Math-Bridge: short summary of features
▪ Tools for students: ▪ Static Courses ▪ Adaptive Course Generation ▪ Micro Course Generation ▪ Intelligent search ▪ Interactive exercises ▪ Student progress indicators
▪ What is the target audience? ▪ How do students work with the
system? ▪ Which features are useful? ▪ Which pedagogical approaches
are suitable?
Math-Bridge is a family of technologies made by a community of researchers
ActiveMath-‐EUActive
Math
Le-‐ActiveM
ath
Math-‐Bridge
Math-‐Bridge+ MathCoach
ATuF 2
2000 2004
Matheführerschein
ATuF
ALOE
Mathe-‐Brücke
Math-‐Bridge final
20072009 2011
2013?
eChalk
First Version of ActiveMath
• Course Generation • User Model • Progress indicators • Multiple Choice
Questions • CAS exercises
Math-Bridge is a family of technologies made by a community of researchers
ActiveMath-‐EUActive
Math
Le-‐ActiveM
ath
Math-‐Bridge
Math-‐Bridge+ MathCoach
AtUF 2
2000 2004
Matheführerschein
AtUF
ALOE
Mathe-‐Brücke
Math-‐Bridge final
20072009 2011
2013
?
eChalk
Matheführerschein (Driving License for Math)
▪Matheführerschein Online helps preparing learners for college/university
▪ It was initiated by FH Dortmund
▪ Content: wide range of school mathematics needed for University
▪ Fractions, Equations, Term Manipulation, Functions, Differentiation and Integration
▪ The pedagogical approach is constructivist, starting from complex real world problems
▪ ActiveMath interface was modified ▪ Specific strategy for interactive exercises was developed
▪ The ActiveMath possessed a library of terms with a novel structure (flavours and links to exercises) !!
Matheführerschein
• The system received positive reviews for its intuitive design and didactic approach
• Matheführerschein is available online for wide public
• Freshly enlisted students from FH Dortmund were recommended to use the system
• Hundreds of Students tested their knowledge using the system
• No records of learning effect !
Math-Bridge is a family of technologies made by a community of researchers
ActiveMath-‐EUActive
Math
Le-‐ActiveM
ath
Math-‐Bridge
Math-‐Bridge+ MathCoach
AtUF 2
2000 2004
Matheführerschein
AtUF
ALOE
Mathe-‐Brücke
Math-‐Bridge final
2007
2009 2011
2013
?
eChalk
eChalk: Algebraic Geometry on a Smartboard
▪ This project connects three systems: ▪ ActiveMath ▪ Computer Algebra System
Singular ▪ Smartboard technology eChalk
▪ A Course of Algebraic Geometry given by Prof. Schreyer ▪ Contents of a Course Book
encoded in ActiveMath ▪ Handwriting recognition and
Computer Algebra work together to help the lecturer manipulate interactive visualizations
▪ The Course was held at the Mathematics Faculty at Saarland University
Math-Bridge is a family of technologies made by a community of researchers
ActiveMath-‐EUActive
Math
Le-‐ActiveM
ath
Math-‐Bridge
Math-‐Bridge+ MathCoach
AtUF 2
2000 2004
Matheführerschein
AtUF
ALOE
Mathe-‐Brücke
Math-‐Bridge final
2007
2009 2011
2013
?
eChalk
Features of Le-ActiveMath
• Tutorial Dialogue in exercises • Better design • Concept Mapping Tool • Elaborate pedagogical scenarios
Example Usage of Le-ActiveMath
Practical Calculus Course !238 Practical Calculus students, Edinburgh University, UK. Mean Age = 19 !• 11 week course, 1 tutorial every fortnight. • Traditionally, tutorials and homework paper-‐
based. • Le Active Math used instead.
• Content: University first year Calculus • Pre-‐recorded books authored for course and each
homework/tutorial. à LeAM could be used in 3 homework/tutorials.
