D2.1 Content Release version 2€¦ · D-2.1 Content Release, version 2 Math-Bridge Project ref.no. ECP-2008-EDU-428046 Project title Math-Bridge European Remedial Content for Mathematics

ECP-2008-EDU-428046

Math-Bridge

Content Release, version 2

Deliverable number D-2.1

Dissemination level Public

Delivery date July 31st 2011

Status Final

Authors Franz Embacher (University of Vienna)

Michael Dietrich (Saarland University)

Gergely Wintsche (Eotvos Lorand University)

eContentplus

This project is funded under the eContentplus programme1 ,a multiannual Community programme to make digital content in Europe more accessible, usable and exploitable.

1OJ L 79, 24.3.2005, p. 1.

D-2.1 Content Release, version 2 Math-Bridge

Project ref.no. ECP-2008-EDU-428046

Project title Math-Bridge

European Remedial Content for Mathematics

Deliverable dissemination level Public

Contractual date of delivery July 31st, 2011

Actual date of delivery July 31st, 2011 / March 7th, 20122

Deliverable number D-2.1

Deliverable title Content Release, version 2

Type Demonstrator

Status & version Final

Number of pages 49

WP contributing to the WP2, WP3, WP5

deliverable

WP/Task responsible Franz Embacher

Authors Franz Embacher (University of Vienna)

Michael Dietrich (Saarland University)

Gergely Wintsche (Eotvos Lorand University)

EC Project Officer Francesca Borrelli

Keywords content, quality management, knowledge repre-sentation

2First date is delivery date for the Demonstrator/second date is delivery date for this report

Page 2 of 49


Contents

1 Progress achieved since July 2010 6

1.1 Translation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2 Filling of gaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3 Reuse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4 Quality control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.5 Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Overview of the content 9

3 Collections 10

3.1 Collection: BasWis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.2 Collection: Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.3 Collection: ounlContent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.4 Collection: Schulmathematik . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.5 Collection: LeAM calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.6 Collection: kasselContent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.7 Collection: UV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.8 Collection: tutCollection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.9 Collection: Bevezeto matematika (Introduction to Math) . . . . . . . . . . . . 18

4 Pre-recorded books 19

4.1 Pre-defined course: Basiscursus wiskunde . . . . . . . . . . . . . . . . . . . . 19

4.2 Pre-defined course: Basiscursus Wiskunde deel 2 . . . . . . . . . . . . . . . . 20

4.3 Pre-defined course: Ideas Exercises . . . . . . . . . . . . . . . . . . . . . . . 21

4.4 Pre-defined course: Curso Cero UC3M . . . . . . . . . . . . . . . . . . . . . . 22

4.5 Pre-defined course: Fraction Calculation . . . . . . . . . . . . . . . . . . . . . 23

4.6 Pre-defined course: Introduction to Calculus . . . . . . . . . . . . . . . . . . 24

Page 3 of 49


4.7 Pre-defined course: Short Introduction to Calculus . . . . . . . . . . . . . . . 26

4.8 Pre-defined course: General Functions . . . . . . . . . . . . . . . . . . . . . . 28

4.9 Pre-defined course: VEMA-Content (Kassel/Paderborn) . . . . . . . . . . . . 29

4.10 Pre-defined course: enriched VEMA-Content (Kassel/Paderborn) . . . . . . . 30

4.11 Pre-defined course: Application relevant LOs: Engineering . . . . . . . . . . . 31

4.12 Pre-defined course: Application relevant LOs: Mathematics . . . . . . . . . . 32

4.13 Pre-defined course: Application relevant LOs: Science . . . . . . . . . . . . . 33

4.14 Pre-defined course: Application relevant LOs: Pedagogy . . . . . . . . . . . . 34

4.15 Pre-defined course: Application relevant LOs: Others . . . . . . . . . . . . . . 35

4.16 Pre-defined course: Wiederholung des Schulstoffes . . . . . . . . . . . . . . . 36

4.17 Pre-defined course: Mathematics Remedial Instruction . . . . . . . . . . . . . 37

4.18 Pre-defined course: Remedial Exercises . . . . . . . . . . . . . . . . . . . . . 38

4.19 Pre-defined course: UV ANW collection (UV alkalmazasi peldak) . . . . . . . 39

4.20 Pre-defined course: Szintfelmero collection (assessment test) . . . . . . . . . . 40

5 External Content 41

5.1 Collection: AMorContent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.1.1 Pre-defined course: Mathematics, Physics and Chemistry Exercises . . 42

5.2 Collection: mathebrHTW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.2.1 Pre-defined course: Bruckenkurs HTW . . . . . . . . . . . . . . . . . 44

5.2.2 Pre-defined course: Ubungen zum Bruckenkurs HTW . . . . . . . . . 45

5.3 Collection: Statistik . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.3.1 Pre-defined course: Grundlagen der Wahrscheinlichkeitsrechnung Kapi-tel 1: Ereignisse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.3.2 Pre-defined course: Grundlagen der Wahrscheinlichkeitsrechnung Kapi-tel 2: Zufallsgroßen . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6 Summary 49

Page 4 of 49


Introduction

In the first version of the deliverable D-2.1 Content Release, the type and sources of contentprovided by various partners to the Math-Bridge project was described. In addition, thetransformation steps necessary to bring that content into a form that can be used in Math-Bridge were described, together with an outline of the quality management. Finally thestate of the content as of July 2010 was summarized.

