brief history of math-bridge and its usage

Brief History of Math-Bridge and its Usage

George Goguadze Leuphana Universität Lüneburg

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

ActiveMath: The breakthrough

First Version of ActiveMath

• Course Generation • User Model • Progress indicators • Multiple Choice

Questions • CAS exercises

First Version of ActiveMath

• Next Best Suggestion Engine

• „Poor man‘s“ eye-‐ tracker „DFKeye“

Second Version of ActiveMath

• Dashboard-‐style main screen • „better“ design • Open User Model

First Users of ActiveMath



Math

Le-‐ActiveM

ath

Math-‐Bridge


AtUF 2

2000 2004

Matheführerschein

AtUF

ALOE

Mathe-‐Brücke


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

Le-‐ActiveM

ath

Math-‐Bridge


AtUF 2

2000 2004

Matheführerschein

AtUF

ALOE

Mathe-‐Brücke


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

Le-‐ActiveM

ath

Math-‐Bridge


AtUF 2

2000 2004

Matheführerschein

AtUF

ALOE

Mathe-‐Brücke


2007

2009 2011

2013

?

eChalk

Le-ActiveMath: The next generation

Features of Le-ActiveMath

• Tutorial Dialogue in exercises • Better design • Concept Mapping Tool • Elaborate pedagogical scenarios

Features of Le-ActiveMath

• „Scrutable“ User Model

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 Tutorials

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

Le-‐ActiveM

ath

Math-‐Bridge


AtUF 2

2000 2004

Matheführerschein

AtUF

ALOE

Mathe-‐Brücke


2007

2009 2011

2013

?

eChalk

ActiveMath-EU: Dissemination and Exploitation of LeActiveMath

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

Le-‐ActiveM

ath

Math-‐Bridge


ATuF 2

2000 2004

Matheführerschein

ATuF

ALOE

Mathe-‐Brücke


2007

2009 2011

2013

?

eChalk

ATuF and ALOE projects

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 !!!

Interactive Exercises

ALOE Users



Math

Le-‐ActiveM

ath

Math-‐Bridge


AtUF 2

2000 2004

Matheführerschein

AtUF

ALOE

Mathe-‐Brücke


2007

2009 2011

2013

?

eChalk

Math-Bridge

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)


(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


Bridging-‐course

(7 Weeks)

Pretest

Posttest


(7 Weeks)


(4 Weeks)


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


Bridging-‐course

(7 Weeks)

Pretest

Posttest


(7 Weeks)


(4 Weeks)


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

Term-manipulation- and Animation tool „Termania“

„Termania“: Example

GeoGebra- Visualization

24.09.14 49

Geogebra Portal: Bridging Course Collection

24.09.14 50

Visualizations and animations of various concepts

Youtube channel: Math-Bridge Leuphana

24.09.14 51

Videos of Term-‐Manipulation

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

Future?

24.09.14 57

Classroom of the future (1969, Shōnen Sunday magazine)

E-‐Lecture

Working with Math-‐Bridge

Flag Feedback

24.09.14 58

Classroom of the future: the future is NOW!

Thanks!

The Mathematical Bridge, Cambridge, England

brief history of math-bridge and its usage

Education