Source: Tim Smith
Tutorial Structure
▪Before Tutorial ▪ Lecturer sets homework on LeActiveMath. ▪ Students complete exercises at home/computer lab. ▪ Answers automatically logged. ▪ Links in LeActiveMath between homework content and other
content assist students. ▪ In preparation ▪ Admin Pages developed to allow tutors to view student progress. ▪ Reporting Tool produces reports on a group of user’s attempts at
exercises. ▪ In Tutorial ▪ Students completed exercises and browsed the content if needed
Source: Tim Smith
LeActiveMath Usage
▪Expected regular usage ▪ Peak of usage prior to tutorials ▪ Increasing mean usage prior to exam. ▪Observed very low usage. ▪Most users were those recruited for in-depth tasks. ▪Usage was mostly on exercises and searching for content. ▪Advanced components rarely used. !▪There were also some technical problems, so the usage
statistics is not reliable
Source: Tim Smith
▪Users found navigation of the content easy. ▪Users liked the book metaphor, search tool, and
hyperlinks. ▪But ▪ The content was often confusing, too scattered with jargon, and
the difficulty level incorrect. ▪ They found the search tool too complicated e.g. they had to
select too many options to find the content in a book.
In-depth Evaluation: Summary Source: Tim Smith
In-depth Evaluation: Summary
▪Formula Editor
▪ Is seen as a useful tool ▪ But it is unintuitive, too particular in its syntax, and frustrates
users. ▪Hints and feedback
▪ Learners find them useful ▪ But could have more levels of hints and always bottom out at
solution. ▪Exercise Types
▪ Learners see the benefit of most types of exercises
▪ But prefer MCQ, SCQ, and computations without the input editor.
Source: Tim Smith
Math-Bridge is a family of technologies made by a community of researchers
ActiveMath-‐EUActive
Math
Le-‐ActiveM
ath
Math-‐Bridge
Math-‐Bridge+ MathCoach
AtUF 2
2000 2004
Matheführerschein
AtUF
ALOE
Mathe-‐Brücke
Math-‐Bridge final
2007
2009 2011
2013
?
eChalk
ActiveMath-EU: Using LeActiveMath in classroom
▪ ActiveMath usage for multilingual pre-service teachers ▪ In Charles University in Prague for pre-service teacher students learning math in
Czech and English in parallel ▪ In Eötvös Lorand University in Budapest for pre-service teacher students learning
math in Hungarian and German
▪Other Sample Usage Scenarios ▪ Blended Learning in a classroom moderated by a teacher in Eötvös Lorand
University Budapest ▪ Solving interactive Exercises in a secondary school in Germany ▪ Blended Learning and learning assignments with particular learning paths for pre-
service teachers in Université Pierre Marie Curie, Paris 6 ▪ Blended-Learning with homework assignments at St. Michael College in the
Netherlands (own content)
Math-Bridge is a family of technologies made by a community of researchers
ActiveMath-‐EUActive
Math
Le-‐ActiveM
ath
Math-‐Bridge
Math-‐Bridge+ MathCoach
ATuF 2
2000 2004
Matheführerschein
ATuF
ALOE
Mathe-‐Brücke
Math-‐Bridge final
2007
2009 2011
2013
?
eChalk
ALOE Project
• ALOE project investigated the Effects of erroneous examples in the domain of decimals
• Several school experiments were conducted in Germany and U.S. • 6th grade, 7th grade, and 8th grade • Interactive exercises were solved in a classroom in teacher-‐
assisted exercise sessions • Pupils worked with fixed sequences of learning objects
• General comments on the usage of the system • After just 1 hour of familiarization, pupils are able to cope with
the system navigation and formula input • Intuitive user interfaces are important for school context
• Good observations: • Students find and describe errors, but cannot correct
➢declarative vs. practical knowledge • Students solve similar exercises, but cannot correct errors
➢Memorized solution practice, but lack of deeper knowledge !!!
School Fraction Course and ATuF Project
• A Fraction Course for School was authored in ActiveMath by a teacher (Mr. Kessler)
• He used this course for teaching fractions in a secondary school in Saarbrücken for 2 Semesters
• The Course was further reworked within the DFG Project ATuF (Adaptive Tutorial Feedback)
• ATuF investigates various feedback strategies for interactive exercises, based on the feedback framework of Prof. S. Narciss
• A structured user interface for solving interactive exercises in the domain of fractions was developed
• Several feedback strategies have been tested with students • Lab experiments with about 200 students were conducted !!!