In this report, D-2.1 Content Release, version 2, we give a complete description of thecontent as it is provided to Math-Bridge users by January 2012.

Section 1 summarizes the progress achieved since July 2010 in completing the content andin the improvement of its quality and appearance.

In Section 2 we give an overview of the current content.

Section 3 lists all collections of Math-Bridge, and relevant information about each is dis-played.

Section 4 lists the pre-defined courses generated from the existing collections.

Section 5 lists the content collections which were provided to Math-Bridge by externalcontributors.

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1 Progress achieved since July 2010

As described in the first part of the deliverable D-2.1 Content Release, the steps necessaryto convert the content sources to the target format had been performed for the major partof the content by July 2010. When counted in terms of content provided by 7 contentproviding partners or partner groups (German Research Center For Artifcial Intelligence,University of Kassel/University of Paderborn, Open Universiteit Netherlands, SaarlandUniversity, University of Vienna, Tampere University of Technology and Eotvos LorandUniversity), the status was:

• The content transformation

– was completed in 4 cases

– and in progress in 2 cases.

• The content slicing


– and in progress in 1 case.

• The metadata enrichment

– was completed in 1 case


• The formula transformation



• Finally the quality control

– was in progress in all 7 cases.

Since then, the outstanding tasks have been completed. Besides the completion of thetechnical procedures and the advancement of translations into various languages, the mainemphasis has been put on the detection and filling of content gaps and the general qualitycontrol.

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1.1 Translation

The complete collection LeAM calculus has been translated into all partner languages. Itis now available in English, German, Hungarian, Spanish, French, Dutch and Finnish.

Based on the original English and Finnish text, the collection tutCollection has been trans-lated to German, Hungarian, French and Spanish.

The collection UV is now available in English, German and Hungarian.

1.2 Filling of gaps

The Gap Detection Tool was used to automatically identify structural gaps in the content.In addition, the content was reviewed for gaps in terms of pedagogical goals and coursestructures. The procedures and the results have been described in the deliverable D-3.1Report on Content Gaps Detected and Filled from May 2011.

1.3 Reuse

The detection of structural gaps was the opportunity to put forward the cross-partner use(“reuse”) of learning items. The information which pre-defined courses contain contentprovided by other partners is displayed in the listing of courses in Section 4.

1.4 Quality control

Extensive reviews of the content led to the correction of a number of errors, ranging fromsimple typos to problems with the formula representation.

1.5 Layout

In addition to the quality enhancement of the content as such, the layout of its presentationhas been improved. With the evolution of web browsers the opportunity arose to useMathML for presentation of mathematical contents which provides a much better renderingof formulae compared to HTML, as the following example illustrates:

Page 7 of 49


Formulae rendered using MathML

Formulae rendered using HTML

One big advantage of native MathML support, besides the excellent rendering of formulas,is the integration of MathML objects into the Document Object Model. With that it ispossible to attach JavaScript functions to MathML objects which allows us to port usefulfunctionalities from the old user interface to the new one.

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2 Overview of the content

The learning content of Math-Bridge as delivered to students consists of collections andpre-defined courses.

A collection may be understood as a structured pool of learning items out of whichcourses may be generated. Although Math-Bridge allows the individual generation ofcourses by its users, the content relevant for a given bridging course is usually delivered tothe students as a pre-defined course, comprizing all material necessary for the studentsto work with and showing the overall scope of the course.

In total, the current content of Math-Bridge provided by members of the Math-Bridgeconsortium contains 9 collections, consisting of 10408 learning items (learning objects).From these 9 collections, 20 pre-defined courses were generated.

• 10 of these courses are suitable for presentation to students in bridging courses. Intotal, these 10 courses consist of 595 pages and display 8323 learning items to thestudents using Math-Bridge (where items appearing in several courses are multiplycounted).

• The remaining 10 courses were used to collect learning items of certain types that willhelp future teachers and tutors in generating further courses for various purposes.

The transformation of external content brought three more collections into Math-Bridgescontent database. These collections add an additional 1018 learning objects and 5 morepre-defined courses.

Alltogether the number of available learning objects sums up to 11426.

The next two Sections give detailed information about the collections and courses. Forcompleteness, these lists also include the collections LeAM calculus and Schulmathematikand the courses generated from them, although they were authored in previous projects:The calculus course has been developed in the LeActiveMath project during January 2004through December 2006. The fractions calculation course was developed and encodedby Edgar Kessler, a German highschool teacher, who visited the ActiveMath group foralmost two years. The course has been further improved over time by ActiveMath groupmembers.

