maple t.a. in mathematical education of engineers in austria...maple t.a. in mathematical education...
TRANSCRIPT
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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
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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
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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
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Problem 2
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Problem 3
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Skills
Understanding
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• 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
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Results 2
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Result 3
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Skills
Understanding
Skills
Understanding
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• 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
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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
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Refresher Course – Structure
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Anonymous Test AKMATH First Turnus AKMATH Second Turnus Final Exmaination
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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
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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
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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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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
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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
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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?
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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