Math-Bridge is a family of technologies made by a community of researchers
ActiveMath-‐EUActive
Math
Le-‐ActiveM
ath
Math-‐Bridge
Math-‐Bridge+ MathCoach
AtUF 2
2000 2004
Matheführerschein
AtUF
ALOE
Mathe-‐Brücke
Math-‐Bridge final
2007
2009 2011
2013
?
eChalk
Math-Bridge: Intelligent Remedial Mathematics
• The goal of the project was to create a European portal for mathematical bridging courses
• The final product should be disseminated to the educational institutions and used for teaching
• Project partners have used the system for teaching in their institutions, there is a community of associate partners
• Leading Universities in Europe and Industrial Partners and Sub-‐contractors have contributed to the project
Some Users of Math-Bridge
▪Math-Bridge was used in bridging courses at Eötvös Lorand University for pre-service teachers ▪ HTW Saarland uses Math-Bridge in combination with Math-Coach
System ▪ Universities of Kassel and Paderborn used Math-Bridge for
Mathematics bridging courses for technical faculties ▪ University of Brandenburg used Math-Bridge for their Mathematics
bridging course for Computer Scientists ▪Math-Bridge is currently used at Leuphana University of Lüneburg in a
Mathematics bridging course for economists.
Mathematics Bridging Course at Leuphana University
Bridging-‐course
(7 Weeks)
Pretest
Posttest
Blended-‐Learning Bridging Course
(7 Weeks)
Blended-‐Learning Bridging Course
(4 Weeks)
Lecture– Mathematics for Economics Exam
Repeated Exam
The first semester at Leuphana University (so-‐called Leuphana Semester) is divided into two halves: !
• The first half is devoted to introductory courses and bridging courses • In the second half some major Mathematics lectures build upon the
introductory courses
Mathematics Bridging Course at Leuphana University
Bridging-‐course
(7 Weeks)
Pretest
Posttest
Blended-‐Learning Bridging Course
(7 Weeks)
Blended-‐Learning Bridging Course
(4 Weeks)
Lecture– Mathematics for Economics Exam
Repeated Exam
• Pretest determines the knowledge gaps • Bridging course in the first 7 weeks is using math-‐bridge and other technologies
• Math-‐Bridge is used for information and training at home • Other teacher tools are used during the classes • Lecture materials are linked to Math-‐Bridge
• Posttest shows the improvement for those who attended the first bridging course
Mathematics Bridging Course at Leuphana University
Bridging-‐course
(7 Weeks)
Pretest
Posttest
Blended-‐Learning Bridging Course
(7 Weeks)
Blended-‐Learning Bridging Course
(4 Weeks)
Lecture– Mathematics for Economics Exam
Repeated Exam
• A blended learning bridging course using Math-‐Bridge is given in the next 7 weeks
• The main Mathematics lecture is running in parallel to the second bridging course, offering the students with difficulties to join right away and train with Math-‐Bridge system.