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3 Collections

3.1 Collection: BasWis

Collection name: BasWis

Content providing partner: Open Universiteit Nederlands (OUNL)

Authors(s) and affiliation: Arjan Kok (OUNL), Math Dicker (OUNL) andJosje Lodder (OUNL)

Editor(s): Nike van Vugt, Jan Timmerman

Translator(s): Arjan Kok, Nike van Vugt, Bert Esmeijer

License: Creative Commons Attribution-NonCommercial3.0 Unported (CC BY-NC 3.0): http://

creativecommons.org/licenses/by-nc/3.0/

Available language(s): Dutch, English

Number of learning items: 568

Description: Basic skills: calculating with numbers, roots andexponents.

Available courses (mainly)based on this collection:

Basiscursus wiskundeBasiscursus wiskunde deel 2

The collection is availablefrom the server(s):

http://system.math-bridge.org/

Page 10 of 49

http://creativecommons.org/licenses/by-nc/3.0/




3.2 Collection: Ideas

Collection name: Ideas


Authors(s) and affiliation: Johan Jeuring (OUNL) and Bastiaan Heeren(OUNL)

Editor(s): Authors

Translator(s): Thomas Wassong, Christian Mercat, Thumas Mi-ilumaki, Tomas de la Rosa, Angel Garcia Olaya,Johan Jeuring, Rozsa Gabor, Wintsche Gergely



Available language(s): Dutch, English, Hungarian, Finnish, German,French, Spanish


Description: Multistep exercises.


Ideas Exercises



Page 11 of 49





3.3 Collection: ounlContent

Collection name: ounlContent


Authors(s) and affiliation: R. Beerends, J.S. Lodder, H.M. Mulder, E.M. vande Vrie

Editor(s): Authors

Translator(s): Collection available in Dutch only



Available language(s): Dutch


Description: This collection contains several learning objectsconcerning typical bridging course subjects: defini-tion of a function; descriptions of special functionslike polynomials, rational functions, absolute value,trigoniometric, exponential and logarithmic func-tions; inverse functions and composition of func-tions; equations and inequalities. There are alsosome more extensive lessons on subjects from dis-crete mathematics: number theory, graphs, trees,sets of numbers, relations and function.


No courses have been derived from this collectionyet


Collection has not been put online yet

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3.4 Collection: Schulmathematik

Collection name: Schulmathematik

Content providing partner: German Research Center for Artificial Intelligence(DFKI)

Authors(s) and affiliation: Edgar Kessler (teacher), PD Dr. Erica Melis(DFKI)

Editor(s): Adrian Frischauf, Michael Dietrich

Translator(s): Miriam Kunold



Available language(s): English, German


Description: This collections aims at supporting teaching of frac-tions in middle school.


Fraction Calculation


http://service.math-bridge.org/ and http://

system.math-bridge.org/

Page 13 of 49



http://service.math-bridge.org/




3.5 Collection: LeAM calculus

Collection name: LeAM calculus

Content providing partner: Saarland University (USAAR)

Authors(s) and affiliation: Christian Groß (University of Augsburg), MarianneMoormann (Ludwigs Maximilian University Mu-nich)

Editor(s): Christian Groß, Carsten Ullrich, Erica Melis, EvaVasarhelyi, Johan Jeuring, Jussi Kangas, MartinHomik, Marianne Moormann

Translator(s): Christian Bokhove, Eva Vasarhelyi, Rui Dong,Veronica Guzman, Paul Libbrecht, Hana Moraova,Johan Heuring, Julianna Zsido, Angel GarciaOlaya, Tomas de la Rosa, Hanna Sarikka, AlainBruguieres, Nike van Vugt, Katona Janos, PeterMijnheer



Available language(s): Czech, Dutch, English, French, Finnish, German,Hungarian, Spanish


Description: LeAM calculus is a multi-lingual content-collectionfor calculus.


Introduction to CalculusShort Introduction to Calculus


http://math.tut.fi/math-bridge, http:

//euler.math.univ-montp2.fr/mathbridge/,http://service.math-bridge.org/ andhttp://system.math-bridge.org/

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http://math.tut.fi/math-bridge

http://euler.math.univ-montp2.fr/mathbridge/





3.6 Collection: kasselContent

Collection name: kasselContent

Content providing partner: University Kassel and University Paderborn

Authors(s) and affiliation: see VEMA project: http://www.mathematik.

uni-kassel.de/vorkurs

Editor(s): Authors

Translator(s): Miriam Kunold, Nadine Camin, Sabrina AlexandraLohmann, Tomas de la Rosa, Angel Garcia Olaya

License: Creative Commons Attribution Noncommercial NoDerivative

Available language(s): Complete: German, English. Parts: Hungarian,Spanish, French, Dutch, Finnish


Description: The collection comprises the complete VEMA ma-terial, as provided by the Universities Kassel andPaderborn.


