination going online
• Mathematics 3 for electrical engineers
Moodle Usage • Administraion of lectures
• Offering lecture materials • Administration e-exams
• Administration of Homeworks (Kreuzerlliste) • Uploading the homework examples • On Monday they have the say which
example they prepared • Administration of exercises
• Group administraion • Creation of marks
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MTA connection • Since winter 2013 connection to
MTA (Tool of Moodle) • Former times 3 accounts necessary • Example pools linked in TUWEL • Tests are linked in TUWEL • Test results stored in TUWEL • Results directly useable in assessment
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Course Structure
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First Use of Maple T.A.
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First Use of Maple T.A.
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• Create a common mathematical level • Short course duration • Big amount of students • Using of e-learning • Focus on practice • Coordination with regular lectures
Refresher Course – Structure
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Anonymous Test AKMATH First Turnus AKMATH Second Turnus Final Exmaination
AKMATH – Course Structure • 6-8 modules focusing on different topics • one module contains:
o 2 h classical lecture o 2 h classical exercises combined with Maple T.A. , guided self education o→∞ practising on MTA
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AKMATH Content
• Basics and Introduction • Number Ranges • Basics of Equations • Linear equation systems
• Elementary functions and equations • Vector calculus
• Geometry in plane • Geometry in space • Vector products • Matrix calculations (for some field of studies)
• Complex numbers • Differential Calculus • Integral Calculus
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AKMATH – Teilnehmer
2014 ET MB TPH BI INF VG DIV total
total 212 546 295 268 275 35 282 1913
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0 100 200 300 400 500 600
AKMATH ET
AKMATH MB
AKMATH TPH
AKMATH BI
AKMATH RP
AKMATH
AKMATH INF
2014
2013
2012
2011
2010
2009
AKMATH Lecture
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AKMATH Exercice & Practice
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Refresher Course: The Start
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Refresher Course: Advanced Examples
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Advanced Use of Maple T.A.
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Basic Mathematical Courses
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• Classic lectures 3-4 times a week • Homework
o 8-10 examples per week, 60% necessary o Presentation of the prepared examples
• Examples in MTA o 1-3 assignements per week o 10-20 examples
• 3 Tests o Spread through semester o Pass 2 of 3 tests o Bonus points for pretests
Content Mathematics 1
• Real Numbers • Sequences and Series • Complex Numbers • Elementary functions • Rational functions • Continuity of real functions • Differential Calculus • Integral Calculus
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ò
Content Mathematics 2
• Linear Algebra • Vector spaces • Orthogonality • Matrix calculus • Eigenvalues, Eigenvactors
• Multivariate Functions • Pre-calculus • Derivatives, Taylorpolynom, etc.
• Differential Equations • Ordinary differential equations • Initial Value Problem
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Advanced Mathematical Courses
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• Classic lectures 4 times a week • Homework
o 8-10 examples per two weeks, 60% necessary o Presentation of the prepared examples
• Examples in MTA o 1-3 assignements per topic o 10-20 examples
• 3 Tests o Spread through semester o Pass 2 of 3 tests
Content Mathematics 3
• Vector Analysis: • grad, rot, div • Intgration
• Integral Transformation: • Laplace-Transform • Fourier Transform
• Statistics: descriptive • Numerical Mathematics
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Examples Mathematics 1
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Examples Mathematics 1
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Content Mathematics 1
• Real Numbers • Sequences and Series • Complex Numbers • Elementary functions • Rational functions • Continuity of real functions • Differential Calculus • Integral Calculus
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Maple T.A. - Grading
• Grade[Expr], Grade[ExprDiff]
• Grade[Set]
• Grade[ParFrac]
• Grade[Vec]
• Grade[Mat]
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Maple T.A. - Creating
• Random[FromSet]
• Random[VecInts]
• Random[MatInts] • rows, cols • zerocount, rank
• Random[MatsIntsDef]
• Random[MatRatsEig]
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Examples Mathematics 2
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Examples Mathematics 3
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Numerical Examples Mathematics 3
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MMT Mathematics, Modelling and Tools
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MMT Server structure
User Adam Ries(e)
Standard Matlab
Octave
Weitere Moodle 06.10.2014 47
MMT: Example
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E-Exams
Examination for electrical engineers: written exams (2h)
New regulations: written & oral exams written exams: e-test or ordinary
oral exam
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E-Exams
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Any Questions?
Maple T.A. in Mathematical Education of Engineers in Austria
A. Körner, S. Winkler, F. Breitenecker Vienna University of Technology
Institute for Analysis and Scientific Computing