• Another intensive blended-‐learning course using Math-‐Bridge is offered between two exams (duration 4 weeks)
How to teach it? Old and new Technologies for Mathematics Lecture
24.09.14 40
• Conflict: Blackboard vs. Computer & Projector • Blackboard:
• Chalk supports arbitrary formula input and visualizations • Full freedom for improvisation with examples
• Computer: • Power Point Slides: complex diagrams and animations • GeoGebra Animations: examples to touch • Intelligent Computer Algebra Systems
• Commonly used solutions: • Use Smartboards to combine blackboard and computer • Use tablet computers connected to a projector
Our solution: E-Learning / E-Teaching Technologies!‣ Structured interfaces for teacher to interact with presented content ‣ Termania – tool for visualizing term manipulation ‣ GeoGebra
‣ Intelligent Learning Environment Math-Bridge ‣ VEMINT Portal Contents
First Bridging Course: Structure & Learning Materials
24.09.14 42
!• Course: Bridging Course Mathematics for Economics • Number of students: max 250 • Lecture
• Two times a week two hours each time • One book chapter per week (in total 6 Chapters) • Power Point Slides
• Animations in the slides • External Animations
• Learning materials • Book „Mathematics for Economics“ Chapters 1-‐6 • Slides including video recorded animations from the
lecture • Additional materials in Math-‐Bridge • Animations in Youtube und GeoGebra portals as extra
channels
Self-learning & Social Learning
▪ Micro-prelearning (Math-Bridge): ▪ Animated worked solutions (Math-Bridge, youtube) ▪ Training exercises with feedback (similar to homework exercises)
▪ Self-learning (Math-Bridge) ▪ Working with additional materials: ▪ Math-Bridge books, interactive exercises, (micro) course generation
▪ Social Browsing: ▪ Youtube channel of Math-Bridge ▪ One can browse related videos brought by youtube keyword matching ▪ Students can add own videos
▪ Browse GeoGebra Animation portal ▪ Animations from the lecture are uploaded and linked to ▪ Similar animations from GeoGebra portal can be browsed, they are
automatically linked by common keywords
24.09.14 43
Math-Bridge Contents
▪ Each content book corresponds to a chapter of the course book ▪ The structure of each chapter is fixed and the students are suggested to follow particular
learning paths, depending on their goals
45
Interactive Power Point Slides
=+b +a
+b
a+b=b+a a-b=a+(-b)
+a -‐b -‐b +a
a-(-b)+2a+b-a= a+b+2a+b-a= bereinigen
+a
+a +b =
+2a +b -a
+2a +2b
46
Pascal´s Triangle
52
!
"#
$
%&=
5!2!3!
=4 ⋅52
=10
52
!
"#
$
%&= 4
1
!
"#
$
%&+ 5
2
!
"#
$
%&= 4+ 6 =10
Geogebra Portal: Bridging Course Collection
24.09.14 50
Visualizations and animations of various concepts
Blended-Learning Bridging Course (using Math-Bridge) running in parallel to the main Mathematics Lecture
!▪ Number of Students: max 60 ▪ Course is given in a computer equipped seminar room ▪ Topics: ▪ Static and Personalized Courses in Math-Bridge corresponding
the the contents of Chapters 1-6 of the reference book ▪ Visualizations and Examples ▪ Special examples for economists ▪ Animations (GeoGebra)
▪ Exercises: ▪ Demonstration of worked solutions ▪ interactive exercises in Math-Bridge
24.09.14 52
Blended-Learning Scenario: „Teach & Train“!‣ Introduction to a lecture topic ‣ Definitions, interactive examples using Termania and GeoGebra !!
‣ Solving problems in Math-Bridge ‣ Interactive exercises with feedback and hints ‣ Self-assessment exercises solved on the paper and compared to the
master solution in the system ‣ Multimedial exercises correct/wrong feedback
Students about using Math-Bridge
▪ Course Materials are easy to browse, intuitive and well structured ▪ However ▪ Most of the students did not notice that the search function exists ▪ Not all chapters of static books were structured in the same way, which
introduced some confusion ▪ Most of the students did not use the micro course generation feature, even after
explicitly introducing them to the feature ▪ Solving interactive exercises was too much effort for some students ▪ Formula editor is complex and slow means of entering formulas ▪ Many students prefer to write the solution of the paper and submit the final
result into the system ▪ Multiple choice questions, graphical puzzles and one step exercises with simple
input were more popular
Further Steps!‣ Automatic Generation of Termania Examples ‣ How? ‣ Use integrated domain reasoners to generate the annotated
solutions ‣ Why do we need this? ‣ The teacher can generate on the fly a worked solution of an
improvised example and show it right away ‣ Automatic Integration of the lecture slides in the system ‣ Generation of annotated e-Lectures ‣ Automatic annotation of parts of videos with links to corresponding
concepts ‣ Evaluation of the learning effect of the „Teach & Train“
strategy and comparison to the classical lecture
24.09.14 57
Classroom of the future (1969, Shōnen Sunday magazine)
E-‐Lecture
Working with Math-‐Bridge
Flag Feedback