VEMA-Content(Kassel/Paderborn)


http://moodle.math.uni-paderborn.de/

mathbridge and http://system.math-bridge.

org/

Page 15 of 49

http://www.mathematik.uni-kassel.de/vorkurs

http://www.mathematik.uni-kassel.de/vorkurs

http://moodle.math.uni-paderborn.de/mathbridge





3.7 Collection: UV

Collection name: UV

Content providing partner: University of Vienna (UV)

Authors(s) and affiliation: Franz Embacher (UV), Petra Oberhuemer (UV)

Editor(s): Franz Embacher, Attila Mandy, Balint Kreka,Christian Spreitzer, Katalin Fried, GergelySuranyi, Katalin Gosztonyi, Eva Vasarhelyi,Tamas Gilinger, Pal Maus, Katharina Brazda,Peter Tomosy, Nora Repasy, Judit Torok, AnnaNemeth, Bernat Kallo, Amy Besamusca, GabriellaAmbrus, Gabor Vidra, Katalin Munkocsy, GaborRozsa, Marianna Pinter, Agnes Borszeki, BalintBelinszki, Gergely Wintsche

Translator(s): Christian Spreitzer, Katharina Brazda, Franz Em-bacher

License: Creative Commons Attribution Noncommercial

Available language(s): German, English, Hungarian


Description: This collection comprises background chapters andinteractive tests from mathe online.


Wiederholung des Schulstoffes



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3.8 Collection: tutCollection

Collection name: tutCollection

Content providing partner: Tampere University of Technology (TUT)

Authors(s) and affiliation: Janne Kauhanen, Markku Luhtalahti, Markus Ur-ponen, Kari Suomela, Pasi Hakkinen, Sanna Maki-Turja, Olli Perttula, Seppo Pohjolainen, TeemuMakela, Thumas Miilumaki, Emilia Rautiainen(TUT)

Editor(s): Thumas Miilumaki, Jussi Kangas, Hanna Sarikka,Juha Tiihonen, Markku Akerblom

Translator(s): Hanna Sarikka, Juha Tiihonen, Aino Ylinen,Markku Akerblom


Available language(s): Finnish, English, Dutch, German, Spanish, Hun-garian, French


Description: The collection includes study material for TUT En-gineering Mathematics courses, an introduction tothe University mathematics course at TUT and in-teractive STACK exercises.


Mathematics Remedial Instruction


http://system.math-bridge.org and http://

math.tut.fi/mathbridge

Page 17 of 49

http://system.math-bridge.org

http://math.tut.fi/mathbridge



3.9 Collection: Bevezeto matematika (Introduction to Math)

Collection name: Bevezeto matematika (Introduction to Math)

Content providing partner: Eotvos Lorand University (ELTE)

Authors(s) and affiliation: Kallo Bernat, Kreka Balint, Eva Vasarhelyi(ELTE)

Editor(s): Kallo Bernat, Kreka Balint, Eva Vasarhelyi

Translator(s): none

License: Creative Commons License Attribution-SharealikeGeneric: http://creativecommons.org/

licenses/by-sa/2.0/

Available language(s): Hungarian


Description: Test exercises for practicing.


Szintfelmero collection (assessment test)


http://rgabgab.eu:8080/mathbridge/#!

bevmat_hu-collinfo/1/

Page 18 of 49

http://creativecommons.org/ licenses/by-sa/2.0/


http://rgabgab.eu:8080/mathbridge/#!bevmat_hu-collinfo/1/

http://rgabgab.eu:8080/mathbridge/#!bevmat_hu-collinfo/1/


4 Pre-recorded books

4.1 Pre-defined course: Basiscursus wiskunde

Book title: Basiscursus wiskunde

Project partner: Open Universiteit Nederlands (OUNL)

Authors(s) and affiliation: Authors of the collections Baswis, kasselContent,UV and Ideas

Editor(s): Josje Lodder

Translator(s): Peter Mijnheer, Amy Besamusca, Nike van Vugt,Arjan Kok



Number of pages: 59


Learning time: 60 hrs

Difficulty: easy

Available language(s): Complete: Dutch, English. Parts: Hungarian,Finnish, German, French, Spanish

(Mainly) part of collection: BasWis

Description: Basic skills, computations with numbers and let-ters, functions, linear and quadratic functions andequations.

Reuse of objects: The course contains items from the collections kas-selContent and UV.

This course was used in lec-ture(s):

Basis cursus Wiskunde

It is available from theserver(s):


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4.2 Pre-defined course: Basiscursus Wiskunde deel 2

Book title: Basiscursus Wiskunde deel 2


Authors(s) and affiliation: Authors of the collections Baswis, UV and Ideas

Editor(s): Josje Lodder

Translator(s): Amy Besamusca, Bert Esmeijer



Number of pages: 16


Learning time: 40 hrs

Difficulty: medium

Available language(s): Complete: Dutch, English. Parts: Hungarian,Finnish, German, French, Spanish

(Mainly) part of collection: BasWis and Ideas

Description: Exponential functions, more complex equations, in-troduction to differentiating.

Reuse of objects: The course contains items from the collection UV.


Basiscursus wiskunde



Page 20 of 49





4.3 Pre-defined course: Ideas Exercises

Book title: Ideas Exercises


Authors(s) and affiliation: Johan Jeuring, Bastiaan Heeren, Alex Gerdes(OUNL)

Editor(s): Authors

Translator(s): Thomas Wassong, Christian Mercat, Thumas Mi-ilumaki, Angel Garcia Olaya, Johan Jeuring, RozsaGabor, Wintsche Gergely



Number of pages: 26


Learning time: unknown

Difficulty: easy, intermediate, and difficult

Available language(s): Dutch, English, Hungarian, Finnish, German,French, Spanish

(Mainly) part of collection: Ideas

Description: Multistep exercises for many different kinds ofproblems: solving various kinds of equations orinequations, differentiation, manipulating expres-sions, etc.

Reuse of objects: The course contains no items provided by otherpartners.


Basiscursus wiskunde, Basiscursus wiskunde deel 2



Page 21 of 49





4.4 Pre-defined course: Curso Cero UC3M

Book title: Curso Cero UC3M

Project partner: Universidad Carlos III de Madrid (UC3M)

Authors(s) and affiliation: Authors of the collection tutCollection

Editor(s): Pedro J. Hernando, Tomas de la Rosa, Angel Gar-cia

Translator(s): Tomas de la Rosa, Angel Garcia Olaya


licenses/by-sa/2.0/

Number of pages: 55


Learning time: 2 weeks

Difficulty: easy

Available language(s): English, Finish, Spanish. Partly: Hungarian,French, German

(Mainly) part of collection: tutCollection

Description: Book used for the Spanish Bridging Course.

Reuse of objects: The course has been generated from the collectiontutCollection.


Spanish Bridging Course


http://hilbert.plg.inf.uc3m.es:8080

Page 22 of 49



http://hilbert.plg.inf.uc3m.es:8080


4.5 Pre-defined course: Fraction Calculation

Book title: Fraction Calculation

Project partner: German Research Center for Artificial Intelligence(DFKI)

Authors(s) and affiliation: Edgar Kessler (teacher), PD Dr. Erica Melis(DFKI)

Editor(s): Michael Dietrich, Adrian Frischauf

Translator(s): Miriam Kunold



Number of pages: 54


Learning time: approx 20 hrs (for university students)

Difficulty: easy

Available language(s): English, German

(Mainly) part of collection: Schulmathematik

Description: This course aims at supporting teaching of fractionsin middle school.



none


http://service.math-bridge.org/ and http://

system.math-bridge.org/

Page 23 of 49







4.6 Pre-defined course: Introduction to Calculus

Book title: Introduction to Calculus

Project partner: Saarland University (USAAR)



Translator(s): Christian Bokhove, Eva Vasarhelyi, Rui Dong,Veronica Guzman, Paul Libbrecht, Hana Moraova,Johan Heuring, Julianna Zsido, Angel GarciaOlaya, Hanna Sarikka, Peter Mijnheer, AlainBruguieres, Nike van Vugt, Katona Janos



Number of pages: 220


Learning time: 2 – 4 weeks

Difficulty: easy and medium


(Mainly) part of collection: LeAM calculus

Description: This course contains the complete content of dif-ferential calculus in one variable, on school lev-els as well as on university level. In addition,it contains all the required basics on functionsand relations, on sequences and series, and onproofs (by induction). Numerous exercises, exam-ples and interactive applets, including many fromnon-mathematical fields of application, support thecomprehension of the mathematical contents.

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Book title: Introduction to Calculus (cont’d)



none


http://math.tut.fi/math-bridge, http:

//euler.math.univ-montp2.fr/mathbridge/,http://rgabgab.eu:8080/mathbridge/,http://service.math-bridge.org/ andhttp://system.math-bridge.org/

Page 25 of 49

http://math.tut.fi/math-bridge



http://rgabgab.eu:8080/mathbridge/




4.7 Pre-defined course: Short Introduction to Calculus

Book title: Short Introduction to Calculus




Translator(s): Christian Bokhove, Eva Vasarhelyi, Rui Dong,Veronica Guzman, Paul Libbrecht, Hana Moraova,Johan Heuring, Julianna Zsido, Angel GarciaOlaya, Hanna Sarikka, Peter Mijnheer, AlainBruguieres, Nike van Vugt, Katona Janos

License: Creative Commons Attribution-NonCommercial3.0 Unported (CC BY-NC 3.0):urlhttp://creativecommons.org/licenses/by-nc/3.0/

Number of pages: 40





(Mainly) part of collection: LeAM calculus

Description: This course is an introduction into differential cal-culus. Using a hiking tour as an example, wesuccessively introduce the notions “difference quo-tient”, “derivative”, and “derivative function”. Fi-nally, the most important rules of differentiationare treated.

Page 26 of 49


Book title: Short Introduction to Calculus (cont’d)



none


http://system.math-bridge.org/, http:

//demo.math-bridge.org/ and http:

//rgabgab.eu:8080/mathbridge/

Page 27 of 49


http://demo.math-bridge.org/





4.8 Pre-defined course: General Functions

Book title: General Functions


Authors(s) and affiliation: identical with those of the collection kasselContentplus Christian Groß (University of Augsburg), Mar-ianne Moormann (Ludwigs Maximilian UniversityMunich), Johan Jeuring (OUNL)

Editor(s): identical with those of the collection kasselContentplus Eric Andres and Michael Dietrich

Translator(s): all translators of the Math-Brigde consortium


Number of pages: 7


Learning time: not defined

Difficulty: not defined

Available language(s): German, English. Hungarian, Spanish, French,Dutch, Finnish

(Mainly) part of collection: kasselContent, but contains also material from allother content providing partners

Description: This pre-defined course serves as a showcase course.It is based on the module “General functions” en-riched with learning objects from the collectionsLeAM calculus, Ideas and tutCollection.

Reuse of objects: This course contains learning objects from the col-lections LeAM calculus, Ideas and tutCollection.


none



Page 28 of 49



4.9 Pre-defined course: VEMA-Content (Kassel/Paderborn)

Book title: VEMA-Content (Kassel/Paderborn)

Project partner: University Kassel and University Paderborn

Authors(s) and affiliation: identical with those of the collection kasselContent

Editor(s): identical with those of the collection kasselContent

Translator(s): identical with those of the collection kasselContent







(Mainly) part of collection: kasselContent

Description: The complete VEMA-Collection in the establishedorder.



none


none

Page 29 of 49


4.10 Pre-defined course: enriched VEMA-Content (Kassel/Paderborn)

Book title: enriched VEMA-Content (Kassel/Paderborn)


Authors(s) and affiliation: identical with those of the collection kasselContent

Editor(s): identical with those of the collection kasselContent

Translator(s): identical with those of the collection kasselContent







(Mainly) part of collection: kasselContent, but contains also material from allother content providing partners

Description: The complete VEMA-Collection in the establishedorder, enriched by learning objects from all otherpartners.

Reuse of objects: The course contains learning items from all otherpartners.


Kassel/Paderborn bridging courses


http://moodle.math.uni-paderborn.de/

mathbridge (split into several smaller pre-definedcourses) and http://system.math-bridge.org/

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4.11 Pre-defined course: Application relevant LOs: Engineering

Book title: Application relevant LOs: Engineering


Authors(s) and affiliation: all partners

Editor(s): The course was recorded by Kassel-Paderbornteam: Rolf Biehler, Pascal Fischer, ReinhardHochmuth and Thomas Wassong



licenses/by-sa/2.0/

Number of pages: none


Learning time: none

Difficulty: none

Available language(s): Complete: English. Parts: all other languages

(Mainly) part of collection: all collections from all partners

Description: Collection of the application relevant learning ob-jects concerning engineering. The course has thesame topics and order as was used for the domainontology.

Reuse of objects: The course contains learning items from all otherpartners.


none

Remark: This was a result of T3.8.



Page 31 of 49

http://creativecommons.org/licenses/by-sa/2.0/




4.12 Pre-defined course: Application relevant LOs: Mathematics

Book title: Application relevant LOs: Mathematics





License: Creative Commons License Attribution Share-alike Generic: http://creativecommons.org/

licenses/by-sa/2.0/



Learning time: none

Difficulty: none



Description: Collection of the application relevant learning ob-jects concerning mathematics. The course has thesame topics and order as was used for the domainontology.

Reuse of objects: The course contains items from all other partners.


none




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4.13 Pre-defined course: Application relevant LOs: Science

Book title: Application relevant LOs: Science






licenses/by-sa/2.0/



Learning time: none

Difficulty: none



Description: Collection of the application relevant learning ob-jects concerning science. The course has the sametopics and order as was used for the domain ontol-ogy.



none




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4.14 Pre-defined course: Application relevant LOs: Pedagogy

Book title: Application relevant LOs: Pedagogy






licenses/by-sa/2.0/



Learning time: none

Difficulty: none



Description: Collection of the application relevant learning ob-jects concerning Pedagogy. The course has thesame topics and order as was used for the domainontology.



none




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4.15 Pre-defined course: Application relevant LOs: Others

Book title: Application relevant LOs: Others






licenses/by-sa/2.0/



Learning time: none

Difficulty: none



Description: Collection of the application relevant LOs concern-ing others than engineering, maths, science andpedagogy. The course has the same topics and or-der as was used for the domain ontology.



none




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4.16 Pre-defined course: Wiederholung des Schulstoffes

Book title: Wiederholung des Schulstoffes

Project partner: University of Vienna (UV)

Authors(s) and affiliation: Franz Embacher (UV), Petra Oberhuemer (UV)

Editor(s): Franz Embacher, Christian Spreitzer, Fabio Tonti

Translator(s): Christian Spreitzer, Katharina Brazda, Franz Em-bacher

License: Creative Commons Attribution Noncommercial

Number of pages: 33




Available language(s): English, German, Hungarian

(Mainly) part of collection: UV

Description: Complete content of the collection UV with an ad-ditional chapter on sequences.

Reuse of objects: The course contains items from the collectionLeAM calculus.


Einfuhrung in das mathematische Arbeiten (Intro-duction to mathematical working) at the Univeristyof Vienna



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4.17 Pre-defined course: Mathematics Remedial Instruction

Book title: Mathematics Remedial Instruction

Project partner: Tampere University of Technology (TUT)

Authors(s) and affiliation: Markku Luhtalahti, Markus Urponen, KariSuomela, Pasi Hakkinen, Sanna Maki-Turja, OlliPerttula, Seppo Pohjolainen, Teemu Makela, Thu-mas Miilumaki (TUT)

Editor(s): Thumas Miilumaki, Hanna Sarikka, Jussi Kangas

Translator(s): Hanna Sarikka


licenses/by-sa/2.0/

Number of pages: 68



Difficulty: medium

Available language(s): Finnish, English, Spanish, Hungarian, German,French


Description: Mathematics Remedial Instruction Math-Bridgecourse.



Mathematics Remedial Instruction at TUT



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4.18 Pre-defined course: Remedial Exercises

Book title: Remedial Exercises

Project partner: Tampere University of Technology (TUT)

Authors(s) and affiliation: Pasi Hakkinen, Seppo Pohjolainen, Teemu Makela,Thumas Miilumaki (TUT)

Editor(s): Thumas Miilumaki, Hanna Sarikka, Jussi Kangas

Translator(s): Hanna Sarikka


licenses/by-sa/2.0/

Number of pages: 10



Difficulty: medium

Available language(s): Finnish, English, Spanish, Hungarian, German,French


Description: Mathematics Remedial Instruction Math-Bridgecourse, only interactive STACK exercises.



Mathematics Remedial Instruction at TUT



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4.19 Pre-defined course: UV ANW collection (UV alkalmazasi peldak)

Book title: UV ANW collection (UV alkalmazasi peldak)

Project partner: Eotvos Lorand University (ELTE)

Authors(s) and affiliation: Franz Embacher (UV), Eva Vasarhelyi (ELTE)

Editor(s): Eva Vasarhelyi

Translator(s): none


licenses/by-sa/2.0/

Number of pages: 9

Number of learning items: n.a.

Learning time: n.a.

Difficulty: n.a.


(Mainly) part of collection: UV

Description: Collected examples of the collection UV.

Reuse of objects: The course contains items from the collection UV.


Matematikai felzarkoztato kurzus (Bridgingcourses for mathematics at ELTE)


http://rgabgab.eu:8080/mathbridge/#!UV_

ANW-collinfo/1/

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http://rgabgab.eu:8080/mathbridge/#!UV_ANW-collinfo/1/

http://rgabgab.eu:8080/mathbridge/#!UV_ANW-collinfo/1/


4.20 Pre-defined course: Szintfelmero collection (assessment test)

Book title: Szintfelmero collection (assessment test)

Project partner: Eotvos Lorand University (ELTE)

Authors(s) and affiliation: Balint Kreka, Eva Vasarhelyi (ELTE)

Editor(s): Balint Kreka, Eva Vasarhelyi

Translator(s): none


licenses/by-sa/2.0/

Number of pages: 4


Learning time: 45 min

Difficulty: unknown


(Mainly) part of collection: Bevezeto matematika

Description: Test exercises for practicing.



Matematikai felzarkoztato kurzus (Bridgingcourses for mathematics at ELTE)


http://rgabgab.eu:8080/mathbridge/#!

szintfelmero-collinfo/1/

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http://rgabgab.eu:8080/mathbridge/#!szintfelmero-collinfo/1/

http://rgabgab.eu:8080/mathbridge/#!szintfelmero-collinfo/1/


5 External Content

This section gives a description of the content collection which have been added to theMath-Bridge content database by contributors from outside the consortium.

We were able two win Prof. Dr. Barbara Grabowski and Prof. Michael Springborg ascontent providing contributors. Prof. Grabowski is teaching statistics and applied mathe-matics at Saarlands technical university and Prof. Springborg is physical and theoreticalchemistry professor at the Saarland University.

Their provided material resulted in three collections containing 5 pre-defined courses. Hereare the details of the collections and contained courses.

5.1 Collection: AMorContent

Collection name: AMorContent

Content providing partner: Prof. Dr. Michael Springborg (External)

Authors(s) and affiliation: Prof. Dr. Michael Springborg

Editor(s): Simona Helmsmuller, Andreas Schumacher,Michael Clayton Davis, Matthias Jacob, StephanieSchreiner, Thomas Geber

Translator(s): Content available in German only



Available language(s): German


Description: This collections provides exercises to train all nec-essary mathematical topics necessary for chemistrystudies.


Mathematics, Chemistry and Physics Exercises



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5.1.1 Pre-defined course: Mathematics, Physics and Chemistry Exercises

Book title: Mathematics, Physics and Chemistry Exercises

Content provider: Prof. Dr. Michael Springborg (external)

Authors(s) and affiliation: Prof. Dr. Michael Springborg

Editor(s): Simona Helmsmuller, Andreas Schumacher,Michael Clayton Davis, Matthias Jacob, StephanieSchreiner, Thomas Geber

Translator(s): none



Number of pages: 32



Difficulty: Easy


(Mainly) part of collection: AMorContent

Description: This course provides a huge number of exercisesstudents can use to train all necessary mathemat-ical concepts needed to study Chemisty. It cov-ers mathematical topics like elementary arithmeticsoperations, fractions calculus, functions and equal-ities, differentiation, integration, vector and matrixcalculation, linear equality systems and complexnumbers.



None



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5.2 Collection: mathebrHTW

Collection name: mathebrHTW

Content providing partner: Prof. Dr. Barbara Grabowski (External)

Authors(s) and affiliation: Prof. Dr.Barbara Grabowski and Melanie Kaspar

Editor(s): Barbara Grabowski, Melanie Kaspar


License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported (CC BY-NC-ND 3.0):http://creativecommons.org/licenses/

by-nc-nd/3.0/



Description: This collection is an online bridging course whichis taught at the University of Applied SciencesSaarbrucken.


Bruckenkurs HTW, Ubungen zum Bruckenkurs HTW



Page 43 of 49

http://creativecommons.org/licenses/by-nc-nd/3.0/




5.2.1 Pre-defined course: Bruckenkurs HTW

Book title: Bruckenkurs HTW

Content provider: Prof. Dr. Barbara Grabowski(external)

Authors(s) and affiliation: Prof. Dr. Barbara Grabowski, Melanie Kaspar

Editor(s): Prof. Dr. Barbara Grabowski, Melanie Kaspar

Translator(s): none


by-nc-nd/3.0/

Number of pages: 53



Difficulty: Easy


(Mainly) part of collection: mathebrHTW

Description: This course is used as an online bridging course atUniversity of Applied Sciences Saarbrucken. It cov-ers mathematical basics like arithmetics, fractionscalculus, powers, roots, logarithm, sets, equalitiesand inequalites, calculation with units, functions,limits, differentiation, integration and vector cal-culation.



None



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5.2.2 Pre-defined course: Ubungen zum Bruckenkurs HTW

Book title: Ubungen zum Bruckenkurs HTW


Authors(s) and affiliation: Prof. Dr. Barbara Grabowski, Melanie Kaspar


Translator(s): none


by-nc-nd/3.0/

Number of pages: 99



Difficulty: Easy


(Mainly) part of collection: mathebrHTW

Description: This course is an excerpt of the BruckenkursHTWcourse which only contains exercises.



None



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5.3 Collection: Statistik

Collection name: Statistik

Content providing partner: Prof. Dr. Barbara Grabowski (External)

Authors(s) and affiliation: Prof. Dr.Barbara Grabowski

Editor(s): Barbara Grabowski, Melanie Kaspar



by-nc/3.0/



Description: This collection contains an introduction to statis-tics course


Grundlagen der Wahrscheinlichkeitsrechnung Kapitel1: Ereignisse, Grundlagen der Wahrscheinlichkeit-srechnung Kapitel 2: Zufallsgroßen



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5.3.1 Pre-defined course: Grundlagen der Wahrscheinlichkeitsrechnung Kapitel 1: Ereignisse

Book title: Grundlagen der Wahrscheinlichkeitsrechnung Kapitel1: Ereignisse


Authors(s) and affiliation: Prof. Dr. Barbara Grabowski


Translator(s): none


by-nc-nd/3.0/

Number of pages: 26


Learning time: 2-4 weeks

Difficulty: Easy-Medium


(Mainly) part of collection: Statistik

Description: This course serves as an introduction to events usedin probability and statistics.



None



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5.3.2 Pre-defined course: Grundlagen der Wahrscheinlichkeitsrechnung Kapitel 2: Zu-fallsgroßen

Book title: Grundlagen der Wahrscheinlichkeitsrechnung Kapitel2: Zufallsgroßen


Authors(s) and affiliation: Prof. Dr. Barbara Grabowski

Editor(s): Prof. Dr. Barbara Grabowski

Translator(s): none


by-nc-nd/3.0/

Number of pages: 14


Learning time: 1-2 weeks

Difficulty: Easy-Medium


(Mainly) part of collection: Statistik

Description: This course serves as an introduction to randomvariables used in probability and statistics..



None



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6 Summary

In this report, we described the progress made since July 2010 in providing viable learningcontent, and the final status of the content as delivered to the users of Math-Bridge.

Page 49 of 49

Documents

D2.1 Content Release version 2€¦ · D-2.1 Content Release, version 2 Math-Bridge Project ref.no. ECP-2008-EDU-428046 Project title Math-Bridge European Remedial Content for Mathematics